Download Super-charging nonlinear optical processes through collective effects

FIP
Super-charging nonlinear
optical processes through
collective effects
Joel A. Greenberg and Daniel J. Gauthier
Duke University
7/6/2010
Introduction
• Long-term goal:
– Realize few-photon nonlinear optical (NLO)
effects (for quantum/optical info. networks )
• Short-term goal:
– Study nonlinear wave mixing processes
• Approach:
– use collective (rather than single atom) effects
to ‘super charge’ NLO processes
• reduce instability thresholds, enhanced scalings, etc.
Optical FWM
• Optical four-wave mixing (FWM) involves the exchange of
energy between four optical fields
Es
Epc
e
h∆
Ein
X(3)
Ein
medium
Ein
Es
Ein
Epc
g
• To occur efficiently, energy and momentum must be conserved
in the optical fields
Boyd, Nonlinear optics.
Ultracold Atoms
2D Rb Magneto-optical
Trap (MOT)
3 cm
Experimental Scheme
Cooling and
Trapping
FWM
Experiment
Cold atoms
Long. Optical path length = 50-100
Temp = 20-40 µK
Dimensions: R = 150 µm, L = 3 cm
Greenberg, Oria, Dawes, Gauthier, Opt. Express 15, 17699 (2007)
FWM with Cold Atoms
Initial homogenous
distribution of cold atoms
FWM with Cold Atoms
Initial homogenous
distribution of cold atoms
FWM pump beam
Dipole force
begins to spatially
organize atoms
Gattobigio et al., PRA 74, 043407 (2006)
Collective FWM (CFWM)
• Grating self-phase-matches additional FWM processes
(Bunching allows higher order wave mixing processes to occur)
Es
Epc
Ψ1
Ein
G
matter waves
Ψ2
Ein
• Lamb-Dicke effect enhances CFWM through
- Confining atoms ∆x<<λ (enhances bunching gain)
- Reducing inelastic scattering while allowing elastic scattering
(increases coherence time)
PCR Setup
IPC
Iprobe
Pump
θ
θ =10 deg
∆ = -6 Γ
|R|2 =IPC/Iprobe
Cold atoms
Investigate importance of bunching by comparing phaseconjugate reflectivity (PCR) for different pump polarizations
Co-rotating Polarization
(BUNCHING)
Counter-rotating Polarization
(NO BUNCHING)
PCR Results: No Bunching
Counter-rotating pumps
100
|R|2
10
|R|2 = tan(β Ιp)2
1
exp. data
0.1
0.01
1
Is = 1.6 mW/cm2
2
3
Ip/ Is
4
5
6
Self-oscillation (|R|=∞)
for β Ιp = π/2
Gaeta et al. IEEE J. Quant. Elec. 22, 1095 (1986)
PCR Results: With Bunching
Co-rotating pumps
100
|R|2 = tan(β Ip )2
|R|2
10
exp. data
1
0.1
0.01
0.5
1.0 1.5
Ip/ Is
2.0
2.5
PCR Results: With Bunching
Co-rotating pumps
100
|R|2 = tan(β Ip )2
|R|2
10
exp. data
1
|R|2 = tan(β (1+b(Ιp) Ιp )2
0.1
0.01
bunching
0.5
1.0
1.5
Ip/ Is
2.0
2.5
Degree of Bunching
b(Ι)
1.0
0.8
0.6
0.4
0.2
0.0
• semi-classical, 1D model
• only pump-pump grating
• phenomenological
rethermalization rate
0.5
1.0 1.5
Ip/ Is
2.0
2.5
PCR Results: With Bunching
Co-rotating pumps
100
|R|2 = tan(β Ip )2
|R|2
10
exp. data
1
|R|2 = tan(β (1+b(Ιp) Ιp )2
0.1
0.01
bunching
0.5
1.0
Ip
1.5
2.0
2.5
Predicted threshold
observed threshold
Observation of Self-oscillation
SF
ΙSF (mW/cm )
2
3
off
Forward
2
Backward
1
0
0
on
Pump
100
200
Pump beams
300
t (µs)
MOT beams
Collective Instability
Initial homogenous
distribution of cold atoms
Dipole force
begins to spatially
organize atoms
Generated light acts back on
atoms to self-organize atoms
and further enhance scattering
Experimental Results
Pump
SF
ΙSF (mW/cm )
2
3
2
off
Backward
1
0
0
on
Forward
100
200
F/B Pumps
300
t (µs)
MOT beams
Experimental Results
Pump
SF
ΙSF (mW/cm )
2
3
off
Forward
2
Backward
1
0
0
on
Cloud expansion
terminates self-oscillation
100
200
F/B Pumps
300
t (µs)
MOT beams
Persistent CFWM via Trapping
ΙSF (mW/cm )
2
time (s)
on
time (ms)
MOT
beams
F/B Pumps
off
τc ~ 300 µs
(2)
(2)
g
(τ )
g (τ)
g ( 2) (τ ) =
τ (µs)
I2
I
2
Decoherence Mechanisms
Atomic Motion
• Expect gratings to decay due to ballistic atomic motion in a time τc
τc = 1/Λgvav = 0.76 µs for T=30 µK, Λg~400nm
Atoms confined to wells diffuse much more slowly
Λg = grating
wavelength
vav = av. velocity
Incoherent Scattering
• Free atom scattering rate of Γfree~300 kHz
Lamb-Dicke effect reduces inelastic scattering
Γ free
Er
=
~ 50 − 100 Γbound ~3 – 6 kHz
Γbound hΩ vib
Εr = recoil energy
Ωvib = vibrational
frequency
Conclusions/Outlook
Conclusion: Self-organization can reduce NLO
instability thresholds and give rise to new, more
sensitive parameter dependences
Future: Study how collective effects may enhance
other NLO processes
• quantum correlated photon pair generation
• quantum memories