Nonlinear Spectroscopy of Cold, Trapped Atoms: Atomic

Nonlinear Spectroscopy of Cold, Trapped Atoms: Atomic Recoil and Localization Effects in a MOT

T. M. Brzozowski M. M¹czyñska M. Zawada J. Zachorowski and W. Gawlik

Marian Smoluchowski Institute of Physics, Jagiellonian University, Reymonta 4, 30-059 Cracow, Poland

Experimental setup Simplistic predictions

| e,N-1>

|e,N>

| g,N>

| g,N+1>

| 2(N-1)>

| 1(N-1)>

| 2(N)>

|1(N)>

d

d

W’

w+

W’

w+

W’

w-

W’

w-

W’

w

wwww

W’

The simplest model: dressed two level atom

resonances @ , , w - W’ w w + W’@

absorption ~ Im ( r )eg

2four wave mixing ~ |r |eg

Different shapes of the absorption and FWM spectra, but resonances occur at the same frequencies!

Experimental results

ab

sorp

tion

[a

rbitr

ary

un

its]

-4 -3 -2 -1 0 1 2 3 4

I/I =4.60

I/I =10.40

I/I =23.60

D (0,±1) D (0,±1)

D (±1,±2)

a

b

c

probe - pump detuning [MHz]

detuning of the trapping beams d=14 MHz

Changes in absorptionwith trapping beam intensity

D [MHz]

w0 - trapping beam frequency

w0

absorption

four-wave mixing

-60 -40 -20 0 20

w0

Wide scan spectra Narrowed scan spectra: central structure

s+ s-lin

-2 -1 0 1 2 3 -2 -1 0 1 2 3 -2 -1 0 1 2 3

s+ s-lin

absorption

four-wave mixing

pump - probe detuning [MHz]

(s+/-, lin - polarization of the probe beam)

Conclusions

J. Zachorowski, T. M. Brzozowski, T. Pa³asz, M. Zawada, and W. Gawlik, Acta Phys. Polonica A 101, 61 (2002)

trap beam frequency

absorption

four-wave mixing

frequencyRequirements

Spectroscopy of cold atomsin the magneto-optical trap

Experiment principle

Investigation of atom energy levels perturbed by light

Investigation of localization of atoms in the light field

Investigation of atom dynamics in the trap

Motivation

Nonlinear Spectroscopy of Cold, Trapped Atoms: Atomic Recoil and Localization Effects in a MOT

T. M. Brzozowski M. M¹czyñska M. Zawada J. Zachorowski and W. Gawlik

Marian Smoluchowski Institute of Physics, Jagiellonian University, Reymonta 4, 30-059 Cracow, Poland

Experimental setup Simplistic predictions

| e,N-1>

|e,N>

| g,N>

| g,N+1>

| 2(N-1)>

| 1(N-1)>

| 2(N)>

|1(N)>

d

d

W’

w+

W’

w+

W’

w-

W’

w-

W’

w

wwww

W’

The simplest model: dressed two level atom

resonances @ , , w - W’ w w + W’@

absorption ~ Im ( r )eg

2four wave mixing ~ |r |eg

Different shapes of the absorption and FWM spectra, but resonances occur at the same frequencies!

Experimental results

ab

sorp

tion

[a

rbitr

ary

un

its]

-4 -3 -2 -1 0 1 2 3 4

I/I =4.60

I/I =10.40

I/I =23.60

D (0,±1) D (0,±1)

D (±1,±2)

a

b

c

probe - pump detuning [MHz]

detuning of the trapping beams d=14 MHz

Changes in absorptionwith trapping beam intensity

D [MHz]

w0 - trapping beam frequency

w0

absorption

four-wave mixing

-60 -40 -20 0 20

w0

Wide scan spectra Narrowed scan spectra: central structure

s+ s-lin

-2 -1 0 1 2 3 -2 -1 0 1 2 3 -2 -1 0 1 2 3

s+ s-lin

absorption

four-wave mixing

pump - probe detuning [MHz]

(s+/-, lin - polarization of the probe beam)

Conclusions

J. Zachorowski, T. M. Brzozowski, T. Pa³asz, M. Zawada, and W. Gawlik, Acta Phys. Polonica A 101, 61 (2002)

trap beam frequency

absorption

four-wave mixing

frequencyRequirements

Spectroscopy of cold atomsin the magneto-optical trap

Experiment principle

Investigation of atom energy levels perturbed by light

Investigation of localization of atoms in the light field

Investigation of atom dynamics in the trap

Motivation

Nonlinear Spectroscopy of Cold, Trapped Atoms: Atomic Recoil and Localization Effects in a MOT

T. M. Brzozowski M. M¹czyñska M. Zawada J. Zachorowski and W. Gawlik

Marian Smoluchowski Institute of Physics, Jagiellonian University, Reymonta 4, 30-059 Cracow, Poland

Experimental setup Simplistic predictions

| e,N-1>

|e,N>

| g,N>

| g,N+1>

| 2(N-1)>

| 1(N-1)>

| 2(N)>

|1(N)>

d

d

W’

w+

W’

w+

W’

w-

W’

w-

W’

w

wwww

W’

The simplest model: dressed two level atom

resonances @ , , w - W’ w w + W’@

absorption ~ Im ( r )eg

2four wave mixing ~ |r |eg

Different shapes of the absorption and FWM spectra, but resonances occur at the same frequencies!

