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arXiv:quant-ph/0401012 · Physical Review A

Nonadiabatic effects of atomic motion inside a high- Q optical cavity

Peng Zhang, Y. Li, C. P. Sun, Li You

Published Dec 8, 2004• 3 citations
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Abstract

We revisit the topic of atomic center of mass motion of a three level atom Raman coupled strongly to an external laser field and the quantum field of a high-$Q$ optical cavity. We focus on the motion related nonadiabatic effects of the atomic internal dynamics and provide a quantitative answer to the validity regime for the application of the motional insensitive dark state as recently suggested by Duan, Kuzmich, and Kimble [Phys. Rev. A 67, 032305 (2003)].

DOI
10.1103/physreva.70.063804

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We consider the motion of the end mirror of a cavity inside which a two-level atom trapped. The fast vibrating mirror induces nonlinear couplings between the cavity field and the atom. We analyze this optical effect by showing the population of the atom in its internal degrees of freedom as a function of time. On the other side, fast atom-field variables result in an additional potential for the atomic center-of-mass motion and the mirror vibration, leading to entanglement in the motion and the vibration. The entanglement has been numerically simulated and discussed.
We consider an atom inside a ring cavity, where a plane-wave cavity field together with an external coherent laser beam induces a two-photon Raman transition between two hyperfine ground states of the atom. This cavity-assisted Raman transition induces effective coupling between atom’s internal degrees of freedom and its center-of-mass motion. In the meantime, atomic dynamics exerts a back-action to cavity photons. We investigate the properties of this system by adopting a mean-field and a full quantum approach, and show that the interplay between the atomic dynamics and the cavity field gives rise to intriguing nonlinear phenomena.
We present two schemes for driving Raman transitions between the ground-state hyperfine manifolds of a single atom trapped within a high-finesse optical cavity. In both schemes, the Raman coupling is generated by standing-wave fields inside the cavity, thus circumventing the optical access limitations that free-space Raman schemes must face in a cavity system. These cavity-based Raman schemes can be used to coherently manipulate both the internal and motional degrees of freedom of the atom, and thus provide powerful tools for studying cavity quantum electrodynamics. We give a detailed theoretical analysis of each scheme, both for a three-level atom and for a multilevel cesium atom. In addition, we show how these Raman schemes can be used to cool the axial motion of the atom to the quantum ground state, and we perform computer simulations of the cooling process.
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In order to study quantum effects such as state superposition and entanglement, one would like to construct simple systems for which the damping rates are slow relative to the rate of coherent evolution. One such system is strong-coupling cavity quantum electrodynamics (QED), in which a single atom is coupled to a single mode of a high finesse optical cavity. In recent years, optical trapping techniques have been applied to the cavity QED system, allowing an individual atom to remain coupled to the cavity for long periods of time. For the purpose of future cavity QED experiments, one would like to gain as much control over the trapped atom as possible; in particular, one would like to cool the center of mass motion of the atom, to measure the magnetic field at the location of the atom, and to be able to prepare the atom in a given internal state. In the first part of this thesis, I present a scheme for driving Raman transitions inside the cavity that can be used to achieve these goals. After giving a detailed theoretical treatment of the Raman scheme, I describe how it can be implemented in the lab and discuss some preliminary experimental results. In the second part of this thesis, I present a number of simple field theory models. These models were developed in an attempt to understand some of the central ideas of theoretical physics by looking at how the ideas work in a highly simplified context. The hope is that by reducing the mathematical complexity of an actual theory, the underlying physical concepts can be more easily understood.