Work towards Creating a Quantum Gas of Strontium and Construction of 3P0 & 3P2 Clock lasers

(1)

MSc Chemistry

Molecular sciences

Master Thesis

Work towards creating a

quantum gas of strontium and

the construction of

3

_P

0

&

3

_P

2

ultranarrow-linewidth lasers

by

Alexander

Urech

11108037

September 2017

42 EC

January 2017- September 2017

Supervisor/Examiner:

Examiner:

(2)

Abstract

In the last quarter century, the study of ultracold quantum gases has been a rapidly developing area of physics. From the realization of the first degen-erate quantum gases around the turn of the millennium, to the use of these highly controlled and tunable environments for explorations into quantum simulation and computation experiments today, these systems have devel-oped from the area of study themselves to the experimental medium for further investigations into interesting physics. The ongoing improvement in laboratory technology, such as ultra-stable laser systems, has lead to a plethora of new opportunities in the area of quantum simulation. Specif-ically the alkaline-earth atoms have desirable atomic properties for both cooling to degeneracy, and for quantum simulation experiments. The fol-lowing thesis will discuss the elements necessary for bringing a thermal gas of strontium to quantum degeneracy. A brief discussion will also be provided on the construction of ultra-stable laser systems for two differ-ent narrow-linewidth electronic transitions in strontium know as the clock transitions.

(3)

Acknowledgements

I would like to acknowledge everyone who has helped me in writing this thesis. First of all I would like to thank Florian Schreck for the opportunity to join his strontium quantum gas group and for the amazing introduction into the world of ultracold quantum gases. It has been an unbelievable opportunity that has allowed for me to learn so much.

I would like to especially thank the team working on the strontium gas microscope project with me. Thank you Georgios for letting me help you with getting the first MOTs in the machine that you have designed and for everything that you have taught me along the way. Thank you Oleksiy for all the great explanations, spirited conversations, and all the help you gave me. Thank you Sergei for the tips and tricks you’ve taught me from injecting fibers and slaves to explaining the blue system to me, and teaching me how to get the lasers locked and stable. Thank you also to Oleksiy for constructing the red laser system, and Sergei for constructing the blue laser system. Also thanks to the whole team for all the design work, and assembly of the vacuum chamber and magnets that was completed before I joined the group.

Additionally, thank you Vincent Barb´e and the rest of the RbSr team for providing us with the resonant light from their spectroscopy setups neces-sary for making our machine work. Also thank you for conversations on the methods and sequences that you use in making a degenerate gas of stron-tium. Thank you Alessio Ciamei for the discussions related to setting up the metastable state lasers and your ideas into the best way to accomplish the desired ultranarrow-linewidth.

I would also like to say thank you to the SrCal team as well for sharing your lab space with us, and for all the advice and knowledge. Thank you

(4)

Benjamin Pasquiou for your great Wikipedia files explaining so many dif-ferent tasks, and for the great explanations and answers you were able to provide to my questions. Thank you Chun-Chia Chen and Shayne Bennetts for all the tips and additional knowledge that you were able to pass on to me as well I am extremely grateful for it.

Thank you as well to the electronic and mechanical workshops for all the help you have provided in making all the custom pieces needed for this project.

Finally, I would like to thank my parents, Ron and Soraya, for the support and encouragement that has lead me to this point. I wouldn’t be here without your support and I will always be grateful for that. Thank you as well to my siblings, Diandra and Daniel, for your encouragement as well.

I am extremely thankful for the opportunity I have had to be a part of the amazing research team, and work on this amazing project. Thank you again to all that have made this possible. I want to emphasize that this thesis shows the work that has been completed on the machine and tries to provide an overview of the processes and equipment that are involved in getting to the current status. I was part of the group and offered my help wherever was needed, and do not want to take undeserved credit. I specifically constructed the MOT optics, ultranarrow-linewidth laser optics, and wrote the experimental sequences to name some of my specific contri-butions. It would not have been possible to complete near the amount that was described in this thesis without the help and efforts of our entire team and I am extremely grateful for all the help of everyone involved!

(5)

Introduction

In quantum physics, there are two important statistical classes of particles based on their total spin; for half integer spin fermions, and integer spin bosons. The combi-nation of the electrons, protons and neutrons gives the total spin of the atom. In the 1920’s, the statistics of bosons was first described by Satyendra Bose for photons and shortly after extended by Albert Einstein to all bosons. Based the statistics of bosons a phase transition was predicted at low enough temperatures that would cause particles to condense into a single macroscopic quantum state. The statistics of fermions were first described by Enrico Fermi and Paul Dirac a few years later which predicts a de-generate Fermi quantum gas (DFG) at low temperatures (1). Although the predictions of a Bose-Einstein condensate (BEC) and DFG both came almost 100 years ago, they were not realized experimentally until the early 90’s (2).

The first step our group uses in creating ultracold quantum gases is laser cool-ing, which was proposed in 1975 by Ted Hänsch and Arthur Schawlow (3). The first neutral atoms were cooled in 1981. This lead to Steven Chu, Claude Cohen-Tannoudji, and William D. Phillips receiving the Nobel prize in 1997 (4). This achievement along with the method of evaporative cooling led to the observation of quantum gases (5). The first atoms for quantum gas experiments were alkali metals such as rubidium, sodium, and lithium. The study soon continued on to alkaline earth metals as well such as calcium and strontium (1,2,6).

Now that quantum gases are obtainable they have became a platform for further ex-periments, rather than just the actual area of study. This has opened doors to many

(8)

1.1 Quantum Simulation

new areas of study, specifically to the use of ultracold atoms in quantum simulation and computing (7,8,9,10).

Two-electron atoms such as strontium and ytterbium have gained particular interest in such proposals because of their 1_S

0 ground state, metastable states and

narrow transitions (2,5, 11). For the fermionic isotopes, the atoms have nuclear spin that can be decoupled from the electronic states since there is no spin or angular mo-mentum in the ground state (J = 0). This leads to degenerate nuclear spin states that have an SU(N ) spin symmetry and are quite immune to environmental perturbations. This makes them great candidates for different quantum simulation and computation experiments (5, 7, 8, 9, 10). The purpose of the machine described in this thesis is quantum simulation experiments, and strontium is the atom used due to its appealing properties.

1.1 Quantum Simulation

In the early 80’s Richard Feynman first mentioned the idea of observing the evo-lution of a controllable quantum system and directly comparing it to another physical system. If the two systems could be explained by the same evolution and behavior, one can be used to simulate the other (10). A great quantum simulator is a fully controllable and tunable system allowing for models to be probed over a wide range of parameters. This type of system is provided by ultracold quantum gases, and it can be used to explore different areas of physics such as solid state systems, distant neutron stars, topological insulators, and high temperature superconductors (2).

One area of interest is the study of SU(N ) symmetries which are expected to lead to exotic many body phenomena at large N . An example can be seen in the behavior of quarks and gluons that is described by SU(3) symmetry (9). The under-lying Hubbard model describing alkaline earth metals takes on the SU(N ) symmetry because decoupling of the nuclear spin and electronic angular momentum causes nu-clear spin independent of the scattering between two atoms (9, 10). This opens up the possibilities SU(N _{≤ 2I + 1) symmetries to be observed in the interaction physics,} where I is the nuclear spin (2, 9). The fermionic isotope of strontium has a nuclear

(9)

1.1 Quantum Simulation

spin of I = 9/2 which allows for up to 10 spin states to be used. Some examples of higher order SU(N ) spin Hamiltonians that could be investigated with strontium in-clude the Kugel-Khomskii model used to describe transition metal oxides and quantum many body phases, and the Kondo lattice model for describing heavy fermion materials (2,10).

