Squeezed Light and Quantum
Imaging with Four-Wave Mixing in
Hot Atoms
Squeezed Light and Quantum Imaging
with Four-Wave Mixing in Hot Atoms
Alberto Marino
Ulrich Vogl
Jeremy Clark (U Maryland)
Quentin Glorieux
Neil Corzo Trejo (CINVESTAV, Mexico)
Ryan Glasser
PDL
Zhifan Zhou (ECNU)
Andrew Lance (Quintessence Labs)
Raphael Pooser (Oak Ridge)
Kevin Jones (Williams College)
Vincent Boyer (Birmingham)
Atomic Physics Division
National Institute of Standards and Technology
Gaithersburg, MD
also with the
Joint Quantum Institute (NIST/U Maryland)
$ JQI NSF-PFC, DARPA, AFOSR $
something for (almost) everyone
squeezed light from 4WM in Rb vapor
• squeezed light
– bright beams
– vacuum
•
•
•
•
•
slow light
continuous-variable entanglement
images (multiple-spatial-mode)
narrowband at Rb color (atom optics)
relatively simple experiments!
really cool! if only this were 20 years ago!
history
First observations of squeezed light in 1985 (Slusher, et al.)
were based on degenerate 4WM in atomic vapors.
Most experimental reports of squeezing by 4WM in atomic
vapors were published more than 10 years ago... mostly
based on 2-level systems; these ended with several
attempts in cold atom samples.
Most recent squeezed-light results use OPO’s and OPA’s
with c(2) materials in a cavity; strong squeezing achieved.
4WM in fibers generates correlated photons and ~7 dB of
squeezing.
Lots of theoretical examinations...... but none that actually
predicted squeezing under our conditions.
Goals
We are trying to perform quantum optics and
“quantum atom optics” experiments:
create non-classical photon beams that can, in turn, be
used to produce non-classical atom beams.
also try to do “real” quantum optics and image
processing experiments with non-classical light
amplifiers.
Producing correlated atoms
from correlated photons drive the “upward-going”
“dress” the atoms
in the BEC with the
“downward-going”
frequency of a Raman
transition
transition with correlated
photon beams
k1
twin beams
of atoms
out
klaser
BEC
k2
k1
ki
klaser
hk
2hk
0hk
Raman transition
hk
√2/2hk
hk
k2
P. Lett, J. Mod Opt. 51, 1817 (2004)
Single-mode squeezing
Two-mode squeezing:
phase-insensitive amplifier
p1
x1
Coupled
Gain
correlations
p2
x2
two vacuum
modes
two noisy, but entangled,
vacuum modes
Squeezing quadratures
squeezing from 4WM in hot
Rb vapor
85Rb
in a double-L
scheme
~120 C cell temp.
~1 GHz detuned
~400 mW pump
~100 mW probe
- narrowband
- no cavity
strong intensity-difference
squeezing measured
1 MHz detection
frequency
RBW 30 kHz
VBW 300 Hz
pump detuning
800 MHz
Raman detuning
4 MHz
noise
“squeezed light” implies, in some form, reduced
fluctuations
this is usually compared to “shot noise”
N particles/second => noise ~ N1/2
state of the art; (linear and log)
3 dB = factor of 2; 10% noise = -10 dB
Two-Mode: We have -8.8 dB (13% of “shot noise”)
“project” lossless squeezing level of -11 dB at source
world record (using an OPO): -9.7 dB (11%) twin beam;
-11.5 dB for single-mode quadrature squeezing
We have -3 dB of single-mode squeezing
previous best with 4WM in atoms: -2.2 dB
LIGO will use -6 dB of squeezing in phase II
intensity-difference squeezing
at low frequencies
better than
8 dB noise
suppression
if backgrounds
subtracted!
image correlations
no cavity
means fewer
constraints
on modes!
image correlations in space
amplified probe
(spatially filtered + )
pump relic
generated conjugate
(spatially filtered)
expect that correlations are “reflected” radially through the pump
note that “images” do not constitute multiple spatial modes!
4.7 dB intensity difference squeezing between images at 1 MHz
demonstrating
entanglement
scan LO phase
alignment and
bright beam entanglement
+ or -
probe
pump
pzt
mirror
conjugate
phase stable local
oscillators at +/- 3GHz
from the pump
pzt
mirror
demonstrating
entanglement
unsqueezed
vacuum
vacuum
squeezing
+ and -
probe
pumps
conjugate
50/50
BS
signal pump
LO pump
pzt
mirror
pzt
mirror
scan LO phase
“twin beam” vacuum
quadrature entanglement
measurements at 0.5 MHz
entangled images
measurements at 0.5 MHz
• V. Boyer, A.M. Marino, R.C. Pooser, and P.D. Lett, Science 321, 544 (2008).
seeded, bright modes
cone of vacuum-squeezed modes
(allowed by phase matching)
entangled “images”
arbitrarily-shaped local oscillators can be used
(we used a “T”-shaped beam)
squeezing in both quadratures;
(equivalent results in all quadratures)
Gaussian bright-beam (-3.5 dB) or
vacuum (-4.3 dB); T-shaped vacuum (-3.7 dB)
implies EPR-levels of CV-entanglement could
be measured in each case
no feedback loops or mode cleanup cavities!
