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arXiv:cond-mat/0112372 · Physical Review Letters

Stability of Continuously Pumped Atom Lasers

Simon A. Haine, J. J. Hope, Nicholas P. Robins, Craig M. Savage

Published Apr 11, 2002• 28 citations
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Abstract

A multimode model of a continuously pumped atom laser is shown to be unstable below a critical value of the scattering length. Above the critical scattering length, the atom laser reaches a steady state, the stability of which increases with pumping. Below this limit the laser does not reach a steady state. This instability results from the competition between gain and loss for the excited states of the lasing mode. It will determine a fundamental limit for the linewidth of an atom laser beam.

DOI
10.1103/physrevlett.88.170403

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A multimode model of a continuously pumped atom laser is shown to be unstable below a critical value of the scattering length. Above the critical scattering length, the atom laser reaches a steady state, the stability of which increases with pumping. Below this limit the laser does not reach a steady state. This instability results from the competition between gain and loss for the excited states of the lasing mode. It will determine a fundamental limit for the linewidth of an atom laser beam.
In this thesis we theoretically model a continuously pumped atom laser using the mean-field description. We find that it is unstable below a critical scattering length. Above the critical scattering length, the atom laser reaches a steady state, the stability of which increases with pumping. Below this limit the atom laser does not reach a steady state. We show that this instability results from the competition between gain and loss for the excited states of the lasing mode, and show how the nonlinearities stabilise the system. The requirement for a minimum scattering length will determine a fundamental limit for the linewidth of an atom laser beam. We propose a method of stabilising the system below the critical scattering length and investigate its effectiveness.
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.
The linewidth of an atom laser can be limited by excitation of higher energy modes in the source Bose-Einstein condensate, energy shifts in that condensate due to the atomic interactions, or phase diffusion of the lasing mode due to those interactions. The first two are effects that can be described with a semiclassical model, and have been studied in detail for both pumped and unpumped atom lasers. The third is a purely quantum statistical effect and has been studied only in zero-dimensional models. We examine an unpumped atom laser in one dimension using a quantum field theory using stochastic methods based on the truncated Wigner approach. This allows spatial and statistical effects to be examined simultaneously, and the linewidth limit for unpumped atom lasers is quantified in various limits.
We investigate the intensity stability of the superradiant laser. Our study focuses on the architecture where a continuous beam of atoms in an electronically excited state crosses the mode of a high-finesse Fabry-Perot cavity, which has been proposed as a new architecture of an active optical clock. We show that such superradiant laser can become unstable and develop chaotic behavior. We derive an analytical criterion for this instability and find that it may only occur when the lifetime of photons in the cavity is significantly shorter than the lifetime of atoms. This criterion allows for refining the necessary parameters to run a superradiant laser as a frequency reference in the optical domain. In particular, we point-out the consequences of the instability on intensity fluctuations and laser linewidth. On the other hand, we also point out that the superradiant laser, when in the unstable regime, can become an interesting playground for studying chaos. At the mean-field level, there is a direct mapping to the Bénard instability associated with fluid turbulence; however quantum fluctuations associated with photon out-coupling and atom re-filling substantially modify the expected behaviors. Finally, we point-out the existence of a regular self-pulsing regime at large atom numbers.
A continuous wave (cw) atom laser will most likely be realised by outcoupling from a reservoir containing a Bose-Einstein condensate at finite temperature. This will mean that the correlation properties and linewidth of the cw atom laser beam will be influenced by the thermal nature of the reservoir. Here we report on simulations using the stochastic Gross-Pitaevskii formalism for finite temperature dynamics to find the steady state properties of the outcoupled beam. We determine how the linewidth and correlation length depend on the condensate size, temperature, and outcoupling properties, and determine the optimum parameters for cw atom laser operation.