Another area of interest is the study of artificial gauge fields created with neutral atoms, since magnetic effects are important in the description of many quantum phenomena. The coupling of charge carrying particles to electromagnetic fields leads to many ideas including the quantum hall effect, topological insulators, the Aharonov-Bohm effect, and gauge invariance (12). The problem with simulating these effects is that the neutral atoms do not have any charge, but this can be rectified in a number of ways. An example can be seen when comparing the Lorentz force to the Coriolis force. The Lorentz force of a charged particle, q, moving at a velocity of v, in the presence of a magnetic field, B, is (12)

FL= qv× B. (1.1)

The Coriolis force describes the force experienced by a particle of mass M rotating at an angular velocity of Ω around an axis, and moving at a velocity f v with respect to a rotating frame (12,13);

Fc= 2M v× Ω. (1.2)

Without going into the details it can still be seen how these two forces can be compared. With the proper trapping potential the rotation of a neutral cloud of atoms can be described by a Coriolis force that is equivalent to the Lorentz force experienced by a charged particle in a magnetic field. The comparison of the two Hamiltonians shows the equivalence of the two schemes. Experimentally the equivalence can be seen by the appearance of vortices in the ultracold cloud (13). This was one of the first methods in which a gauge field was simulated in an ultracold gas, but it is not one that will be pursued in our lab, and is just presented here as a quick example. Other possibilities include using long-lived excited states, such as the metastable states of strontium, to accumulate a phase on the atoms based on their movement through an optical lattice, or by the movement of atoms in the weak binding regime of a lattice that is known as an optical flux lattice. A flux lattice can be can be thought of as a tight binding

(10)

1.2 Strontium

isotope natural abundance statistics nuclear spin

84_Sr _0.56% _bosonic ₀

86_Sr _9.86% _bosonic ₀

87_Sr _7.00% _fermionic _9/2

88_Sr _82.58% _bosonic ₀

Table 1.1: Naturally occurring isotopes of strontium, taken from Ref.(2).

lattice in momentum space (12). For a review of some of the many possibilities in the simulation of artificial gauge fields see Ref. (12).

Neutral atoms can also be directly used in the field of quantum information pro-cessing where computational algorithms are carried out as unitary transformations on a many body quantum system. For the implementation of a real world quantum com-puter the system must have strong correlation between the individual qubits (two-level quantum systems) and driving fields, while having weak correlations to environmental noise (14). This is exactly the type system that can be provided in ultracold fermionic strontium atoms. The decoupling of the nuclear and electronic states along with the control offered by the two metastable states, 3_P

0 and 3P2, allows for the execution

of phase gates through state dependent lattices, and for single sites to be addressed through the use of the3_P

2’s large Zeeman shift (8).

1.2 Strontium

The large number of possible simulations and other experiments with ultracold strontium has made it an appealing atom to work with and one studied in labs around the world. The different isotopes and rich electronic structure of strontium allow for a diverse set of problems to be explored.

1.2.1 Atomic Properties

strontium is an alkaline earth metal with three naturally occurring bosonic iso-topes;84_Sr,86_{Sr, and the most abundant}88_{Sr. There is also a single fermionic isotope,} 87_{Sr, which has the nuclear spin I = 9/2.The nuclear spin of fermionic} 87_{Sr causes a}

(11)

nu-1.2 Strontium 1_S 0 - 1P1 1S0 - 3P1 3P1 - 3S1 3P25s5d3D2 3P25s5d3D3 84_Sr _-270.8 _351.49 _{≈ 200} _-91.8 _-91.6 86_Sr _-124.8 _-163.81 _{≈ 100} _-47.5 _-46.6 87_Sr _-46.5 _-62.15 ₅₄ 88_Sr ₀ ₀ ₀ ₀ ₀

Table 1.2: ”Isotope shifts of the Sr isotopes, given in MHz. All values are referenced to

the most abundant isotope 88Sr. The hyperfine structure of the fermionic isotope 87Sr is much larger than the isotope shift, which is stated here for an assumed J = 0 state.” Text and figure taken from Ref. (2).

and even atomic mass numbers (for Sr; 38) (2, 11). The natural abundance of each isotope is recorded in Tab.1.1.

The electronic structure of strontium is [Kr]5s2 _{making it a group II element.}

The ground state of1_S

0 has two paired electrons that must fill the orbital in opposite

orientations due to the Pauli exclusion principle leading to a singlet ground state in addition to other excited singlet configurations. strontium can be seen as a helium like atom, so it also contains electronic configurations in which the spins of the two valence electrons are parallel leading to additional triplet states in the level scheme. The relevant electronic states can be seen in Fig. 1.1. The availability of transitions in the visible spectrum at wavelengths easily accessible by commercial diodes makes strontium a great candidate for laser cooling and state selective control.

1.2.2 Energy shifts

The isotopes in strontium have shifted energies for the relative electronic states due to the charge distributions of the different nuclei and the nuclear spin of the fermionic isotope (16). These shifts are large enough that they must be addressed for proper tuning of the lasers for the desired isotope. The coupling of the atomic states with light fields also causes a shift in the energy levels know as the AC Stark shift. This can be used to tune the energy levels and transition frequencies (2).

(12)

1.2 Strontium

Figure 1.1: A selection of the relevant energy level scheme in strontium. ”The position

of the manifolds are drawn to scale, but the fine structure splittings are not. The MOT and repump transitions (solid arrows), decay paths from the1_P

1state (dashed arrows) and

branching ratios, a proposed quenching transition (dotted arrow), and the clock transition (thin arrow) are depicted. The 3_P

2 reservoir state is indicated by a short arrow. The

ionization threshold is at 45932.09 cm1 _{(5.69485 eV).” Text and figure taken from Ref. (2).}

The 671 nm3_P

(13)

1.2 Strontium

Figure 1.2: ”Hyperfine structure for relevant states of 87_{Sr. The splittings are given in}

MHz and calculated with respect to an assumed I = 0 state, indicated by a dashed line. The calculation is based on the A and Q interaction constants taken from Ref. (11) and determined in measurements found in Ch. 9.” Text and figure taken from Ref. (2).

The nuclear spin of 87_{Sr leads to a hyperfine structure for atomic states with}

J ̸= 0. The splitting of the hyperfine levels for the relevant states is on the order of

10 MHz to 1 GHz and therefore is easily covered by traditional tuning methods such as acousto-optic modulators (AOMs). The hyperfine, F-states of strontium are shown in Fig. 1.2 for the important states where F = (I + J) denotes the total angular momentum. The order of these F-states can be inverted or the energies perturbed based on the different hyperfine parameters for each state (2).

