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Asia Pacific Physics Conference (APPC)

Quantum Dissipation in Rotating Wave Approximation

Hiroki Majima

Published Mar 19, 2014• 0 citations
Publisher

Abstract

We study composite quantum systems, like atom-cavity systems and coupled optical resonators, in the absence of external driving by resorting to methods from quantum field theory. It is shown that the usually neglected counter-rotating part of the Hamiltonian relates to the vacuum instability and generates an irreversible time evolution. To discuss the stability of the quantum dissipative system due to the influence of an Jaynes-Cummings Hamiltonian and the dissipative force (counter-rotating term) under situation, we derive a behavior for large time for transition amplitudes of the dissipative system with the help of the perturbation analysis.

DOI
10.7566/jpscp.1.012134

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We study composite quantum systems, like atom-cavity systems and coupled optical resonators, in the absence of external driving by resorting to methods from quantum field theory. It is shown that the usually neglected counter-rotating part of the Hamiltonian relates to the vacuum instability and generates an irreversible time evolution. To discuss the stability of the quantum dissipative system due to the influence of an Jaynes-Cummings Hamiltonian and the dissipative force (counter-rotating term) under situation, we derive a behavior for large time for transition amplitudes of the dissipative system with the help of the perturbation analysis.
We study composite quantum systems, like the Dicke model (or the generalized quantum Rabi model), in the absence of external driving by resorting to methods from quantum field theory.It is shown that the usually neglected counter-rotating part of the Hamiltonian relates to the vacuum instability and generates an irreversible time evolution.To discuss the stability of the quantum dissipative system due to the influence of an Jaynes-Cummings Hamiltonian and the dissipative force (counter-rotating term) under situation, we derive a behavior for large time for a vacuum survival probability of the dissipative system.In the ultra-strong coupling regime, we show that the timedependent coherent state generated by an interaction Hamiltonian behaves non-unitary irreversible time evolution.
This thesis studies counter-rotating terms part of an Hamiltonian usually neglected in the so-called Rotating Wave Approximation. Generalising the usual description of light-matter interactions and open quantum systems it is demonstrated that normally neglected counter-rotating terms have the potential to allocate energy among different system degrees of freedom. It is pointed out in examples that this aspect can affect the energy concentration in quantum systems. Initially, a composite quantum system is considered, i.e. bipartite systems like atom-cavity systems and coupled optical resonators without decay. By resorting to methods from quantum field theory it is shown that for such bosonic systems, the Rotating Wave Approximation cannot be applied far off resonance. In fact, the counter-rotating terms are related to an entropy operator that is capable of generating an irreversible time evolution. The vacuum state of the system is shown to evolve into a generalised coherent state exhibiting entanglement of the modes in which the counter-rotating terms are expressed. Furthermore, it is demonstrated that a non-trivial behaviour of the photon emission rate of such composite quantum system can occur when the counter-rotating terms are not dropped. In such a system, there is a coupling to infinitely many modes with most of them being far off resonance. An energy concentrating mechanism is discussed which cannot be described by the Rotating Wave Approximation. Its result is the continuous leakage of photons from open quantum system, even in the absence of external driving. Finally, a model is proposed to explain the origin of the sudden energy concentration in the intriguing phenomenon of sonoluminescence. The model is based on the quantum dynamics of trapped particles and assumes the presence of a weak but highly inhomogeneous electric field. It is shown that the counter-rotating terms can significantly contribute to the energy focussing mechanism in terms of quantum coherences.
We have investigated vacuum Rabi oscillation of an atom coupled with single-mode cavity field exactly, and compared the results with that of the Jaynes–Cummings (J–C) model. The results show that for resonant case, there is no Rabi oscillation for an atom. For small detuning and weak coupling case, the probability for the atom in excited state oscillates against time with different frequencies and amplitudes from that of the J-C model. It exhibits that the counter-rotating wave interaction could significantly effect the dynamic behaviour of the atom, even under the condition in which the RWA is considered to be justified.
A microscopic derivation of the master equation for the Jaynes–Cummings model with cavity losses is given, taking into account the terms in the dissipator which vary with frequencies of the order of the vacuum Rabi frequency. Our approach allows us to single out physical contexts wherein the usual phenomenological dissipator turns out to be fully justified and constitutes an extension of our previous analysis (Scala et al 2007 Phys. Rev. A 75 013811 ), where a microscopic derivation was given in the framework of the rotating wave approximation.
Abstract. A microscopic derivation of the master equation for the Jaynes-Cummings model with cavity losses is given, taking into account the terms in the dissipator which vary with frequencies of the order of the vacuum Rabi frequency. Our approach allows to single out physical contexts wherein the usual phenomenological dissipator turns out to be fully justified and constitutes an extension of our previous analysis [Scala M. et al. 2007 Phys. Rev. A 75, 013811], where a microscopic derivation was given in the framework of the Rotating Wave Approximation. PACS numbers: 42.50.Lc, 03.65.Yz, 42.50.PqCavity losses for the dissipative Jaynes-Cummings Hamiltonian beyond RWA 2
The fully-coupled Jaynes-Cummings model contains both counter-rotating and rotating wave terms. It is usual to solve for the rotating wave dynamics exactly and to include the counterrotating contributions as a perturbation. In this paper we choose an alternative approach in which the counterrotating terms are treated exactly and the rotating wave interaction is included as a perturbation. We find that, under the influence of the counterrotating terms, the field Q-function undergoes an oscillatory bifurcation in phase space. The cycle-averaged splitting of the Q-function is found to be of the same order in the interaction as the Bloch-Siegert shift.