Images
no cavity, so
freedom for
complex and
multiple spatial
modes!
phase-sensitive amplifier
the phase of the injected beam, with respect to those of the
pumps, will determine whether the beam will be amplified or
de-amplified
One can design an amplifier for given field quadratures - useful
for signal processing!
phase-insensitive
w-
w+
w0
f+ = 2f0 - f-
given the
phase of 3
“input” beams
the 4th phase
is free to
adjust for gain
phase-sensitive
no free
w+
parameters
w0
w-
gain:
0 = 2f0 - f- - f+
phase-sensitive amplifier set-up
Phase lock each
pump beam to
the probe.
ti:sapph laser
Double-pass 1.5 GHz AOM
-3 GHz
Double-pass
semiconductor
tapered amp
optics
pzt for phase lock
~1 mW
~ 500 mW
+3 GHz
probe
Rb cell
problems
- tapered amps noisy; astigmatic output beams;
feedback adds laser noise
- detuning needs to be large to avoid other 4WM
- 500 mW is marginal power
- non-co-linear geometry helps separate the beams
but makes the (distorted) wavefronts not match
(getting a fixed phase for amplification is hard)
phase relation varies
across probe beam
(phase fronts are
distorted)
competing 4WM processes
pump 1
“extra conjugate”
pump 2
“probe”
extra 4WM can be suppressed by putting “pump1”
mid-way between the absorptions (more power needed)
Experimental Setup - PSA
5P1/2
Probe
Pumps
5S1/2
3GHz
Probe
3GHz
Experimental Parameters
Pump ~200mW each
Probe ~ 0.1mW
Cell ~12mm
Gain ~ 2
Angle ~ 0.5°
Orthogonal Linear Pol.
The probe gets amplified or deamplified depending on its phase . Cell Temperature 86 C
Double Lambda Scheme in
85Rb
“single mode” quadrature squeezing
PSA (phase-sensitive amplifier)
seeded
direct detection
squeezing calculated
from probe gain
“vacuum seeded”
homodyne detection
lower cell temp ~90 C
than for phaseinsensitive case
Vacuum Squeezing
Squeezing trace at 1 MHz (zero span, RBW: 30 KHz, VBW: 100 Hz) for the
vacuum squeezed state, normalized to the shot noise. One-photon detuning
0.8 GHz. Two-photon detuning 4MHz.
Squeezing [dB]
Vacuum Squeezing vs Pump Power
Squeezing at 1 MHz (zero span, RBW: 30 KHz, VBW: 100 Hz) for the vacuum
squeezed state, normalized to the shot noise. One-photon detuning 0.8 GHz.
Vacuum Squeezing Bandwidth
Vacuum Squeezing Bandwidth
Squeezing trace (RBW: 10 KHz, VBW: 100 Hz) for the vacuum squeezed state,
normalized to the shot noise. One-photon detuning 0.8 GHz. Two-photon
detuning 4MHz. Pump1 = 225 mW. Pump 155mW.
Vacuum Squeezing Bandwidth
Squeezing trace (RBW: 10 KHz, VBW: 100 Hz) for the vacuum squeezed state,
normalized to the shot noise. One-photon detuning 0.8 GHz. Pump1 = 225
mW. Pump 155mW.
Vacuum Squeezing Bandwidth
Squeezing trace (RBW: 10 KHz, VBW: 100 Hz) for the vacuum squeezed state,
normalized to the shot noise. One-photon detuning 0.8 GHz. Pump1 = 225
mW. Pump 155mW.
Vacuum Squeezing Bandwidth
Squeezing trace (RBW: 10 KHz, VBW: 100 Hz) for the vacuum squeezed state,
normalized to the shot noise. One-photon detuning 0.8 GHz. Pump1 = 225
mW. Pump 155mW.
phase-sensitive amplifier
To avoid other phase-insensitive 4WM processes
the detuning is much different than with the phaseinsensitive version of the 4WM amplifier.
These processes can be suppressed, however, not
completely. This leads to excess noise and limits
the gain at which the PSA can be operated.
It still operates with multiple spatial modes, but the
symmetry of the spatial modes will be an issue to
some (unknown) extent.
multi-spatial mode
“single-mode quadrature squeezing”
attenuating
beam (modes)
by blocking
in different
manners
Summary
• 4WM should add to
our ability to perform
quantum imaging
and amplifier
experiments
• narrowband source
should allow us to
use this to interface
with Rb atom
quantum memories
group photo
Quentin Glorieux Ulrich Vogl
Zhifan Zhou Alberto Marino
Ryan Glasser
Jeremy Clark
Neil Corzo Trejo