Setup of optical system for laser light distribution between two atomic chip experiments

(1)

University of Amsterdam

Bachelor Thesis

Setup of optical system for laser light

distribution between two atomic chip

experiments

Author:

Milo Stroink

Supervisor:

Dr Robert Spreeuw

Daily

supervisor:

David Davtyan

Abstract

In this thesis, a optical system is discussed that will increase the power available for lasers for one atomic physics experiment and supply laser light for an experiment currently under construction. For both experiments it will supply the light for the MOT (probe and repump) and cooling. The increased intensity for the cooling light is 200 mW, and for the optical pump 60 mW. The thesis also discusses the many challenges that are still faced.’

(2)

1 Introduction

Optical system’s are one of the essential building blocks in atomic physics. Detuning lasers, changing polarisation and coupling in to fibres are all tools for manipulation of atoms. A well constructed optical-system is one of the key-essentials for making quantum computers, which is a hot-topic in physics and also in society. Quantum computers have the ability to stretch the limit of modern computers and can in theory calculate faster than any current computer can ever do. The optical system in these quantum computers, can be seen as the motherboard in present day computers, creating connection between the different components. Laser light that is moved through a optical system carrying information from a processor driven by mere atoms can be sent through an optical setup to other components, where the information from the atoms is read, processed, or stored for calculation of impossible algorithms or other uses that a modern computer can do. One of these optical systems is discussed in this thesis. This system is built to switch light between two experiments with the use of optical switches. One experiment is already built and running, while the other experiment is still being assembled. For the already existing experiment, the optical setup being built, will give more intensity for the cooling laser. For the other experiment, the setup will give the laser-light needed for running the experiment. The laser that is detuned and distributed over different parts in the setup, will power the MOT (Magneto-Optical Traps), to trap, cool, probe, and repump the atoms in the experiment and getting closer of achieving quantum computing. For the existing experiment investigating Rydberg atoms, different parts of the optical setup are spread around the laboratory in different locations. This setup is made to increase the efficiency, making higher intensity available for the two experiments, while keeping the already working set-up running. The setup will be built so that there is minimal interference for the experiment currently running in the lab and the experiment can continue without hold-up or time lost.

1.1 Rydberg atoms on a chip

To understand the reason for doing the atom optical experiment, a understanding of what Rydberg atoms are and why they are so essential in atomic quantum computing, is needed. Rydberg atoms are atoms that have a high excitation level meaning that they have a high principle quantum number. Due to there high quantum numbers, their is a possibility that they create strongly interacting systems and therefore they are a candidate for making Q-bits[1]. To create the Rydberg atoms in this experiment, Rubidium-87 vapour is released near the MOT (Magneto-Optical Trap). MOT is a magneto-optical trap and uses optical pumping in a linear inhomogeneous magnetic field to trap the atoms[2]. The MOT is also used to cool the atoms from room temperature to microkelvin temperatures. If an atom drifts away from the trap, the Zeeman shift of the atom, is increased and therefore the atomic resonance, shift closer to the frequency of the laser. This causes the atom to scatter with the light moving back in the trap, trapping the atom in the MOT. The different frequency of detuning needed to achieve different levels in he hyperfine structure of Rybidium-87 and how the different laser are called inside the experiment and the MOT is given in figure (1). The laser for the MOT is set to a wavelength of 780 nm and is detuned by AOM’s (acousto-optic modulators) in different arms and frequencies, for the different purposes it must achieve. In figure (1) the

(4)

Figure 1: The hyperfine scheme for Rb-87. The 52_S

1

2 ground state and 5

2_P

3

2 excited state is

(5)

cooling laser is closely tuned to the F=2 to F’=3 transition. The electron that is excited, has insufficient energy for the whole transition, and uses its external energy to make the whole transition, cooling the atom in the progress. This cools the atoms trapped in the MOT. The optical pumping laser changes the spin polarisation. This is needed to trap the atoms further. A repump laser,exciting the atoms from F=2 to the F’=2 state, repumps the atoms that have decayed to the F=1 grounds state, back to the F’=2 state. This brings the atoms back in the cooling cycle. The probe laser is tuned to the F=2 to F’=3 transition. This laser is used to detect the atoms and to excite the atoms. This laser with the combination with the Rydberg laser, creates a two-step excitation, exciting the atoms in a Rydberg state. The two-step excitation, creates a low possibility for the decay of electron[1]. The vapour of Rubidium is released in a vacuum chamber. Magnetic coils are placed around the vacuum chamber for the initial MOT stage. For the later trapping of the rubidium vapour an atomic chip is used. Beneath this chip that is permanently magnetised,small gold wires run. This creates a magnetic field, trapping the atoms further.

