Mesoscopic physics deals with three fundamental issues: quantum coherence, fluctuations and correlations. Here we analyze these issues for atom optics, using a simplified model of an assembly of atoms (or detectors, which are particles with some internal degree of freedom) moving in arbitrary trajectories in a quantum field. Employing the influence functional formalism, we study the self-consistent effect of the field on the atoms, and their mutual interactions via coupling to the field. We derive the coupled Langevin equations for the atom assemblage and analyze the relation of dissipative dynamics of the atoms with the correlation and fluctuations of the quantum field. This provides a useful theoretical framework for analysing the coherent properties of atom-field systems.
Mesoscopic physics deals with three fundamental issues: quantum coherence, fluctuations and correlations. Here we analyze these issues for atom optics, using a simplified model of an assembly of atoms (or detectors, which are particles with some internal degree of freedom) moving in arbitrary trajectories in a quantum field. Employing the influence functional formalism, we study the self-consistent effect of the field on the atoms, and their mutual interactions via coupling to the field. We derive the coupled Langevin equations for the atom assemblage and analyze the relation of dissipative dynamics of the atoms with the correlation and fluctuations of the quantum field. This provides a useful theoretical framework for analysing the coherent properties of atom-field systems.
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.
In this paper, we dwell on three issues: (1) revisit the relation between vacuum fluctuations and radiation reaction in atom-field interactions, an old issue that began in the 1970s and settled in the 1990s with its resolution recorded in monographs; (2) the fluctuation–dissipation relation (FDR) of the system, pointing out the differences between the conventional form in linear response theory (LRT) assuming ultra-weak coupling between the system and the bath, and the FDR in an equilibrated final state, relaxed from the nonequilibrium evolution of an open quantum system; (3) quantum radiation from an atom interacting with a quantum field: We begin with vacuum fluctuations in the field acting on the internal degrees of freedom (idf) of an atom, adding to its dynamics a stochastic component which engenders quantum radiation whose backreaction causes quantum dissipation in the idf of the atom. We show explicitly how different terms representing these processes appear in the equations of motion. Then, using the example of a stationary atom, we show how the absence of radiation in this simple cases is a result of complex cancellations, at a far away observation point, of the interference between emitted radiation from the atom and the local fluctuations in the free field. In so doing we point out in Issue 1 that the entity which enters into the duality relation with vacuum fluctuations is not radiation reaction, which can exist as a classical entity, but quantum dissipation. Finally, regarding issue 2, we point out for systems with many atoms, the co-existence of a set of correlation-propagation relations (CPRs) describing how the correlations between the atoms are related to the propagation of their (retarded non-Markovian) mutual influence manifesting in the quantum field. The CPR is absolutely crucial in keeping the balance of energy flows between the constituents of the system, and between the system and its environment. Without the consideration of this additional relation in tether with the FDR, dynamical self-consistency cannot be sustained. A combination of these two sets of relations forms a generalized matrix FDR relation that captures the physical essence of the interaction between an atom and a quantum field at arbitrary coupling strength.
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.
Abstract Recent experimental results point to the existence of coherent quantum phenomena in systems made of a large number of particles, despite the fact that for many-body systems the presence of decoherence is hardly negligible and emerging classicality is expected. This behaviour hinges on collective observables, named quantum fluctuations , that retain a quantum character even in the thermodynamic limit: they provide useful tools for studying properties of many-body systems at the mesoscopic level, in-between the quantum microscopic scale and the classical macroscopic one. We herein present the general theory of quantum fluctuations in mesoscopic systems, and study their dynamics in a quantum open system setting, taking into account the unavoidable effects of dissipation and noise induced by the external environment. As in the case of microscopic systems, decoherence is not always the only dominating effect at the mesoscopic scale: certain types of environment can provide means for entangling collective fluctuations through a purely noisy mechanism.
We study the nonequilibrium dissipative dynamics of the center of mass of a particle coupled to a field via its internal degrees of freedom. We model the internal and external degrees of freedom of the particle as quantum harmonic oscillators in 1+1D, with the internal oscillator coupled to a scalar quantum field at the center of mass position. Such a coupling results in a nonlinear interaction between the three pertinent degrees of freedom---the center of mass, internal degree of freedom, and the field. It is typically assumed that the internal dynamics is decoupled from that of the center of mass owing to their disparate characteristic timescales. Here we use an influence functional approach that allows one to account for the self-consistent backaction of the different degrees of freedom on each other, including the coupled nonequilibrium dynamics of the internal degree of freedom and the field, and their influence on the dissipation and noise of the center of mass. Considering a weak nonlinear interaction term, we employ a perturbative generating functional approach to derive a second order effective action and a corresponding quantum Langevin equation describing the non-equilibrium dynamics of the center of mass. We analyze the resulting dissipation and noise arising from the field and the internal degree of freedom as a composite environment. Furthermore, we establish a generalized fluctuation-dissipation relation for the late-time dissipation and noise kernels. Our results are pertinent to open quantum systems that possess intermediary degrees of freedom between system and environment, such as in the case of optomechanical interactions.
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 N harmonic oscillators, modeling the internal degrees of freedom (IDFs) of N 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 N 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.