M. G. Moore

Theory of Superradiant Scattering of Laser Light from Bose-Einstein Condensates

In a recent MIT experiment, a new form of superradiant Rayleigh scattering was observed in Bose-Einstein condensates. We present a detailed theory of this phenomena in which the directional dependence of the scattering rate and condensate depletion lead to mode competition which is ultimately responsible for superradiance. The nonlinear response of the system is highly sensitive to initial quantum fluctuations which cause large run to run variations in the observed superradiant pulses.

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

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.

EFFECTS OF ATOMIC DIFFRACTION ON THE COLLECTIVE ATOMIC RECOIL LASER

We formulate a wave atom optics theory of the Collective Atomic Recoil Laser, where the atomic center-of-mass motion is treated quantum mechanically. By comparing the predictions of this theory with those of the ray atom optics theory, which treats the center-of-mass motion classically, we show that for the case of a far off-resonant pump laser the ray optics model fails to predict the linear response of the CARL when the temperature is of the order of the recoil temperature or less. This is due to the fact that in theis temperature regime one can no longer ignore the effects of matter-wave diffraction on the atomic center-of-mass motion.

Optical control and entanglement of atomic Schrödinger fields

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.

Generating entangled atom-photon pairs from bose-einstein condensates

We propose using spontaneous Raman scattering from an optically driven Bose-Einstein condensate as a source of atom-photon pairs whose internal states are maximally entangled. Generating entanglement between a particle which is easily transmitted (the photon) and one which is easily trapped and coherently manipulated (an ultracold atom) will prove useful for a variety of quantum-information related applications. We analyze the type of entangled states generated by spontaneous Raman scattering and construct a geometry which results in maximum entanglement.

Eliminating the mean-field shift in two-component Bose-Einstein condensates

We demonstrate that the nonlinear mean-field shift in a multicomponent Bose-Einstein condensate may be eliminated by controlling the two-body interaction coefficients. This modification can be achieved by engineering the environment of the condensate. We consider the case of a two-component condensate in a quasi-one-dimensional atomic waveguide, achieving modification of the atom-atom interactions by varying the transverse wave functions of the components. Eliminating the density-dependent phase shift represents a promising potential application for multicomponent condensates in atom interferometry and precision measurements.

Gravity-induced Wannier-Stark ladder in an optical lattice

We discuss the dynamics of ultracold atoms in an optical potential accelerated by gravity. The positions and widths of the Wannier-Stark ladder of resonances are obtained as metastable states. The metastable Wannier-Bloch states oscillate in a single band with the Bloch period. The width of the resonance gives the rate transition to the continuum.

Monte Carlo investigation of an atom laser with a modulated quasi-one-dimensional cavity

Abstract The dynamics of a recently proposed atom laser scheme based on a modulated quasi-one-dimensional atom cavity are investigated. A three-mode model is developed which includes the effects of dipole–dipole collisions as well as pump and loss mechanisms. It is shown that the Monte Carlo wavefunction simulation technique is superior to a direct solution of the resulting master equation because of the existence of constants of motion which are present in the Monte Carlo wavefunctions but not in the full density operator. Under suitable parameter choices, the solution to the master equation leads to Poissonian atom statistics in the occupation of a single-atomic-cavity mode, analogous to the photon statistics of the optical laser. A threshold behaviour is predicted as the losses are varied relative to the gain for the laser mode.

Parametric Amplification of Coupled Atomic and Optical Fields

One of the earliest and still most important spin-offs of the invention of the laser is without a doubt nonlinear optics. Following the pioneering experiments carried out by P. A. Franken and his students [1], N. Bloembergen, Y. R. Shen and their collaborators made a series of crucial advances that led to the rapid development of the field [2]. In the early days, it was generally understood that what made nonlinear optics possible was the high optical powers provided by lasers. For such fields, a classical description of the light fields was clearly sufficient. Yet, a few visionaries insisted on a fully quantum mechanical description of radiation in the analysis of nonlinear optical phenomena such as parametric amplification. A central character in these developments was R. J. Glauber, who, together with his students, developed many of the tools, and much of the early quantum theory of nonlinear optics [3],[4]. One of his students was DanWalls, who upon his return to New Zealand after spending a short time in Germany developed one of the leading schools of quantum optics in the world.

Cavity atom optics and the 'free atom laser'

Abstract The trap environment in which Bose–Einstein condensates are generated and/or stored strongly influences the way they interact with light. The situation is analogous to cavity QED in quantum optics, except that in the present case, one tailors the matter-wave mode density rather than the density of modes of the optical field. Just as in QED, for short times, the atoms do not sense the trap and propagate as in free space. After times long enough that recoiling atoms can probe the trap environment, however, the way condensates and light fields are mutually influenced differs significantly from the free-space situation. We use as an example the condensate collective atomic recoil laser, which is the atomic matter-wave analog of the free-electron laser.