Construction and calibration of a magnetic atom chip experiment

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University of Amsterdam

Bachelor thesis physics and astronomy

Construction and calibration of a magnetic

atom chip experiment

Author:

Elmer Gr¨

undeman

10424512

Supervisor:

Dr. Robert Spreeuw

Daily supervisor:

A.L. La Rooij

July 28, 2015

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Abstract

To overcome some of the limititions in the current Rb-87 magnetic chip experiment a new experiment is being built. This thesis gives the results of the calibration of the new radiofrequency (RF) wire antennas, microwave (µW) patch antennas and one set of coils. The new configuration of the antennas was tested, this will improve the power of their field which will speed up the transitions between hyperfine states of the atoms. The field and the heating of the coil pair was characterized and compared to models. Lastly some of the construction work is covered in this thesis.

Nederlandse samenvatting

Feynman voorspelde in 1982 al dat klassieke computers niet in staat zijn om quantum-systemen met veel deeltjes te simuleren, de benodigde ruimte in het geheugen neemt exponentieel toe met het aantal deeltjes. Hij stelde voor om deze veel-deeltjes quantum-systemen te simuleren door een vergelijkbaar quantumsysteem te maken en hiervan de parameters te beheersen. Dit wordt gedaan in de Quantum Gases & Quantum Infor-mation onderzoeksgroep in Amsterdam. Hier worden deze quantumsystemen gemaakt door een gas van rubidiumatomen te vangen in een magneetveld en ze af te koelen met lasers. Hierna worden de heetste atomen uit de wolk verwijderd met radiogolven, hierdoor koelt het gas verder af tot ongeveer 10µK. Uiteindelijk worden deze atomen gevangen in een rooster van magnetische microvallen, dit rooster wordt opgewekt door een chip waar met magnetisch materiaal een patroon op ge-etst is. In elke val zitten enkele honderden atomen, deze vormen nu 1 qubit, dit zijn elementaire eenheden van een quantumcom-puter. Doordat qubits zich in een superpositie van 0 en 1 bevinden kunnen ze veel meer waardes aannemen dan een klassieke bit, die alleen 0 of 1 kunnen zijn.

Voor mijn project heb ik meegewerkt aan de constructie en kalibratie van een nieuwe opstelling die gebouwd wordt in deze groep. Ik heb de antennes voor de radiogolven en microgolven afgesteld, de radiogolven worden gebruikt om de atomen af te koelen. De microgolven worden gebruikt om de atomen van de 0 toestand naar de 1 toestand te krijgen, dus om de qubit te vormen. Daarnaast heb ik ook de spoelen, deze wekken het magneetveld op waar de atomen in worden gevangen, getest. Alle onderdelen zijn afgesteld en zullen de komende tijd ingebouwd worden in de nieuwe opstelling. Deze zal in staat zijn om effici¨enter atomen te vangen in de microvallen en kan nog uiteenlopendere quantumsystemen simuleren. Hiermee hopen wij meer te weten te komen over hoe veel-deeltjes quantumsystemen zich gedragen.

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1 Introduction

In 1982 Feynman explained why classical computers cannot easily simulate quantum-mechanical problems [1]. The ammount of memory needed scales exponentially with the number of quantum particles, so many-body systems would be impossible to simulate. He suggested using other quantumsystems to simulate quantummechanics. A way to simulate a many-body quantum system is to make a similar system and control its parameters. In the group of Dr. Robert Spreeuw this is done by trapping ultracold Rb-87 atoms in the magnetic field of a magnetic chip. On the chip a pattern of permanently magnetized FePt is etched on Si, creating a lattice of magnetic minima with a spacing of 10µm, see figure 1. The atoms are first trapped in a Magneto-Optical Trap (MOT), then cooled to 1-10 µK using laser cooling and evaporative cooling. They are then loaded into the microtraps, this results in a lattice with a few hundred atoms per trap.