Experimental results

ab

sorp

tion

[a

rbitr

ary

un

its]

-4 -3 -2 -1 0 1 2 3 4

I/I =4.60

I/I =10.40

I/I =23.60

D (0,±1) D (0,±1)

D (±1,±2)

a

b

c

probe - pump detuning [MHz]

detuning of the trapping beams d=14 MHz

Changes in absorptionwith trapping beam intensity

D [MHz]

w0 - trapping beam frequency

w0

absorption

four-wave mixing

-60 -40 -20 0 20

w0

Wide scan spectra Narrowed scan spectra: central structure

s+ s-lin

-2 -1 0 1 2 3 -2 -1 0 1 2 3 -2 -1 0 1 2 3

s+ s-lin

absorption

four-wave mixing

pump - probe detuning [MHz]

(s+/-, lin - polarization of the probe beam)

Conclusions

J. Zachorowski, T. M. Brzozowski, T. Pa³asz, M. Zawada, and W. Gawlik, Acta Phys. Polonica A 101, 61 (2002)

trap beam frequency

absorption

four-wave mixing

frequencyRequirements

Spectroscopy of cold atomsin the magneto-optical trap

Experiment principle

Investigation of atom energy levels perturbed by light

Investigation of localization of atoms in the light field

Investigation of atom dynamics in the trap

Motivation

Nonlinear Spectroscopy of Cold, Trapped Atoms: Atomic Recoil and Localization Effects in a MOT

T. M. Brzozowski M. M¹czyñska M. Zawada J. Zachorowski and W. Gawlik

Marian Smoluchowski Institute of Physics, Jagiellonian University, Reymonta 4, 30-059 Cracow, Poland

Experimental setup Simplistic predictions

| e,N-1>

|e,N>

| g,N>

| g,N+1>

| 2(N-1)>

| 1(N-1)>

| 2(N)>

|1(N)>

d

d

W’

w+

W’

w+

W’

w-

W’

w-

W’

w

wwww

W’

The simplest model: dressed two level atom

resonances @ , , w - W’ w w + W’@

absorption ~ Im ( r )eg

2four wave mixing ~ |r |eg

Different shapes of the absorption and FWM spectra, but resonances occur at the same frequencies!

Experimental results

ab

sorp

tion

[a

rbitr

ary

un

its]

-4 -3 -2 -1 0 1 2 3 4

I/I =4.60

I/I =10.40

I/I =23.60

D (0,±1) D (0,±1)

D (±1,±2)

a

b

c

probe - pump detuning [MHz]

detuning of the trapping beams d=14 MHz

Changes in absorptionwith trapping beam intensity

D [MHz]

w0 - trapping beam frequency

w0

absorption

four-wave mixing

-60 -40 -20 0 20

w0

Wide scan spectra Narrowed scan spectra: central structure

s+ s-lin

-2 -1 0 1 2 3 -2 -1 0 1 2 3 -2 -1 0 1 2 3

s+ s-lin

absorption

four-wave mixing

pump - probe detuning [MHz]

(s+/-, lin - polarization of the probe beam)

Conclusions

J. Zachorowski, T. M. Brzozowski, T. Pa³asz, M. Zawada, and W. Gawlik, Acta Phys. Polonica A 101, 61 (2002)

trap beam frequency

absorption

four-wave mixing

frequencyRequirements

Spectroscopy of cold atomsin the magneto-optical trap

Experiment principle

Investigation of atom energy levels perturbed by light

Investigation of localization of atoms in the light field

Investigation of atom dynamics in the trap

Motivation

absorptiondetectionabsorptiondetection

four-wave mixingsignal detection

four-wave mixingsignal detection

trapping & pump beamstrapping & pump beams

probe beamprobe beam

Simultaneous detection of absorptionand four-wave mixing (FWM) and

lockedmaster

oscillator

probelaser

trappinglaser

double-passAOM

double-passAOM

frequency offset

probe tuning

single-passAOM

single-passAOM

frequency offset

frequency offset

trapping beam

probe beam

injection

injection

High spectroscopic resolution

Laser stabilization and tuning precision up to single kHz

D - detuning from atomic resonance F=3 - F’=4

s+ s-

frequency reference &stabilization

Enhanced resolution spectraabsorption

four-wave mixing

pump - probe detuning [MHz]

(s+/- - polarization of the probe beam)

Raman transitionsbetween the vibrational levels in optical lattices

Transitions between the states in continuum:Recoil induced resonances

absorption four-wave mixing

Mechanisms responsible for central structure

Raman transitionsbetween light shifted Zeeman sublevels

absorption four-wave mixing

2 D

(±1,

±2)

[k

Hz]

2 D (0,±1)

[kHz]

The plot of D vs. D(0,±1) (±1,±2)

23,

13,

03,

73

72

715

21

D (0,±1)

D (±1,±2)

-13,

-23, D (±1,±2)

73

715

21

Light-shifted Zeeman sublevels 85

of F=3 level of Rb atom

500 600 700 800 900 1000 1100 1200 1000

1500

2000

2500

3000

3500

a

b

Fitting: y = a + b x

= -392.1 ± 65.3

= 3.16 ± 0.08

slope: 3.0weak intensity pól

2(~W / d)

slope: 3.22strong intensity limit(~W)

Trapping beams detunung d = 14 MHz

D(0

,±1)

D (±1,±2)

a

b

c

D(0

,±1)

Interpretation

-2 -1 0 1 2 -2 -1 0 1 2

four-wave mixingabsorption

Our spectra probe the dynamics of trapped atoms.

results from transitions between:Central structure

Light-perturbed Zeeman subleveles

Vibrational levels in optical lattice

Kinetic continuum states

Four-wave mixing signals reveal more detailsbut require explanation of:

differences between resonances in the absorption and FWM spectra

dynamic effects: signal dependence on scan speed and direction

signal dependence on the probe polarization

References

pump photon(from trapping beam)

probe photon