(14)

1.3 Thesis Overview

1.3 Thesis Overview

The purpose of this thesis is give an introduction to the new quantum gas machine being built in the lab of Florian Schreck. The main goal of this new experimental setup is the exploration of artificial gauge fields and other quantum simulation and computation experiments. The machine will eventually include a quantum gas micro-scope capable of single atom imaging. This thesis will outline the steps that have been completed on the path to creating an ultracold quantum gas of strontium (Ch. 2 & 3), specifically focusing on the capturing and cooling of atoms in a Magneto Optical Trap (Ch. 4). Finally the thesis will conclude with a brief discussion of the strontium ultra-narrow linewidth transitions and the progress that has been made on the construction of ultra-stable laser setups to address them. If the reader is interested in more detailed explanations of the processes described here, the doctoral theses of Simon Stellmer (2), Andrew Ludlow (15), and Martin Boyd (11) are recommended.

(15)

2

Theory and Overview

Cooling an atomic gas to quantum degeneracy can be seen as an elimination of the thermal fluctuations. Removing these fluctuations allows for the control necessary for quantum simulation experiments. To get to the desired ultralow temperatures for experiments, we must reduce the energy (or lower the temperature) by a factor of the same order as the energy that must be increaesd (or that the temperature must be raised) to create a quark-gluon plasma at the large hadron collider (17)! At room temperature, _{∼ 290 K a gas of atoms behave as individual particles travelling with an} average velocity on the order of 100 m/s. As the temperature is decreased, the atoms quantum behavior becomes more important and the atomic wavepackets typically have a size of the de Broglie wavelength. If the de Broglie wavelength exceeds the average spacing between the atoms in the gas it leads to a BEC phase transition for identical bosons (17).

The cooling of strontium to quantum degeneracy takes place in four different steps: transverse cooling, Zeeman slowing, magneto optical trapping and finally evapo-rative cooling. The first three steps can all be explained through some basic principles and parameters that will be briefly outlined in the following sections. An overview of the exact processes used in cooling strontium to quantum degeneracy will then be provided in the final section of the chapter.

(16)

2.1 Cooling parameters Transition Γ/2π λ TD Tr Isat 1_S 0 - 1P1 30.5MHz 461 730 µK 1.02µK 40.7 mW/cm2 1_S 0 - 3P1 7.4 kHz 689 nm 180nK 460 nK 3.0 µW/cm2 3_P 2− 5s5d3D2 2.7MHz 497 nm 64.8 µK 880 nK 2.9 mW/cm2

Table 2.1: Some of the important cooling parameters for the three transitions used in our

group for cooling strontium. For more details see text. Transition rates and wavelengths obtained from (2).

2.1 Cooling parameters

To choose which transitions are best for laser cooling it is good to look at some param-eters such as the saturation intensity of a transition, the recoil temperature, and the Doppler limit. The minimum temperature that can be reached with Doppler cooling of a given atomic transition is the Doppler limit (11,15),

TD = ℏΓ

2kB

. (2.1)

which is determined by the transition (FWHM) linewidth Γ = 2π_{× γ. Mechanisms to} reach sub Doppler limit temperatures do exist, such as polarization gradient cooling, Sisyphus Cooling, and Raman cooling (15), but will not be discussed in these basic considerations.

Another cooling limit is given by the recoil temperature (11),

Tr=

h2 λ2_{M k}

b

, (2.2)

which gives the energy gained upon the absorption of a single photon based on the wavelength of the cooling light λ and the mass of the atom M .

Using λ and the excited state lifetime, τ , the saturation intensity, I_sat, can be calculated (11),

Isat=

hcπ

3τ λ3, (2.3)

giving the laser intensity for useful cooling and trapping (11). If the intensity of cooling light is below the saturation intensity the rate of absorption - spontaneous emission cycles is still limited by the intensity of light (1). Table 2.1 provides the calculated values for the relevant transitions used for cooling strontium.

(17)

2.2 Zeeman slowing

As many photons are absorbed from a beam in a given direction, the spon-taneous emissions of the atom will cancel each other out since they are emitted into random directions. This causes a net force to be exerted in the direction of the cooling beam. This force can be quantified by solving the optical Bloch equations (1),

⃗

F = ℏ⃗ksΓ/2

1 + s + (2δ/Γ)2, (2.4)

where s = I/Is is the saturation parameter and δ/2π is the detuning of the laser from

the optical transition of the atoms. The saturation parameter quantifies the effect that the force saturates at higher intensities. As the intensity is increased, so is the rate of stimulated emissions experienced by the atom. Since the stimulated emission will take place in the same direction as the slowing beam, it will lead to a net force of zero because the absorption-emission events will cancel each other out. Only the sponta-neous emission events lead to a cooling force. Since the rate of spontasponta-neous emissions is limited, this leads to a limiting force and acceleration that can be experienced by the atoms for a given beam,

⃗ Fmax= ℏ⃗kΓ 2 ⇒ ⃗amax= ℏ⃗kΓ 2M. (2.5)

2.2 Zeeman slowing

The slowing of atoms can be accomplished by exploiting two physical principles. The first is the Doppler effect; For a given atomic transition the frequency of a photon required to excite the electron is ω_atom. As the atoms travel at a velocity, v, towards an incoming beam, the frequency of the laser, ω_L, required to excite the atom is red shifted, or decreased, to compensate for the velocity, ⃗v of the atom (1,18),

ωatom= ωL+ ⃗k· ⃗v, (2.6)

where ⃗k is the laser’s wave vector. However, if only a red detuned laser was sent onto the atoms, it would only slow atoms of a particular velocity that fulfilled this relation.To overcome this limitation we exploit the Zeeman effect. When an atom is placed in a magnetic field, atomic energy levels, specifically mJ states with an angular momentum

(18)

Figure 2.1: ”Graph showing the Zeeman splitting in Rb-87, the energy levels of the 5s

orbitals, including fine structure and hyperfine structure. Here, the quantum number F = J + I, where I is the nuclear spin. (for Rb-87, I = 3/2). The original splitting is due to zero-field fine structure + hyperfine splitting. Graph was produced in MATLAB by plotting the Breit-Rabi equation. The code can be viewed here: https://github.com/ delton137/Breit_Rabi_Zeeman_Plotter.” Text and figure taken from Wikipedia.

field as illustrated in Fig 2.1.

For low magnetic fields the energy shift caused by the field is

ωa(B) = ωa,0+

µ′

ℏB, (2.7)

where µ′= (mege− mggg)µB is the effective magnetic potential between the ground(g)

and excited states, with m_e,g the magnetic quantum numbers and g_g,e Land´e g-factors (1). From Eqn. 2.6and Eqn. 2.7it can be seen, by substitution, that if done properly the two effects can compensate each other (1);

ωL= ωa,0+

µ′

ℏB− ⃗k · ⃗v. (2.8) If the magnetic field decreases at the same rate as the velocity of the atoms, a single laser frequency is able to stay resonant with the atomic transition over a range of ve-locities.

