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arXiv:0807.0931 · Physical Review A

Theory of Raman transitions in cavity QED

A. David. Boozer

Published Sep 9, 2008• 4 citations
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Abstract

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.

DOI
10.1103/physreva.78.033406

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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.
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.
A single neutral atom is trapped in a three-dimensional optical lattice at the center of a high-finesse optical resonator. Using fluorescence imaging and a shiftable standing-wave trap, the atom is deterministically loaded into the maximum of the intracavity field where the atom-cavity coupling is strong. After 5 ms of Raman sideband cooling, the three-dimensional motional ground state is populated with a probability of (89±2)%. Our system is the first to simultaneously achieve quantum control over all degrees of freedom of a single atom: its position and momentum, its internal state, and its coupling to light.
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 report on recent progress in our lab involving cavity quantum electrodynamics with optically trapped atoms. \n \nIn particular, we will focus on a recent measurement of the Vacuum-Rabi splitting for one atom strongly coupled to the field of a high finesse optical resonator. This splitting is characteristic of the normal modes in the eigenvalue spectrum of the atom-cavity system. A new Raman scheme for cooling atomic motion along the cavity axis enables a complete spectrum to be recorded for an individual atom trapped within the cavity mode, in contrast to all previous measurements in cavity QED that have required averaging over many atoms.
We propose a quantum simulation of a two-level atom coupled to a single mode of the electromagnetic field in the ultrastrong-coupling regime based upon resonant Raman transitions in an atom interacting with a high finesse optical cavity mode. We show by numerical simulation the possibility of realizing the scheme with a single rubidium atom, in which two hyperfine ground states make up the effective two-level system, and for cavity QED parameters that should be achievable with, for example, microtoroidal whispering-gallery-mode resonators. Our system also enables simulation of a generalized model in which a nonlinear coupling between the atomic inversion and the cavity photon number occurs on an equal footing with the (ultrastrong) dipole coupling and can give rise to critical-type behavior even at the single-atom level. Our model takes account of dissipation, and we pay particular attention to observables that would be readily observable in the output from the system.
In recent years, remarkable advances in the science of laser cooling and trapping of atomic samples have lead to breakthroughs in quantum optics and, in particular, in cavity quantum electrodynamics (QED). The ability to optically trap an atom within the mode of a ultra-high finesse cavity of small mode volume for experimentally significant periods of time now allows for the continuous observation of fundamental quantum optical effects. This dissertation will focus on experiments conducted to fully characterize and exert quantum control over a strongly-coupled atom-cavity system consisting of single cesium atoms isolated by a dipole trapping in the mode of a Fabry-Perot optical resonator. In particular, we describe techniques developed and implemented for exerting coherent control over the internal and quantum motional state of these atoms using stimulated Raman processes. We also focus on the applications of this system to quantum networking and quantum information science, particularly within the context of coherently transferring quantum states from atom to quantum optical fields and back. Finally, we describe a series of measurements carried out to explore the characteristic dynamics of the Jaynes-Cummings Hamiltonian which governs the system. This includes spectroscopic measurement of the signature vacuum Rabi splitting for strongly-coupled cavity QED as well as evidence in the time domain for coherent Rabi nutation of excitation between atom and field on resonance.