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arXiv:quant-ph/0301180 · Physical Review A

Moving atom-field interaction: Quantum motional decoherence and relaxation

Sanjiv Shresta, B. L. Hu

Published Jul 24, 2003• 10 citations
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Abstract

The reduced dynamics of an atomic qubit coupled both to its own quantized center of mass motion through the spatial mode functions of the electromagnetic field, as well as the vacuum modes, is calculated in the influence functional formalism. The formalism chosen can describe the entangled non-Markovian evolution of the system with a full account of the coherent back-action of the environment on the qubit. We find a slight increase in the decoherence due to the quantized center of mass motion and give a condition on the mass and qubit resonant frequency for which the effect is important. In optically resonant alkali-metal atom systems, we find the effect to be negligibly small. The framework presented here can nevertheless be used for general considerations of the coherent evolution of qubits in moving atoms in an electromagnetic field.

DOI
10.1103/physreva.68.012110

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The reduced dynamics of an atomic qubit coupled both to its own quantized center of mass motion through the spatial mode functions of the electromagnetic field, as well as the vacuum modes, is calculated in the influence functional formalism. The formalism chosen can describe the entangled non-Markovian evolution of the system with a full account of the coherent back-action of the environment on the qubit. We find a slight increase in the decoherence due to the quantized center of mass motion and give a condition on the mass and qubit resonant frequency for which the effect is important. In optically resonant alkali-metal atom systems, we find the effect to be negligibly small. The framework presented here can nevertheless be used for general considerations of the coherent evolution of qubits in moving atoms in an electromagnetic field.
This dissertation treats quantum open system dynamics, focusing on the coherent evolution of a two-level atom (as the system) interacting with an electromagnetic field (as the bath), for purposes relevant to quantum computing. In order to maintain the quantum correlations that develop between the system and bath throughout the evolution path integral formalisms such as the influence functional and closed time path formalisms are used. Predictions of effects due to the quantum correlations in the composite interacting system are computed. Conventional treatments using Schr\"odinger-master equation and Heisenberg-Langevin approaches usually ignore system+bath quantum correlations as a technical simplification. It is argued that although neglect of system+bath correlations is generally a good approximation when the bath has a large continuous set of degrees of freedom, a residual coherence effect remains due to the non-zero bath correlation time. Though small, these effects are becoming more relevant as, with the advent of ultra cold atom sources, atom optics experiments are reaching levels at which such residual effects are becoming measurable. Three specific problems are investigated in this thesis: First is a self-dressing rederivation of the Casimir-Polder retardation force. The well known stationary atom result is reproduced and a result for a slowly moving atom is obtained which is up to twice the stationary atom correction. Second is the entangled evolution of a qubit with an initially thermal low temperature bath. The diagonal matrix elements are found to thermalize and the off-diagonal elements to decohere as expected, however they do so non-exponentially due to the quantum correlations that develop between the qubit and bath. Third is a calculation of qubit dynamics in the presence of quantized atomic motion as well as zero point fluctuations of the electromagnetic field. The decoherence rate of the qubit is found to increase slightly in that case due to the additional degree of freedom.
We perform a first-principles derivation of the general master equation to study the non-Markovian dynamics of a two-level atom (2LA) interacting with an electromagnetic field (EMF). We use the influence functional method, which can incorporate the full back reaction of the field on the atom, while adopting Grassmannian variables for the 2LA and the coherent-state representation for the EMF. We find exact master equations for the cases of a free quantum field and a cavity field in the vacuum. In response to the search for mechanisms to preserve maximal coherence in quantum computations in ion trap prototypes, we apply these equations to analyze the decoherence of a 2LA in an EMF, and find that decoherence time is close to relaxation time. This is at variance with the claims by authors who studied the same system but used a different coupling model. We explain the source of difference and argue that, contrary to common belief, the EMF, when resonantly coupled to an atom, does not decohere it as efficiently as a bath does on a quantum Brownian particle. The master equations for non-Markovian dynamics derived here are expected to be useful for exploring new regimes of 2LAEMF interaction, which is becoming physically important experimentally.
We study the non-Markovian dynamics of a qubit made up of a two-level atom interacting with an electromagnetic field (EMF) initially at finite temperature. Unlike most earlier studies where the bath is assumed to be fixed, we study the complete evolution of the combined qubit-EMF system, thus allowing for the coherent backaction from the bath on the qubit and the qubit on the bath in a self-consistent manner. In this way we can see the development of quantum correlations and entanglement between the system and its environment, and how that affects the decoherence and relaxation of the system. We find nonexponential decay for both the diagonal and nondiagonal matrix elements of the qubit's reduced density matrix in the pointer basis. The former shows the qubit relaxing to thermal equilibrium with the bath, while the latter shows the decoherence rate beginning at the usually predicted thermal rate, but changing to the zero-temperature value as the qubit and bath become entangled. The decoherence and relaxation rates are comparable, as in the zero-temperature case. On the entanglement of a qubit with the EMF we calculated the fidelity and the von Neumann entropy, which is a measure of the purity of the density matrix. The present more accurate non-Markovian calculations predict lower loss of fidelity and purity as compared with the Markovian results. Generally speaking, with the inclusion of quantum correlations between the qubit and its environment, the non-Markovian processes tend to slow down the drive of the system to equilibrium, prolonging the decoherence and better preserving the fidelity and purity of the system.
The entanglement dynamics of a two-level atom with center-of-mass motion in a single-mode quantized field is investigated.The behavior of the entropy changes of the subsystems,as well as the concurrence of the coupled atom-field system is explored.These results show that when the atom is initially prepared in ground state anti-correlation behavior occurs,but a positively correlated behavior appears gradually as the increasing of the probability of the atom initially in excited state.Also,the amplitude of the concurrence increases with the increasing of the probability of the atom initially in excited state.In addition,with increasing of the atomic center-of-mass motion,both the amplitudes of the partial entropy changes and the concurrence are reduced.
In general, decoherence destroys quantum-mechanical interference originating from the coherent superposition of complex probability amplitudes. In this paper we show how decoherence of a quantized electromagnetic field inside a cavity influences atomic motion. This motion is entangled with the internal states of the atom and with the quantized field via the Jaynes-Cummings interaction. As a result, we present the effect of generating coherence in the subspace of the atomic motion via decoherence of the cavity field. The quantum trajectory method is used for the description of the relaxation process.
We discuss the dynamical properties of quantum entanglement and partial entropy for moving three-level atom interacting with single-mode quantized field inside a phase-damped cavity for more general cases.The results show that the atomic motion and decoherence effects play an important role on the evolution of the system dynamics and quantum entanglement.Moreover, we show that the phenomena of long lived nonlocal correlation and short temporal disentanglement can be generated through specific values of phase damping and atomic motion parameter.