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

TL;DR

This paper develops non-Markovian stochastic equations for two-level atoms in a common quantum field, revealing new insights into entanglement dynamics, including finite-time disentanglement at zero temperature and conditions for Dicke subradiance.

Contribution

It introduces a non-perturbative approach to analyze non-Markovian dynamics of atoms without the rotating-wave approximation, improving understanding of entanglement and subradiance.

Findings

All initial states undergo finite-time disentanglement at zero temperature.

Subradiant states can be temperature dependent or independent at finite temperature.

Standard perturbative master equations cannot accurately capture these effects.

Abstract

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.