Atom trapping laboratory for upper level undergraduate...
1
λ/2 Experiment Rb Cell Reference Rb Cell M3a M3b M4 M5 HeNe Laser Telescope AOM Detector Beam block f 1 f 2 RF Mirror Lens Sample of glass beads on slide Condenser lens Back light CCD Camera To computer Laser Gaussian beam focussed on glass slide Neutral density filter Dichroic mirror Translation stage Microscope objective Two courses introduced in 2007: PHYS 4061 - Laser Spectroscopy PHYS 4062 - Atom Trapping – Laser spectroscopy course includes 9 experiments. – Each experiment is completed in two 3-hour lab sessions. – Experiments involve techniques in laser spectroscopy with focus on atom trapping. – Weekly short-form lab reports focus on data analysis. – Atom trapping course has two 3-hour lab sessions per week. – Students typically take four to five weeks to obtain a MOT and spend an additional three weeks on cold atom experiments. – Long-form lab report is completed during the last 3 weeks. Variation in average density as a function of atom number. The atom number was varied by changing the trap laser power. Graduate studnets: M.Weel I. Chan S. Beattie E. Rotberg A. Carew Undergraduate students: S. Chudasama D. Gosset K. Sowka V. Popovici H. Morrison A. Sibilia C. Guimaraes Other possible experiments include: – Absorption spectroscopy of cold atoms – Transition probablity measurements – Trapping 85 Rb or 87 Rb 200mV = 10 6 atoms PHYS 4061 - Laser Spectroscopy PHYS 4062 - Atom Trapping – Absorption and Emission Spectroscopy - EOM – Zeeman Shift – Lock-In – Linewidth & Fabry Perot – Optical Tweezers – Gaussian Beams – RF & Heterodyne – Vacuum Systems – Optical Detectors – Steady State Atom Number – Trap Number Density – Temperature – Loading Rate – Optical Pumping – Magetic Gradients – Beam Diameter Saturated absorption setup used in three experiments: EOM, Zeeman Shift, and Lock-in Detection Spatial profile of a laser before (black) and after (grey) passing through an optical fiber. CW and pulsed Heterodyne de- tection are demonstrated using an AOM. Plots of the trapped atom number as a function of inci- dent trapping and repump laser powers. The trapped atom number is inferred from fluorescence. – Hands-on approach for teaching experimental physics. – Students describe course as demanding, but rewarding. – Highly popular because modern techniques and equipment used. – – Research environment flexibility and advanced data analysis skills are excellent preparation for graduate studies in AMO laboratories and industrial careers. Phosphor fluorescence from an oscilloscope electron beam sweep is recorded by a trig- gered CCD camera. The dips correspond to grid lines on the oscilloscope screen. An expo- nential fit gives a 1/e decay time of 1.30(3) ms. Students calibrate and investi- gate noise characteristics of a photodiode and a photomulti- plier tube using pulsed and CW light. A measurement of the tem- perature of an atom trap using the release and re-capture method. The most probable speed from the fit gives a tem- perature of T = 420(20) µK. A measurement of the optical molasses decay time. A fit to a decaying exponential gives a time constant of 0.165(2) s. These courses are designed to be accessible for all undergraduate streams in physics and applied physics as well as incoming gradu- ate students. PHYS 4061- Laser Spectroscopy has been expanded to two sections with a maximum of 20 students and is a mandatory course for all physics streams. PHYS 4062 - Atom Trapping can ac- comodate up to 10 students. The