Figure 1: Magnetic potential due to the etched magnetized FePt pattern, there are a few hundred Rb-87 atoms per trap.

Now each ensemble can be defined as a qubit, α|0> + β|1>, which is a superposition of the |0> state, where all atoms are in the hyperfine ground state 5S1/2|F=1, mF=-1>,

and the |1> state, which has one atom in 5S1/2|F=2, mF=1> and the rest in 5S1/2|F=1,

mF=-1>. These qubits have infinitely more possible configurations than a classical bit,

which has 2, and can be used to store quantum information. Numerous proposals exist to exploit these qubits to speed up calculations that would be impossible due to the scaling of classical bits. The energy difference between the F =1 and F = 2 state for Rb-87 is 6.835 GHz, so the transition from |0> and |1> can be driven by microwaves.

1.1 The magchips experiment II

To create these magnetic lattices a setup was constructed between 2003 and 2007. The chip is located in ultrahigh vacuum in a glass cuvette of 30 x 30 x 70 mm, the chip is at the center of 3 pairs of coils which generate the magnetic field for the MOT, see figure 2.

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This setup has a couple of limitations; due to cooling limits the maximum current through the coils is 20 A and it takes 10 ms to reverse the polarity of the current, in that time atoms can escape from the trap, also the microwave (µW) and radio frequency (RF) fields are rather weak and due to lack of space the antennas cannot be brought closer to the chip, finally there is (too) little optical access, the lens is fixed and exchanging chips takes up to several months.

Figure 2: Schematic image of the coils in the current experiment. 1) The MOT coils, 2) the small coils 3), the big coils. The coils are used to cancel background fields, for the Magneto-Optical Trap and moving atoms [2].

1.2 Nanochips III

To overcome these limitations a new setup was designed. Bigger coils with better cooling will generate a larger magnetic field and with new power supplies the polarity can be re-versed within a millisecond. A larger vacuum chamber with better optical access is being built, see figure 3, the RF and µW antennas are placed inside this vacuum chamber, next to the chip, this will result in a stronger field. In figure 4 the placement of the antennas is shown, the RF wire antennas are labeled with 1 and the µW patches with 2. There are 2 antennas for a more uniform field. Also a loadlock system will be included to exchange chips within 1 week. Because of the easier chip exchange chips with shorter lattice spacing and different geometries, so different quantum systems, can be simulated.

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Figure 3: Model of the new vacuum chamber and coils of the new setup, the new vacuum chamber is about the size of the coils of the current setup.

Figure 4: Vacuum chamber with antennas as seen from below. The RF antennas are marked with a 1, the µW with a 2.

This thesis covers the calibration of the new radiofrequency and microwave antennas, the measurements on the coils and some of the construction I performed.

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2 Radio frequency antennas

2.1 RF-induced evaporative cooling

One of the applications of the RF antennas lies in evaporative cooling. This technique is used to further cool the atoms in the MOT below the Doppler limit [3]. This is necessary to reach the temperatures where the atoms can be loaded onto the chip. This is also used to reach the phase transition to a Bose Einstein Condensate (BEC), a macroscopic occupation of lowest energy state. The first BEC was achieved in 1995 [4], this discovery has led to many new insights and may be used as building block for quantum simulators.

To understand evaporative cooling it is important to understand how atoms are trapped in a magnetic field. Rb-87 atoms are neutral, but have a magnetic moment. The component of the magnetic moment of atoms along the direction of a magnetic field is given by the following formula:

µ = −mFgjµB (1)

Where mF is the magnetic quantum number, gj the Land´e g-factor and µB the Bohr

magneton. There is a minus sign because electrons have a negative charge. Atoms with a magnetic moment experience an energy shift in a magnetic field:

