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Communications in Theoretical Physics

On the Quantum Dynamic Theory of the MIT Output Coupler for the Bose-Einstein Condensation

Sun Changpu, Zhan He, Miao Yuan-Xiu, Jianming Li

Published Mar 15, 1998• 16 citations
Publisher

Abstract

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.

DOI
10.1088/0253-6102/29/2/161

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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.
Based on the Bogoliubov approximation in the thermodynamical limit, a linear quantum many-body theory is presented to deal with the output of the bosonic atoms to a free propagating mode from a magnetic trap. It is shown that, when atoms are prepared initially in the Bose-Einstein condensation inside a trap, the output will be described by a macroscopic quantum state, a many-body coherent state. This is due to the factorization structure of the total wave function, showing that the output atom beam is coherent. The general expressions for the spectral density of the output and its spatial distribution are given in terms of our linear quantum many-body theory.
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.
The regions of validity of the Markov approximation for the coupling of atoms out of an atomic trap are determined. We consider radio-frequency output coupling in the presence of gravity and collisional repulsion, and Raman output coupling. The Markov approximation is crucial in most theoretical descriptions of an atom laser that assume a continuous process of output coupling from a trapped Bose-Einstein condensate. In this regime many techniques that have proved to be useful for modeling the optical laser, such as master equations, can be used to describe the dynamics of the damping of the condensate mode undergoing output coupling.
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.
The analogies between coherent matter waves in Bose-Einstein condensates of atomic gases and coherent photons have been discussed in connection with possible realization of an “atom laser”. Theoretical discussions of the atom laser have considered the case in which atoms are fed into and coupled out of the condensate continuously. Here we discuss the analogy between the output coupler for the trapped coherent matter waves and collective nonlinear energy transfer in a system of three coupled pendulums with variable parameters. One pendulum in the system is weakly coupled through a spring with the pair of pendulums, which are tightly bound through a common string. We show that self-sustained oscillations of the energy distribution between the weakly coupled and tightly bound subsystems can occur. In our simulations, the coherent fraction of the total mechanical energy of the system, which is periodically transferred to the weakly linked subsystem, can be of the order of 1/4000 and even smaller. These periodic oscillations in the energy distribution are similar, and their time evolution is described by similar functions of time, to the quantum Rabi oscillations in the populations of the trapped and untrapped (out-coupled) states in the coherent output coupler in Bose-Einstein condensed atoms. The described effects can be used for the coherent control of the transfer of mechanical energy on the micro- and nano-scales.