(19)

calculated. This can be done by assuming the atoms experience a constant deceler-ation, a = ηa_max with 0 < η < 1, when bombarded with photons travelling in the opposite direction. The repeated absorption and spontaneous emission of atoms causes the velocity to decrease to v(x) =√v2

0− 2ax from an initial velocity v0. Using the

re-lationship between the B-field strength, atomic velocity, the resonant frequency of the atomic transition, Eqn.2.8, and including an overall offset of ∆B =_ℏδ/µ′, the Zeeman B-field is obtained (1), B(x) = ℏδ µ′ + ℏkv0 µ′ √ 1− 2ax v2 0 = ∆B + B0 √ 1− x x0 . (2.9)

The offset ∆B of the field has no influence on the deceleration of the atoms. The remaining parameters, which are important for the design of a Zeeman slower, are B₀ and x₀;

B0= ℏkv0

µ′ , x0 = M v0

ηℏkΓ. (2.10)

To obtain x0 the formula for ⃗amax in Eqn. 2.5was used. These parameters can be used

to design what is known as a Zeeman slower, which is typically used as a first laser cooling stage to slow a beam of fast atoms emanating from an oven.

Two counterpropagating beams can be used in another important process when slow moving atoms are in the center. Considering a 1-D system where the atoms can only move parallel to the beams the optical force is ⃗FOM = ⃗F++ ⃗F− where ⃗F± are

the forces of the two opposing beams. Using Eqn.2.4and Eqn.2.6the forces of the two beams can be written as (18)

⃗

F_±=±ℏ⃗kΓ 2

s

1 + s + (∆_±)2, where ∆± = (2δ∓ |kv|)/Γ. (2.11)

If δ < 0 the force exerted by the two beams opposes the velocity, so can be considered to dampen the atomic motion. This is known as an optical molasses and can be used for the cooling of atoms, or to decrease their velocity in a given direction, but it does not provide any trapping potential. When the ⃗FOM is calculated for large detunings

of the laser, (2δ/Γ_s)2≫ 1 maxima can be seen to appear near v = ±(δ/k). The power broadened line width of the transition has been used here where Γ_s= Γ√s + 1. In the

(20)

2.3 Overview of the cooling procedure

⃗

FOM, is nearly linear,|v| ≤ Γ/k (18).

One of the ways to both increase the capture velocity and tocreate a trapping force is to introduce a gradient magnetic field B_m = a1∗ x. By again considering two

counterpropagating beams as was done for ⃗FOM in Eqn. 2.11, and by using Eqn.2.8

instead of Eqn. 2.6, the force becomes(18)

⃗ FM OT = ℏ⃗kΓ 2 ( s 1 + s + ∆2 +M OT − s 1 + s + ∆2 −MOT ) , (2.12) where ∆_±MOT = (2δ∓ |kv| ∓ µ ′_B(x) ℏ /Γ. (2.13)

With the proper orientation of the gradient B-field and polarization of the incoming laser beams, this force can create what is known as Magneto Optical Trap(MOT) where the combination of light and magnetic fields leads to the trapping and cooling of atoms. A more detailed discussion of how this trap is created can be found in Ch. 4. From these basic details on light forces experienced the processes of cooling atoms to microkelvin temperatures can be explained.

2.3 Overview of the cooling procedure

Initially a gas of strontium atoms leaves an oven that produces an atomic beam with an initial velocity of around 500 m/s in one direction and are slightly expanding radially. Although the velocity at which atoms are spreading is small in comparison to their longitudinal velocity, as the atoms are slowed this expansion can become a more substantial issue. For example, if the atoms are travelling at initial velocity of 500 m/s and have an angular spread of .05 radian, and the atoms are slowed to 25 m/s this spread will become .1 radian at the end of the slowing region (18). To minimize this effect, Doppler cooling is used to further collimate the atomic beam to increase the number of atoms that will make it to the final stage of the machine. An optical molasses is formed by pairs of counter propagating lasers placed perpendicular to the desired paths of the atoms and is used to reduce their undesired velocity in the radial directions. This step is not required, but can lead to a 2 or 3 fold increase in the atom

(21)

number caught later on by the MOTs.

The following step is a Zeeman slower, which uses both a magnetic field and a red detuned laser beam to slow the atoms from 500 m/s to approximately 25-50 m/s. The Zeeman slower uses a beam detuned from the1_S

0 - 1P1 atomic transition, see Sec.

2.2. The beam is tuned into resonance for the different velocity atoms by a magnetic field as they travel. As the atoms are slowed the magnetic field strength is reduced and the laser beam stays resonant. The length of the Zeeman slower and the initial field strength required were designed based on the values presented in Eqn. 2.10 (1). The Zeeman slower reduces the atoms to a low enough velocity that they are able to be captured by a MOT.

Bringing a strontium gas to quantum degeneracy once it has been through the Zeeman slower is done in three stages; a blue MOT, a red MOT, and evaporative cooling in a far off-resonance dipole trap. A 3D MOT is created by three back reflected beams. The three beams are positioned on Cartesian axes, (x, y, z), with the z axis aligned to the center of a quadrupole magnetic field. Atoms from the Zeeman slower are loaded directly into a broad transition MOT, also called blue MOT because it uses the 1_S

0 − 1P1 transition at 461nm. The atoms are eventually transferred from the

blue MOT transition cycle into the metastable 3_P

2 state through the 1D2 transition.

This can be a good or a bad thing depending on what one wants to achieve. We use it to our advantage since the 3_P

2 state has a magnetic moment and long lifetime. This

allows the atoms to be magnetically trapped by the MOT field, and creates a reservoir to collect atoms (2).

Atoms are ”repumped” back into the1_{S ground state with a laser tuned to the} 3_P

2 - 5s5d3D2 transition. The repumping openss a decay pathway through the short

lived (τ _{≈ 21µs)}3_P

1 state, and allows the atoms to easily return to the ground state.

The blue light and influx of new atoms from the oven is stopped before the repump light is flashed. As the repumping occurs the magnetic field is dropped to a weaker gradient, and the atoms are captured by the second MOT referred to as the red MOT. The laser beams of this trap are detuned from the1_S

0−3P1 (698 mn) transition, and has a much

(22)

detailed descriptions of both MOTs and can be found in Ch. 4.

There are certain limitations to how much you can cool with a MOT. The lasers are only detuned by at most a few linewidths from the atomic transition. This means that even when the atoms are standing still they continue scattering photons at a non negligible rate. The scattering of a single photon by an atom will increase the temperature of an atom by_{∼ 1 µK, which raises the temperature too much for a BEC} to form (17). Secondly, the probability that a photon emitted by one atom is absorbed by another atom increases as the atoms are cooled, and as the density inside the trap increases (17). The resonant light that has helped us in the initial cooling now prevents the formation of a BEC. However, the atoms must still be trapped against gravity and cooled further. This leads to the use of a dipole trap to perform evaporative cooling (17).

After the red MOT sequence is completed, the atoms are transferred into the dipole trap. The trap is made of two infrared (1064 nm) beams; one strong ( 5 W) elliptical, and one weaker ( 1 W) circular beam. The light polarizes the atoms and attracts them to the intensity maximum, thereby forming a trap (17). The two beams propagate through the chamber at a 90◦ angles to each other in the (x, y)-plane of the MOT. Dichroic mirrors are used to combine the absorption imaging paths and the dipole trap paths by transmitting the blue absorption beams and reflecting the IR beams. The dipole trap intensity can be controlled via AOMs placed on each path, so that the depth of the trap can be varied allowing for proper evaporative cooling to occur. After the beams have travelled through the chamber, the IR light is sent to water cooled beam dumps. The second beam of the trap is is not necessary, but is added to help with lateral confinement since a 1D trap will have a weak potential along the beams propagation axis. The infrared beams are focused by lenses so that they create a focusing beam shape, with the trap occurring at the focus of the beams.