∆E = −~µ · ~B (2) If there is a magnetic field gradient atoms can move to a higher or lower field to minimize their energy. Depending on the sign of gj and mF the atoms will either seek a low or a

high magnetic field. If an atom has a negative magnetic moment it will seek a minimum in the magnetic field. Atoms with a positive magnetic moment will seek a maximum in the magnetic field. Because it is only possible to produce a local magnetic field minima in free space atoms with a negative magnetic moment can be trapped if they have too little kinetic energy to escape the minimum. For F= 2 the Land´e factor is positive, so atoms with a positive mF can be trapped, for F = 1 the Land´e factor is negative, so

atoms with a negative mF can be trapped.. The atoms in the MOT will all be in the low

field-seeking trapped state |F=2, mF=2> in this experiment. The energy distribution of

the atoms in the trap is a Boltzmann distribution, [5]. A way to lower the temperature in the trap is to remove the atoms with the highest energy and let the cloud rethermalize, see figure 5. To remove only the hottest atoms RF-induced evaporation is used. In figure 6 a schematic drawing of a parabolic magnetic minimum is shown. Hot atoms with high energy can get to positions with a higher magnetic field than the cold atoms which stay closer to the magnetic minimum. Because of the Zeeman splitting the energy difference between trapped and untrapped states is higher at a higher magnetic field.

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Figure 5: The red line gives the initial energy distribution in the system, when the red area is removed the system will rethermalise through collisions until the distribution of the blue line is reached. The temperature of system 2, T2, is lower than the initial temperature T1.

Figure 6: Energy levels of Rb-87 vs positions in a parabolic trap. For different mFthe atoms experience

a different magnetic potential. The higher the distance from the center the higher the energy differential between trapped and untrapped states. The energy difference is typically in the order of several MHz and can thus be induced by RF (Radio Frequency) waves.

With a high frequency RF signal it is possible to only send the atoms in a high magnetic field, thus the hottest, from a trapped to an untrapped state. When the hottest atoms are removed the system then rethermalizes to a system with a lower temperature. After the rethermalization the hottest atoms of the new system can be driven to an untrapped state by the same procedure, but now the energy, or frequency, of the RF needs to be lower.

2.2 Placement of the antennas

Because the RF is used for a broad range of frequencies, up until 50 MHz, the antennas have to produce a strong field at all these frequencies. Because the RF is too weak in the current experiment a new configuration was tested by Roos Jehee [6]. This configuration

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has 2 antennas and is based on the RF setup built by Marcius Extavour [7], here there were RF wires next to the Z-wire. Because there will be a chip on top of the Z-wire the field of wire antennas would be shielded, so 2 wire antennas next to the chip were chosen. With this configuration the field of the RF was stronger than in the current experiment up to a factor 4 [6].

2.3 Number of windings RF antennas

The antennas in the vacuum chamber will have 2 windings each. To see the influence of the number of windings on the power of the RF field an antenna was manufactured with 5 windings. This antenna was placed next to a copper block with the dimensions of the magnetic chip and the field was measured at the position of the atom cloud above the copper, see figure 7. The following equipment was used:

-Agilent 33220A 20MHz signal generator -ENI 420 LA +43dB linear amplifier -Aaronia 6mm probe

-Rigol DSA 815 spectrum analyzer

The probe is calibrated between 0 and 1000 MHz and gives an output in dBm. The formula to convert the power in dBm to field amplitude in mG is deduced from the manual and is given by:

field (mG) = 10Measured(dBm)−20∗log(f )20 ∗ 105 (3)

With f is the frequency of the RF in MHz. The antenna was connected after the amplifier, its field was measured with the probe which was connected to the spectrum analyzer. The field in the y-direction for different frequencies for different numbers of windings is shown in figure 8.

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(a) View from the top. (b) View from the side.

Figure 7: Setup used to measure the influence of the number of windings on the output power. The field was measured in the y-direction. The blue rod is the aaronia 6 mm probe.

Figure 8: RF power in dBm and magnetic field in mG for different numbers of windings, measured in the y-direction.