2 Optical background

To understand the optical system that is assembled, some optical background is presented.

2.1 Polarisation: Jones matrices

Polarisation is an aspect of every photon beam and a nice tool, in most optical set-ups. Monochromatic light that moves in the z-direction can be written in it’s complex form by equation[3] [4]1

Ex = Ex0ei(ωt−kz+δx) (1a)

Ey = Ey0ei(ωt−kz+δy) (1b)

Where Ex and Ey is the component of the electric field in the x and y direction respectively.

E0x and E0y, are the amplitude of the electric field, ω is the angular velocity, k is the wave

number and δx,y is the phase shift for the different xy-components. This equation can be

written in a vector form.

~ E =Ex Ey =Ex0e i(ωt−kz+δx) Ey0ei(ωt−kz+δy) (2)

This vector ~E is called the Jones vector. Jones vectors are an orthogonal set of vectors and can be normalised making it orthonormal, meaning that equation(3) most hold.

~

E†_{E = 1}_~ ₍₃₎

Where ~E† _{is the complex transpose of the Jones vector. Jones vectors are only used to}

de-scribe fully polarised light. Different states of the Jones vector dede-scribe different polarisation. If Ey0= 0, the Jones vector becomes

~ E =E0 0 =1 0 (4)

(6)

This describes a linear polarised light in the x-direction. It is a similar for the situation E0x = 0, however in this case the light would be polarised in the y-direction. For the

situation E0x= E0y, the Jones matrix becomes

~ E =E0x E0y = √1 2 1 1 (5) With √1

2 being the normalisation factor, so the vector holds to equation 3. This

corre-sponds to a linear polarised light with a angle of 45◦, between the x-axis and the polarised line. If the angle between x-axis and the polarisation is −45◦, the Jones-vector becomes:

~ E =E0x E0y = √1 2 1 −1 (6)

(a) Polarised light propagating in the z-direction (b) The linear polarised Jones vector plotted on the XY-plane

Figure 2: The left figure is polarised light moving in the Z-direction. There is no y-component. The right figure is the same however, plotted in the XY-plane

Light can also be circular polarised. This occurs when

δx− δy = ±

1

2π (7)

meaning that the phase-shift difference between Ex and Ey is 90◦. In amplitude for

XY-component, is the same meaning: E0x = E0y . The ± indicates the direction of rotation of

the light. For circular polarised light, the Jones vector becomes.

~ E =E0x E0y = √1 2 1 ±i (8)

For phase-shift difference higher or lower then 1₂π, the circular polarised light becomes elliptical.

(7)

(a) 3D plot of circular light (b) Plot of circulair light on the XY-plane

Figure 3: The left image is a 3D-plot of a circular polarised light and the right image is circular light on the xy-plane. Light moves in this direction

2.1.1 Quarter wave and half wave plates

To change the polarisation of light, quarter wave and half wave plates can be used.In a quarter or half wave plate, a birefringent crystal is placed. Birefringent material, has the property to have different refraction index for different polarisation travelling through the birefringent material[4].This gives a difference in the speed between the x and y component and therefore, a phase-shift occurs. The XY-components of the Jones vector, undergo therefore different phase changes as they pass through the matter. Describing it in a more mathematical way, it is a transformation of the Jones vector.

To transform a vector, a transformation matrix can be used. ~

E0 = ~T · ~E (9) Where ~E0 is the transformed Jones vector and ~T is the transformation matrix or Jones matrix. In the case of the wave plates, the Jones matrix becomes.