cost of equipment based on commercially available compo- nents is $150,000. This budget is dominated by the cost of four diode laser systems (total $80,000). The laser budget can be sub- stantially reduced to ~$30k by using home-built external cavity diode lasers and master oscillator-power amplifier systems. Student training opportunities could include building Faraday isolators, lock-in circuits, and Rb reference cells. The laboratory manual con- taining a list of equipment relating to the individual experiments is available upon request. The California Institute of Technology, University of Michigan and State University of New York: Stony Brook as well as several liberal arts colleges have developed courses in related areas. An alternative format to this work can involve a small subset of these experiments. The spectral shift of a transition is measured with respect to a refer- ence spectrum. Expected value for F = 3, m F = 3→F’ = 4, m F’ = 4 sublevel transition is 1.4 MHz/G. The horizontal error bars are 5%, vertical error bars are comparable to the point size. Doppler-free data is fit to a Lorentzian lineshape to obtain a typical FWHM of 15 MHz. This is compared to the natu- ral linewidth. Doppler-broadened data is fit to a Gaussian curve obtaining typical FWHM of 750 MHz. This is compared with theory. The effect of EOM sidebands is studied. FPI peaks with (grey) and without grating feedback (black). The free running lin- ewidth is 91(5) MHz. The instrument limited linewidth is 58(5) MHz. Analog RF components such as couplers, splitters, mixers, amplifiers, and attenuators are investigated. RF power mea- surements are taken. The pressure insdie a vacuum system as a function of time is measured during pump down. The pumping speed is varied by adding bellows lengths and apertures. The conductances of the com- ponents are found from the slope. Leaks are demon- strated by loosening seals and outgassing is demonstrated by heating the chamber. A fit to the form (1-e -Γt ) gives 1/Γ = 1.17(3) s. Variation of the collisional rate with background density. A plot of the fluorescence from the F’ = 4 → F = 3 tran- sition as a function of time after the repump laser is shut off using an AOM. An expo- nential fit gives a time con- stant of 42.42(5) µs. The atom number has a sensi- tive dependence on the trap beam size. A power law fit is shown by the solid line. The atom 1/e cloud radius as a function of magnetic field gradient along the vertical axis of the MOT. The average operational maintenance budget is $3,000/year. This is sufficient to cover minor equipment failure. Items that typically re- quire replacement are laser diodes, ($1,000 commercial) and control electronics. Ion pumps ($1,000) may need to be replaced on a tim- escale of 10 years. The maintenance budget is comparable to the budget for other upper-year laboratory courses. Ideally, the course can be maintained by two trained graduate teach- ing assistants with a research concentration in AMO physics and one technical staff member. At York University, these courses have been in operation for more than five years. – Data analysis skills are emphasized in Mathematica – Mathematica tutorial during first two weeks of PHYS 4061 – Mandatory Laser Safety tutorial and training – LabVIEW tutorial included Students are exposed to an actual laboratory environ- ment. They must calibrate equipment for absolute mea- surements. Teamwork is necessary to op- timize data taking and to pre- pare a long-form lab report. Courses were