Because the antenna had to be repositioned each time a winding was removed it was not in the same postition every measurement, this explains the differing distances between the lines and the corresponding power. It is clear though that the power increases with the number of windings, but since more windings take up more room the antennas in the vacuum chamber will have 2 windings each.

2.4 Impedance matching with tuners

Inspired by conversations with R. Sprik optimisation of the antenna performance by matching the impedance of the antenna with the output impedance of the function gen-erator was tested. For this a MFJ-971 portable antenna tuner and 2 MFJ-16010 random

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wire tuners were used. The effect of impedance matching was measured for either 1 an-tenna or both anan-tennas.

The impedance matching was first tested for one antenna with the MFJ-971. The impedance was optimised for 10 MHz and the field was compared to the field of the untuned antenna, see figure 9a. There is a clear increase in output power around 10 MHz, but the field at other frequencies is decreased. Because the field is very low for all the other frequencies, even zero before the peak, this tuner will not be useful for a frequency sweep needed for evaporative cooling, but could improve the power for dedicated frequen-cies.

(a) Impedance matching with a MFJ-971 portable antenna tuner for 10MHz compared to the field without tuner, for one antenna.

(b) The 2 antennas tuned seperately for 13 MHz, then measured together. Two MFJ-16010 were used.

Figure 9

To find the potential gain in power for 1 frequency with 2 antennas another tuner was needed. Two MFJ-16010 tuners were borrowed and tested. These tuners gave a different spectrum compared to the MFJ-971, the field was not zero at all other frequencies but could only boost the field for frequencies above 13 MHz. The effect of these tuners was measured by matching both antennas seperately for the same frequency and the connect-ing them together, see figure 9b. Because the signal came from 1 function generator and was then split between the 2 antennas there is no significant gain, when the antennas were tested seperately the signal was not split. This measurement could be improved by using 2 different signal generators and 2 amplifiers. Because there are 2 antennas used it is also important to have a 180◦ phase difference between the 2 antennas. Because of the experiment design there currently is no need for these tuners, but boosting a dedicated frequency could be useful at a later time.

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2.5 Vacuum antennas

The antennas Roos Jehee used to measure the field of the new configuration were larger, had different windings and were made of another material than the antennas designed for inside the vacuum chamber [6]. When the vacuum antennas were finished the field of the 2 new antennas could be characterized and compared to the conclusion of Roos Jehee. For this the setup seen in figure 10 was used. The same equipment was used as before, but since there was only 1 amplifier the signal from the generator was split after the amplifier. To get an idea of the power and direction the field was measured at different points between the two antennas, so the field in the y-direction at different points on the y-axis. The results are shown in figure 11a.

(a) View from below, lab system included. (b) View from the side.

Figure 10: Setup used to measure the field of the RF antennas. With the placement of the probe in (b) the field in the x-direction is measured.

(a) Output power in the direction along the y-axis.

(b) The power of the single antennas and the power of both antennas connected.

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First of all, the field is the strongest near the antenna to the right in figure 10a and the spectrum has a distinct shape with a dip around 8MHz. Secondly the field is rather weak near the left antenna, here the spectrum also has another shape. Lastly there is a clear dip in the power between 2mm and 5mm. To understand what happens here the power of the single antennas was measured and compared to situation where they are both connected, see figure 11b. The fields of both antennas are comparable in magnitude, but seem to cancel eachother at the frequencies where their power is equal. Around 8 MHz there is a dip in the right antenna and a peak in the left antenna. By fastening the connection between the antenna and the feedthrough this dip/peak disappeared. It seems like these home built connections can cause resonance in the antennas, this should be tested before the antennas are installed in the experiment.