~ Tφ₌ " eiφ₂ ₀ 0 e−iφ2 # (10)

Where eiφ2 is the fast axis and e−i φ

2 is the slow axis. This gives a difference in speed for the

differentte axis and given it a small phase differente. For the half wave plate φ = π and the quarter wave plate φ = π₂. Filling these values in equation 10, give the equations:

~ Tπ ₌e iπ 2 0 0 e−iπ2 = i1 0 0 −1 (11) and ~ Tπ2 e iπ 4 0 0 e−iπ4 = eiπ4 1 0 0 −i (12)

letting matrix (11), (12) work on a 45◦ linear polarised light Jones vector, gives i1 0 0 −1 1 1 = i 1 −1 (13a)

(8)

eiπ4 1 0 0 −i 1 1 = eiπ4 1 −i (13b)

The polarisation has changed with 90◦ for the half wave plate. For the quarter waveplate, the polarisation changed from linear to circular.

The phase-shift in fast axis and slow axis in a wave plate, can be calculated by equation

δ = 2π∆nL λ0

(14)

Where δ is the phase-shift along the axis, λ is the wavelength of light in vacuum, ∆n is the birefringence of the materiel and L is the thickness of the crystal.

2.1.2 PBS:Polarising beam splitting

In optical setups, light has to be distributed between different paths. To do so, PBS (po-larising beam splitting) are used. PBS’s are two dielectric materiel with different refractive indexes, in a prism form fused together to make a cube. The materials have different trans-mittance or reflectivity between polarisation direction. In Jones matrices this gives two matrices. One for transmittance and one for the reflection.

t =tx 0 0 ty ≈1 0 0 0 (15a) r =rx 0 0 ry ≈0 0 0 1 (15b)

With t being the transmission coefficient and r the reflection coefficient. If the polarisation of light is changed with a half wave plate, the intensity in one component of the light increases. This causes light to be more or less, transmitted or reflected. With this you can control the intensity in the transmitted or reflected part in a optical setup.

2.2 AOM: Acoustic-optic modulator

The AOM is a device to modulate the frequency, amplitude and propagation direction of laser light. In a AOM, a piezo vibrates with a frequency against a crystal, causing the crystal to vibrate with the same frequency as the piezo. The vibration of the crystal causes sound waves in the crystal. Sound waves are longitudinal waves, that create a pressure distribution in the crystal. As the pressure changes, the reflective index changes with it [5]. This occurs with the formula.

n(z, t) = n0 + ∆n cos(ωt − kz) (16)

With n0 the refraction index of the material, ∆n the amplitude of change of the refraction

index and k the propagation constant[6]. These changes in diffraction, creates wave fronts in the crystal where light can scatter from[7]. Because these wavefront travels through the crystal, creating a moving surface where the light scatters from, Doppler shift occurs, red or blue shifting the frequency of the laser. The light that is scattered interferes under Braggs condition, giving diffraction. For interference to occur, the interference condition must hold.

(9)

Figure 4: Light interfering constructively in Bragg diffraction/reflection [8]

nλ = Λ(sin θi+ sin θd) (17)

with n a integer, λ the wavelength of the light in the material, Λ the wavelength of the sounds, θi is the angle of light coming in and θd is the angle of light deflected. In figure (4)

shows the condition in a overview. Other light that scatters not in the interference condition, interferes destructively and therefore is not seen. Because of reflection; θi = θdand this gives

in combination with equation (17), the formula.

nλ = 2Λ sin θ (18)

In practice there are multiple angles possible, creating more orders [8], however the intensity in these orders can be lowered to a minimum with prober alignment AOM. The change of frequency caused by the Doppler shift, can also beseen as the result of phonon’s of the sounds wave being absorbed or emitted by the photons of the light. With the equation the change in frequency can be calculated

∆f = mEphonon

h = mfacoustic (19) where ∆f is the change in frequency of the laser and Ephonon is the energy of the phonon’s.

m is the number of phonon’s created or destroyed in the wavefront in other words, the Bragg diffraction order Depending on the angle of the incoming photons, the photons can be absorbed or be emitted by the interaction of the photon with the wavefront, gaining or losing energy in the process. The losing energy decreases the frequency of the photon and gaining energy increases the energy of the photon.

