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Journal of Experimental and Theoretical Physics Letters

Generation of nonclassical states of light in the Bose-Einstein condensate under electromagnetically induced transparency

A. V. Prokhorov, A. P. Alodjants, Sergei M Arakelyan

Published Dec 1, 2004• 10 citations
Publisher

Abstract

A quantum theory of the interaction of the atomic Bose condensate with external optical fields has been developed for a two-beam Λ-scheme close to resonance. Regimes have been obtained where the coefficients of Kerr nonlinearity and nonlinear absorption reach giant values and even become negative, which gives rise to the effect of nonlinear electromagnetically induced transparency. The possibility of the efficient generation of quadrature-squeezed light under the condition of the nonlinear compensation of optical losses has been shown.

DOI
10.1134/1.1868797

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A quantum theory of the interaction of the atomic Bose condensate with external optical fields has been developed for a two-beam Λ-scheme close to resonance. Regimes have been obtained where the coefficients of Kerr nonlinearity and nonlinear absorption reach giant values and even become negative, which gives rise to the effect of nonlinear electromagnetically induced transparency. The possibility of the efficient generation of quadrature-squeezed light under the condition of the nonlinear compensation of optical losses has been shown.
We consider a $\ensuremath{\Lambda}$-type model of the Bose-Einstein condensate of sodium atoms interacting with the light. Coefficients of the Kerr nonlinearity in the condensate can achieve large and negative values, providing the possibility for effective control of group velocity and dispersion of the probe pulse. We find a regime when the observation of the ``slow'' and ``fast'' light propagating without absorption becomes achievable due to the strong nonlinearity. An effective two-level quantum model of the system is derived and studied. Our approach is based on a possibility of establishing a connection of the underlying algebra with the su(2)su(2)su(2) algebra within the formalism of the polynomial algebras of excitations (PAE). We propose an efficient way for the generation of sub-Poissonian fields in the Bose-Einstein condensate at time-scales much shorter than the characteristic decay time in the system. We show that the quantum properties of the probe pulse can be controlled in BEC by the classical coupling field.
We have investigated the optical properties of Λ-configuration ultracold dense Bose gas interacting with two laser pulses, which usually result in electromagnetically induced transparency. With the nonrelativistic quantum electrodynamics and taking into account the atomic dipole-dipole interaction and local field effect, we have derived the Maxwell-Bloch equations of the system. The dispersion relation of an ultracold Bose gas has been obtained and the light-induced nonlinear effects have been analysed. The light-induced nonlinear effects are different from the effects induced by two-body collision of Bose-Einstein condensation atoms which have a frequency shift of transparent window.
We study linear and nonlinear optical properties of an electromagnetically induced transparency (EIT) medium interacting with two quantized laser fields in the adiabatic EIT case. We show that the EIT medium exhibits normal dispersion. Kerr and higher-order nonlinear refractive index coefficients are also calculated in a completely analytical form. It is indicated that the EIT medium exhibits giant resonantly enhanced nonlinearities. We discuss the response of the EIT medium to nonclassical light fields and find that the polarization vanishes when the probe laser is initially in a nonclassical state of no single-photon coherence.
We study the nonlinear effect in a three-level atomic system in Λ configuration. As two or more fields are confined within the common electromagnetically induced transparency (EIT) window, they directly disturb EIT dark state at the same time, which leads to the self- and cross-Kerr nonlinear interactions. Our scheme is different from the existed schemes based on three-level or multilevel systems only existing single type of nonlinear interactions. In the common EIT windows, the self- and cross-Kerr nonlinearities are established with suppressed linear absorption and our scheme can be generalized polychromatic Kerr nonlinearity. Because the atoms are almost trapped in the ground states and the atom population becomes unchanged, the scheme is robust to the atomic spontaneous emission. Our scheme is a promising avenue for preparation of squeezing and entanglement .
In this paper, we investigate the squeezing properties of the output of an atom laser which consists of an ensemble of three-level atoms in Bose–Einstein condensate state interacting with two quantized and classical laser fields in the presence of a Kerr medium. We represent the Hamiltonian of the system under an electromagnetically induced transparency regime and using the adiabatical elimination process, in terms of angular momentum operators, and then deduce the corresponding analytical state vector with the help of the Dicke model. We give our attention to the evaluation of atomic and field squeezings via numerical calculations. The results show that nonlinear sources in the system, i.e., “interatom collisions” and “Kerr medium,” lead to squeezing of atoms and photons. In this respect, the squeezing values can be controlled by adjusting the strength of interatom collisions, the Kerr medium, as well as other involved parameters in the considered model. Also, the collapse-revival phenomenon as a pure quantum feature can be observed in the behavior of atomic squeezing, while only irregular oscillations appeared in the field squeezing.