Since the antennas are connected to the same function generator both waves are in phase. Because of this the fields are in the opposite direction in the y-direction and they cancel eachother out. If the fields cancel if they are in phase, they should add up when there is a phase difference of 180◦. To control the relative phase a RIGOL DG4000 function generator was used. This function generator has 2 independent signal outputs of which the relative phase can be controlled. The power was measured in the center of the cloud for 0◦, 90◦ and 180◦ phase difference, see figure 12. At different relative phases the field behaves as expected, where at 180◦ the field is maximal. Because there were 2 outputs no amplifier was used, this explains the weaker output power.

Figure 12: The influence of the phase difference of the antennas on the power of the RF field at the center of the chip. This is maximal for a phase difference of 180◦.

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Now that the fields add up correctly the antennas can be calibrated. The cloud of atoms will be in a long cigar-like shape along the x-axis, so the power was measured on these positions. Because of the almost rectangular shape of the antennas, it is expected that the field in the y-direction is the same for all positions on the x-axis close to the center. This is confirmed by the measured field, see figure 13. The field was roughly the same on every position. Because one of the antennas moved at 4mm this measurement is omitted from the graph. The field there is expected to be the same as on the neighbouring positions

Figure 13: Field along the x-axis measured in the y-direction of the antenna pair with a phase difference of 180◦.

2.6 Absolute power calibration

Because different equipment was used compared to Roos it was difficult to compare the absolute field of the antennas. The only comparable measurement performed was the absolute field for different numbers of windings, presented in figure 8. If one would measure the field of the antenna with 2 windings and would use 2 amplifiers, the field would be twice as strong as in the current experiment, see figure 14.

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(a) Absolute field in current setup. (b) Absolute field of the new configuration. Figure 14

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3 Microwave patch antennas

The energy difference between F = 1 and F = 2 for Rb-87 is 6.835 GHz, and can thus be driven by microwaves. Because microstrip (or patch) antennas have a strong near field, are compact and robust, have a higher efficiency than an open cable and can be tuned for a particular resonance frequency it was decided to use these. In figure 15 a schematic drawing of the patch is shown. Roos Jehee tested different vacuum compatible materials for the dielectric substrate on the patch and found that teflon gave the best results, [6]. Based on the patch used by Roos the new patches had a teflon substrate with a constant height h, the patch itself was made of silver. The L and W were chosen such that the resonance frequency was expected at 6.835 GHz. The following formula shows the (theoretical) proportionality between the resonance frequency frand the width W of

the patch [8]: fr∝ c 2W r 2 r+ 1 (4) With c the speed of light and rthe dielectric constant of teflon. Although the resonance

frequency also strongly depends on the other parameters, it was decided to only use the width of the patch as variable to tune the patch for the right resonance frequency.

Figure 15: Schematic drawing of a microstrip antenna from Antenna theory[8].

3.1 Tuning the patches antennas

To tune the antennas the reflection was measured using a R&S ZVA 67 vector network analyzer at AMOLF. With a network analyzer it is possible to see the reflection of an antenna for a broad range of frequencies. If there is a dip in the reflection, there will most likely be a peak in the transmission. So by measuring the reflection it is possible to see where the resonance frequency lies. Because the antennas only have to emit 6.835 GHz the resonance peak should be a this frequency for the antennas to work optimally.

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The first patch had a resonance peak at 6.55 GHz, but the peak was very narrow and the network analyzer was not calibrated the right way. Because the resonance frequency was too low the width was decreased. In an attempt to broaden the peak it was decided to taper the patch, in the first version this was done by keeping one edge straight and tapering the other side. The resonance peak shifted to a higher frequency and the peak seemed broader. To further increase the resonance frequency and width the patch was cut to a trapezium. This trapezium was cut 2 more times until the resonance peak included 6.835 GHz. In figure 16a the resonance peaks of these patches are shown. Each time the patch was cut the width of the silver was reduced by 1mm at both sides, this was done by Hugo Schlatter and took a couple of days.

