Collective Nonlinear Optical Effects in an Ultracold Thermal Vapor
Joel A. Greenberg, Daniel J. Gauthier
Duke University, Physics Department and the Fitzpatrick Institute for Photonics · Durham, NC
2
Effects
Collective
Introduction
Nonlinear Optics (NLO) with Cold Atoms
• Few-photon NLO elements are critical for quantum
information applications, but large atom-photon
interaction strengths are needed
• We obtain large nonlinear couplings in cold atoms by
controlling the atoms’ internal and external states
• Collective nonlinear effects allow for a drastic
enhancement of the atom-photon coupling strength over
single-atom effects, and may lower NLO thresholds to the
single-photon limit
We observe SF light generated along the trap’s long axis in
both the forward and backward directions3
Collective optical effects occur when the radiative properties
of an atom are effected by the presence of additional atoms
Amplified Spontaneous
Emission (ASE)
Spontaneous
Emission (SE)
Experimental Setup
Superfluorescence (SF)
SF Thresh
Pump (B)
 ~ 10
SF light
The influence of the radiators on one another can take on a
continuum of values (described by a collectivity parameter). On
one end, atoms radiate independently (SE) – on the other, all
atoms release their energy at the same time (SF)
SF light
Pump (F)
Cold atoms
Forward
Cell
Magnets
Example: Absorption
atom
Trapping laser beam configuration
atom
p
Photo of MOT setup
before
1) J.A. Greenberg, M. Oria, A.M.C. Dawes, D.J. Gauthier, Opt. Express 15, 17699 (2007)
2) M. Malcuit, Univ. of Rochester, PhD Dissertation (1987)
3) J.A. Greenberg and D.J. Gauthier, OSA Opt. Photonics Cong. Tech. Digest, ISBN 978-1-55752-873-5 (2009)
Funding
NSF AMO Grant # PHY-0855399; DARPA Slow Light Contract PO #412785-G-2
The degree of atomic organization affects the radiation field,
thus producing a nonlocal atom-atom coupling. The net result
is a runaway process that gives rise to the collective emission
of light
Scattering
enhances grating
Grating enhances
scattering
Ppeak (mW)
SF light
Atomic density grating
Citations
PF/B (mW)
SF Power vs N

CCD image of trapped atoms
PF/1B/ 2
PF/B (mW)
3 cm
• Length: 3 cm, Radius: 150 mm
• Optical Depth ~55 (Iout/Iin = e-OD)
• Density 7x1010 atoms/cm3
• Temperature ~30 μK
• 87Rb trapped on F=2F’=3
 PF / B
after
The forces exerted on atoms by multiple light beams give rise
to a global spatial organization of the atoms
MOT Characteristics:
cold atoms
Laser timing scheme
We find good agreement with the predictions of superfluorescent
collective atomic recoil lasing (CARL) theory
An atom recoils when it absorbs or a emits a photon
Cooling
MOT beams
tD (ms)

F/B Pump beams
SF Light Trends
Self-organization
Mirror
Probe
on
time
Ppeak (mW)
z
• SF light is nearly degenerate
with pump frequency
• Light persists until atomic
density falls below threshold
• F/B SF temporal correlations
• ~1 photon emitted/atom
3 cm
MOT
x
• Cooperative emission produces a
short, intense pulse of light
• Ppeak N2 (N times larger than SE!)
• Delay time (tD) before pulse occurs
• Threshold density/ pump power
off
Vacuum
y
Backward
t (ms)
tD
MOT Setup:
Trapping
tSE
SF Characteristics
Power (mW)
Our magneto-optical trap (MOT) uses lasers and magnetic
fields to trap and cool atoms
tSFtSE/N
Power
Anisotropic
1
MOT
Detector (F)
SF Light Observed on Detectors
Collective Emission Characteristics
Ppeak
• Counter-propagating
pump beams
• Detect emitted light in
forward (F) and
backward (B) directions
Detector (B)
Collectivity
1
Goal: Single-photon NLO
Superfluorescence
 Exp(N )
 ( N  Nt )2
We may be seeing a
nonlinear (N2) scaling of
the peak SF power with
atom number
OD  N
Applications
• New insight into free electron laser dynamics
• Possible source of correlated photon pairs
• Optical/Quantum memory