(23)

3

The Machine

This Chapter will provide an outline of the machine being constructed by our group, which includes Florian Schreck, Georgios Siviloglou, Oleksiy Onishchenko, Sergey Pyatchenkov, and myself.

3.1 Machine Overview

The setup is divided on two optical tables; one which is known as the vacuum, or experimental, table containing the vacuum chamber of the machine, and one known as the laser, or optical, table and containing the majority of the laser systems and optics. Figure 3.1shows the experimental table of the machine in its current form.

Atoms are initially heated in the oven, from which they leave through a

col-Figure 3.1: A photo of the machine being constructed by our group taken in August

(24)

3.1 Machine Overview

lection of small capillaries, known as micro tubes, into the vacuum chamber of the machine. These tubes are used to select atoms flying along the tubes from the thermal cloud formed through the sublimation of the heated strontium. This creates an almost collimated atomic beam. The atoms proceed to the following chamber in which trans-verse cooling takes place to reduce the radial expansion of the atomic beam which is slightly diverging emerges from the oven.

After a differential pumping tube the atoms enter the Zeeman slower. The Zeeman slower is composed of two sections with magnetic fields along the z-axis but pointing in opposite directions. The two fields connect. The laser beam for slowing the atoms enters through the back window which is heated to prevent the deposition of strontium atoms on the surface. If the window was left unheated a mirror made of strontium atoms would form over time (2).

The Zeeman slower ends at the MOT chamber. This is where the atoms will be brought to quantum degeneracy. The MOT Chamber has a total of 14 openings. The z-axis of the chamber is oriented parallel to the force of gravity. 12 of the open-ings are in the horizontal plane, and two are centered on the z axis currently used for the vertical MOT beams. Four horizontal openings are connected to the Zeeman slower the back window where the Zeeman and repump beams enter, the quantum gas microscope (QGM) chamber, and the glass chamber. The glass and QGM cham-bers are not yet in use. The other 8 openings are all windows currently in use; the MOT beams (2 back reflected beams occupying 4 windows), 2 windows for absorption imaging beam inputs and dipole trap beam outputs, and 2 windows for FLIR Black-fly (Model BFLY-PGE-23S6M-C) imaging cameras and dipole trap IR beam inputs. The dipole trap beams and absorption imaging beams are superimposed with dichroic mirrors and travel through the same window pairs. The beams are divided again on the opposite side of the MOT chamber where the absorption beams continue onto the Blackfly cameras and the dipole trap beams are sent to beam dumps. The chamber is surrounded by two magnetic coils that are also centered on the z axis and separated by the horizontal windows.

(25)

3.1 Machine Overview

3.1.1 Vacuum

In order to perform well-controlled experiments and prevent unwanted atomic col-lisions a very high level of vacuum is necessary in the machine chamber. This is accom-plished through the use of four different pumping systems. To achieve the first step in pressure reduction a traditional rotary pump is used to reach 10−3 mbar. After that a turbo molecular pump is used, which operates on slightly different vacuum principles and allows pressures down to 10−8 mbar to be reached (19). During this initial period the steel, which makes up the majority of the vacuum chamber, must be heated to help with the outgassing process. This causes an accelerated loss of hydrogen and other volatile gases from the stainless steel (20). The turbo molecular pump is used to bring the pressure of the system down, but is then disconnected and removed from the lab.

Once the pressure becomes too low for the turbo pump to properly function,

∼ 10−8_{mbar, additional vacuum pumps are required to further lower the pressure,}

tita-nium sublimation (Ti sub) pumps. A Ti sub pump reduces the pressure in the chamber further through the high reactivity of titanium (19). There are four Ti sub pumps on the vacuum chamber of the machine attached near the MOT chamber, quantum gas microscope chamber, back window, and oven of the machine.

The last piece of the vacuum pumping are the ion pumps, which in contrast to Ti Sub pumps can pump noble gases and which allow for the final pressure to be obtained. Ion pumps, also known as ”getter” or sputter ion pumps, consist of a cath-ode, an anode and a small magnetic field (21). Ion pumps allow for extremely low pressures to be obtained, but one disadvantage is that they are unable to operate at higher pressures, which is why they are used only as the final stage. The ion pumps on the experiment are continuously operated, aside from the times that Ti sub pumps are flashed. The final pressure is somewhere around 10−11 mbar.

3.1.2 The Oven

The oven is used for heating the solid strontium into a gas. It is heated with a collection of wire heaters to a temperature of 450◦C. This lead to a vapor pressure of

(26)

3.2 Magnetic Fields

about 10−3 Torr (22).

3.2 Magnetic Fields

All of the necessary magnetic fields are created with electromagnetic coils made of wire or tubing. The choice of wire or tubing depends on the operation current needed for the desired B-field. High current fields will create extra heat so extra precautions must be taken to prevent over heating. The coils meant to carry high current are made from tubing instead of normal wire allowing for water cooling to be performed. To insure that none of the coils become too warm, a series of interlocks were placed on each coil. DC power supplies used to provide the required current are separated from the experiment in a different room to minimize external noise. Other options also exist for making the necessary magnetic fields, but this was the choice used in our group.

3.2.1 Zeeman slower

The Zeeman slower is constructed of three separate coils. They have been deemed the long, the short and the high current (HC) Zeeman coils in the lab. The magnetic field of each coil points along the direction of the atomic beam. The long Zeeman coil, which is the majority of the slower’s length, is the first after the transverse cooling chamber and starts with a large magnetic field that decreases in magnitude along the slower. It is attached to a section of differential pumping tube, which connects to the short Zeeman coil whose field points in the opposite direction to create the spin flip Zeeman slower (1, 23). The short coil, however, does not provide a fast enough in-crease in field, which is why an additional high current coil has been added with the same orientation as the short Zeeman coil. The HC Zeeman Coil is constructed out of copper tubes and water cooled because of the large current that runs through it. The operating currents for the long, short and HC coils are 4.5, 6, and 85 A respectively. The long and short Zeeman coils are powered with EA-PS-3032 power supplies, and the HC Zeeman coil is powered with a HP 6626A power supply capable of up to 500 A.

(27)

3.2 Magnetic Fields

3.2.2 Magneto Optical Trap Coils

The MOT Coil consists of 6 coils; two sets of 3 concentric coils. Each set has three concentric coils connected in series to form one large coil. They are positioned above and below the horizontal windows and positioned so that the center of the coils is aligned to the center of the vertical MOT chamber windows. Since these coils re-quire a high current in certain cases, and are so close to the atoms, copper tubing was used to construct the coils so that they can be water cooled as well. The large coils are also connected in series so that they can be operated from a single power supply. The power supply currently being used is a TDK lambda ZUP 6-132 capable of a 132 Amp output. When making a MOT, the coils must be in an anti-Helmholtz configuration to insure the desired quadrupole field. An anti-Helmholtz configuration causes the magnetic field of the two large coils to not add up but instead also create a quadrupole field. However, later on certain experiments will require a Helmholtz con-figuration. An H-bridge was installed between the power supply and coils consisting of four high current switches that can be used to switch between the two configurations.

