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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