(10)

Figure 5: A schematic overview off the process of a driver. The VCO creates a RF-signal, with the voltage it receives. The sign ale is send to the VVA, where the power of the RF-signal can be changed with a applied voltage. The RF-signal is then send to the amp, where the signal is boosted and ends at the AOM.[8].

2.2.1 Controling the AOM

The AOM works with frequency of the order of 100 MHz. The frequencies are called radio frequency or RF. To create the RF signal, a VCO (Voltage Controlled Oscillator) is needed. A VCO is a device that changes the freqeuncy of the RF-signal it put outs, to the voltage it receives. A increase of voltage applied to the VCO is a increase of frequency of the RF-signal. The intensity can be controlled by the VVA (Voltage Variable Attenuator). Variation of the voltage on the VVA, change the attenuation, which changes the intensity. The intensity can be increased using an amplifier, which increases the intensity of the signal. The RF-signal goes from the amplifier to the AOM. The RF-signal powers the piezo that makes the crystal in the AOM to vibrate. The frequency of the vibration is equal to the frequency of the RF signal. The detuning is therefore the same as the RF-signal. In figure (5) a schematical overview is given.

2.2.2 Double pass AOM

The double pass AOM, can be used for higher detuning of the laser. The laser passes the AOM twice, giving it twice the detuning. To set-up a double pass, a single pass system is build. A AOM is placed in the focal point of a lens. Another lens, with the same focal lens is placed, twice the length of the focal length. This will increase efficiency of the AOM[6] and changes the waist of the laser beam back to normal size. An iris is placed, to block out the other diffraction orders, only passing the order that is needed. As the laser moves out the other lens, it passes a quarter wave plate, and is deflected on a mirror back in the direction of the AOM. If the beam is reflected precisely on the same path as the beam coming, time reversely symmetry gives that it will travel the same path as the light coming in. Amn iris is the placed after the AOM for the beam coming back, blocking other diffraction orders. Turning the quarter wave plate, can change the amount of light that passes or is reflected

(11)

Figure 6: Schematic overview of a double pas setup AOM setup[8].

by the PBS at the begin of the arm. A schematic overview of a double pass AOM is shown in figure (6). One of the Main advantage of a double pass AOM setup is that if the RF frequency changes and therefore the diffracted light of the AOM, has a different angle, the alignment does not change. This makes it easier for detuning laser at different freqeuncies.

2.3 Focal length measurement: knife-edge and photos

Knife edge measurement is a method to calculate the focal length of a lens. Light from a laser, is a Gaussian beam: The intensity is not concentrated in a point, but rather distributed as a Gaussian in the XY-plane. Due to the Gaussian field distribution, the actual focus might not coincide with the geometrical focus. This means that the focus point must be calculated to be certain that the focal point coincide with, the focal point given by the supplier of the lens. If a Gaussian beam is focused, it does not converge totally. There is a point where the waist of the beam is at its minimum. This gives a equation for the waist given by: The

Figure 7: The intensity as function of waist of the beam, is seen in the left figure. If the knife moves from the 10% mark to the 90% mark, the light is blocked. The amount of light that is blocked can be seen in figure on the right. The x-axis is the movement of the knife and the y axis is amount intensity of light that is blocked.

waist of the a Gaussian beam through a lens follows the equation[9].

w(z) = w0 s (1 + z 2 z2 R ) (20)

(12)

Figure 8: A knife-edge measurement done on one of the lenses in the experiment. The function fitted in this graph is (20). The measured focal length, is 20,68

Where w0is the smallest part of the waist and zRis the Rayleigh length. the Rayleigh length

is defined by equation.

zR=

πw2₀

λ (21)

To measure the waist of a beam on a position z, a razor-knife is placed on the position on moved in to the beam. After Two points, the intensity is measured. One where the knife blocks 10 % of the intensity (starting position) and the end point where the knife blocks 90 % of intensity (end position). The knife is moved from the starting position to the end position. The distance the knife is moved to achieve the intensity drop from 10 to 90 % is measured, plotted in a graph and fitted to the equation 20. The focal length is then read-out from the fitting parameters. An other way of calculating the focal length, is using a camera to photograph the beam. If a camera is placed in the beam, the profile of the beam, can be seen on a computer. As it moves through the beam that has past a lens, the beam image on the computer appear smaller. Where beam is the smallest, is the focal point. This technique is faster, however the positioning is not exact, making a knife-edge measurement a more exacter way of measuring the focal point.