3.2.3 Earth & Additional Compensation Coils

One extra issue is the need to compensate the magnetic field of the earth as well as other stray fields. This is accomplished by a number of compensation coils. The first is the Zeeman slower compensation coil located at the opposite side of the MOT chamber from the Zeeman slower. This coil is used for elimination of any extra field from the Zeeman coils that may interfere with the MOT field. This is more important for the creation and position of a blue MOT since during this period the Zeeman coils are still on.

The next set of important compensation coils is for the compensation of the earth’s magnetic field. They consist of three sets of coils that form a cage around the machine. These pairs of coils are orientated in Helmholtz configuration, so that fields can be placed in each Cartesian direction to help zero any stray fields. These fields are not so important in the blue MOT stage since the coils can only produce fields much weaker than those used in the MOT and Zeeman slower, but once the transition to the red MOT occurs, they become of great importance. In the red MOT the field is much

(28)

3.3 Laser Systems

weaker which leads to a large influence by even the earth’s magnetic field. All the compensation coils are also powered using EA-PS-3032-10 power supplies. The values used for creating a blue MOT can be seen in Table4.1.

3.3 Laser Systems

Bringing strontium atoms to quantum degeneracy requires four different laser sys-tems. For each atomic transition that is utilized in the cooling process, multiple laser beams with different detunings and intensities are necessary.

3.3.1 The Blue Lasers

The broad1_S

0 - 1P1 transition is the first used in the cooling of strontium. This

transition has a line width Γ = 2π×30.5MHz, which allows for a large capture range as well as very fast cycling of photons since the life time (τ = 1

Γ) of the 1_P

1 state is only

∼ 370 ns. The high capture velocity and saturation intensities also make this a great

candidate for the Zeeman beam, initial MOT cooling stage, as well as other tasks. The 461nm blue light is also used for transverse cooling and absorption imaging. However, for each of these four tasks a different detuning from resonance is necessary.

Laser beams with the desired detuning from resonance can be obtained with Acousto-Optic Modulators (AOMs). The resonance of the1_S

0 - 1P1transition is found

through the use of a strontium vapor cell heated to approximately 500◦C. Once the cell is heated, Doppler free Spectroscopy (24) 1 is used to lock the laser’s frequency to the transition. The initial plan was to use an External Cavity Diode Laser (ECDL) built by Tim van Leent (25), but unfortunately due to technical difficulties the stability of this new setup was too hard to work with. The setup was used to obtain the first blue MOT on the machine, but still has not been fixed since no solution to the stability problem could be found. Instead, initial seed resonant light is currently acquired from the spectroscopy setup of the RbSr experiment.2

1_{See Ref. (}₂_,₂₅_{) for details of the setup} 2_{See Ref. (}₂_{) for details.}

(29)

A small portion of the blue light is split off for locking to the 1_S

0 - 1P1

tran-sition of 88_{Sr, and to send seed resonant light to both other experiments in Florian}

Schreck’s group for seeding slave lasers.1

A total of five 461nm slave lasers are used in the experiment to create the power required for all of the blue beam paths, and each one is injected with fiber cou-pled light through the side port of a Thorlabs IO-5-532-HP optical isolator (OI). The OI ensures that back reflected light does not reach the diode. An additional benefit of this setup is the ability to easily optimize the coupling of the seed light into the diode. This is done by optimizing the coupling efficiency of the leakage diode light reflected by the first cube of the isolator into the seed fiber (See Fig3.2). To further confirm that the spatial modes of the two beams matches, the coupling efficiency of the leakage light is compared with the one of the seed light. If the two beams have similar spatial modes, the efficiencies will be similar. To make the side port of the isolator’s first cube function as the injection path for the diode a λ/4 waveplate between the slave laser and the isolator is required. Because the beam passes through the waveplate twice, the polarization is rotated by 90◦ in comparison to the incoming beam. The rotated polarization of the beam allows for the beam to exit through the front of the OI. All of the slaves are injected this way, but it will not be included in the continued explanation below for simplicity. A simplified layout of blue system can be seen in Fig. 3.2

The resonant light sent from the Rb-Sr lab has a power of 0.40 mW once it arrives on the laser table. This light is used to seed an initial slave laser called the ”Amplifier slave” in the set up because its main function is to amplify the light that has been received from the RbSr experiment. The slave light is sent through an ad-ditional PBS cube after the OI for extra polarization cleaning of the light and is then injected into a fiber for mode cleaning. The slave light is distributed into three beam paths via a series of λ/2 waveplates and PBS cubes. The first path goes to a Toptica Fabry Perot FPI-100 cavity with a scanning piezo to confirm that the slave is running in single mode and is properly injection locked.

(30)

Figure 3.2: A simplified diagram of the blue laser system. A legend of optical elements

has been included. The legend applies to all laser diagrams in this thesis. The slave lasers each have a fiber that brings the seed light to them. If the modes of the incoming light and the light produced by the diode spatially overlap, the coupling efficiency of the leakage diode light reflected from the OI going back through the fiber will be similar to the coupling efficiency of the seed light into the fiber. For the rest of the system, see the text further details. The blue system was constructed primarily by Sergey Pyatchenkov.

(31)

To test that the slave laser is properly injection locked, the current sent to the diodes is varied around the known lasing value. An oscilloscope attached to the pho-todiode of the Fabry-Perot cavity monitors the transmission signal of the cavity. Once modes are seen on the oscilloscope, the current is adjusted slightly until a single stable mode is seen that recovers when the seed light is momentarily interrupted. If this is not possible the injection into the diode must be touched. The procedure consists of adjusting the current so that side bands of the mode can be seen, and then adjusting the mirror that injects light until only the central peak of the mode remains. This is done with four of the slave lasers, while for the fifth a beat note is used.

The second path of light from the Amplifier slave travels through a single pass AOM, and a double pass AOM. The operating frequency of the single pass AOM has a small tuning range since a change in frequency will change the direction of the diffracted beam significantly. It is used mainly for the initial offset of the resonant light. The second AOM is used for compensating the isotope shift of the energy levels, so is adjusted based on the desired isotope. The additional AOM’s do not need to be changed for different isotopes since the frequency shifts of Tab. 1.2are fully compensated in this stage. Light travels from here to inject the following slave laser known as the ”Master slave”. The frequency shifts of different AOMs is shown in Fig. 3.3.

The light produced by the Master slave is distributed, again through a series of λ/2 waveplates and PBS cubes. A small portion of light is sent to the Fabry Perot cavity for monitoring, while the rest travels through 4 different AOMs; Zeeman AOM, MOT AOM, TC AOM, and Imaging AOM. These 4 AOMs are all placed into double pass configuration to allow for larger frequency tuning ranges and offsets. The fre-quency offsets are shown in Fig. 3.3. Once shifted to the correct frequency for each task the light continues on to seed one of the additional slaves. The three remaining slaves are for the transverse cooling, MOT, and Zeeman light. The light after the ab-sorption imaging AOM is sent directly to the experimental table. Aside from tuning the light back to resonance the other purpose of the imaging AOM is to act as a fast switch for flashing the imaging light at the appropriate times. At the table, the light has a power of about 1.0 mW and is expanded to a beam diameter of about 30 mm before passing through the MOT chamber onto a Blackfly Camera. There is a lens that

(32)

Figure 3.3: The frequency shifts caused by different AOMs in the blue laser system. Light

resonant with the1_S

0-1P0 is tuned to the proper frequency for each specific process. The

frequency shifts are to scale. The AOM for selecting the isotope selecting is shown tuned for88_{Sr. This AOM shifts the frequency by different offsets depending on the isotope being}

captured; 286MHz for88_{Sr, 348.4MHz for}86_{Sr, 421.4MHz for}84_{Sr, and 309.25MHz for the}

fermionic isotope87_Sr.

focuses the beam onto the CCD Chip of the camera.

