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arXiv:1011.2760 · Physical Review A

Emission characteristics of laser-driven dissipative coupled-cavity systems

Michael Knap, Enrico Arrigoni, Wolfgang von der Linden, Jared H. Cole

Published Feb 24, 2011• 54 citations
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Abstract

We consider a laser-driven and dissipative system of two coupled cavities with Jaynes-Cummings nonlinearity. In particular, we investigate both incoherent and coherent laser driving, corresponding to different experimental situations. We employ Arnoldi time evolution as a numerical tool to solve exactly the many-body master equation describing the nonequilibrium quantum system. We evaluate the fluorescence spectrum and the spectrum of the second-order correlation function of the emitted light field. Finally, we relate the measured spectra of the dissipative quantum system to excitations of the corresponding nondissipative quantum system. Our results demonstrate how to interpret spectra obtained from dissipative quantum systems and specify what information is contained therein.

DOI
10.1103/physreva.83.023821

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We consider a laser-driven and dissipative system of two coupled cavities with Jaynes-Cummings nonlinearity. In particular, we investigate both incoherent and coherent laser driving, corresponding to different experimental situations. We employ Arnoldi time evolution as a numerical tool to solve exactly the many-body master equation describing the nonequilibrium quantum system. We evaluate the fluorescence spectrum and the spectrum of the second-order correlation function of the emitted light field. Finally, we relate the measured spectra of the dissipative quantum system to excitations of the corresponding nondissipative quantum system. Our results demonstrate how to interpret spectra obtained from dissipative quantum systems and specify what information is contained therein.
We calculate the emission spectra, the Glauber g(2){g}^{(2)}g(2) function, and the entanglement of formation for two-level emitters coupled to a single cavity mode and subject to an external laser excitation. To evaluate these quantities we couple the system to environmental degrees of freedom, which leads to dissipative dynamics. Because of the periodic time dependence of the system Hamiltonian, the coefficients of the Markovian master equation are constant only if Floquet states are used as the computational basis. Studying the emission spectra, we show that the dynamic Stark effect first appears in second order of the laser intensity. For the Glauber function, we find clearly distinguished parameter regimes of super- and sub-Poissonian light emission and explain the additional features appearing for finite laser intensity in terms of the quasienergy spectrum of the driven emitter-cavity system. Finally, we analyze the temperature and emitter-cavity-coupling regimes where entanglement among the emitters is generated and show that the laser excitation leads to a decrease of entanglement.
We explore the role of quantum fluctuations in the strong-coupling limit of the dissipative Jaynes–Cummings oscillator driven on resonance. For weak excitation, we derive analytical expressions for the spectrum and the intensity correlation function for the photons scattered by the two-state atom coupled to the coherently driven cavity mode. We do so by writing down a birth–death process adding the higher orders in the excitation strength needed to go beyond the pure-state factorization, following the method introduced in Carmichael (2008). Our results for the first and second-order correlation functions are complemented by the numerical investigation of the waiting-time distribution for the photon emissions directed sideways, and the comparison with ordinary resonance fluorescence. To close out our discussion, we increase the driving field amplitude and approach the critical point organizing a second-order dissipative quantum phase transition by depicting the excitation pathways in the intracavity field distribution for a finite system size.
We study the non-equilibrium behavior of optically driven dissipative coupled resonator arrays. Assuming each resonator is coupled with a two-level system via a Jaynes–Cummings interaction, we calculate the many-body steady state behavior of the system under coherent pumping and dissipation. We propose and analyze the many-body phases using experimentally accessible quantities such as the total excitation number, the emitted photon spectra and photon coherence functions for different parameter regimes. In parallel, we also compare and contrast the expected behavior of this system assuming the local nonlinearity in the cavities is generated by a generic Kerr effect as described by the Bose–Hubbard (BH) model rather than a Jaynes–Cummings interaction. We find that the behavior of the experimentally accessible observables produced by the two models differs for realistic regimes of interactions even when the corresponding nonlinearities are of similar strength. We analyze in detail the extra features available in the Jaynes–Cummings–Hubbard (JCH) model originating from the mixed nature of the excitations and investigate the regimes where the BH approximation would faithfully match the JCH physics. We find that the latter is true for values of the light–matter coupling and losses beyond the reach of current technology. Throughout the study we operate in the weak pumping, fully quantum mechanical regime where approaches such as mean field theory fail, and instead use a combination of quantum trajectories and the time evolving block decimation algorithm to compute the relevant steady state observables. In our study we have assumed small to medium size arrays (from 3 up to 16 sites) and values of the ratio of coupling to dissipation rate g / γ ∼ 20, which makes our results implementable with current designs in circuit QED and with near future photonic crystal set ups.
We study the emission spectra of the dissipative Rabi and Jaynes-Cummings models in the non-Markovian and ultrastrong coupling regimes. We have derived a polaron-transformed Nakajima-Zwanzig master equation (PTNZE) to calculate the emission spectra, which eliminates the well-known limitations of the Markovian approximation and the standard second-order perturbation. Using the time-dependent variational approach with the multiple Davydov ansatz as a benchmark, the PTNZE is found to yield accurate emission spectra in certain ultrastrong coupling regimes where the standard second-order Nakajima-Zwanzig master equation breaks down. It is shown that the emission spectra of the dissipative Rabi and Jaynes-Cummings models are, in general, asymmetric under various initial conditions. Direct comparisons of spectra for the two models illustrate the essential role of the qubit-cavity counter-rotating term and the spectral features under different qubit-cavity coupling strengths and system initial conditions.
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.
Understanding nonequilibrium transport and fluctuations driven by nonclassical light in nonlinear quantum optical systems is challenging. Here, we formulate a driven quantum master equation in the rotating frame combined with full counting statistics, retaining the drive-induced frequency shifts in the system-reservoir interactions and providing a unified description of drive-assisted incoherent transitions based on the rotated system dressed-basis. Applied to a Kerr resonator and a nonlinear Jaynes-Cummings model, the approach reveals pronounced multiphoton-resonant enhancement of the drive input energy current, with significant high peaks under two-photon driving compared to the single-photon case. The two-photon resonance relations are analytically obtained. Resonance structure in the nonlinear Jaynes-Cummings model nonlinearly relies on qubit-photon couplings, with additional dressed-state branches. A low-energy-state approximation attributes the resonant current enhancement to dressed-state hybridization and efficient activation of incoherent energy exchange processes. Beyond the average current, two-photon-driving induced energy exchange picture near resonance also substantially modifies the second-order current fluctuation and higher-order current cumulant, while increasing the time-normalized signal-to-noise ratio. Adding two-photon loss introduces extra incoherent photon-pair exchange pathways and further reshapes the current and its fluctuations. We hope these results may deepen interpretation of photon driving and quantum dissipation cooperatively governing nonequilibrium energy transport and fluctuations.