Bei Lok Hu

A bstract: We compute the quantum radiation emitted by wavepackets of relativistic single electrons, both at rest and undergoing uniform acceleration in the Minkowski vacuum of the electromagnetic field. We find that the cubic terms in the original nonlinear action of electrodynamics should be considered in obtaining the quantum radiation to the leading order. We show that the quantum radiation from a single-electron wavepacket at rest vanishes exactly. For a uniformly accelerated electron, the quantum radiated power has secular growth in the long-time regime. We demonstrate that this secular growth has a classical interpretation, and argue that the resummed quantum radiation at late times would not diverge. Regarding experimental proposals for the detection of the Unruh effect from the quantum radiation in the ‘blind spots’ of classical radiation we ascertain that quantum corrections in the two blind spots are fully contributed by the transverse-deviation correlators, where the dominant contributions are irrelevant to the Unruh effect in electron microscopes.

This third paper in this series continues the investigation of atom-field interactions in the presence of a conductor or a dielectric medium, focusing on quantum information related basic issues such as decoherence and entanglement. Here we consider the entanglement between two atoms with internal degrees of freedom modeled by a harmonic oscillator, with varying separations between them and varying distances between them and a conducting surface. These are configurations familiar in the Casimir-Polder effect, but the behavior of atom-surface entanglement is quite different from the well-studied behavior of field-induced forces. For one, while the attractive force between an atom and a conducting surface increases as they come closer, the entanglement between the atom and the quantum field actually decreases as the atom gets closer to the conductor, as shown in \cite{Rong,AFD2}. We show how different factors play out, ranging from the coupling between the atoms and the field to the coupling between the atoms, going beyond the weak coupling restrictions often found necessary in the literature. Gathering our results for the entanglement dependence on each variable concerned, we can provide a spatial topography of quantum entanglement, thus enabling a visualized understanding of the behavior of quantum field-mediated entanglement. In particular we can quantify the definition of a three-dimensional \textit{entanglement domain} between the two atoms, how it varies with their coupling, their separation and their distances from the conducting surface, and for practical applications, how to exercise effective control of the entanglement between two atoms by changing these parameters. Our findings are expected to be useful for studies of atom-field-medium interactions in vacuum and surface physics.

A quantum master equation describing the stochastic dynamics of a quantum massive system interacting with a quantum gravitational field is useful for the investigation of quantum gravitational and quantum informational issues such as the quantum nature of gravity, gravity-induced entanglement and gravitational decoherence. Studies of the decoherence of quantum systems by an electromagnetic field shows that a lower temperature environment is more conducive to successful quantum information processing experiments. Likewise, the quantum nature of (perturbative) gravity is far better revealed at lower temperatures than high, minimizing the corruptive effects of thermal noise. In this work, generalizing earlier results of the Markovian ABH master equation [1,2] which is valid only for high temperatures, we derive a non-Markovian quantum master equation for the reduced density matrix, and the associated Fokker-Planck equation for the Wigner distribution function, for the stochastic dynamics of two masses following quantum trajectories, interacting with a graviton field, including the effects of graviton noise, valid for all temperatures. We follow the influence functional approach exemplified in the derivation of the non-Markovian Hu-Paz-Zhang master equation [62,64] for quantum Brownian motion. We find that in the low temperature limit, the off-diagonal elements of the reduced density matrix decrease in time logarithmically for the zero temperature part and quadratically in time for the temperature-dependent part, which is distinctly different from the Markovian case. We end with a summary of our findings and a discussion on how this problem studied here is related to the quantum stochastic equation derived in [77] for gravitational self force studies, and to quantum optomechanics where experimental observation of gravitational decoherence and entanglement may be implemented.

Moving mirrors as analogue sources of Hawking radiation from black holes have been explored extensively but less so with cosmological particle creation (CPC), even though the analogy between the dynamical Casimir effect (DCE) and CPC based on the mechanism of the parametric amplification of quantum field fluctuations has also been known for a long time. This ‘perspective’ essay intends to convey some of the rigor and thoroughness of quantum field theory in curved spacetime, which serves as the theoretical foundation of CPC, to DCE, which enjoys a variety of active experimental explorations. We have selected seven issues of relevance to address, starting from the naively simple ones, e.g., why one should be bothered with ‘curved’ spacetime when performing a laboratory experiment in ostensibly flat space, to foundational theoretical ones, such as the frequent appearance of nonlocal dissipation in the system dynamics induced by colored noises in its field environment, the existence of quantum Lenz law and fluctuation–dissipation relations in the backreaction effects of DCE emission on the moving atom/mirror or the source, and the construction of a microphysics model to account for the dynamical responses of a mirror or medium. The strengthening of the theoretical ground for DCE is not only useful for improving conceptual clarity but needed for the development of the proof-of-concept type of future experimental designs for DCE. The results from the DCE experiments in turn will enrich our understanding of quantum field effects in the early universe because they are, in the spirit of analogue gravity, our best hopes for the verification of these fundamental processes.