developed with a gift of $125,000 from Optech Inc. and matching funds from the Faculty of Science and Engineering. For more information, visit us: datamac.phys.yorku.ca Fabry Perot Interferometry Vacuum Systems Impact Course Format Maintenance Mageto-Optical Trap Setup Steady State Atom Number Atom Trap Density Temperature Measurements Budget Acknowledgements Effect of Beam Diameter and B Gradient Optical Pumping Time Optical Tweezers Loading Rate Measurements Laboratory Environment RF Circuitry and Heterodyne Spectroscopy Experiments Zeeman Effect Experiment Optical Detectors Gaussian Beams and Spatial Filtering Lock-In Amplifier Spectroscopy Setup List of Experiments I ( )= I 0 exp − M Rb c 2 2k B T ( ∆ν ν 0 2 ν ( [ [ α(ν)= α 0 Γ 2 N (ν−ν 0 ) 2 +(Γ N /2) 2 ∆ E = µ B B (g F ‘ m F ‘ − g F m F ) The optical dipole force is used to trap 3.14 µm polysty- rene beads. The spring constant and auto- correlation are measured. h Ω 2 0 4∆ = U OD = k s <r 2 > 2 I (δ)= I 0 1+ F sin 2 (δ/ 2) F = 4R (1 − R ) 2 dN dt = R −ΓN 1+ z λ π nw 2 0 ( ( w = w 0 2 2 R = reflectance, F = Finesse, I = Intensity δ = phase F=[ R d /R(t)] 3 , R(t) = R 2 0 + (ut) 2 u= 2k B T /M R = loading rate, Γ = collisional rate N = atom number w = waist, = minimum waist n = index of refraction, λ = laser wavelength w 0 u = most probable speed C A Probe beams Beam block Laser Mirror Beam block Solenoid EOM Polarizing beam splitter Rb cell Pump beam Glass slide Time [ms] 3.0 2.0 1.5 1.0 0.5 0 10 18 2.5 Photodiode Signal [arb. units] 12 14 16 Frequency [GHz] -4 -2 0 2 4 6 Photodiode Signal [arb. units] 0 5 10 15 20 Doppler -broadened spectrum with EOM Doppler -free spectrum Time [ms] -4 0 2 4 0 20 40 60 80 0 5 10 15 20 25 30 0 10 20 30 40 Ma g netic Field [Gauss] Frequency [MHz] Ln[Pressure] -2.0 -1.5 -1.0 -0.5 0.0 0 10 20 30 40 50 60 Time [s] 0 1 2 3 4 0 2 4 6 8 10 Time [ms] Fluorescence [arb. units] -2 Intensity [mV] 0.02 0.06 0.10 0.000 0.005 0.010 0.015 Time [ms] 0.0 -0.4 -0.8 45 50 55 60 0.0 -0.4 -0.8 20 60 100 Time [ms] Lock-in signal Time [ms] -0.4 0.0 0.4 0.8 90 30 50 70 Trap beam diameter [cm] 0.0 0.2 0.4 0.8 Trap Fluorescence [mV] 0.6 0 50 100 150 3 4 5 6 7 8 9 10 0.8 1.0 1.2 1.4 1.6 Magnetic Field Gradient [G/cm] Trap Radius [mm] 1/P [1/mW] <r 2 > [ m 2 ] 0 0.0010 0.0020 0.0030 Autocorrelation Function [V 2 ] t’ [ms] 0 1 2 Power [mW] [ms] 20 40 60 80 1 2 3 4 50 100 150 200 0 50 100 150 200 250 Time [µs] Trap Fluorescence [mV] Photodiode Signal [mV] Time [s] 2 4 6 8 0 15 5 10 Background Fluorescence [mV] 40 50 60 0 12 4 8 Γ [1/s] Time [ms] 10 15 20 25 FPI Signal [V] 0 0.05 0.10 0.15 0.20 0.25 50 100 0 10 20 30 40 50 60 Atom Number [ x10 6 ] Average Atom Density [ x10 9 /cm 3 ] 75 25 Incident Trap Power [mW] 10 30 50 70 0 100 200 Photodiode Signal [mV] Incident Repump Power [mW] 0.2 0.6 50 100 150 200 1.0 Photodiode Signal [mV] AOM Incident Laser LO Beam Splitter Photodiode Function generator TTL Pulse RF Signal RF Pulse Switch Amplifier VCO Phosphor decay Spatially filtered beam Spring constant Position autocorrelation Correlation time B Slope = 1.49(8) MHz/G -20 0.08 0.12 0.16 0.20 10 Beam radius [mm] -10 Position [cm] 0 HeNe beam waist MOT loading curve Trap Fluorescence [arb. units] 10 20 30 Time [s] 0 0.5 1.0 1.5 2.0 Optical molasses decay Fraction of Atoms Remaining Expansion Time [ms] 2 4 6 8 0.3 0.9 0.5 0.7 Release and recapture 0 Background pressure variation Repump laser powers red squares: 0.60(6) mW green circles: 1.0(1) mW blue triangles: 50(5) mW 1 0 1 2 3 4 -1 50 -1 00 -50 0 50 Time [µs] Photodiode