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Acta Sinica Quantum Optica

The Memory Function of Non-Markovian Spontaneous Emission Decay Process of a Two-level Atom Embedded in a Sandwich Structure

Nian-Hua Liu

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

The memory function of non-Markovian spontaneous emission decay process is investigated.We obtained the non-Markovian memory function and the reservoir coupling spectrum of a two-level atom embedded in a sandwich structure by the means of quantum optics.Because the modes interact with different weights to the atom,a weight factor is considered in the spectrum.As the emission field is perturbed by the sandwich structure,some pulse-like oscillations occur in memory function.The memory function is related to the Fourier transform of the spectrum,thus the wider spectrum leads to the shorter memory time.

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The memory function of non-Markovian spontaneous emission decay process is investigated.We obtained the non-Markovian memory function and the reservoir coupling spectrum of a two-level atom embedded in a sandwich structure by the means of quantum optics.Because the modes interact with different weights to the atom,a weight factor is considered in the spectrum.As the emission field is perturbed by the sandwich structure,some pulse-like oscillations occur in memory function.The memory function is related to the Fourier transform of the spectrum,thus the wider spectrum leads to the shorter memory time.
A two-level atom coupled to a reservoir with Lorentzian spectral response function is considered. It is shown that if the free oscillations of the atomic dipole are suitably modulated by an external field, then the dynamics of the spontaneous decay can be strongly modified. As a result, the probability of finding the atom in an excited state can be large even for very long times. This is because the frequency modulation may lead to both effective detuning of the atom from the resonance with reservoir modes and to effective cancellation of the coupling between the atom and the reservoir. Non-Markovian features of the reservoir are found to be essential for this effect to be observable. Conditions of experimental verifications are provided.
The dynamic evolution of atomic spontaneous emission in one-dimensional photonic crystals (1DPC) is investigated by using mode functions for the 1DPC. Our attention is focused on the non-Markovian processes in the first several optical cycles of the spontaneous emission decay. The integral-differential dynamic equation is directly solved by numerical calculation without using the Markovian approximation. The interference of the multireflected fields plays an important role in the non-Markovian processes. Due to the interference of the fields successive arrived at the atom due to the reflection at the interfaces, the decay rate shows a series of pulselike peaks. If the interference is constructive, the spontaneous decay is enhanced, while if the interference is destructive, the spontaneous decay is suppressed. The steady decay rate is approximately equal to the vacuum decay rate, when the atomic transition frequency corresponds to an allowed normal mode of the 1DPC. The spontaneous emission decay is suppressed if the atomic transition frequency is within the forbidden gap of the 1DPC.
We present a formula to evaluate the spontaneous emission spectra of an atom in contact with a radiation field with non-Markovian effects. This formula is written in terms of a two-time correlation of system observables and the environmental correlation function, and depends on the distance between the emitting atom and the detector. As an example, we use it to analyze the fluorescence spectra of a two level atom placed as an impurity in a photonic crystal. The radiation field within those materials has a gap or discontinuity where electromagnetic modes cannot propagate in the stationary limit. In that situation, the atomic emission occurs in the form of evanescent waves which are detected with less efficiency the farther we place the detector. The methodology presented in this paper may be useful to study the non-Markovian dynamics of any quantum open system in linear interaction with a harmonic oscillator reservoir and within the weak-coupling approximation.
The dynamics of a three-level atom in a cascade (or ladder) configuration with both transitions coupled to a single structured reservoir of quantized electromagnetic field modes is treated using Laplace transform methods applied to the coupled amplitude equations. In this system two-photon excitation of the reservoir occurs, and both sequences for emitting the two photons are allowed and included in the theory. An integral equation is found to govern the complex amplitudes of interest. It is shown that the dynamics of the atomic system is completely determined in terms of reservoir structure functions, which are products of the mode density with the coupling constant squared. This dependence on reservoir structure functions rather than on the mode density or coupling constants alone, shows that it may be possible to extend pseudomode theory to treat multiphoton excitation of a structured reservoir---pseudomodes being introduced in one-one correspondence with the poles of reservoir structure functions in the complex frequency plane. A general numerical method for solving the integral equations based on discretizing frequency space, and applicable to different structured reservoirs such as high-QQQ cavities and photonic band-gap systems, is presented. An application to a high-QQQ-cavity case with identical Lorentzian reservoir structure functions is made, and the non-Markovian decay of the excited state shown. A formal solution to the integral equations in terms of right and left eigenfunctions of a non-Hermitian kernel is also given. The dynamics of the cascade atom, with the two transitions coupled to two separate structured reservoirs of quantized electromagnetic field modes, is treated similarly to the single structured reservoir situation. Again the dynamics only depends on reservoir structure functions. As only one sequence of emitting the two photons now occurs, the integral equation for the amplitudes can be solved analytically. The non-Markovian decay of the excited state is shown for the same high-QQQ-cavity case of identical Lorentzian reservoir structure functions, and differs from that for the single reservoir situation.
The interaction of a traveling pulse of quantum light with a localized quantum system shows non-Markovian features when scattering takes place in a structured environment. Here, we devise a non-Markovian input-output theory by coherently coupling the scatterer to a pseudomode, which decays into a Markovian reservoir. This incorporates memory effects of a structured environment without altering the cascaded nature of the Lindblad master equation, whose solution provides the quantum state of the output field of any desired mode. We apply our theory to the stimulated emission by a two-level atom, and to transmission of a Gaussian pulse through a cavity. We observe that the non-Markovian revival of coherence in the scatterer distorts the single-mode nature of the incoming pulse, thus resulting in a multimode output field.
Manipulating the dynamics of open quantum systems is a crucial requirement for large-scale quantum computers. Finding ways to overcome or extend decoherence times is a challenging task. Already at the level of a single two-level atom, its reduced dynamics with respect to a larger environment can be very complex. Structured environments, for instance, can lead to various regimes other than memoryless Markovian spontaneous emission. Here, we consider an atom coupled to an array of coupled cavities in the presence of on-site correlated disorder. The correlation is long-ranged and associated with the trace of a fractional Brownian motion following a power-law spectrum. With the cavity modes playing the role of the environment, we study the dynamics of the spontaneous emission. We observe a change from non-Markovian to Markovian decay in the presence of disorder by tuning the correlation parameter. This is associated with a localization-delocalization transition involving the field modes. Two dissipative models that effectively reproduce the behavior of the non-Markovianity are discussed. The dissipation dynamics of the atom can thus be used to extract information about the phase of the environment. Our results provide a direction in the engineering of disordered quantum systems to function as controllable reservoirs.