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Journal of Laser Applications

Model of the atom laser with Raman outcoupling

Chasib A. Emshary, Shaker I. Esa, Arafat J. Almanea

Published Apr 6, 2011• 0 citations
Publisher

Abstract

In the present paper, the authors start from the interaction of a system of two-level atoms with an electromagnetic field to drive the interaction Hamiltonian between these two-level atoms. Second, introduce the equations of motion which describing the dynamics of atom laser depending on the interaction Hamiltonian, this interaction Hamiltonian will be used to describe the outcoupling process in a Raman atom laser. Also, the authors model the dynamics of an atom laser produced by outcoupling three-level atoms from a Bose-Einstein condensate (BEC) via a Raman transition and investigate the transfer of quantum statistics from one of the optical modes to the atomic field. Finally, the authors mathematical treatment leads to the same as equations appears in literature which allowed obtaining the dynamics for any atom laser systems.

DOI
10.2351/1.3544220

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In the present paper, the authors start from the interaction of a system of two-level atoms with an electromagnetic field to drive the interaction Hamiltonian between these two-level atoms. Second, introduce the equations of motion which describing the dynamics of atom laser depending on the interaction Hamiltonian, this interaction Hamiltonian will be used to describe the outcoupling process in a Raman atom laser. Also, the authors model the dynamics of an atom laser produced by outcoupling three-level atoms from a Bose-Einstein condensate (BEC) via a Raman transition and investigate the transfer of quantum statistics from one of the optical modes to the atomic field. Finally, the authors mathematical treatment leads to the same as equations appears in literature which allowed obtaining the dynamics for any atom laser systems.
We have studied the characteristics of an atom laser created by removing atoms from a Bose-Einstein condensate (BEC) via a two-photon Raman process. In contrast with outcoupling by RF transitions, Raman outcoupling offers spatial selectivity within the condensate and delivers significant momentum transfer to the outcoupled atoms. We develop a version of zero-temperature mean-field theory for BECs which includes the internal state of the atom and the effect of laser fields focused into the cloud. For a model condensate we find that the outcoupled matter wave develops sharp peaks at spatial positions where the two-photon Raman process is resonant with the hyperfine splitting of the atomic ground state. As time proceeds the width of the outcoupled wave expands and a steady stream of matter waves travels outside the condensate volume.
We introduce a scheme for creating continuous variable entanglement between an atomic beam and an optical field, by using squeezed light to outcouple atoms from a Bose-Einstein condensate via a Raman transition. We model the full multimode dynamics of the atom laser beam and the squeezed optical field and show that, with appropriate two-photon detuning and two-photon Rabi frequency, the transmitted light is entangled in amplitude and phase with the outcoupled atom laser beam. The degree of entanglement is controllable via changes in the two-photon Rabi frequency of the outcoupling process.
Atom lasers have been demonstrated in both pulsed and semi-continuous modes. The dynamics of these devices is predicted to be dramatically different to the optical laser due to fundamental differences between the two types of boson fields, however to date it is the similarities that have been emphasized. Here we show how the atom laser dynamics are strongly affected by coupling of the output beam back to the condensate. Typically research in the field of Bose-Einstein condensation (BEC) 1 relates to studies of fundamental properties, such as collective modes 2 or to the response of the BEC to external stimuli 3. In contrast, the atom laser is one of the most promising technologies to arise from BEC, being the di-rect atomic equivalent of the optical laser 4. Mewes et al. 5 demonstrated the first atom laser, based on the application of pulsed radio-frequency (RF) fields to induce controlled spin flips from magnetically trapped to un-trapped states of a Bose-Einstein condensate. Later it was shown by Hagley et al. 6 that a pulsed Raman out-coupling could be used to achieve a quasi-continuous multi-state atomic beam. Bloch et al. 7 achieved con-tinuous RF out-coulping for up to 100ms, producing a single state atom laser beam, and showed that this beam could be coherently manipulated in direct analogy to the optical laser 8. These experiments, and others 9,10, have conclusively demonstrated that the outcoupling process can be made coherent. They have also demonstrated a number of other similarities be-tween the optical and atomic lasers such as high flux and low divergence of the output beam. In all these works, the similarities between the two sys-tems have been emphasized, however, ultimately it is the differences such as mass and wavelength that will lead to applications of the atom laser. 1
We investigate the dynamics of a continuous atom laser based on the merging of independently formed atomic condensates. In a first attempt to understand the dynamics of the system, we consider two independent elongated Bose–Einstein condensates which approach each other and focus on intermediate inter-trap distances so that a two-mode model is well justified. In the framework of a mean-field theory, we discuss the quasi-steady-state population of the traps as well as the energy distribution of the outcoupled atoms.