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Progress in Natural Science Materials International

Quantum many-body theory of coherent output of Bose-Einstein condensation (I)——Factorization and atom coherence

CP Sun, Y. X. Miao, Huijuan Zhan, JM Li

Published Jan 1, 1999• 0 citations
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Abstract

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.

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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 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.
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.
For a dilute, interacting Bose gas of magnetically-trapped atoms at temperatures below the critical temperature T0 for Bose-Einstein condensation, we determine the second-order coherence function g(2)(r1, r2) within the framework of a finite-temperature quantum field theory. We show that, because of the different spatial distributions of condensate and thermal atoms in the trap, g(2)(r1, r2) does not depend on |r1 - r2| alone. This means that the experimental determinations of g(2) reported to date give only its spatial average. Such an average may underestimate the degree of coherence attainable in an atom laser by judicious engineering of the output coupler.
Tunneling of atoms between two trapped Bose-condensed gases at finite temperatures is explored using a many-body linear-response tunneling formalism similar to that used in superconductors. To lowest order, the tunneling currents can be expressed quite generally in terms of the single-particle Green's functions of isolated Bose gases. A coherent first-order tunneling Josephson current between two atomic Bose-Einstein condensates is found, in addition to coherent and dissipative contributions from second-order condensate-noncondensate and noncondensate-noncondensate tunneling. Our work is a generalization of Meier and Zwerger, who recently treated tunneling between uniform atomic Bose gases. We apply our formalism to the analysis of an out-coupling experiment induced by light wave fields, using a simple Bogoliubov-Popov quasiparticle approximation for the trapped Bose gas. For tunneling into the vacuum, we recover the results of Japha, Choi, Burnett, and Band, who recently pointed out the usefulness of studying the spectrum of out-coupled atoms. In particular, we show that the small tunneling current of noncondensate atoms from a trapped Bose gas has a broad spectrum of energies, with a characteristic structure associated with the Bogoliubov quasiparticle u2{u}^{2}u2 and v2{v}^{2}v2 amplitudes.
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.
For a dilute, interacting Bose gas of magnetically-trapped atoms at temperatures below the critical temperature T0 for Bose-Einstein condensation, we determine the second-order coherence function g (2) (r1 ; r2) within the framework of a finite-temperature quantum field theory. We show that, because of the different spatial distributions of condensate and thermal atoms in the trap, g (2) (r1 ; r2) does not depend on jr1 r2j alone. This means that the experimental determinations of g (2) reported to date give only its spatial average. Such an average may underestimate the degree of coherence attainable in an atom laser by judicious engineering of the output coupler.