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Physical Review A

Non-Markovian decay of an atom coupled to a reservoir: Modification by frequency modulation

Maciej Janowicz

Published Jan 12, 2000• 25 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.61.025802

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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 dynamics of a three-level Λ-atom coupled to a structured reservoir has been investigated. Comparing the Lorentzian time-dependent decay rate and population dynamics for the weak coupling regime with those for the strong coupling regime, we note that non-Markovian features exist in both regimes, but population dynamics shows fairly different behaviors. Moreover, the different positions of the two transition frequencies with respect to the structured reservoir reduces the influence of non-Markovian effects on population dynamics. Based on the non-Markovianity, we give an intuitive interpretation of the result that the non-Markovian effects have little influence on population dynamics in the weak coupling regime, but have an obvious influence in the strong coupling regime.
We demonstrate how a time-dependent dissipative environment may be used as a tool for controlling the quantum state of a two-level atom. In our model system the frequency and coupling strength associated with microscopic reservoir modes are modulated, while the principal features of the reservoir structure remain fixed in time. Physically, this may be achieved by containing a static atom-cavity system inside an oscillating external bath. We show that it is possible to dynamically decouple the atom from its environment, despite the fact that the two remain resonant at all times. This can lead to Markovian dynamics, even for a strong atom-bath coupling, as the atomic decay becomes inhibited into all but a few channels; the reservoir occupation spectrum consequently acquires a sideband structure, with peaks separated by the frequency of the environmental modulation. The reduction in the rate of spontaneous emission using this approach can be significantly greater than could be achieved with an oscillatory atom-bath detuning using the same parameters.
We study the spontaneous emission of atoms coupled to frequency-dependent photon-mode reservoirs, and find atomic emission spectra qualitatively different from those of free space. Frequency-dependent photon-mode reservoirs are found in a variety of physical situations (e.g., in waveguides, microcavities, dielectrics, systems with photonic spectral gaps, etc.), and are shown to lead to nonexponential decay and concomitant complicated non-Lorentzian emission line shapes. By studying Autler-Townes spectra in the presence of a frequency-dependent photon-mode density, we present simple examples of dynamical modifications of spontaneous decay properties.
Interesting new aspects of atomic behavior in the presence of strong driving fields appear when the driven atom resides not in free space, but in a region (such as an optical cavity) that displays a frequency-dependent photon-mode density. Under such conditions, it is found that a strong driving field can modify the spontaneous decay properties of an atom, and thereby give rise to interesting new features in the spectrum of strong-field resonance fluorescence. It is also found that a high level of dressed-state polarization can be maintained in a sample of resonantly or nonresonantly driven atoms by appropriate tuning of an enclosing cavity. Furthermore, for appropriate laser and cavity tunings, it is found that the atomic states become highly squeezed. In the course of analyzing these effects, a set of modified Bloch equations is derived that explicitly accounts for the finite response time associated with a frequency-dependent photon-mode density.
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.
Abstract We study the non-Markovianity and quantum speedup of a two-level atom (quantum system of interest) in a dissipative Jaynes-Cumming model, where the atom is embedded in a single-mode cavity, which is leaky being coupled to an external reservoir with Ohmic spectral density. We obtain the non-Markovianity characterized by using the probability of the atomic excited state and the negative decoherence rate in the time-local master equation. We also calculate the quantum speed limit time (QSLT) of the evolution process of the atom. The results show that, the atom-cavity coupling is the main physical reasons of the transition from Markovian to non-Markovian dynamics and the transition from no speedup to speedup process, and the critical value of this sudden transition only depends on the Ohmicity parameter. The atom-cavity coupling and the appropriate reservoir parameters can effectively improve the non-Markovianity in the dynamics process and speed up the evolution of the atom. Moreover, the initial non-Markovian dynamics first turns into Markovian and then back to non-Markovian with increasing the atom-cavity coupling under certain condition. Finally, the physical interpretation is provided.