Once the three slaves are injected by the Master slave, the slaves are each prop-erly tuned and ready for their specific experimental tasks. Light from each slave is sent to the experimental table through optical fibers. The light from the Zeeman slave is sent through a dichroic mirror so that the beams of the green repump laser (next sec-tion) and Zeeman slower can be sent to the experimental table through the same fiber. Once on the experimental table the beam has about 30 mW of power. It is expanded with a telescope and then a slowly converging beam is sent through the back window. The beam has an initial diameter after the telescope of about 25 mm and focuses the beam is about 3 meters from the last lens, or about a meter past the oven. The Zeeman beam has shutters to stop light both before and after the fiber that brings it to the experimental table related to the fact that repump light uses the same path. There is a shutter for each beam on the laser table and and a fast shutter on the vacuum table. This is done to better control the length of the repump light pulse sent into the machine.

(33)

The TC slave light must be monitored differently than the other four slaves because only four beams can be aligned into the cavity. This is where the third beam path of the Amplifier laser comes in. A small portion of the TC slave light is split off and then superimposed using a 50/50 beamsplitter with the last beam of the Amplifier slave. The two beams, which have very similar intensities, are sent onto a photodiode whose signal is monitored on an oscilloscope. When the two lasers are both single mode they will create a beat note on the photodiode if the difference between the two laser frequencies is less than the bandwidth of the detector, and the polarization’s are not orthogonal.

The rest of the TC light is sent to the machine through a fiber with approx-imately 28 mW arriving at the experimental table. The light is then collimated and expanded in the horizontal axis to make an elliptical beam. The beam is then split in two paths with a 50/50 beamsplitter, one for horizontal transverse cooling and one for vertical. The horizontal beam is brought to the level of the TC chamber window with a periscope and sent through the chamber perpendicular to the propagation of the atomic beam. The TC beam is reflected by 90◦ to shift the beam about 10 cm over before sending it back through the chamber a second time. The laser is retro reflected from the same side of the chamber that it entered creating two retro reflected horizontal paths. The same configuration is done for the vertical TC path without the periscope since the initial beam enters from the bottom window. The optimiza-tion of the alignment of these beams was done via fluorescence of the blue MOT and a factor of approximately ten increase in fluorescent counts was the final result. The TC light can be turned on and off at the machine via a shutter installed before the fiber.

The final slave is the MOT slave. The path can be blocked with a fast Uniblitz shutter, and the slave light is sent onto the experimental table where approximately 25 mW arrives. Further details of the MOT paths can be found in Ch. 4.

3.3.2 The Green Repump Laser

The laser used in our group for repumping atoms from the metastable 3_P 2 state

is 497nm green light resonant with the 3_P

2− 5s5d3D2 transition. There exists an

in-finite ladder of 3_D

(34)

as well, but the availability of light at 994nm that can be doubled to 497nm made this an appealing option. The green laser is sent from the RbSr experiment. A detailed description of the without laser system and light that is generated can be found in Simon Stellmer’s thesis (2) and will not be provided here. The repump light arrives on the laser table of our experiment through a fiber and is superimposed with the Zee-man beam and sent to the experimental table. There is a slow shutter that blocks the repump light on the laser table so that when the Zeeman slower is functioning and the metastable reservoir is being loaded, the repump light is blocked. Once the Zeeman light is switched off, the fast shutter on the experimental table is closed and the slow repump shutter is opened. This allows for repump pulses as short as a few ms.

3.3.3 The Red Lasers

The second transition used for laser cooling is the1_S

0 - 3P1 transition at 689nm

has a much narrower linewidth of 7.4 kHz. This transition can be used to cool the atoms to much lower temperatures, but this means that the possible capture velocity is much lower. The blue MOT takes care of this issue by cooling the atoms to a low enough temperature that they are able to be captured by the red MOT. The only 689nm light used currently in the experiment is for the MOT. The initial seed light is again obtained from the RbSr experiment. The initial laser light is produced by a Toptica DL Pro ECDL. The laser is locked via current and grating piezo to the TEM₀₀ mode of a high finesse Fabry Perot cavity with a Toptica FALC PID controller. In Ch. 4 a detailed description of this procedure can be found for the clock lasers. The cavity also has a piezo that can adjust the length between the mirrors and the resonant frequency. The cavity length is locked to a narrow line width spectroscopy cell with a very slow PID (2) to the 1_S

0 - 3P1 of 88Sr. The resonant light is shifted by +80MHz

with an AOM before being sent to our laser table where approximately 0.3 mW arrives.

The red laser setup for our experiment contains three slave lasers with a fourth soon to be added, and the light from the RbSr experiment is used to seed the first slave, S0R. The light from this laser is used for seeding the other slaves similar to the Master slave in the blue setup. A small portion of light is sent to a Toptica Fabry Perot

(35)

FPI-3.4 The Control System

in the setup tend to always run single mode, the frequency will drift when not properly locked. The rest of the light goes on to a series of AOMs aside for light that can be used to directly inject a slave when working with the 88_{Sr isotope. The configuration}

of the red system is a bit different than the blue and does not have dedicated slave lasers or fibers to the experimental table. Depending on the desired isotope, or multiple isotopes, for the experiment that will be performed different light can be used to inject different slaves. Each slave will address a single isotope or hyper-fine transition in87_Sr.

When working with 88_{Sr the next slave injected is S2R.}

The remaining S0R light is sent to seven AOMs used for creating the light necessary for the different isotopes and hyper-fine transitions. The different frequency shifts can be seen resented in Fig. 3.4. See Fig. 1.2 for the shifts of the hyperfine transitions, and Tab. 1.2 for the isotope shifts. The light from each AOM is fiber coupled and is used to seed the desired slave laser.

For the three remaining slaves, an 80MHz AOM is placed in single pass (-1 order) alignment to compensate the +80MHz added to the 88_{Sr resonant light before it is}

sent from the RbSr experiment. The slave lasers can be injected with light shifted to any of the isotopes or the hyper-fine transitions mentioned above. The 80MHz AOM introduces the detuning from resonance along with providing the extra frequency modulation that creates a comb of different frequencies. This process will be explained further in the following Chapter. The three slaves are then combined using a multiplexer made of four 50:50 beamsplitters that superimpose three beams into four paths as can be seen in Fig. 3.5. The four paths are each injected into a fiber and sent to the experimental table. The four fibers are for MOT beams and each have their own shutters on the laser table. Further explanation of the red MOT setup including the optical setup on the laser table can also be found in Ch. 4.

3.4 The Control System

The control system used for the experiment was designed for BEC experiments by Florian Schreck and Todd Meyrath when working in Mark Raizen’s group at the University of Texas at Austin. All software and circuit designs are available free for

(36)

non-3.4 The Control System

Figure 3.4: The different frequency shifts for the AOMs in the red laser system. The

different shifts are labelled with their respective isotope for the bosonic isotopes. The relevant transitions in the fermionic isotope are labelled with their respective hyperfine transitions. The transitions with two arrows represent shifts that required the use of two AOMs, and are shown at 2/3 scale for compactness.

