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Physical Review A

Theory of an atom laser

Murray Holland, Keith R. Burnett, Crispin W. Gardiner, J. I. Cirac, P. Zoller

Published Sep 1, 1996• 150 citations
Publisher

Abstract

Superconductivity, superfluidity, Bose-Einstein condensation, and laser amplification are all examples of a general mechanism involving the stimulated transfer of bosons into a specific quantum state. When the occupation number of the state is large, this mechanism may generate a macroscopic coherence for the state amplitude. In this paper, we demonstrate that the stimulated transfer of bosonic atoms into a given state of an optical or a magnetic trap can give rise to a coherent atomic source in analogy with the photon laser and we present a general model for such a device.

DOI
10.1103/physreva.54.r1757

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Superconductivity, superfluidity, Bose-Einstein condensation, and laser amplification are all examples of a general mechanism involving the stimulated transfer of bosons into a specific quantum state. When the occupation number of the state is large, this mechanism may generate a macroscopic coherence for the state amplitude. In this paper, we demonstrate that the stimulated transfer of bosonic atoms into a given state of an optical or a magnetic trap can give rise to a coherent atomic source in analogy with the photon laser and we present a general model for such a device.
The transition of atoms from the disorder of the gaseous phase into the “disciplined” behavior of the condensate can be compared with the transformation of chaotic incoherent light into a laser light beam. This analogy leads directly to the definition of the atom laser: a device that produces a beam of boson atoms that have “escaped” from a trapped Bose–Einstein condensate. The operation of our well-known optical laser requires essentially three things: an optical cavity, an active medium, and a mechanism that allows light to escape from the cavity. Within the cavity, a huge number of atoms of the active medium interact with photons. The cavity consists essentially of two mirrors with very high reflectivity onto which the photons are reflected many times. Multiple reflections cause photons to interact continuously with atoms in the cavity, leading to a continuous generation of new photons by stimulated emission. The result is an increase in the number of photons, i.e., amplification of the beam traveling within the cavity. All of the photons have the same frequency and phase (i.e., they oscillate synchronously). Since one of the mirrors is not perfectly reflective, the photons manage to escape from the cavity, resulting in the well-known, monochromatic, and directional laser beam.
The experimental observation of Bose–Einstein condensation (BEC) in rubidium in 1995 demonstrated that a macroscopic number of bosons could be produced in a single quantum state of trapped atoms. The occupation of a single quantum state by a large number of identical bosons is the matter-wave analog of the storage of photons in a single mode of a laser cavity. In a conventional laser, one extracts a coherent beam of photons from a cavity by using a partially transmitting mirror as an output coupler. In 1997, Wolfgang Ketterle and his collaborators at MIT built a pulsed output coupler that extracted matter waves from a condensate, and they observed interference between atoms from two separate condensates, thereby demonstrating an atom laser for the first time (see PHYSICS TODAY, March 1997, page 17).
We develop the quantum-mechanical description of output coupling of macroscopic coherent matter waves from a Bose-Einstein condensate (BEC) via a radio-frequency field in the pulsed and cw limits for both strong and weak field coupling. The theory is converted into a Fock state description to point out the stimulated (in Bose particle) nature of the output coupling. A useful analogy with the theory of molecular photodissociation is used to explain the various regimes of output coupling BECs using radiation sources. We present specific calculations of the rates of output coupling as a function of the number of Bose atoms in the condensate and the frequency, detuning, and intensity of the radio-frequency field.
Summary form only given.Recent experiments show signatures of exciton Bose-Einstein condensation in semiconductors. Thus a device that creates a coherent population of excitons while being pumped by a thermal source may be possible. Such an exciton matter laser could consist of a quantum well, possibly embedded in an optical microcavity. In it hot excitons slightly below the bandgap are created by a thermal distribution of free electrons and holes (generated by electrical injection or optical pumping). The excitons interact with (LA) phonons. At low densities excitons are bosonic, and their scattering is affected by statistical enhancement into states with large occupation. Under certain conditions the excitons can condense into a single state, with statistics similar to a coherent state. Light emitted by radiative recombination has the coherence properties of the condensate and is similar to laser light. However, the electronic population in the device does not need to be inverted. We consider 1S heavy-hole excitons in a two-dimensional harmonic trap, realized by a quantum well where interface roughness inevitably localizes low-energy excitons, or by strain fields in lattice mismatched structures. We treat the lowest two trap levels quantum mechanically, and the higher lying states act as a reservoir. Our model is valid at low density, where phase space filling and collisions are negligible. While simplistic, the model displays the main features of an exciton matter laser. Our model is described by the master equation.
An analysis is made of the condition for stimulated precipitation of Bose particles to form a coherent Bose condensate. Experimental observations of the interference of Bose condensates are described. A system of equations is proposed for the dynamics of a generator of coherent atomic beams, i.e. an 'atom laser'. This system of equations takes account of the interaction of a Bose condensate with incoherent particle subsystems. A description is given of experimental observations of stimulated amplification of an exciton bunch. The possibility of generation of a coherent state of excitons by direct binding of free carriers in semiconductors and insulators is considered.