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arXiv:1904.02164

Environment-Induced Rabi Oscillations in the Optomechanical Boson-Boson Model

Y. Minoguchi, Peter Kirton, Peter Rabl

Published Apr 3, 2019• 2 citations
arXivHTMLPDF

Abstract

We analyze the strong-coupling dynamics of a driven harmonic oscillator whose energy is modulated by a continuum of other bosonic modes. This type of system-bath interaction appears, for example, in optomechanical or equivalent circuit QED setups, where the frequency of a confined photonic mode depends linearly on a fluctuating boundary. Compared to the canonical spin-boson model, where coupling to bath modes only leads to decoherence, the role of the environment in such systems is more complex, since it also provides the only source of nonlinearity. We show that even for an unstructured bath, these environment-induced nonlinearities can dominate over decoherence processes resulting in Rabi oscillations and the formation of highly non-classical states. These findings provide important insights into the non-Markovian dynamics of higher-dimensional open quantum systems and for realizing few-photon optical nonlinearities through strong interactions with a bath.

DOI
10.48550/arxiv.1904.02164

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Quantum mechanics describes the unitary time evolution of closed systems. In practice, every quantum system interacts with the environment, leading to an irreversible loss of coherence. The spin-boson model (SBM) is central to the understanding of the fundamental process of decoherence of a two-state quantum system interacting with a bosonic heat bath, but the nature of transient dynamics in the presence of hybrid diagonal and off-diagonal system-bath interactions remains much less explored. Here, we investigate how the hybrid system-bath interactions of an Ohmic environment induce localization in the bias-free SBM. For strong coupling to the environment, localization is strongly affected by a dynamically generated bias via the renormalization of the tunneling amplitude. We find that counteracting effects of Hamiltonian parameters on non-exponential short-time dynamics and long-time population equilibration can lead to a separation of timescales and transient quantum coherent dynamics that can persist even for ultra-strong system-bath interaction. The findings offer novel insight into the equilibration behavior of quantum devices operating in the ultra-strong coupling regime.
For many open quantum systems, a master equation approach employing the Markov approximation cannot reliably describe the dynamical behaviour. This is the case, for example, in a number of solid state or biological systems, and it has motivated a line of research aimed at quantifying the amount of non-Markovian behaviour in a given model. Within this framework, we investigate the dynamics of a quantum harmonic oscillator linearly coupled to a bosonic bath. We focus on Gaussian states, which are suitably treated using a covariance matrix approach. Concentrating on an entanglement based non-Markovian behaviour quantifier (NMBQ) proposed by Rivas et. al. [1], we consider the role that near resonant and off-resonant modes play in affecting the NMBQ. By using a large but finite bath of oscillators for both Ohmic and super Ohmic spectral densities we find, by systematically increasing the coupling strength, initially the near resonant modes provide the most significant non-Markovian effects, while after a certain threshold of coupling strength the off-resonant modes play the dominant role. We also consider the NMBQ for two other models where we add a single strongly coupled oscillator to the model in extra bath mode and 'buffer' configurations, which affects the modes that determine non-Markovian behaviour.
The interplay between an open quantum system and its environment can lead to both coherent and incoherent behavior. We explore the extent to which strong coupling to a single bosonic mode can alter the coherence properties of a two-level system in a structured environment. This mode is treated exactly, with the rest of the environment comprising a Markovian bath of bosonic modes. The strength of the coupling between the two-level system and the single mode is varied for a variety of forms for the bath spectral density in order to assess whether the coherent dynamics of the two-level system are modified. We find a clear renormalization of the site population oscillation frequency that causes an altered interaction with the bath. This leads to enhanced or reduced coherent behavior of the two-level system, depending on the form of the spectral density function. We present an intuitive interpretation, based on an analytical model, to explain the behavior.
We introduce a new analytical method for studying the open quantum systems problem of a discrete system weakly coupled to an environment of harmonic oscillators. Our approach is based on a phase space representation of the density matrix for a system coupled to a two-tiered environment. The dynamics of the system and its immediate environment are resolved in a non-Markovian way, and the environmental modes of the inner environment can themselves be damped by a wider 'universe'. Applying our approach to the canonical cases of the Rabi and spin-boson models we obtain new analytical expressions for an effective thermalization temperature and corrections to the environmental response functions as direct consequences of considering such a tiered environment. A comparison with exact numerical simulations confirms that our approximate expressions are remarkably accurate, while their analytic nature offers the prospect of deeper understanding of the physics which they describe. A unique advantage of our method is that it permits the simultaneous inclusion of a continuous bath as well as discrete environmental modes, leading to wide and versatile applicability.
In this paper we investigate non-Markovian evolution of a two-level system (qubit) in a bosonic bath under influence of an external classical fluctuating environment. The interaction with the bath has the Lorentzian spectral density, and the fluctuating environment (stochastic field) is represented by a set of Ornstein-Uhlenbeck processes. Each of the subenvironments of the composite environment is able to induce non-Markovian dynamics of the two-level system. By means of the numerically exact method of hierarchical equations of motion, we study steady states of the two-level system, evolution of the reduced density matrix and the equilibrium emission spectra in dependence on the frequency cutoffs and the coupling strengths of the subenvironments. Additionally, we investigate the impact of the rotating wave approximation (RWA) for the interaction with the bath on accuracy of the results.