Signal [mV] Pulsed heterodyne 0.30 87 Rb F=2 →1,2,3 85 Rb F=3 →2,3,4 85 Rb F=2 →1,2,3 87 Rb F=1 → 0,1,2 EOM on EOM off F' = 4 F' =2 F' = 3 F' = (2,3) crossover F' = (2,4) crossover F' = (3,4) crossover 0 4 8 12 0 4 8 Position [mm] Intensity The fit gives a correlation time of 0.422(5) ms blue: single bellows red: double bellows green: aperture Photodetector Trigger Pulse λ /2 µ τ φ = 0 φ = π/2 φ = π E = energy, m F = magnetic quantum number µ Β = Bohr magneton, g F = Lande g factor Properties of Gaussian beams such as divergence and Ray- leigh range are measured with a scanning knife edge profiler. The cloud radius is deter- mined from Gaussian fits along two dimensions that were summed in quadrature. Inset: The integrated spatial profile of an atom cloud imaged by a CCD camera. A Gaussian fit gives a 1/e 2 cloud radius of 0.66(1) mm. Performance of lock-in components: mixers, filters, and phase shift- ers are investigated. Laser is locked using commercial lock-in module for durations of 10-15mins. The frequency stability is measured. Lock-in error signals obtained by scanning a laser across an atomic resonance for different phase shifts φ. Atom trapping laboratory for upper level undergraduate students C. Mok, S. Winter, H. Beica, B.Barrett, R. Berthiaume,A. Vorozcovs, F. Yachoua, N.N. Afkhami-Jeddi, R. Marants, M.Aggarwal, and A. Kumarakrishnan, Department of Physics, York University Work supported by Optech Inc. and York University
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Transcript of Atom trapping laboratory for upper level undergraduate...
λ/2
Experiment Rb Cell
Reference Rb Cell
M3a
M3b
M4M5
HeNe Laser
Telescope AOM
DetectorBeamblock
f1 f2
RF
Mirror
Lens
Sample ofglass beadson slide
Condenser lens
Back light
CCDCamera To computer
Laser
Gaussian beamfocussed onglass slide
Neutral densityfilter
Dichroicmirror
Translation stage
Microscopeobjective
Two courses introduced in 2007: PHYS 4061 - Laser Spectroscopy PHYS 4062 - Atom Trapping
– Laser spectroscopy course includes 9 experiments. – Each experiment is completed in two 3-hour lab sessions. – Experiments involve techniques in laser spectroscopy with focus on atom trapping. – Weekly short-form lab reports focus on data analysis.
– Atom trapping course has two 3-hour lab sessions per week.– Students typically take four to five weeks to obtain a MOT and spend an additional three weeks on cold atom experiments. – Long-form lab report is completed during the last 3 weeks.
Variation in average density as a function of atom number. The atom number was varied by changing the trap laser power.
Graduate studnets:M.WeelI. ChanS. BeattieE. RotbergA. Carew
Undergraduate students:S. ChudasamaD. GossetK. SowkaV. PopoviciH. MorrisonA. SibiliaC. Guimaraes
Other possible experiments include: – Absorption spectroscopy of cold atoms – Transition probablity measurements – Trapping 85Rb or 87Rb
200mV = 106 atoms
PHYS 4061 - Laser Spectroscopy PHYS 4062 - Atom Trapping
– Absorption and Emission Spectroscopy - EOM– Zeeman Shift– Lock-In– Linewidth & Fabry Perot– Optical Tweezers– Gaussian Beams– RF & Heterodyne– Vacuum Systems– Optical Detectors
– Steady State Atom Number– Trap Number Density– Temperature– Loading Rate– Optical Pumping– Magetic Gradients– Beam Diameter
Saturated absorption setup used in three experiments: EOM, Zeeman Shift, and Lock-in Detection
Spatial profile of a laser before (black) and after (grey) passing through an optical fiber.
CW and pulsed Heterodyne de-tection are demonstrated using an AOM.