Because the quality of the patch did not suffer from the cutting of the silver a second patch was manufactured. The dimensions of this patch were based on the measurements on the first patch, this patch was made as a square because this was easier to make and adjust. The reflection measurements are shown in figure 16b. The last measurements on both patches in figure 16 are incomplete because the data was not exported the right way, the peaks of the reflection are still visible and show resonance peaks including 6.834GHz. The final patches are shown in figure 17. Although the shapes of the patches differ the resonance frequency is roughly the same.

(a) Reflection at 6.835 GHz is -14.87 dBm. (b) Reflection at 6.835 GHz is -9.89 dBm. Figure 16

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Figure 17: Final shapes of the square (left) and trapezium (right) patches before cleaning.

After the antennas were tuned they were made ready for ultrahigh vacuum. This involved cleaning the patch and replacing the SMA cable with the vacuumproof SMA cable. Dur-ing the cleanDur-ing the tapered silver patch detached from the teflon and the teflon of the square patch came loose. The square patch could be salvaged by reglueing the teflon, this way the peak stayed at roughly the same position. The tapered patch was also reglued but had a very different reflection. See figure 18 for the reflection of the reglued vacuum antennas. The square patch had an acceptable resonance peak and is considered finished. Because the resonance peak of the trapezium patch was very small it was decided to re-place the trapezium with another silver patch with the dimensions of the square. Because this patch was not finished in time it is not included in this report.

Figure 18: Reflection of both patches after the reglueing, the resonance peak of the trapezium patch has almost disappeared compared to before.

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These measurements show that efficient vacuum compatible microwave patches can be made and can be tuned for the right frequency by cropping the width of the silver. The quality of the patch did not suffer from these adjustments.

3.2 Influence vacuum chamber & phase adjuster

While the antennas were being tuned other measurements were performed using 2 an-tennas Roos Jehee used to test the dielectric. These anan-tennas did not have the right resonance frequency but were still useful for testing the influence of a vacuum chamber and the relative phase between the antennas.

Because the wavelength of microwaves is rather small, 4.9 cm for 6.835 GHz, the nearby stainless steel vacuum chamber is expected to have a large influence on the magnitude of the field due to reflection. To get an idea of this effect the 2 antennas were set up in the configuration of the experiment. A piece of aluminum foil was shaped in the form of the chamber and the field was measured inside this chamber. The magnitude of the field strongly depended on the shape of the chamber. By slightly deforming the aluminum foil the magnitude of the field could be changed by a factor of 40. The reflecting fields of the 2 antennas cause interference in the chamber, where the positions of the positive and destructive interference depend on the reflected field and thus on the position of the wall. The position of the minima and maxima in the field is also dependent on the relative phase of the antennas. To test the influence of the relative phase a phase adjuster was placed in the cable towards one of the antennas and the aluminum chamber was shaped in such a way that the field was 0 above the chip. At 12 GHz the range of the phase adjuster is 520◦. Because the maximum range is dependent on the wavelength of the signal, and thus the frequency, the maximum phase shift at 6.83 GHz is 296◦. The influence of the phase adjuster on the magnitude of the field is shown in figure 19a.

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(a) Output power of the pair of µW patches above the chip for different phase shifts.

(b) Power of the pair of µW patches for different phase shifts when using different cables.

Figure 19

At a phase shift of 180◦_{the signal increased by 16dB. Although the full range is not 360}◦

for this frequency, it is possible to come close to the maximum µW field power for every shape of vacuum chamber.

The phase adjuster creates a phase difference by increasing the length of the path the signal has to travel. By turning the knob the length of the cable inside is increased or decreased. This means that the relative phase of the 2 antennas depends on the length of the cable between the signal generator and the antenna. This is shown in figure 19b, here the cable towards one of the antennas is longer than the cable towards the other antenna. This has been tested for 2 different cables, where cable 2 is longer than cable 1, because of the length difference the the maximum of the field has shifted. The inclusion of an apparatus to control the phase of the µW signal can make up for the influence of a vacuum chamber and a possible difference in cables.

