Theory of non-Markovian decay of a cascade atom in high-Q cavities and photonic band-gap materials

Abstract

The dynamics of a three-level atom in a cascade configuration with both transitions coupled to a single structured reservoir of quantized field modes is treated using Laplace transform methods applied to the coupled amplitude equations. Results are also obtained from master equations by two different approaches, that is, involving either pseudomodes or quasimodes. Two different types of reservoir are considered, namely a high-Q cavity and a photonic band-gap system, in which the respective reservoir structure functions involve Lorentzians. Non-resonant transitions are included in the model. In all cases non-Markovian behaviour for the atomic system can be found, such as oscillatory decay for the high-Q cavity case and population trapping for the photonic band-gap case. In the master equation approaches, the atomic system is augmented by a small number of pseudomodes or quasimodes, which in the quasimode approach themselves undergo Markovian relaxation into a flat reservoir of continuum quasimodes. Results from these methods are found to be identical to those from the Laplace transform method including two-photon excitation of the reservoir with both emitting sequences. This shows that complicated non-Markovian decays of an atomic system into structured EM field reservoirs can be described by Markovian models for the atomic system coupled to a small number of pseudomodes or quasimodes.

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Cited by in corpus (13)

• General Non-Markovian structure of Gaussian Master and Stochastic Schrödinger Equations
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• Non-perturbative effects in corrections to quantum master equation arising in Bogolubov-van Hove limit
• Pseudomode approach and vibronic non-Markovian phenomena in light harvesting complexes
• Gaussian entanglement induced by an extended thermal environment
• Convergence guarantees for discrete mode approximations to non-Markovian quantum baths
• Non-Markovian evolution of multi-level system interacting with several reservoirs. Exact and approximate
• Time evolution of cascade decay
• Long-time Markovianity of multi-level systems in the rotating wave approximation
• How to Project onto an Arbitrary Single-Photon Wavepacket
• Integral representation of finite temperature non-Markovian evolution of some RWA systems
• Cascade atom in high-Q cavity: The spectrum for non-Markovian decay
• Susceptibility of a two-level atom near an isotropic photonic band edge: transparency and band edge profile reconstruction