(13)

3 Setup

The optical system that has been build has as purpose to detunne a 780nm laser, to the probe,cooling and optical pump transitions seen in figure (1). After light is detunned for these transitions, the light is coupled to a fibre that is connected to optical switches. These switches, switch the light between two experiment. A high efficiency is needed. The op-tical scheme is given in figure (9). The laser for this opop-tical setup, comes from a Toptica laser (model:TA-780), placed in an adjacent lab. The laser is coupled in the other lab and transferred with a single-mode polarization maintaining fibre, to the optical setup. The laser light propagates through a PBS, where large portion of light is reflected in to the cooling arm. It passes a double pass AOM(model MT110-B50a1-IR from AA optoelectronics) set to 99, 5 MHz, detuning the laser to 199 MHz slightly blue detuned below the F=2 to F’=3 transition, this to cool the cloud of atoms. The lenses used for the AOM’s have a focal length of f = 200mm. After the double pas AOM, the beam is moved through the PBS to the coupling part of the setup. The beam passes to a Glan-Thomson polarizer cleaning up the polarisation of the beam. A half wave plate is placed so the polarisation can be chosen to match the fibre’s axis. The beam is coupled to a fibre and the fibre is connected to an optical switch. The part of the beam that is not been reflected in to the cooling arm, is transported to the next arm that is responsible for the probe. It is the same as the cooling arm, however the AOM is set to 106M Hz, making the total detuning to 212 MHz. For the F=2 to F’=3 transition. The last arm is made for the optical pump. This arm is red detuned by 55 MHz and passes the AOM once before it is coupled with a fibre. After the laser passes through the AOM (model 46045-1-.78-TE02 from NEOS), the laser is coupled to a fibre. The optical switches, switch between the experiments if needed. The setup uses one inch high post, that can not be changed in the vertical direction. This increases the stability of the setup and decrease the effect of vibrations to a minimum. Shutters are placed, to send pulses to the experiment. The shutters are from Uniblitz and are powered by an Uniblitz driver. The shutters are hung from a plate, and lowered by a rails into place. The shutters stand free from the optical board, to lesser the effect of vibrations from the shutters on the optical equipment. Most of the mirror holders, are from Radiant Dyes, who are known for there stability.

3.1 Electronics

The AOM’s are powered by drivers. In the setup the cooling and probe AOM’s are controlled by Isomet model 323-b drivers and the optical pump AOM is controlled by isomet model 322-b driver. The drivers are characterised and therefore, the needed voltages for the different frequency that the VCO gives, is known. The drives need 28 V to operate. Every driver needs around of 400 mA. The current comes from one power supply where the drives are all connected to in a parallel circuit. The power supply gives out about 1.31 to 1.37 A of current. The current changes over time. This is the result of temperature increase over time of the drivers. The VCO and modulator, are controlled by the computer. The DAC from the computer gives out maximum of 10V . The needed voltage for the detuning, are about 6,8 6,4 and 3 V. These voltages can be created by the computer and therefore, the computer can be used for control the AOM. For the modulation, a total of 5 V is needed. This also can

(14)

(15)

be achieved using the computer, so the whole setup can be computer controlled. The drivers used from Isomet, give out a powerful enough signal for the AOM to work without any amplification. To characterise the drivers, the drivers are connected to a spectrum analyser and the voltage to the VCO is changed. The drivers have two parts in the characterisation graph. A non-linear part and a part after 4V that is linear. Over the linear part, a linear function is fitted to have a linear relation between voltage and frequency. The linear part for

Figure 10: The left graph, is whole characterisation for the driver for cooling. The first part has more measurements, to be certain of the behaviour of the Driver at lower voltage. The right is zoomed in onto te linear part of left graph, giving the right formula for the linear part

the cooling laser, gives a linear formula of fc = 4.67(5)U + 63.8(4) where fc is the frequency

in MHz and U the voltage. With this equation, frequency can be calculated and applied for detuning the laser to the wanted frequency. The same is done for the probe laser. The linear