Plots of the trapped atom number as a function of inci-dent trapping and repump laser powers.
The trapped atom number is inferred from fluorescence.
– Hands-on approach for teaching experimental physics. – Students describe course as demanding, but rewarding. – Highly popular because modern techniques and equipment used. –– Research environment flexibility and advanced data analysis skills are excellent preparation for graduate studies in AMO laboratories and industrial careers.
Phosphor fluorescence from an oscilloscope electron beam sweep is recorded by a trig-gered CCD camera. The dips correspond to grid lines on the oscilloscope screen. An expo-nential fit gives a 1/e decay time of 1.30(3) ms.
Students calibrate and investi-gate noise characteristics of a photodiode and a photomulti-plier tube using pulsed and CW light.
A measurement of the tem-perature of an atom trap using the release and re-capture method. The most probable speed from the fit gives a tem-perature of T = 420(20) µK.
A measurement of the optical molasses decay time. A fit to a decaying exponential gives a time constant of 0.165(2) s.
These courses are designed to be accessible for all undergraduate streams in physics and applied physics as well as incoming gradu-ate students. PHYS 4061- Laser Spectroscopy has been expanded to two sections with a maximum of 20 students and is a mandatory course for all physics streams. PHYS 4062 - Atom Trapping can ac-comodate up to 10 students.
The cost of equipment based on commercially available compo-nents is $150,000. This budget is dominated by the cost of four diode laser systems (total $80,000). The laser budget can be sub-stantially reduced to ~$30k by using home-built external cavity diode lasers and master oscillator-power amplifier systems. Student training opportunities could include building Faraday isolators, lock-in circuits, and Rb reference cells. The laboratory manual con-taining a list of equipment relating to the individual experiments is available upon request.
The California Institute of Technology, University of Michigan and State University of New York: Stony Brook as well as several liberal arts colleges have developed courses in related areas. An alternative format to this work can involve a small subset of these experiments.
The spectral shift of a transition is measured with respect to a refer-ence spectrum. Expected value for F = 3, mF = 3→F’ = 4, mF’ = 4 sublevel transition is 1.4 MHz/G. The horizontal error bars are 5%, vertical error bars are comparable to the point size.
Doppler-free data is fit to a Lorentzian lineshape to obtain a typical FWHM of 15 MHz. This is compared to the natu-ral linewidth.
Doppler-broadened data is fit to a Gaussian curve obtaining typical FWHM of 750 MHz. This is compared with theory. The effect of EOM sidebands is studied.
FPI peaks with (grey) and without grating feedback (black). The free running lin-ewidth is 91(5) MHz. The instrument limited linewidth is 58(5) MHz.
Analog RF components such as couplers, splitters, mixers, amplifiers, and attenuators are investigated. RF power mea-surements are taken.
The pressure insdie a vacuum system as a function of time is measured during pump down. The pumping speed is varied by adding bellows lengths and apertures.
The conductances of the com-ponents are found from the slope. Leaks are demon-strated by loosening seals and outgassing is demonstrated by heating the chamber.
A fit to the form (1-e-Γt ) gives 1/Γ = 1.17(3) s.
Variation of the collisional rate with background density.
A plot of the fluorescence from the F’ = 4 → F = 3 tran-sition as a function of time after the repump laser is shut off using an AOM. An expo-nential fit gives a time con-stant of 42.42(5) µs.
The atom number has a sensi-tive dependence on the trap beam size. A power law fit is shown by the solid line.
The atom 1/e cloud radius as a function of magnetic field gradient along the vertical axis of the MOT.
The average operational maintenance budget is $3,000/year. This is sufficient to cover minor equipment failure. Items that typically re-quire replacement are laser diodes, ($1,000 commercial) and control electronics. Ion pumps ($1,000) may need to be replaced on a tim-escale of 10 years. The maintenance budget is comparable to the budget for other upper-year laboratory courses.
