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arXiv:quant-ph/0012014 · Physical Review A

Quantum-dynamical theory for squeezing the output of a Bose-Einstein condensate

Hui Jing, Jing‐Ling Chen, Mo‐Lin Ge

Published Nov 29, 2000• 48 citations
arXivHTMLPDF

Abstract

A linear quantum dynamical theory for squeezing the output of the trapped Bose-Einstein condensate is presented with the Bogoliubov approximation. We observe that the nonclassical properties, such as sub-Poisson distribution and quadrature squeezing effect, mutually oscillate between the quantum states of the applied optical field and the resulting atom laser beam with time. In particular, it is shown that an initially squeezed optical field will lead to squeezing in the outcoupled atomic beam at later times.

DOI
10.1103/physreva.63.015601

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A linear quantum dynamical theory for squeezing the output of the trapped Bose-Einstein condensate is presented with the Bogoliubov approximation. We observe that the nonclassical properties, such as sub-Poisson distribution and quadrature squeezing effect, mutually oscillate between the quantum states of the applied optical field and the resulting atom laser beam with time. In particular, it is shown that an initially squeezed optical field will lead to squeezing in the outcoupled atomic beam at later times.
A model for the squeezed output coupler of the trapped Bose-Einstein condensed atoms is established with a simple many-boson system of two states with linear coupling, by preparing an initially squeezed light field. In the Bogoliubov approximation, its solutions show that the quadrature squeezing effect mutually oscillates between the coupling light field and the output atomic field. This manifests that the initially squeezed light will transform into a coherent state after some period of coupling interaction while the output atomic field is in a squeezed state.
We have investigated quantum statistical behaviors of photons and atoms in interaction of an atomic Bose Einstein condensate with quantized laser field. When the quantized laser field is initially prepared in a superposition state which exhibits holes in its photon-number distribution, while the atomic field is initially in a Fock state, it is found that there is energy exchange between photons and atoms. For the input and output states, the photons and atoms may exhibit the sub-Poissonian distribution. The input and output laser fields may exhibit quadrature squeezing, but for the atomic field, only the output state exhibits quadrature squeezing. It is shown that there exists the violation of the Cauchy-Schwartz inequality, which means that the correlation between photons and atoms is nonclassical.``
We have investigated quantum statistical behaviors of photons and atoms in interaction of an atomic Bose–Einstein condensate with quantized laser field. When the quantized laser field is initially prepared in a superposition state which exhibits holes in its photon-number distribution, while the atomic field is initially in a Fock state, it is found that there is energy exchange between photons and atoms. For the input and output states, the photons and atoms may exhibit the sub-Poissonian distribution. The input and output laser fields may exhibit quadrature squeezing, but for the atomic field, only the output state exhibits quadrature squeezing. It is shown that there exists the violation of the Cauchy–Schwartz inequality, which means that the correlation between photons and atoms is nonclassical.
A linear quantum dynamic theory for output coupler of Bose–Einstein condensed atoms in a trap is considered with the Bogoliubov approximation in the thermodynamical limit based on the recent MIT experiment ( Phys. Rev. Lett. 78 (1997) 582) for atomic laser. In evolution of total system, the solution of the many-body problem shows a factorization of dynamic process, i.e., the wave function initially prepared in a direct product of a vacuum state and a coherent state remains in a direct product of coherent states at any instance. Physically, this factorizable structure predicts that an ideal condensate in the trap will remain in such a condensate state after the radiation frequency interaction while the output-coupler pulse of atoms forms a macroscopic quantum state in a propagating mode, i.e., the atomic laser.