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Conference on Lasers and Electro-Optics

Bound mode of an atom laser

John Jeffers, Péter Horák, Stephen Mark Barnett, C. Baxter, PAUL M. RADMORE

Published Aug 29, 2005• 0 citations

Abstract

Summary form only given. Hope, Savage and Moy have presented a model Hamiltonian for an atom mirror. In conjunction with a Bose-Einstein condensate such a device can model the output coupler for an atom laser. The basic structure of the Hamiltonian is identical to the optical output coupler. A cavity mode at a particular wavevector is coupled to a set of output modes over a range of wavevectors. The difference is that the parameter in the Hamiltonian which would be the frequency in the optical case is the square of the wavevector for atoms. This has the consequence that the cavity mode is only coupled to one of the two superposition (sum and difference) modes of the output. We present a Fano diagonalisation of this output coupler model. The Hamiltonian can be expressed in terms of the diagonal operators together with operators representing a bound mode. This mode appears when the coupling is strong compared to the energy of the cavity mode. Any states of the bound mode represent excitations which will not propagate out of the cavity. We give the criterion for the existence of the mode in the cases where the interaction strengths are real and complex.

DOI: 10.1109/iqec.2000.907940

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Summary form only given. Hope, Savage and Moy have presented a model Hamiltonian for an atom mirror. In conjunction with a Bose-Einstein condensate such a device can model the output coupler for an atom laser. The basic structure of the Hamiltonian is identical to the optical output coupler. A cavity mode at a particular wavevector is coupled to a set of output modes over a range of wavevectors. The difference is that the parameter in the Hamiltonian which would be the frequency in the optical case is the square of the wavevector for atoms. This has the consequence that the cavity mode is only coupled to one of the two superposition (sum and difference) modes of the output. We present a Fano diagonalisation of this output coupler model. The Hamiltonian can be expressed in terms of the diagonal operators together with operators representing a bound mode. This mode appears when the coupling is strong compared to the energy of the cavity mode. Any states of the bound mode represent excitations which will not propagate out of the cavity. We give the criterion for the existence of the mode in the cases where the interaction strengths are real and complex.

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.

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.

We present a generalized two-state theory to study the output coupler for Bose-Einstein condensate atoms and its interference. The results show that the fraction of out-coupled atoms can be adjusted between 0% and 100% by varying the amplitude of the rf. radiation, and the interference patterns of the two coherent outputs that are coupled out of a double-well trapped potential vary with time. Moreover, we study the influence of atom-atom interactions on the output Tn contrast with the case without atom-atom interactions, collapses and revivals appear in the number of the output atoms.

We present a fully quantum-mechanical treatment of a single-mode atomic cavity with a pumping mechanism and an output coupling to a continuum of external modes. This system is a schematic description of an atom laser. In the dilute limit where atom-atom interactions are negligible, we have been able to solve this model without making the Born and Markov approximations. When coupling into free space, it is shown that for reasonable parameters there is a bound state which does not disperse, which means that there is no steady state. This bound state does not exist when gravity is included, and in that case the system reaches a steady state. We develop equations of motion for the two-time correlation in the presence of pumping and gravity in the output modes. We then calculate the energy spectrum of the steady-state output flux from the laser. We present a ``self-consistent Markov approximation'' which allows efficient calculation of this energy spectrum well above threshold.