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4 Small coil pair

4.1 Field & gradient

The small coils were the only coils to be finished in time to be tested. The coils were set up in the same configuration as designed for the experiment, connected to the cooling water and to a 0 - 100A Delta power supply borrowed from F. Schreck. The field was measured in the center of the pair for different currents with a GM08 Gauss meter. The field of 1 coil was compared to the field of the pair, see figure 20a. The field of 2 coils is twice the field of a single coil, so it seems like the 2 coils are roughly equal in field. To test whether the coils are equal the gradients of the coils were measured at 60A and compared, see figure 20b. From these figures it is concluded that the coils give an equal field.

(a) Field of one coil and of the pair at the position of the chip.

(b) Comparison between the magnetic field vs the distance of the small coils at 60A.

Figure 20

After the comparison of the 2 coils the field of the coil pair was measured and compared with a model in mathematica, figure 21. The field of the coil pair matches the model well. The model uses the Radia software developed by the ID group of the ESRF [9].

4.2 Heating model

All coils are cooled by running water through 1 side of the brass housing, see figure 24 for a schematic drawing, the brass transports the heat of the wires to the cooling water. The coils have to generate a certain field without getting too hot. To predict the heating of the coils a model was made. To calibrate this model the temperature of the small coils was measured at different points for currents between 0 and 60A. In figure 22 an infrared photo of the 2 small coils is shown for 60A. The infrared camera was used to measure the highest temperature for different currents. The magnetic field and temperature of

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Figure 21: Magnetic field vs the distance from the center of the pair compared with a model in Mathematica. A current of 42A was used.

the coil pair for different currents is shown in figure 23. The highest temperature of the second coil is slightly higher than of the first. This could be because the cooling water first ran throught the first coil and then through the second, so the second coil was cooled by slightly warmer water, the difference was about 1◦C. The temperature at the positions shown in figure 24 for different currents can be seen in table 1. At 60A the maximum temperature is 56◦C, this does not correspond with figure 22a, where the highest temper-ature is 61.3◦C. This is because the temperature in the table was measured at the surface of the coil with a thermo-couple. Though from both measurements it is concluded that the temperature is acceptable for all currents and that the coils are cooled efficiently.

(a) Temperature coil 1 at 60A (b) Temperature coil 2 at 60A Figure 22

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Figure 23: Temperature and field of the coil pair for different currents.

Figure 24: Cross-section of the coil with different positions where the temperature was measured, the coil is cooled from the D-side. The temperatures are shown in table 1.

Temperature small coil vs current

Current (A)

A

B

C

D

50

42.85

◦

C

36.56

◦

C

30.67

◦

C

20.33

◦

C

60

56.38

◦

C

46.34

◦

C

36.54

◦

C

22.35

◦

C

Table 1: Temperatures of small coil 1 measured at the positions A, B, C and D with thermo-couples, these positions correspond with the positions shown in figure 24.

The small coils have 40 windings, 4 wires axially and 10 radially. This means that the thermal conductivity in the radial direction will be lower than in the axial direction

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because there is more material between the wire and the brass. Eric Hennes calculated the values for the thermal conductivity with Finite Element analysis (FEM). He calculated a worst case, k = 1.13W/mK, and best case scenario, k = 3.6W/mK. A naive 1D model is given by the following formula:

∆T = PtotWx 8Akx

(5) Where ∆T is the temperature difference due to heating, Ptotthe total power, Wxthe axial

width of the coil, A the cross-sectional area of the wire and kxthe thermal conductivity

in W/mK.

Using figure 22 ∆T is 40◦C, this gives a kx of 6.8W/mK. Because the temperature can

only go in one direction in this model this will most probably be a overestimation. The best 2D approximation using the measured temperatures gives kr = 2.0W/mK and ka =

3.8W/mK. The difference between the coils and the FEM analysis prompt a new FEM analysis with better parameters. In the end the k-values are not as good as hoped, but the temperatures are manageable.