Figure 11: The same thing is done for the probe driver as by the cooling driver. Left the whole characterisation graph, right only the linear fit part.

equation for the probe becomes becomes fp = 4.58(4)U + 64.6(3). for the optical pump, the

voltage required for the right detuning frequency of the AOM, is lower then 4 volts. Therefore there is no linear equation For the optical pump. This makes it difficult to characterise the

(16)

Figure 12: The frequency needed for the optical pump (55M Hz), is in the non-linear area of the curve, and therefore it uses a non-linear fit

optical-pump. In figure (12) the characterisation is given. The non-linear part where the frequency needed for the experiment is shown and fitted with a special polynomiaal function.

y = Vmax

xn

kn_{+ x}n (22)

which gives a nicely fit for and a formula for the part needed for the optical pump AOM. The values for the fit are k = 32(2) · 102_{, V}

max = 503(9) and n = 0, 29(3). which gives a

formula for the fitting condition:

Fop= 503(9)

x0,29(3)

(32(2) · 102₎0,29(3)_{+ x}0,29(3) (23)

This can be programmed into the computer to have the right frequency for the the right voltage. The intensity over voltage is measured to. The results are given in figure (15), the results show a small change in intensity as the voltage increases. however, the changes are small and therefore not significant for the experiment.

4 Results, conclusion and discussion

These are the results from the optical setup. Most results are about efficiency.

4.1 Intensity of the RF-signal and current increase

One of the first observation seen on the setup, was a steady increase of current as the drivers were on. The current increased from 1.345 to 1.373. The increase in current, can have a effect on the intensity. The measurement done is how the current, temperature, and intensity change over time.The outcome of the measurement was to be certain that there is no change in intensity over time. A infrared temperature camera is focused on a driver while the power-supply, is connected to a ampere-meter. The output from the driver, is connected to a spectrum analyser. The spectrum analyser, has a dBm limit of 25 dBm. The driver,

(17)

Figure 13: The left figure shows the change in temperature and current as a function of time of the probe driver. This clearly show that the temperature and current correlate. The right graph shows current as a function of time. The graph show there is a linear connection between current and temperature

gives out more power and therefor attenuators of total -19dB is placed to lower the intensity of the RF signal from the driver, so the spectrum analyser can measure the output of the driver. The measurement is done over the course of one half hour. The voltage stayed on 28 V, during the measurement. The temperature and intensity of the probe driver is measured The figures (13) show that as the temperature increases, the current increases linear. This means that as the drivers become hotter, the internal resistance drops and therefore more current moves through the drivers. The increase in current is small and therefore not a problem for the set-up. The intensity and current, over time are given in figure(14). The graph shows that the intensity fluctuate between 12.35 and 12.40 dBm. There is no coherence between the current increase and the intensity. This means that the intensity stays the same over time, and doesn’t change as the current changes. With the linear connection between the current and temperature, the conclusion can be made that the intensity doesn’t change as the temperature increases. The intensity has also been measured as the voltage changes on the VCO. The test have been done after the drivers have been receiving a current over a long period of time. The results are given in figure (15). The figure shows that there is a small increase of intensity as the voltage on driver increases. After the initial increase, the intensity drops due to a unknown reason. These changes in intensity are small and therefore don’t have a major effect on the efficiency of the AOM. The conclusion can be made that the Temperature of the driver and the voltage/current applied to the driver, have none to little effect on the intensity of the RF signal. The small changes that where measured are small and do not effect the efficient of the AOM significant.

4.2 Coupling efficiency

The intensity of the laser power changed over time, while the power of the laser itself, stayed stable. The coupling efficiency was measured to look if that had changed over time. To measure the coupling efficiency a power-meter that is placed at output of the fibre, is connected to a computer and then runs over couple of hours collecting samples every minute.

(18)

Figure 14: The figure shows current and intensity of the RF-signal as a function of time. As the current increases, the intensity does not increase with it.

(a) Probe Driver (b) Cooling Driver

Figure 15: Intensity of the RF signal of the drivers as a function of voltage appleid to the VCO of the driver.