Ideally, the course can be maintained by two trained graduate teach-ing assistants with a research concentration in AMO physics and one technical staff member.
At York University, these courses have been in operation for more than five years.
– Data analysis skills are emphasized in Mathematica– Mathematica tutorial during first two weeks of PHYS 4061– Mandatory Laser Safety tutorial and training– LabVIEW tutorial included
Students are exposed to an actual laboratory environ-ment. They must calibrate equipment for absolute mea-surements.
Teamwork is necessary to op-timize data taking and to pre-pare a long-form lab report.
Courses were developed with a gift of $125,000 from Optech Inc.and matching funds from the Faculty of Science and Engineering.
For more information, visit us:datamac.phys.yorku.ca
Fabry Perot Interferometry
Vacuum Systems
ImpactCourse Format
Maintenance
Mageto-Optical Trap Setup Steady State Atom Number
Atom Trap DensityTemperature Measurements Budget
Acknowledgements
Eect of Beam Diameter and B Gradient
Optical Pumping Time
Optical Tweezers Loading Rate Measurements
Laboratory Environment
RF Circuitry and Heterodyne
Spectroscopy Experiments
Zeeman Eect Experiment
Optical Detectors
Gaussian Beams and Spatial Filtering
Lock-In Amplier
Spectroscopy Setup
List of Experiments
I ( ) = I 0 exp −MRbc2
2kBT ( ∆ νν0
2
ν ([ [ α(ν) =α0Γ2
N
(ν − ν0)2 + (ΓN/2)2
∆ E = µB B (gF ‘ m F ‘ − gF m F )
The optical dipole force is used to trap 3.14 µm polysty-rene beads.
The spring constant and auto-correlation are measured.
hΩ 20
4∆= UOD =
ks <r2>2
I (δ) =I0
1 + F sin2(δ/2)F =
4R(1 − R )2
dNdt
= R − ΓN
1 +zλ
πnw 20( (w = w0
22
R = reflectance, F = Finesse, I = Intensity δ = phase
F=[ Rd/R(t)]3 , R(t) = R20 + (ut)2
u = 2kB T/M
R = loading rate, Γ = collisional rateN = atom number
w = waist, = minimum waist n = index of refraction, λ = laser wavelength
w0
u = most probable speed
C
A
Probe beams
Beamblock
Laser
Mirror
Beamblock
Solenoid
EOM
Polarizing beamsplitter
Rb cell
Pump beam
Glass slide
Time [ms]
3.0
2.01.51.00.50
10 18
2.5
Phot
odio
de S
igna
l [ar
b. u
nits
]
12 14 16Frequency [GHz]
-4 -2 0 2 4 6Phot
odio
de S
igna
l [ar
b. u
nits
]
0
5
10
15
20
Doppler-broadened spectrum with EOM Doppler-free spectrum
Time [ms]-4 0 2 4
0
20
40
60
80
0 5 10 15 20 25 30
0
10
20
30
40
Magnetic Field [Gauss]
Freq
uenc
y [M
Hz]
Ln[P
ress
ure]
-2.0
-1.5
-1.0
-0.5
0.0
0 10 20 30 40 50 60Time [s]
0 1 2 3 40
2
4
6
8
10
Time [ms]
Fluo
resc
ence
[arb
. uni
ts]
-2
Inte
nsity
[mV
]
0.02 0.06 0.100.0000.0050.0100.015
Time [ms]
0.0
-0.4
-0.845 50 55 60
0.0
-0.4
-0.8
20 60 100Time [ms]
Lock
-in s
igna
l
Time [ms]
-0.40.00.40.8
9030 50 70
Trap beam diameter [cm]0.0 0.2 0.4 0.8Tr
ap F
luor
esce
nce
[mV
]
0.60
50
100
150
3 4 5 6 7 8 9 10
0.8
1.0
1.2
1.4
1.6
Magnetic Field Gradient [G/cm]
Trap
