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arXiv:quant-ph/0606076 · Physical Review Letters

Polarization Squeezing by Optical Faraday Rotation

Jacob Friis Sherson, Klaus Mølmer

Published Oct 5, 2006• 37 citations
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Abstract

We show that it is possible to generate continuous-wave fields and pulses of polarization squeezed light by sending classical, linearly polarized laser light twice through an atomic sample which causes an optical Faraday rotation of the field polarization. We characterize the performance of the process and we show that an appreciable degree of squeezing can be obtained under realistic physical assumptions.

DOI
10.1103/physrevlett.97.143602

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We show that it is possible to generate continuous-wave fields and pulses of polarization squeezed light by sending classical, linearly polarized laser light twice through an atomic sample which causes an optical Faraday rotation of the field polarization. We characterize the performance of the process and we show that an appreciable degree of squeezing can be obtained under realistic physical assumptions.
We consider an ensemble of trapped atoms interacting with a continuous-wave laser field. For sufficiently polarized atoms and for a polarized light field, we may approximate the nonclassical components of the collective spin angular momentum operator for the atoms and the Stokes vectors of the field by effective position and momentum variables for which we assume a Gaussian state. Within this approximation, we present a theory for the squeezing of the atomic spin by polarization rotation measurements on the probe light. We derive analytical expressions for the squeezing with and without inclusion of the noise effects introduced by atomic decay and by photon absorption. The theory is readily adapted to the case of inhomogeneous light-atom coupling [A. Kuzmich and T.A.B. Kennedy, Phys. Rev. Lett. 92, 030407 (2004)]. As a special case, we show how to formulate the theory for an optically thick sample by slicing the gas into pieces, each having only small photon absorption probability. Our analysis of a realistic probing and measurement scheme shows that it is the maximally squeezed component of the atomic gas that determines the accuracy of the measurement.
The continuous-variable (CV) quadratic phase gate is one of the most fundamental CV quantum gates for universal CV quantum computation, while its experimental realization still remains a challenge. Here we propose a novel and experimentally feasible scheme to realize optical CV quadratic phase gate via Faraday interaction in an atomic ensemble. The gate is performed by simply sending an optical beam three times through an atomic medium prepared in coherent spin state. The fidelity of the gate can ideally run up to one. We show that the scheme also works well as a device to generate optical polarization squeezing. Considering the noise effects due to atomic decoherence and light losses, we find that the observed fidelities of gate operation and the attainable degree of polarization squeezing are still quite high.
When linearly polarized light propagates through a medium in which elliptically polarized light would undergo self-rotation, squeezed vacuum can appear in the orthogonal polarization. A simple relationship between self-rotation and the degree of vacuum squeezing is developed. Taking into account absorption, we find the optimum conditions for squeezing in any medium that can produce self-rotation. We then find analytic expressions for the amount of vacuum squeezing produced by an atomic vapor when light is near-resonant with a transition between various low-angular-momentum states. Finally, we consider a gas of multilevel Rb atoms, and analyze squeezing for light tuned near the D lines under realistic conditions.
A phenomenological (classical) and quantum treatment of the laser light-intensity-induced Faraday effect in isotropic media and crystals is given. The effect, being universal (occurring in all matter), is shown to act as a stimulator controlling the self-squeezing of light: depending on the helicity of circular polarization of the light wave and on the sense of the dc magnetic field, the sign of the pseudoscalar parameter of nonlinear coupling changes leading to an enhancement or weakening of self-squeezing. Moreover, by varying the state of polarization of the light wave or the magnetic field strength, control of the efficiency of light-squeezing generation can be achieved.
The cross-interaction effects for a two-mode light pulse in an optical matrix doped with atoms that are resonant with the light in the presence of two control optical pump pulses (M scheme) have been analyzed. The fundamental possibility of effective generation of polarization-squeezed light in this system at a simultaneous nonlinear amplification of the probe field is shown. The optimal conditions for generating polarization-squeezed light in a doped optical fiber are found for different problem parameters.