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Generation of squeezed vacuum in atomic ensembles
Any electromagnetic signal is subject to the laws of quantum
mechanics. This means that due to the Heisenberg uncertainty principle, any
optical measurement will have on top of it, noise due to quantum fluctuations,
even if you are measuring the vacuum itself. This limits many measurements to
having a minimum non-zero noise, called shot noise, or the standard quantum
limit.
This limit can be beaten however by using a special quantum
state of light called a “squeezed state”. Squeezed light exhibits non-classical
statistics where we can measure noise levels below the shot noise limit. If we
consider light in the quadrature picture, where the electric field is expressed
as E(x, t) =X1(x,t)cos(ωt) +X2(x,t)sin(ωt) we can measure the
quadratures X1 and X2 independently. For classical fields like
coherent lasers or the vacuum, the noise of these quadratures is equal and down
to the shot noise limit. But for squeezed states, we can “squeeze” the noise
of the quadrature we are measuring while “stretching” the other quadrature in
compensation.

Squeezed light finds applications in precision measurements
as well as optical communications where the signal to noise needs to be as low
as possible. Due to it's special quantum nature, squeezing may also be applied
in other related areas of quantum optics and quantum information.
Squeezed states of light may result from one of several
nonlinear interactions of the light with matter such as those caused by
parametric amplifiers, frequency doublers, and Kerr media. The main squeezing
source we study is a nonlinear light-atom interaction called polarization
self-rotation.
The polarization self-rotation (PSR) effect occurs when
elliptically polarized light propagates through an atomic medium (in our case
87Rb vapor) which causes the axis of ellipticity to rotate. Since the
intensity of the left and right circular polarization components are different
in elliptically polarized light, this leads to unequal AC-Stark shifts and
optical pumping of the different atomic Zeeman sublevels resulting in circular
birefringence. Phase differences in the propagation of the two circular components
of the light result in the polarization ellipse rotation.

In our experiment,
we send linearly polarized laser light, made slightly elliptical by vacuum
fluctuations of the horizontal polarization, through a glass cell containing
hot 87Rb atoms. This leads to polarization self-rotation as the light
propagates, resulting in a squeezed vacuum state of the horizontal polarization
at the output of the cell. By mixing this squeezed vacuum field with a strong
local oscillator field in a homodyne detection arrangement and sweeping the
phase between these fields, we can measure the quadrature fluctuations of the
squeezed vacuum. Depending on experimental parameters, we have observed
squeezing at several laser frequencies near the Rubidium atomic transitions
with our highest level of squeezing to date being about 2 dB of noise
suppression.
Our PSR and
squeezing studies have concentrated on optimizing experimental conditions for
the highest degree of noise suppression while gaining a better understanding of
the squeezing process and how differing conditions will influence it. We also
have carried out studies of PSR and quadrature noise in cold Rubidium atoms
held in a trap at temperatures of only hundreds of microkelvin. The current
installment of the squeezing experiment sends the squeezed vacuum through an
atomic medium under the conditions of electromagnetically induced transparency
(EIT) to study the effects of EIT noise filtering and leading up to the slowing
and storage of squeezed vacuum.

References
[1] Horrom, T.; Balik, S.; Lezama, A.; Havey, M.D.; et al. Polarization Self-rotation in Ultracold Atomic Rb. arXiv:1102.4041 2011.
[2] Mikhailov, E.E.; Lezama, A.; Noel, T.W.; et al. Vacuum squeezing via polarization self-rotation and
excess noise in hot Rb vapors. JMO 2009, 56, 1985–1992.
[3] Novikova, I.; Matsko, A.B.; Welch, G.R. Large polarization self-rotation in rubidium vapour: application
for squeezing of electromagnetic vacuum. Journal of Modern Optics 2002, 49 (14), 2565–2581.
[4] Akamatsu, D.; Akiba, K.; Kozuma, M. Electromagnetically Induced Transparency with Squeezed
Vacuum. Phys. Rev. Lett. 2004, 92 (20) (MAY), 203602.
[5] Rochester, S.M.; Hsiung, D.S.; Budker, D.;Ciao, R.Y.; Kimball, D.F.; et al. Self-rotation of resonant
elliptically polarized light in collision-free rubidium vapor. Phys. Rev. A 2001, 63 (4) (Mar), 043814.
[6] Bachor, H.A.; Ralph, T.C. A Guide to Experiments in Quantum Optics, Wiley-VCH: USA, 2004.
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