Rad
ius [
mm
]
1/P [1/mW]
<r2 >
[ m
2 ]
00.00100.00200.0030
Aut
ocor
rela
tion
Func
tion
[V2 ]
t’ [ms]0 1 2
Power [mW]
[ms]
20 40 60 801234
50 100 150 2000
50100150200250
Time [µs]Tr
ap F
luor
esce
nce
[mV
]
Phot
odio
de S
igna
l [m
V]
Time [s]2 4 6 8
0
15
5
10
Background Fluorescence [mV]40 50 60
0
12
4
8
Γ [1
/s]
Time [ms]10 15 20 25
FPI S
igna
l [V
]
00.050.100.150.200.25
50 1000102030405060
Atom Number [ x106 ]
Ave
rage
Ato
m D
ensi
ty [
x109
/cm
3 ]
7525
Incident Trap Power [mW]10 30 50 70
0
100
200
Phot
odio
de S
igna
l [m
V]
Incident Repump Power [mW]0.2 0.6
50
100
150
200
1.0
Phot
odio
de S
igna
l [m
V]
AOM
IncidentLaser
LO
Beam Splitter
Photodiode
Functiongenerator
TTLPulse
RF Signal
RF PulseSwitch
Amplifier
VCO
Phosphor decay
Spatially filtered beam
Spring constant
Position autocorrelation
Correlation time
B
Slope = 1.49(8) MHz/G
-20
0.08
0.12
0.16
0.20
10
Beam
radi
us [m
m]
-10Position [cm]
0
HeNe beam waist
MOT loading curve
Trap
Flu
ores
cenc
e[a
rb. u
nits
]
10
20
30
Time [s]
00.5 1.0 1.5 2.0
Optical molasses decay
Frac
tion
of
Ato
ms R
emai
ning
Expansion Time [ms]2 4 6 8
0.3
0.9
0.5
0.7
Release and recapture
0
Background pressure variation
Repump laser powers red squares: 0.60(6) mWgreen circles: 1.0(1) mWblue triangles: 50(5) mW
1 0 1 2 3 4-150
-100
-50
0
50
Time [µs]
Phot
odio
de S
igna
l [m
V]
Pulsed heterodyne
0.30
87Rb F=2 →1,2,3
85Rb F=3 →2,3,4
85Rb F=2 →1,2,3
87Rb F=1 → 0,1,2
EOM onEOM off
F' = 4F' = 2
F' = 3
F' = (2,3)crossover
F' = (2,4)crossover F' = (3,4)
crossover
0 4 8 120
4
8
Position [mm]
Inte
nsity
The fit gives a correlation time of 0.422(5) ms
blue: single bellowsred: double bellowsgreen: aperture
Photodetector
Trigger Pulse
λ /2
µ
τ
φ = 0 φ = π/2 φ = π
E = energy, mF = magnetic quantum numberµΒ= Bohr magneton, gF = Lande g factor
Properties of Gaussian beams such as divergence and Ray-leigh range are measured with a scanning knife edge profiler.
The cloud radius is deter-mined from Gaussian fits along two dimensions that were summed in quadrature.
Inset: The integrated spatial profile of an atom cloud imaged by a CCD camera. A Gaussian fit gives a 1/e2 cloud radius of 0.66(1) mm.
Performance of lock-in components: mixers, filters, and phase shift-ers are investigated.
Laser is locked using commercial lock-in module for durations of 10-15mins. The frequency stability is measured.
Lock-in error signals obtained by scanning a laser across an atomic resonance for different phase shifts φ.
Atom trapping laboratory for upper level undergraduate studentsC. Mok, S. Winter, H. Beica, B.Barrett, R. Berthiaume,A. Vorozcovs, F. Yachoua, N.N. Afkhami-Jeddi,
R. Marants, M.Aggarwal, and A. Kumarakrishnan, Department of Physics, York University
Work supported by Optech Inc. and York University
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