(19)

Figure 16: The efficiency of the coupling from the fibre going from the one lab to the other lab over 16 hours

At the beginning and at the end, the intensity of the laser that is being coupled is measured. The intensity of the outgoing laser is divided by the incoming laser. The measurement on the begin and the end of the measurement, is done to see if the intensity of the incoming laser had changed. That was in all measurement not the case. The result is shown in figure (16). The intensity drops fast below and start rising as the night progresses. This can be caused by the change in temperature or change of humidity in the lab. The temperature of the lab is monitored, the humidity however is not measured and therefore an unknown factor in the change of efficiency. In graph (17) the temperature against efficiency is shown The small ’bumps’ in the graph fit with the change in temperature, as is seen in the zoomed in part. The dip around the 2 hour mark, can be the effect of change in humidity in the lab. What the humidity does to the efficiency, can not be found out because lack of humidity measurements at the time. Another measurement was done over the weekend. The power meter, collected 1280 samples over the time of 66 hours. Collecting a intensity sample every 2 minutes. The results shown in figure (18). The efficiency of the coupling drops with 7% around the same time there is a increase of temperature. The air conditioning system was probably offline, increasing the temperature and may effect the humidity in the room. In figure (19b) shows the dips in more detail. The dips coincides nicely with the temperature change. The whole weekend, there are small peaks of changing temperature. This is caused that the cooling is turned on when the room hits a certain temperature. The flat-line is a result of the cooling mechanism being in balance with the heat generated in the surrounding. This causes a stable part, in which temperature is roughly stable. The cooling system switches off after a random time, making the lab heat up again till it hits a set temperature where the cooling system

(20)

))

Figure 17: The left graph is the coupling efficiency mauserment done over 16 hours. There are small changes of efficiency correlating with the temperature change. The right graph, show a zoomed in part, with a strong correlation between temperature change and coupling efficiency change. The cause of the dip at 2 hours is not known.

(21)

Figure 19: the left figure is zoomed in figure of the dip of figure (18) and in the right figure is zoomed in on a part of figure (18) where the temperature is in a normal cycle

kicks in again. Another measurement was done over night with a humidity meter, next to the laser. The result can be seen in figure (20). As the night progresses, the efficiency drops significantly about 16%. This can coincide with the increase of humidity however, As the humidity is the same as the humidity at the time of coupling, the efficiency does not turn back to the same efficiency as it had at the same humidity. The humidity has a effect, however, there is know clear evidence how much it effect the efficiency. Further, the temperature has effects on the efficiency as seen in the bumps of efficiency drops around the 15 hour mark, and the increase of efficiency as temperature rises. Overall, the change in efficiency, overnight cannot be explained by mere climate change in the lab. More research has to be done to be conclusive on the change of efficiency over time.

4.3 Conclusion

The maximum efficiency achieved for the coupling of the laser to fibre to one lab to the other lab, was 53.6 %. The double pass AOM for the cooling laser, has a maximum efficiency of 62 %. the efficiency of the optical pump AOM is at maximum at 72%. The AOM of the probe that was ordered and will be delivered too late for this thesis. Further, the optical switches for this experiment are delivered later and therefore a successful coupling to the experiment could not been done. Even if components where delivered late, the conclusion can be made, that there is more intensity available for the experiment already running. With a coupling efficiency of the optical fibres of 50 %, the intensity of the cooling laser, can be increased from 90 mW to 200 mW. With this outlook, the conclusion can be made, that the setup can achieve the goals of increasing the intensity on the already running experiment and achieving the same for the experiment being assembled.

(22)

Figure 20: The results of 21 hours of intensity measurement. The temperature fluctuates with the air conditioning and there is a large change in humidity. Correlations can be seen between efficiency and temperature and humidity.

Figure 21: On the left the figure shows an increase of humidity over time, however the temperature does not change with the increase of humidity and on the right there is a correlation between humidity and coupling efficiency, however it does not explain the high change there is in the efficiency.

