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arXiv:1006.2624 · Optics Express

Non-Markovian dynamics of a microcavity coupled to a waveguide in photonic crystals

Wei-Min Zhang, Meng-Hsiu Wu, Chan U Lei, Heng-Na Xiong

Published Aug 12, 2010• 50 citations
arXivHTMLPDF

Abstract

In this paper, the non-Markovian dynamics of a microcavity coupled to a waveguide in photonic crystals is studied based on a semi-finite tight binding model. Using the exact master equation, we solve analytically and numerically the general and exact solution of the non-Markovain dynamics for the cavity coupled to the waveguide in different coupling regime. A critical transition is revealed when the coupling increases between the cavity and the waveguide. In particular, the cavity field becomes dissipationless when the coupling strength goes beyond a critical value, as a manifestation of strong non-Markovian memory effect. The result also indicates that the cavity can maintain in a coherent state with arbitrary small number of photons when it strongly couples to the waveguide at very low temperature. These properties can be measured experimentally through the photon current flowing over the waveguide in photonic crystals.

DOI
10.1364/oe.18.018407

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In this paper, the non-Markovian dynamics of a microcavity coupled to a waveguide in photonic crystals is studied based on a semi-finite tight binding model. Using the exact master equation, we solve analytically and numerically the general and exact solution of the non-Markovain dynamics for the cavity coupled to the waveguide in different coupling regime. A critical transition is revealed when the coupling increases between the cavity and the waveguide. In particular, the cavity field becomes dissipationless when the coupling strength goes beyond a critical value, as a manifestation of strong non-Markovian memory effect. The result also indicates that the cavity can maintain in a coherent state with arbitrary small number of photons when it strongly couples to the waveguide at very low temperature. These properties can be measured experimentally through the photon current flowing over the waveguide in photonic crystals.
The exact non-Markovian dynamics of a microcavity strongly coupled to a general reservoir at arbitrary temperature are studied. With the exact master equation for the reduced density operator of the cavity system, we analytically solve the time evolution of the cavity state and the associated physical observables. We show that the non-Markovian dynamics are completely determined by the propagating (retarded) and correlation Green functions. Comparing the non-Markovian behavior at finite temperature with those at the zero-temperature limit or Born-Markov limit, we find that the non-Markovian memory effect can dramatically change the coherent and thermal dynamics of the cavity. We also numerically study the dissipation dynamics of the cavity through the mean mode amplitude decay and the average photon number decay in the microwave regime. It is shown that the strong coupling between the cavity and the reservoir results in a long-time dissipationless evolution to the cavity field amplitude, and its noise dynamics undergo a critical transition from the weak to the strong coupling due to the non-Markovian memory effect.
We study the exact non-Markovian dynamics of a multi-qubit system coupled to a photonic-crystal waveguide with infinite cavity-array structure. A general solution of the evolution state of the system is solved for a general initial state in the single-excitation subspace. With this solution, we find that the non-Markovian effect of the environment on the system could be enhanced not only by increasing the system-environment coupling strength but also by adding the qubit number in the system. The explicit non-Markovian dynamics are discussed under two initial states to see the non-Markovian effect on entanglement preservation and entanglement generation. We find that the non-Markovian effect tends to preserve the system in its initial state.
Non-Markovian dynamics go beyond the Markovian approximation by capturing memory effects and information backflow in open quantum systems, which are crucial for describing realistic physical processes. In this work, we study the exact non-Markovian dynamics of a driven cavity coupled to an anisotropic three-dimensional photonic-crystal environment via counterrotating-wave interactions. We derive an exact analytical expression for the cavity amplitude satisfying the integro-differential equation, which includes the contributions of the bound states outside the continuum and the dissipative parts with the continuum spectrum. Based on the characteristic function method, we derive the exact non-Markovian master equation for the cavity, which contributes to the gain of the cavity. We give the physical origin of non-Markovian gain in the presence of bound states in the system consisting of cavity and environment, which has no Markovian counterparts due to the nonexponential gain in the non-Markovian structured environment. We find that three different types of bound states can be formed in the system, containing one bound state with no inversion of photon number, two bound states with the periodic equal-amplitude oscillation, and the gain with two complex roots without the bound states formation. We derive a current equation including the source from the driving field, the transient current induced by the change in the number of photons, and the two-photon current caused by the counterrotating-wave term. The results are compared with those given by the rotating-wave interactions and extended to a more general quantum network involving an arbitrary number of coupled cavities. Our findings may pave the way for a deeper understanding of non-Markovian dynamics with gain in quantum networks involving counterrotating-wave effects.
In this paper, the exact non-Markovian dynamics of open quantum systems in the presence of initial system-reservoir correlations is investigated for a photonic cavity system coupled to a general non-Markovian reservoir. The exact time-convolutionless master equation incorporating with initial system-reservoir correlations is obtained. The non-Markovian dynamics of the reservoir and the effects of the initial correlations are embedded into the time-dependent coefficients in the master equation. We show that the effects induced by the initial correlations play an important role in the non-Markovian dynamics of the cavity but they are washed out in the steady-state limit in the Markovian regime. Moreover, the initial two-photon correlation between the cavity and the reservoir can induce nontrivial squeezing dynamics to the cavity field.
In this work, we investigate the non-Markovian (NM) dynamical evolution of a three-level atom coupled to a semi-infinite one-dimensional photonic waveguide and driven by a classical driving field. The single-end of waveguide behaves as a perfect mirror while light can pass through the opposite end with no backreflection. We derive the exact analytical expressions for the wave function of the driven three-level atom by solving a set of delay differential equations and give the conditions of atom-photon bound state formation that can inhibit the dissipation, which appears in the atom-mirror interspace in order to trap a considerable amount of initial atomic excitation. We show that when the evolution time of the system is shorter than the time delay taken by a photon to perform a round trip between the atom and mirror, the atomic dynamics exhibits Markovian properties, which depend on the driving strength and rescaled parameters. If the evolution time of the system exceeds the time delay, the photon can be reabsorbed by the atom with the photon emitted by the atom having completed the round trip, which exhibits NM memory effects, where the population eventually convergences to the finite-steady values. We also study the influence of the loss and dephasing on the formation of a bound state. Finally, the above results are extended to a more general quantum system involving single-end photonic waveguide coupled to an arbitrary number of noninteracting three-level atoms driven by the driving fields. The presented formalism might open a way to better understand exactly the NM dynamics of driven multilevel atoms coupled to a semi-infinite waveguide.
We predict and analyze boundary-driven exceptional points in semi-infinite Hermitian photonic waveguide lattices with a side-coupled defect. The exceptional points arise from coherent reflections at the lattice termination, which induce strong memory effects in the defect dynamics. Using an exact analytic approach, we derive the defect's non-Markovian memory kernel, revealing the trajectories and coalescence conditions of the resonances, which can be precisely tuned by the defect position and the coupling strength. Our results provide a simple and experimentally accessible platform for exploring memory-enabled non-Hermitian physics in Hermitian photonic lattices.