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Cavity Qed: Adiabatic Atomic Cooling in Cavities and Evaluation of a Technique for Atomic Homodyne Detection of Cotangent States.

T. Zaugg

Published Jan 1, 1994• 0 citations
OpenAlex

Abstract

Part I. We analyze how a decaying cavity field can lead to significant atomic cooling. This cooling can be intuitively understood by invoking the adiabatic theorem to characterize the dynamics of an atom dressed by a classical field. We find numerically that cooling can proceed well into the quantum regime where there are only a few photons left in the cavity, and where the adiabatic theorem ceases to be applicable. A physical interpretation of this final cooling stage is given. Part II. We evaluate a nonlinear atomic homodyne detection scheme for measuring the Wigner characteristic function of a microwave cavity field. We find numerically that the semiclassical approximation, on which this scheme is based, does not give results consistent with a full quantum calculation. We analyze the back-action of the measurements on steady-state 'macroscopic superpositions' that can be generated in high-Q microwave cavities. We show that the measurements required for a full characterization of the state destroys the macroscopic superposition such that it cannot be reconstructed by using the scheme that was used to generate it in the first place.

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•Jun 30, 2006•0 citations
Part I. We analyze how a decaying cavity field can lead to significant atomic cooling. This cooling can be intuitively understood by invoking the adiabatic theorem to characterize the dynamics of an atom dressed by a classical field. We find numerically that cooling can proceed well into the quantum regime where there are only a few photons left in the cavity, and where the adiabatic theorem ceases to be applicable. A physical interpretation of this final cooling stage is given. Part II. We evaluate a nonlinear atomic homodyne detection scheme for measuring the Wigner characteristic function of a microwave cavity field. We find numerically that the semiclassical approximation, on which this scheme is based, does not give results consistent with a full quantum calculation. We analyze the back-action of the measurements on steady-state 'macroscopic superpositions' that can be generated in high-Q microwave cavities. We show that the measurements required for a full characterization of the state destroys the macroscopic superposition such that it cannot be reconstructed by using the scheme that was used to generate it in the first place.
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.
In this poster we characterize the cooling dynamics of atoms confined by an external potential in a high-Q cavity, when the width of the atomic wave packet is much smaller than the field wave-length. Its form allows us to identify novel regimes where the motion can be efficiently cooled to the potential ground state. In particular, parameter regimes are identified where the dynamics is characterized by quantum interference between the mechanical effects of the laser and of the resonator fields, which selectively enhance the cooling transitions and thus the efficiency. In this regime we characterize the state of the system by the spectrum of the intensity of the light scattered by the atom and at the cavity output, when atom and cavity are at steady state of the cooling dynamics. We evaluate the spectrum by implementing the model of M. Bienert et al., (2006) to atoms inside resonators. We find that, in some cases, quantum interference effects lead to the suppression of features of the resonance fluorescence spectrum, which are otherwise visible in the spectrum of atoms in free space.
Every quantum system subjected to measurements is an open quantum system. The cavity QED system is elegant in that it probes the interaction between two quantum systems, the atom and the field, while its loss mechanisms are well understood and can be externally monitored. The study of cross-correlations in cavity QED is important for understanding how entanglement evolves in open quantum systems. As quantum information science grows we need to learn more about entanglement and how it can be quantified and measured. Correlation functions have been used to compare an electromagnetic field (intensity) of one mode with the electromagnetic field (intensity) of the same mode at a later time or different spatial location. In quantum optics, correlation functions have been calculated and measured to probe the nonclassical field that results from the interaction of a single mode of the electromagnetic field and an ensemble of two-level atoms (the canonical cavity QED system). This field can exhibit antibunching, squeezing, and can violate inequalities required for a classical field. Entanglement in the steady state of a cavity QED system cannot be measured directly with traditional correlation functions (Hanbury-Brown and Twiss type experiments). Cross-correlations, however, interrogate directly both modes of the entangled pair, the transmitted (cavity) and the fluorescent (atom) intensities, and can act as an entanglement witness. This thesis presents the implementation of a cross-correlation measurement in a cavity QED system. The work has required the construction of an apparatus that incorporates laser cooling and trapping with quantum optics to carefully control both the external (center of mass motion) and internal (atomic state) degrees of freedom of a collection of atoms that interact with a single mode of a high finesse Fabry-Perot cavity. We examine theoretically and experimentally a new intensity cross-correlation function which probes the evolution of the cavity field conditioned on the detection of a fluorescent photon from an atom in the cavity. The results open the possibility to generalize the dynamics of entanglement as a physical resource necessary for the nascent quantum information science.