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