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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Generalized quantum dynamics and interaction of atoms with quantum fields

R. Kh. Gainutdinov, Aigul A. Mutygullina

Published Jan 24, 2006• 1 citation
Publisher

Abstract

We investigate the effects of the nonlocality in time of the effective interaction of atoms with quantum fields, arising after integrating out certain degrees of freedom. We show that these effects can be described, in a natural way, within the formalism of the generalized quantum dynamics developed in [J. Phys. A 32, 5657 (1999)]. The new possibilities that the generalized quantum dynamics opens for solving the problem are demonstrated by using the example of a muonic atom interacting with the electronic vacuum.

DOI
10.1117/12.675143

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We investigate the effects of the nonlocality in time of the effective interaction of atoms with quantum fields, arising after integrating out certain degrees of freedom. We show that these effects can be described, in a natural way, within the formalism of the generalized quantum dynamics developed in [J. Phys. A 32, 5657 (1999)]. The new possibilities that the generalized quantum dynamics opens for solving the problem are demonstrated by using the example of a muonic atom interacting with the electronic vacuum.
The problem of describing the dynamics of quantum systems generated by a nonlocal-in-time interaction is considered. It is shown that the use of the Feynman approach to quantum theory in combination with the canonical approach allows one to extend quantum dynamics to describe the time evolution in the case of such interactions. In this way, using only the current concepts of quantum theory, a generalized equation of motion for state vectors is derived. In the case where the fundamental interaction generating the dynamics in a system is local in time, this equation is equivalent to the Schrödinger equation. Explicit examples are given for an exactly solvable model. The proposed formalism is shown to provide a new insight into the problem of the description of nonlocal interactions in quantum field theory. It is shown that such a property of the equation of motion, such as nonlocality in time, may be important for describing hadron-hadron interactions at low and intermediate energies.
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.
This paper and planned subsequent ones have two broad aims. First, we construct a theory for multipartite open quantum systems comprising several layers of structure with self-consistent backactions. We develop the graded influence action formalism [Behunin and Hu, Phys. Rev. A 82, 022507 (2010); Phys. Rev. A 84, 012902 (2011)] to account for the influences of successive sublayers on the dynamics of the variables of interest. Second, we apply these methods to the study of atom-field-medium interactions and highlight their merits over conventional methods. We consider a system of NNN harmonic oscillators, modeling the internal degrees of freedom (IDFs) of NNN neutral atoms (A), interacting with a quantum field (F), scalar here, for simplicity, altered by the presence of a dielectric medium (M). In this paper we use the coarse-grained and stochastic effective actions in the influence functional formalism to derive the stochastic equations for the reduced density matrices of the dynamical variables in the successive layers of structure. The term ``graded'' refers to the specific ordering of the coarse-graining procedures. Three layers of coarse graining are performed. First, integrating over the common bath of the dielectric oscillators results not only in the appearance of necessary dissipative properties of the dielectric but also in essential nuanced features such as non-Markovian spatial correlations in the dielectric. Second, integrating over the medium variables as a whole results in a dielectric-modified quantum field, the influence of the medium on the quantum field manifesting through a frequency-dependent permittivity function. Finally, integrating over this dielectric-altered quantum field which interacts with the IDFs of the atoms allows us to derive an equation of motion which describes the nonequilibrium stochastic dynamics of the IDFs of the atoms interacting with a dielectric medium-modified quantum field. In the future we plan to calculate the nonequilibrium covariant matrix elements of the correlation functions of the IDFS of NNN atoms in a dielectric-altered quantum field, which are useful for probing many basic quantum information issues, such as the entanglement dynamics in AFM interactions.
We provide an alternative derivation of a master equation formalism for open quantum systems and apply it to illustrative examples. Using this formalism, we show that generally there can be interference between non-interacting baths on a system's reduced dynamics, confirming results in Phys. Rev. A 89, 042117 (2014). However, we also find that, up to second order, such interference vanishes as long as the baths are initially statistically independent, thereby identifying a satisfiable condition for non-interference. We use a two-dimensional series expansion method to develop a master equation formalism that deals with the effects of both system-environment interaction and classical noise on a system's dynamics in a unified manner. We apply this formalism to the example of a Zeeman-splitted atom in a stochastic B-field interacting with an optical cavity and find that the atom's total decoherence rate is, up to second order, a simple sum of the decoherence rate due to the atom-cavity interaction alone and that due to the stochastic B-field alone. We also develop a formalism for the dynamics of the (marginal) probability density of open classical systems in a similar fashion as the master equation formalism for open quantum systems.