Quantum recoil effects in finite-time disentanglement of two distinguishable atoms

Starting from the requirement of distinguishability of two atoms by their positions, it is shown that photon recoil has a strong influence on finite-time disentanglement and in some cases prevents its appearance. At near-field inter atomic distances well localized atoms, with maximally one atom being initially excited, may suffer disentanglement at a single finite time or even at a series of equidistant finite times, depending on their mean inter atomic distance and their initial electronic preparation.Comment: 13 pages, 1 figure, submitted to Physical Review on august 2

The Rotating-Wave Approximation: Consistency and Applicability from an Open Quantum System Analysis

We provide an in-depth and thorough treatment of the validity of the rotating-wave approximation (RWA) in an open quantum system. We find that when it is introduced after tracing out the environment, all timescales of the open system are correctly reproduced, but the details of the quantum state may not be. The RWA made before the trace is more problematic: it results in incorrect values for environmentally-induced shifts to system frequencies, and the resulting theory has no Markovian limit. We point out that great care must be taken when coupling two open systems together under the RWA. Though the RWA can yield a master equation of Lindblad form similar to what one might get in the Markovian limit with white noise, the master equation for the two coupled systems is not a simple combination of the master equation for each system, as is possible in the Markovian limit. Such a naive combination yields inaccurate dynamics. To obtain the correct master equation for the composite system a proper consideration of the non-Markovian dynamics is required.Comment: 17 pages, 0 figures

Non-Markovian Dynamics and Entanglement of Two-level Atoms in a Common Field

We derive the stochastic equations and consider the non-Markovian dynamics of a system of multiple two-level atoms in a common quantum field. We make only the dipole approximation for the atoms and assume weak atom-field interactions. From these assumptions we use a combination of non-secular open- and closed-system perturbation theory, and we abstain from any additional approximation schemes. These more accurate solutions are necessary to explore several regimes: in particular, near-resonance dynamics and low-temperature behavior. In detuned atomic systems, small variations in the system energy levels engender timescales which, in general, cannot be safely ignored, as would be the case in the rotating-wave approximation (RWA). More problematic are the second-order solutions, which, as has been recently pointed out, cannot be accurately calculated using any second-order perturbative master equation, whether RWA, Born-Markov, Redfield, etc.. This latter problem, which applies to all perturbative open-system master equations, has a profound effect upon calculation of entanglement at low temperatures. We find that even at zero temperature all initial states will undergo finite-time disentanglement (sometimes termed "sudden death"), in contrast to previous work. We also use our solution, without invoking RWA, to characterize the necessary conditions for Dickie subradiance at finite temperature. We find that the subradiant states fall into two categories at finite temperature: one that is temperature independent and one that acquires temperature dependence. With the RWA there is no temperature dependence in any case.Comment: 17 pages, 13 figures, v2 updated references, v3 clarified results and corrected renormalization, v4 further clarified results and new Fig. 8-1

Moving Atom-Field Interactions: Quantum Motional Decoherence and Relaxation

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.Comment: 9 pages, 1 figure, minor change

Entanglement, recoherence and information flow in an accelerated detector - quantum field system: Implications for black hole information issue

We study an exactly solvable model where an uniformly accelerated detector is linearly coupled to a massless scalar field initially in the Minkowski vacuum. Using the exact correlation functions we show that as soon as the coupling is switched on one can see information flowing from the detector to the field and propagating with the radiation into null infinity. By expressing the reduced density matrix of the detector in terms of the two-point functions, we calculate the purity function in the detector and study the evolution of quantum entanglement between the detector and the field. Only in the ultraweak coupling regime could some degree of recoherence in the detector appear at late times, but never in full restoration. We explicitly show that under the most general conditions the detector never recovers its quantum coherence and the entanglement between the detector and the field remains large at late times. To the extent this model can be used as an analog to the system of a black hole interacting with a quantum field, our result seems to suggest in the prevalent non-Markovian regime, assuming unitarity for the combined system, that black hole information is not lost but transferred to the quantum field degrees of freedom. Our combined system will evolve into a highly entangled state between a remnant of large area (in Bekenstein's black hole atom analog) without any information of its initial state, and the quantum field, now imbued with complex information content not-so-easily retrievable by a local observer.Comment: 16 pages, 12 figures; minor change

Relativistic Quantum Information in Detectors-Field Interactions

We review Unruh-DeWitt detectors and other models of detector-field interaction in a relativistic quantum field theory setting as a tool for extracting detector-detector, field-field and detector-field correlation functions of interest in quantum information science, from entanglement dynamics to quantum teleportation. We in particular highlight the contrast between the results obtained from linear perturbation theory which can be justified provided switching effects are properly accounted for, and the nonperturbative effects from available analytic expressions which incorporate the backreaction effects of the quantum field on the detector behaviour.Comment: 21 pages, 3 figures. Prepared for the special focus issue on RQ

Moving Atom-Field Interaction: Correction to Casimir-Polder Effect from Coherent Back-action

The Casimir-Polder force is an attractive force between a polarizable atom and a conducting or dielectric boundary. Its original computation was in terms of the Lamb shift of the atomic ground state in an electromagnetic field (EMF) modified by boundary conditions along the wall and assuming a stationary atom. We calculate the corrections to this force due to a moving atom, demanding maximal preservation of entanglement generated by the moving atom-conducting wall system. We do this by using non-perturbative path integral techniques which allow for coherent back-action and thus can treat non-Markovian processes. We recompute the atom-wall force for a conducting boundary by allowing the bare atom-EMF ground state to evolve (or self-dress) into the interacting ground state. We find a clear distinction between the cases of stationary and adiabatic motions. Our result for the retardation correction for adiabatic motion is up to twice as much as that computed for stationary atoms. We give physical interpretations of both the stationary and adiabatic atom-wall forces in terms of alteration of the virtual photon cloud surrounding the atom by the wall and the Doppler effect.Comment: 16 pages, 2 figures, clarified discussions; to appear in Phys. Rev.