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Physical Review A

Bound mode of an atom laser

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

Published Sep 11, 2000• 25 citations
Publisher

Abstract

We use a Fano diagonalization technique to find the eigenmodes of an atom laser consisting of a single-mode atomic cavity that is coherently coupled to the continuum of free space modes. Under very general conditions the system exhibits a single, stationary bound mode. We discuss the properties of this bound mode depending on the system parameters and investigate its effect on the output beam of the atom laser.

DOI
10.1103/physreva.62.043602

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We use a Fano diagonalization technique to find the eigenmodes of an atom laser consisting of a single-mode atomic cavity that is coherently coupled to the continuum of free space modes. Under very general conditions the system exhibits a single, stationary bound mode. We discuss the properties of this bound mode depending on the system parameters and investigate its effect on the output beam of the atom laser.
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.
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.
We investigate a single-atom nondegenerate cascade laser model, based on a coherently pumped three-level atom coupled to two independently damped cavity modes. We show that while many features predicted within a recently proposed N-atom superradiant laser model [F. Haake et al., Phys. Rev. Lett. 71, 995 (1993)] can readily be obtained in the single-atom case, some of the quantum noise properties are significantly different. The influence of spontaneous decay and nonadiabatic effects due to the finite spectral width of the lower cavity mode are discussed. Finally, we show that the present model has a large potential for the stationary preparation of various nonclassical states of the atom-field system.
A theoretical model of a microscopic laser system incorporating two identical atoms coupled to a single resonator mode is investigated in detail. It is established that a dramatic improvement in laser quality results from the addition of a second atom into the cavity. The enhanced laser action, arising from a cavity-induced mutual atomic coherence, is inferred from comprehensive studies of the steady-state and dynamical properties of the cavity output field. Evidence of laser action is also found in the fluorescence field where position-dependent spectral profiles occur. Counterintuitively, we establish that antibunching phenomena in the fluorescence can be enhanced by incoherent pumping.
We consider a laser model consisting of a single four-level or three-level atom, an optical cavity, and an incoherent pump. Results for photon statistics for varying pump levels are obtained using a quantum trajectory algorithm. In particular, we calculate the mean photon number, Fano factor (which is the variance over the mean). We examine that the behavior of the single-atom device as \ensuremath{\beta}, the fraction of spontaneous emission into the lasing mode, is varied. Typical values considered for \ensuremath{\beta} are $0.01<\ensuremath{\beta}<1.0.$ We find that for large enough \ensuremath{\beta}, lasing action, with properties similar to those predicted by semiclassical theories that factorize atom-field correlations and use a small-noise approximation, can occur. Squeezing can occur as \ensuremath{\beta} is increased. There is no evidence of a sharp phase transition from weakly excited thermal light to coherent light at a particular pump power. This is consistent with work on many-atom lasers with \ensuremath{\beta} values in the range considered here. As \ensuremath{\beta} is increased, the output goes from quasithermal light to coherent and finally to squeezed light, progressing into a fully quantum-mechanical regime. We also consider the effects of cavity damping and spontaneous emission rates on these results.