(23)

5 Populair samenvatting

Quantum computers zijn een van de heetste onderwerpen in de natuurkunde. Ze hebben de potentie om met een veel kleinere oppervlakte, veel snellere berekeningen te maken. Deze kwantum computers gebruiken lasers, om de verschillende berekeningen te maken. De laser exciteert de atomen en kan daarmee de atomen verschillende opdrachten geven. De infor-matie vanuit een atoom gaat via het licht naar andere componenten zodat het daar gebruikt kan worden of zelf opgeslagen. Zo kan een opties system gezien worden als de moederboard van de kwantum computer. Rydberg atomen zijn kandidaten om een onderdeel te zijn van deze kwantum computers. Rydberg atomen zijn atomen, met hoog hoofdkwantumgetal. Dit betekent dat de banen van de elektronen rondom de kern, zeer groot zijn. Hierdoor kunnen er sterke interacties tussen de atomen ondervonden worden, waardoor er ”Q-bit” gemaakt kun-nen worden. De opstelling die in dit verslag beschreven woord, gaat voor twee experimenten het laser licht verzorgen. Een experiment staat er al en een andere word nog gebouwd. De opstelling is zo gemaakt dat het kan schakelen tussen de verschillende experimenten. Voor het experiment zal het extra intensiteit leven voor de koel laser en voor de ‘optical pump’ laser. Een laser zal de opstelling koelen en een andere zal zorgen dat de elektronen van de atomen, niet vervallen in een toestand waar ze niet gekoeld kunnen worden. Licht gaat door verschillende armen en de frequentie van de laser word een beetje veranderd door Acousto-Optic modulator (AOM). Hierdoor kunnen we verschillende tussen niveaus gehaald van elektronen banen gehaald worden. De optische tafel is gemaakt en de componenten die er zijn werken zoals ze horen. Er zijn indicaties dat de opstelling zal werken zoals voor waar hij gemaakt is.

(24)

6 Thanks and acknowledgement

I would begin to thank David for being my help and mentor these weeks and even months. Working with me can be annoying and there is a high probability that the thought of killing me came to mind however, the feedback, mentoring and knowledge given I would always be grateful for. I want to thank Graham for his endless knowledge and a torch in the dark and frustrating world of experimental physics. Arthur for his motivational talks when everything was going wrong. Robert for giving me the opportunity for working in such a great team. Maarten for his tips, tricks and a his toleration for the mess that i had created in the lab. Jullius and nataly for the fun in the lab and for giving there time and patience for explaining and giving the right equipment for me to make this optical system. At last i would like to thank Diederik for untangling my strange sentences in to normal English. With the help of you all, I would not have the ability to do this project and to end with more knowledgee that I will have for the rest of my life.

(25)

References

[1] Atreju Tauschinsky. “Rydberg atoms”. PhD thesis. Universiteit van Amsterdam, 2013. [2] Peter van der Straten Harlod J. Metcalf. Laser Cooling and Traping. Springer-verlag,

1999. isbn: 0-387-98747-9.

[3] Malvin Carl Teich Bahaa E. A. Saleh. Fundamentals of Photonics. John Wiley & Sons Inc, 1991, pp. 192–243. isbn: 0-471-83965-5.

[4] _{Dennis Goldstein. Polarizedlight. 1993. Chap. 11. isbn: 0-8247-4053-X.}

[5] R. M. Waxler and C. E. Weir. “Effect of Pressure and Temperature on the Refractive Indices of Benzene, Carbon Tetrachloride, and Water”. In: (1962).

[6] V.N. Parygin V.I. Balakshy and L.E. Chirkov. “physical principles of acoustotoptics”. In: (1985).

[7] P. Debye and F. W. Sears. “On the scattering of light by supersonic waves”. In: Pro-ceeding of the national academy of sciences 18 (1932).

[8] D. J. McCarron. “A Guide in Acousto-Optic Modulators”. In: (2007).

[9] Dieter Meschede. Optics, Light and Lasers: The Practical Approach to Modern Aspects of Photonics and Laser Physics. KGaA, Weinheim: Wiley-VCH, 2007, pp. 60–61. isbn: 978-3-527-40628-9.

Setup of optical system for laser light distribution between two atomic chip experiments

University of Amsterdam

Bachelor Thesis