(37)

3.4 The Control System

Figure 3.5: A simplified laser diagram of the 689nm light system used for the red

MOT. See text for details. The red laser system was primarily constructed by Oleksiy Onishchenko.

(38)

profit use on the group website (www.strontiumbec.com) where detailed descriptions can also be found of the whole system, this section will just provide a brief summary.

3.4.1 Hardware

The system is controlled from a dedicated computer linked to a parallel bus distri-bution system through a National Instruments NI6534 32-bit digital output card. This links the computer to 16-bit devices such as direct digital synthesizers (DDS) for AOM frequency control, digital outputs for controlling devices such as shutter servos, 16-bit analog output, or 8 digital to analog (DAC) channels for current control or other tasks. The bus has a 2 MHz speed allowing for a timing resolution of 0.5- 3 µs depending on the task and precision required. Three ”sub-busses” are currently used on the system, each addressing up to 256 16-bit devices of which there are three installed into the system currently. The electronics boards are home made and the main types used are the DAC, DDS, and 8 channel digital output boards.

3.4.2 Software

The software used to control everything was written in Visual C++ and Borland C++. There are two main parts of the software the Control code and the Vision system for image processing. The Vision code was written in Borland C++ and is operated from a separate computer linked to the main control computer that does the rest of the processing. Vision is easily made compatible with many different camera types and can perform basic fits and image processing that can be saved and accessed later (26).

The main Control program was written, and is edited, in Visual C++. It contains code dedicated to different functions and menus. The main files create an interactive menu containing different sub-menus for functions like manual controls, setting experimental parameters, defining experimental sequences, determining detec-tion parameters, and creating a cue of measurements (27).

The Manual operation sub-menus directly control the values of different chan-nels, while the initial Parameters sub-menus control the values for the experiment

(39)

the menu contain the Sequence parameter sub-menus that control what happens in an experimental run, such as flashing the repump beam or making a red MOT for example.

There are also camera parameters and detection parameters for the specific camera used or picture taken. A measurement can be made in which up to 5 different parameters can be varied at a time allowing for scans to be done over different detunings or field strengths. Any parameter from either the initial or sequence parameters can be changed. Images are sent to Vision where series of data can be made. This is an extremely brief description of all the control components used in the experiment and it is highly suggested, if the reader has interest in this system, to read the much more detailed and well written descriptions provided (26,27).

(40)

4

Magneto Optical Traps

4.1 Background

A Magneto-optical trap uses a specifically designed configuration of laser beams, and a quadrupole magnetic field, to confine atoms near the quadrupole trap center and dissipate their kinetic energy (4).

A MOT works based on the radiation pressure of light and the Zeeman effect. By looking at Eq.2.12 and the magnetic field created by the anti-Helmholtz coils, it can be seen how a restoring force comes into play. In the center of the quadrupole field the B-field magnitude is zero, and the field magnitude is increasing in strength as the distance from the center increases. The inset of Fig. 4.1shows a simplified example of the field experienced by the atoms on each axis.

The best way to understand the dynamics of a MOT is to look at a singe axis (x-axis). Consider the 1_S

0− 1P1 transition of a bosonic Sr isotope, which does

not have hyperfine structure. The laser beams can be seen as propagating along the axis from either side towards the origin, while the magnetic field is increasing directly proportional to the distance from the origin. The two laser beams contain opposite σ polarization’s oriented such that the beam travelling from +x_{→ 0 has σ}−polarization and vice versa. As seen in Fig. 4.1, the sign of the Zeeman shift induced is directly (inversely) proportional to the sign of the B-field for the m_j = +1 (−1) state.

(41)

4.1 Background

Figure 4.1: The Zeeman shift of a simplified J = 0 → J = 1 transition as in bosonic

strontium. The ground state 1_S

0 state has no magnetic moment so acquires no shift in

energy. Two red detuned lasers are shone onto the atoms. The polarization of the laser beams in relation the B-field allows a restoring force towards the center of the trap to be created. The mj states and corresponding beam that will excite the transition are in the

same color. The green dotted line indicates the detuning, ∆m of the MOT laser. The inset shows the magnitude of the quadruple field created along one of axes. See text for further details.

(42)

4.1 Background

Let us consider the situation without magnetic field as in Eqn. 2.11. As the atoms move in the direction of a particular red detuned beam they see this beam as Doppler shifted to the transition frequency (17). The atoms are slowed down through absorption and spontaneous emission cycles of photons independently of their direction of travel since it will always be in the direction of one of the laser beams. This can also be thought of as the atomic cloud being cooled as the overall energy of the ensemble is being reduced (17). This is called an optical molasses since the atoms are slowed as if they were moving through a thick syrup (17). The beam is red detuned from resonance, so that only atoms moving towards a beam will absorb photons.

To turn an optical molasses into a trap a restoring force is necessary. This is ac-complished through the addition of polarization to the laser beams and a magnetic field as shown in Fig. 4.1. By choosing the x-axis as the quantization axis, and looking at an atom moving in the positive x direction, the m_j =−1 state receives a negative energy shift, while the m_j = +1 state energy is reduced for the opposite direction travel. The second trick used to assure that photons are absorbed from the proper direction creating the desired force is the polarization of the lasers. A σ− polarized beam has an angular momentum of -1 which must shine onto the atom causing only mj = 0 → m′j = −1

transitions to occur. The detuning is larger than the atoms Doppler shift, so as the atom travels in the 0 → +x direction towards the beam it becomes resonant with this laser only. The atom gains a momentum kick in the direction of the laser beam from each photon. This slows the atoms and pushes them back to the center of the trap.

The two processes of slowing and trapping happen simultaneously causing a damped oscillatory motion. As the atoms are being slowed they continue to move outwards at a slower speed decreasing the size of the Doppler shift on their energy, but at the same time the magnitude of the B-field is increasing, which compensates this and keeps the light resonant until atoms are pushed back in the opposite direc-tion. Once this occurs the atoms encounter the other beam travelling −x → 0 with

σ+ polarization and the same process occurs but now with the mj = +1 state. At

low intensities the assumption that a 3D MOT is the combination of three sets of 1-D MOTs on each Cartesian axis (x, y, z) can be made, even though the quantization axis

Work towards Creating a Quantum Gas of Strontium and Construction of 3P0 & 3P2 Clock lasers

MSc Chemistry

Molecular sciences

Master Thesis

Work towards creating a

quantum gas of strontium and

the construction of

P

&

P

ultranarrow-linewidth lasers

by

Alexander

Urech

11108037

September 2017

42 EC

January 2017- September 2017

Supervisor/Examiner:

Examiner:

Abstract

Acknowledgements

Contents

1

Introduction

1.1 Quantum Simulation

1.2 Strontium

1.3 Thesis Overview

2

Theory and Overview

2.1 Cooling parameters

2.2 Zeeman slowing

2.3 Overview of the cooling procedure

3

The Machine

3.1 Machine Overview

3.2 Magnetic Fields

3.3 Laser Systems

3.4 The Control System

4

Magneto Optical Traps

4.1 Background

_P

_P