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.