4.3 Influence steel micrometers screws

Because the entire experiment is dependent on a very precise magnetic field all the com-ponents around the chip are made of non-magnetic material. The 5 micrometers screws which are used to position the lens are made of magnetic hardened steel and are rela-tively close to the atoms, see figure 25. It was tested whether this quantity of steel at this position had a notable impact on the magnetic field of the coils. If this is the case there will be hysteresis when the field is switched. To test this one of the MOT coils was used because these are the largest coils with the highest field in the experiment, so the presence of magnetic material was expected to have the highest impact here. A steel block with the same weight as the 5 micrometer screws combined was used for the test. As seen in figure 26 no visible influence was measured on this range of currents. The blue triangle line shows the field with the steel bock next to the probe, this shows that magnetic material near the atoms could have a large influence. Because the impact of the steel at the position of the micrometers is not noticeable it is concluded that this will not interfere with the magnetic field near the atoms.

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Figure 25: Position of the 5 steel micrometers screws in the experiment. There are 3 screws for the z-direction, 1 for the x-direction and 1 for the y-direction.

Figure 26: Influence of magnetic steel micrometer screws attached to the lens on the magnetic field of one MOT coil measured at the position of the atom cloud. If the steel block would be positioned near the center this would have a large influence, at the position of the micrometer screws the effect is not visible.

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5 Conclusion

The power of the new RF antennas was hard to compare with the current antenna be-cause the measurements performed were done under different circumstances as the mea-surements of Roos Jehee. Still it seems like there is a gain in power, this is probably due to the use of 2 amplifiers instead of 1. Also one of the vacuum antennas has a stronger field than the other one, this could be solved by fastening all the connections tightly. The RF antennas must be used with a 180◦ phase difference to get the maximal field at the position of the atoms. It is also possible to increase the field for a narrow range of frequencies by matching the impedance with a tuner.

The µW patches can be tuned for a specific resonance frequency, this has been done for 6.835 GHz. By adjusting the phase of one of the antennas the negative effects of reflec-tions, interference and difference in cable length can be controlled.

The small coils are equal in field and gradient, the pair produces the required field and are cooled efficiently. The field is well described by the model, the heating model can be improved using the temperatures measured.

6 Thanks and acknowledgements

I would like to thank Arthur for involving me in the construction of the new setup, all the help on the measurements and the very useful discussions. Also for reading and correcting my thesis multiple times.

I would also like to thank Hugo for manufactoring the µW and RF antennas and all the useful disussions about these antennas.

Lastly I am grateful to Thijs for answering all my questions about electronics so patiently, lending me some very useful signal generators and even coming to AMOLF with us to calibrate the network analyzer correctly.

References

[1] R. Feynman, “Simulating physics with computers,” International journal of theoretical physics, 1982.

[2] D. Pijn, “Loading a 2d microtrap lattice on a magnetic atom chip,” Master’s thesis, Universiteit van Amsterdam, 2014.

[3] H. F. Hess, “Evaporative cooling of magnetically trapped and compressed spin-polarized hydrogen,” Physical Review B, vol. 34, no. 5, p. 3476, 1986.

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[4] M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Observation of bose-einstein condensation in a dilute atomic vapor,” science, vol. 269, no. 5221, pp. 198–201, 1995.

[5] O. Luiten, M. Reynolds, and J. Walraven, “Kinetic theory of the evaporative cooling of a trapped gas,” Physical Review A, vol. 53, no. 1, p. 381, 1996.

[6] R. Jehee, “Lab report: Radio frequency and microwave testing for magnetic chips,” 2014.

[7] M. H. Extavour, Fermions and bosons on an atom chip. PhD thesis, University of Toronto, 2009.

[8] C. A. Balanis, Antenna Theory. John Wiley & sons, INC, 1997.

Construction and calibration of a magnetic atom chip experiment

University of Amsterdam

Bachelor thesis physics and astronomy