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arXiv:1607.07396 · The European Physical Journal D

Effect of dissipative environment on collapses and revivals of a non-linear quantum oscillator

Maninder Kaur, Bindiya Arora, Arvind

Published Aug 1, 2018• 5 citations
arXivHTMLPDF
DOI
10.1140/epjd/e2018-80782-x

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Based on the time-convolutionless master-equation approach, we investigate the squeezing dynamics of two atoms in dissipative cavities. We find that the atomic squeezing is related to initial atomic states, atom–cavity couplings, non-Markovian effects and resonant frequencies of an atom and its cavity. The results show that a collapse–revival phenomenon will occur in the atomic squeezing and this process is accompanied by the buildup and decay of entanglement between two atoms. Enhancing the atom–cavity coupling can increase the frequency of the collapse–revival of the atomic squeezing. The stronger the non-Markovian effect is, the more obvious the collapse–revival phenomenon is. In particular, if the atom–cavity coupling or the non-Markovian effect is very strong, the atomic squeezing will tend to a stably periodic oscillation in a long time. The oscillatory frequency of the atomic squeezing is dependent on the resonant frequency of the atom and its cavity.
Solid state-based light emitters such as semiconductor quantum dots (QDs) have been demonstrated to be versatile candidates to study the fundamentals of light–matter interaction. In contrast to optics with isolated atomic systems, in the solid-state dissipative processes are induced by the inherent coupling to the environment and are typically perceived as a major obstacle toward stable performances in experiments and applications. In this theoretical model study we show that this is not necessarily the case. In fact, in certain parameter regimes, the memory of the solid-state environment can enhance coherent quantum optical effects. In particular, we demonstrate that the non-Markovian coupling to an incoherent phonon bath can exhibit a stabilizing effect on the coherent QD cavity-quantum electrodynamics by inhibiting irregular oscillations and allowing for regular collapse and revival patterns. For self-assembled GaAs/InAs QDs at low photon numbers we predict dynamics that deviate dramatically from the well-known atomic Jaynes–Cummings model. Even if the required sample parameters are not yet available in recent experimental achievements, we believe our proposal opens the way to a systematic and deliberate design of photon quantum effects via specifically engineered solid-state environments.
We study the Jaynes-Cummings model (JCM) which describes the interaction between a two-level atom and a single-mode resonant or quasi-resonant electromagnetic field in the non-dissipative and issipative cases. In particular, we study the atomic population inversion whose behavior presents some aspects of purely quantum origin: collapse and revivals. This observables expectation value can be btained analytically without use of approximations for the non-dissipative case and using first-order perturbation in the dissipative case. We make use of the sum of Poisson and the steepest descents method to obtain analytical formulas for the collapse and for each revival. In this way, we can obtain relevant information like the occurrence time, the maximum amplitude, the approximate frequency, and width. The dissipative JCM models the action of the environment on the quantum system. We show that the characteristic time of the revival diminishes as the interaction with the environment enlarges. We consider the limit in which it becomes experimentally impossible to distinguish the obtained curve from the classical one.