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arXiv:cond-mat/0305524 · Journal of Physics B Atomic Molecular and Optical Physics

Effects of interatomic collisions on atom-laser outcoupling

Georgios M. Nikolopoulos, P. Lambropoulos, Nick P. Proukakis

Published Jun 19, 2003• 7 citations
arXivHTMLPDF

Abstract

We present a computational approach to the outcoupling in a simple one-dimensional atom-laser model, the objective being to circumvent mathematical difficulties arising from the breakdown of the Born and Markov approximations. The approach relies on the discretization of the continuum representing the reservoir of output modes, which allows the treatment of arbitrary forms of outcoupling as well as the incorporation of nonlinear terms in the Hamiltonian, associated with interatomic collisions. By considering a single-mode trapped condensate, we study the influence of elastic collisions between trapped and free atoms on the quasi steady-state population of the trap, as well as the energy distribution and the coherence of the outcoupled atoms.

DOI
10.1088/0953-4075/36/13/310

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We present a computational approach to the outcoupling in a simple one-dimensional atom-laser model, the objective being to circumvent mathematical difficulties arising from the breakdown of the Born and Markov approximations. The approach relies on the discretization of the continuum representing the reservoir of output modes, which allows the treatment of arbitrary forms of outcoupling as well as the incorporation of nonlinear terms in the Hamiltonian, associated with interatomic collisions. By considering a single-mode trapped condensate, we study the influence of elastic collisions between trapped and free atoms on the quasi steady-state population of the trap, as well as the energy distribution and the coherence of the outcoupled atoms.
We present a computational approach to the outcoupling in a simple one-dimensional atom-laser model, the objective being to circumvent mathematical difficulties arising from the breakdown of the Born and Markov approximations. The approach relies on the discretization of the continuum representing the reservoir of output modes, which allows the treatment of arbitrary forms of outcoupling as well as the incorporation of nonlinear terms in the Hamiltonian, associated with interatomic collisions. By considering a single-mode trapped condensate, we study the influence of elastic collisions between trapped and free atoms on the quasi steady-state population of the trap, as well as the energy distribution and the coherence of the outcoupled atoms.
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.
We present a steady-state analysis of a quantum-mechanical model of an atom laser. A single-mode atomic trap coupled to a continuum of external modes is driven by a saturable pumping mechanism. In the dilute flux regime, where atom-atom interactions are negligible in the output, we find an analytic form for the linewidth and frequency shift of the laser. This result does not make the Born-Markov approximation, but is based on the far less restrictive ``self-consistent Markov approximation.'' The more exact treatment has a different effective damping rate and occupation of the lasing mode, as well as a shifted frequency and linewidth of the output. We examine gravitational damping numerically, finding linewidths and frequency shifts for a range of pumping rates. We treat mean-field damping analytically, finding a memory function for the Thomas-Fermi regime. The occupation and linewidth are found to have a nonlinear scaling behavior which has implications for the stability of atom lasers.
We present a model for a continuous atom laser in a one-dimensional waveguide. The beam is formed by continuous Raman outcoupling of a trapped one-dimensional (quasi-)condensate, which is created by imposing a tightly confining transverse optical potential on a three-dimensional magnetically trapped ultracold thermal gas. The trapped (quasi-)condensate is modelled by a stochastic Langevin equation, in which pumping arises naturally from the surrounding three-dimensional thermal cloud, which acts as its heat bath. When the outcoupling is turned on, such pumping leads to continuous replenishing of the (quasi-)condensate, and thus to a steady-state operation for the atom laser, which is described by a nonlinear Schroedinger equation, coupled to the Langevin equation for the (quasi-)condensate. This model is used to study the temporal and spatial evolution of the coherence length of the (quasi-)condensate and the atom laser over the entire system.
We discuss the use of the Born and Markov approximations in describing the dynamics of an atom laser. In particular, we investigate the applicability of the quantum optical Born-Markov master equation for describing output coupling. We derive conditions based on the atomic reservoir, and atom dispersion relations for when the Born-Markov approximations are valid and discuss parameter regimes where these approximations fail in our atom laser model. Differences between the standard optical laser model and the atom laser are due to a combination of factors, including the parameter regimes in which a typical atom laser would operate, the different reservoir state which is appropriate for atoms, and the different dispersion relations between atoms and photons. We present results based on an exact method in the regimes in which the Born-Markov approximation fails. The exact solutions in some experimentally relavent parameter regimes give non-exponential loss of atoms from a cavity.