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arXiv:1612.01248

Perturbative dissipation dynamics of a weakly driven Jaynes-Cummings system

S. M. Yu, Gao, Y. B., Hou Ian

Published Dec 5, 2016• 0 citations
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Abstract

We generalize a microscopic master equation method to study the dissipation dynamics of Jaynes-Cummings two-level system with a weak external driving. Using perturbative analysis to extend the damping bases theory, we derive the corrected Rabi oscillation and vaccum Rabi splitting analytically. The evolution of the decoherence factor of the weakly driven system reveals that the off-diagonal density matrix elements are oscillating at a frequency dependent on the driving strength and the initial population inversion. For highly-inverted systems at the weak-driving limit, this frequency reduces to twice the value for the non-driven system, showing the dissipation dynamics unable to be discovered using more conventional approaches.

DOI
10.48550/arxiv.1612.01248

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We generalize a microscopic master equation method to study the dissipation dynamics of Jaynes-Cummings two-level system with a weak external driving. Using perturbative analysis to extend the damping bases theory, we derive the corrected Rabi oscillation and vaccum Rabi splitting analytically. The evolution of the decoherence factor of the weakly driven system reveals that the off-diagonal density matrix elements are oscillating at a frequency dependent on the driving strength and the initial population inversion. For highly-inverted systems at the weak-driving limit, this frequency reduces to twice the value for the non-driven system, showing the dissipation dynamics unable to be discovered using more conventional approaches.
The dynamics of a driven spin-boson model is studied by means of the perturbation approach based on a unitary transformation. Analytical expressions for the population difference and the coherence of the two state system are obtained. The results show that for weak driving, the population difference displays damping coherent oscillation and/or damping quantum beat, depending on the initial preparation. The coherence exhibits damped oscillation with Rabi frequency. When driving is strong enough, the population difference exhibits undamped large-amplitude coherent oscillation. In addition, our theory leads to correct results in two limiting cases: without dissipation and without driving field.
We derive a Born-Markov master equation describing the dissipation induced by a bath of lossy but coherently driven two-level systems (TLSs) coupled to a bosonic system via Jaynes-Cummings interaction. We analytically derive all the master-equation rates. We characterize these rates for the particular case of a single-mode system coupled to identical TLSs. We study the steady state of the system and its exotic properties stemming from the nonthermal stationary state of the driven TLS bath. These properties include dissipative amplification, bath-induced linear instability, and both coherent and dissipative squeezing. The master equation is valid for arbitrarily strong TLS driving and it can be generalized to include multilevel systems or other system-bath interaction terms, among others. Our work provides a tool to study and characterize TLS-induced decoherence, a key limiting factor in quantum technological devices based on, for instance, superconducting circuits, magnonic systems, or quantum acoustics.
Environmental influences on the dynamics of a coupled qubit-oscillator system are studied analytically in a regime where deviations from the exactly solvable Jaynes–Cummings model are important. We investigate the case of a quasi-degenerate qubit within the ultra-strong coupling regime for which the qubit frequency is much smaller than the frequency of the oscillator, and the coupling between the qubit and the oscillator is large, both of which invalidate the usually employed rotating wave approximation. In contrast to the standard quantum optics master equation, we explicitly take the qubit-oscillator coupling into account while microscopically deriving a dressed state master equation. Using the derived master equation, we discuss a spectroscopic technique which can be used to probe the dressed energy-level structure of the qubit-oscillator system.
We analyze the time-dependent physical spectrum of a driven Jaynes-Cummings model in which both the two-level system and the quantized cavity mode are subject to coherent classical driving. The time-dependent Hamiltonian is mapped, via well-defined unitary transformations, onto an effective stationary Jaynes-Cummings form. Within this framework, we derive closed-form expressions for the two-time correlation functions of both the atomic and field operators. These correlation functions are subsequently used to evaluate the time-dependent physical spectrum according to the Eberly-Wódkiewicz definition, which properly accounts for finite spectral resolution and transient emission dynamics. We show that the external driving leads to substantial modifications of the atomic spectral response, including controllable frequency shifts and asymmetric line shapes. Importantly, we identify a regime in which the driving parameters are chosen such that the coherent displacement induced in the cavity field exactly cancels out the initial coherent amplitude. In this limit, the system dynamics reduce to that of an effectively vacuum-initialized Jaynes-Cummings model, and the standard vacuum Rabi splitting is recovered. This behavior provides a clear and physically transparent interpretation of the spectral features as arising from coherent field displacement rather than from modifications of the underlying atom-cavity coupling.
We study the dissipative dynamics of a biased two-level system (TLS) coupled to a harmonic oscillator (HO), the latter interacting with an Ohmic environment. Using Van-Vleck perturbation theory and going to second order in the coupling between TLS and HO, we show how the Hamiltonian of the TLS-HO system can be diagonalized analytically. Our model represents an improvement to the usually used Jaynes-Cummings Hamiltonian as an initial rotating wave approximation is avoided. By assuming a weak coupling to the thermal bath, analytical expressions for the time evolution of the populations of the TLS are\nfound: the population is characterized by a multiplicity of damped oscillations together with a complex relaxation dynamics towards thermal equilibrium. The long time evolution is characterized by a single relaxation rate, which is largest at resonance and whose expression can be given in closed analytic form.
The Jaynes-Cummings and quantum Rabi models are fundamental to cavity and circuit quantum electrodynamics, as they describe the simplest form of light-matter interaction, where a single qubit is coupled to a single bosonic mode. A scenario that is commonly encountered in the experimental practice arises when the bosonic mode interacts with an external dissipative thermal bath, making the qubit-boson system open. In this work, we present a new analytical solution of the Lindblad master equations for the open dispersive Jaynes-Cummings model and a perturbative analytical solution of the open quantum Rabi model in the limit of weak qubit-boson coupling ggg, using the holomorphic formalism in Bargmann space. Specifically, we derive the most general solution of the local Lindblad master equation for the open dispersive Jaynes-Cummings model coupled to a thermal bath, with the only assumptions that the initial state of the qubit-boson system is separable. Additionally, we obtain a perturbative analytical solution for the open quantum Rabi model up to second order in ggg. Notably, our findings include a new formula for the qubit's steady state at zeroth order, showing that the stationary populations depend on both qubit and boson frequencies in the quantum Rabi model, but not in the Jaynes-Cummings model, regardless of the value of ggg. Our results are of general interest to the study of open quantum systems in the context of light-matter interaction.