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arXiv:cond-mat/9902293 · Physical Review A

Quantum optics of a Bose-Einstein condensate coupled to a quantized light field

M. G. Moore, O. Zobay, Pierre Meystre

Published Aug 1, 1999• 125 citations
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Abstract

We consider the interaction between a Bose-Einstein condensate and a single-mode quantized light field in the presence of a strong far-off-resonant pump laser. The dynamics is characterized by an exponential instability, hence the system acts as an atom-photon parametric amplifier. Triggered by a small injected probe field, or simply by quantum noise, entangled atom-photon pairs are created which exhibit nonclassical correlations similar to those seen between photons in the optical parametric amplifier. In addition, the quantum statistics of the matter and light field depend strongly on the initial state which triggers the amplifier. Thus, by preparing different initial states of the light field, one can generate matter waves in a variety of quantum states, demonstrating optical control over the quantum statistics of matter waves.

DOI
10.1103/physreva.60.1491

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We consider the interaction between a Bose-Einstein condensate and a single-mode quantized light field in the presence of a strong far-off-resonant pump laser. The dynamics is characterized by an exponential instability, hence the system acts as an atom-photon parametric amplifier. Triggered by a small injected probe field, or simply by quantum noise, entangled atom-photon pairs are created which exhibit nonclassical correlations similar to those seen between photons in the optical parametric amplifier. In addition, the quantum statistics of the matter and light field depend strongly on the initial state which triggers the amplifier. Thus, by preparing different initial states of the light field, one can generate matter waves in a variety of quantum states, demonstrating optical control over the quantum statistics of matter waves.
We develop a fully quantized model of a Bose-Einstein condensate driven by a far off-resonant pump laser and interacting with a single mode of an optical ring cavity. This geometry leads to the generation of two condensate side modes that grow exponentially and are strongly entangled with the cavity mode. By changing the initial state of the optical field one can vary the quantum-statistical properties of the atomic side modes between thermal and coherent limits, as well as vary the degree of quantum entanglement.
The interaction between Bose Einstein condensates (BECs) and coherent light fields is treated within the framework of nonlinear wave mixing and studied using techniques developed in the fields of nonlinear and quantum optics. We focus in particular on two situations involving a BEC driven by a strong off-resonant 'pump' laser. First, we consider the case where the laser light is scattered into a single mode of an optical ring cavity. We then consider the case where the light is scattered into the continuum of vacuum modes of the electric field. The first problem is an extension of recent theoretical and experimental work on the so-called collective atomic recoil laser (CARL), whereas the second corresponds to a recent condensate-superradiance experiment performed at MIT. In the cavity situation, we develop a CARL model in which both the atomic and optical fields are treated fully quantum mechanically. We first show that the previous CARL model, which treats the atomic motion classically, breaks down at the recoil temperature due to the effects of matter-wave diffraction. We then show that when combined with a BEC the CARL can be viewed as a device which parametrically amplifies atomic and optical fields. The existence of entanglement and non-classical intensity correlations between the amplified atomic and optical fields is demonstrated, as well as the ability to manipulate the quantum statistical properties of the matter and light waves by injecting a weak laser field into the optical cavity to trigger the device. By replacing the cavity mode with a continuum of modes, we are able to formulate a quantum theory of condensate superradiance in which the scattered light field is eliminated in the Markov approximation. This model shows that condensate depletion leads to mode competition which prevents light scattering in all but the preferred direction(s). The outcome of the mode-competition is highly sensitive to the quantum fluctuations which trigger the phenomenon, resulting in large run-to-run variations in the angular pattern of the superradiant light pulse, an effect which is observed experimentally.
In this paper, the influence of dissipation on the dynamics of a recently proposed model [Phys. Rev. A 60,60,60, 1491 (1999)] of a strongly far-off-resonant pumped Bose-Einstein condensate interacting with a quantized light field is studied. It is verified that dissipation induces an exponential instability in the field mean intensities for values of parameters where the undamped system is stable. Also considered is the impact of dissipation on the quantum-statistical properties of the light and atomic fields.
In this paper, we investigate theoretically a system consisting of a one dimensional Bose-Einstein condensate trapped inside the optical lattice of an optical cavity. In the weak-interaction regime and under the Bogoliubov approximation, the wave function of the Bose-Einstein condensate can be described by a classical field (condensate mode) having some quantum fluctuations (the Bogoliubov mode) about the mean value. Such a system behaves as a so-called atomic parametric amplifier, similar to an optical parametric amplifier, where the condensate and the Bogoliubov modes play respectively, the roles of the pump field and the signal mode in the degenerate parametric amplifier and the s-wave scattering frequency of atom-atom interaction plays the role of the nonlinear gain parameter. We show that using the nonlinear effect of atomic collisions, how one can manipulate and control the state of the Bogoliubov mode and produce squeezed states.
In this paper, we investigate theoretically a system consisting of a one-dimensional Bose–Einstein condensate trapped inside the optical lattice of an optical cavity. In the weak-interaction regime and under the Bogoliubov approximation, the wave function of the Bose–Einstein condensate can be described by a classical field (condensate mode) having some quantum fluctuations (the Bogoliubov mode) about the mean value. Such a system behaves as a so-called atomic parametric amplifier, similar to an optical parametric amplifier, where the condensate and the Bogoliubov modes play, respectively, the roles of the pump field and the signal mode in the degenerate parametric amplifier and the s-wave scattering frequency of atom–atom interaction plays the role of the nonlinear gain parameter. We show that using the nonlinear effect of atomic collisions, how one can manipulate and control the state of the Bogoliubov mode and produce squeezed states.
In the present work we propose to realize a macroscopic light-matter entangled state, obtained by the interaction of a multiphoton quantum superposition with a BEC system. The multiphoton quantum state is generated by a quantum-injected optical parametric amplifier (QI-OPA) seeded by a single-photon belonging to an EPR entangled pair and interacts with a Mirror-BEC shaped as a Bragg interference structure. The overall process will realize an entangled macroscopic quantum superposition involving a "microscopic" single-photon state of polarization and the coherent "macroscopic" displacement of the BEC structure acting in space-like separated distant places. This hybrid photonic-atomic system could open new perspectives on the possibility of coupling the amplified radiation with an atomic ensemble, a Bose-Einstein condensate, in order to implement innovative quantum interface between light and matter.