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Physical Review A

Quantum electrodynamics of a single Morse oscillator in a cavity: Spectral aspects

Gautam Gangopadhyay, Deb Shankar Ray

Published Jun 1, 1991• 9 citations
Publisher

Abstract

We consider the finite-temperature cavity electrodynamics with a single Morse oscillator and its spectral aspects. It has been shown that the single-peak structure of the emission spectrum in the presence of weak coupling splits up into a doublet in the limit of strong coupling. In the finite-temperature case, for small average number of photons n\ifmmode\bar\else\textasciimacron\fi{} in the cavity, the line shape first shows doublet structure as the coupling increases. However, these merge to a single peak structure with increasing n\ifmmode\bar\else\textasciimacron\fi{} at values as small as 3 to 4 photons.

DOI
10.1103/physreva.43.6424

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We consider the finite-temperature cavity electrodynamics with a single Morse oscillator and its spectral aspects. It has been shown that the single-peak structure of the emission spectrum in the presence of weak coupling splits up into a doublet in the limit of strong coupling. In the finite-temperature case, for small average number of photons n\ifmmode\bar\else\textasciimacron\fi{} in the cavity, the line shape first shows doublet structure as the coupling increases. However, these merge to a single peak structure with increasing n\ifmmode\bar\else\textasciimacron\fi{} at values as small as 3 to 4 photons.
Spontaneous emission spectra from a single quantum dot embedded in a microcavity characterized by the quality factor ( Q ) are theoretically discussed in the high Q weak coupling region. It is shown that the region should be divided into two subregions in terms of the spectral shape. The spontaneous emission spectrum in one subregion has the Lorentzian line shape, which shows a cavity effect in the line width characterized by Q -1 dependence. In the other subregion, the spectral line shape is found to have a "doublet" structure, although it is in the weak coupling region. This doublet is caused by a quantum interference effect.
By using the method of eigenvalues and eigenstates, the emission and cavity-field spectra of a cascade three-level atom interacting with a single-mode electromagnetic field are studied in both intensity-dependent coupling (IDC) and intensity-independent coupling (IIC) cases. The photon statistics of the field on the spectra are investigated for the initial field in the pure number state, the coherent state and the thermal state. In the resonant case and the strong field limit, the pure-number-state emission spectrum exhibits six peaks and three peaks, respectively, for the IDC case and the IIC case. For a strong initial coherent state field or a strong thermal state field, the central structure of the emission spectrum at the field frequency is a doublet in the IDC case and a singlet in the IIC case. The cavity-field spectrum has three peaks in the IDC case and a single peak in the IIC case in the strong field limit for all of the three kinds of initial fields considered. Results indicate that in the emission spectrum merging of spectral peaks occurs for the IIC case as the initial field becomes stronger while it does not happen for the IDC case.
A single atom in a cavity is the model system of cavity quantum electrodynamics (CQED). The strong coupling regime between the atom and cavity-confined photon corresponds to the reversible exchange of energy between the two modes, and underpins a wide range of CQED phenomena with applications in quantum information science, including for example as quantum logic gates and as sources of entangled states. An important advance was achieved recently when strong coupling between excitons and cavity photons was reported for the first time for localized quantum dots (QDs) in micron-size solid state cavities. This has significance in terms of scalability and integration with other optical devices, and could lead to the emergence of "quantum optics on a chip" technology. However the results presented so far for quantum dots are in the linear regime, corresponding to coupling to the vacuum field (vacuum Rabi splitting); they are not a true QED effect and can equally well be described by classical physics as the coupling between two oscillators. In this paper, we present evidence for a purely quantum phenomenon for the QD/cavity photon system, namely the increase in splitting of the levels when the mean number of photons in the cavity is increased. This corresponds to non-linearities on the single-photon scale: the presence of a single excitation in the cavity changes the level structure, affecting the emission energies for a second photon. Such results are a first step in demonstrating the promise of quantum dots for CQED applications.
We present a systematic study of the properties of systems composed of NNN two-level quantum emitters coupled to a single cavity mode, for light-matter interaction strengths ranging from the weak to the ultrastrong and deep-strong coupling regimes. Beginning with an analysis of the energy spectrum as a function of the light-matter coupling strength, we examine systems with varying numbers of emitters, from a pair to large collections, approaching the thermodynamic limit $(N\ensuremath{\rightarrow}\ensuremath{\infty})$. Additionally, we explore the emission properties of these systems under incoherent excitation of the emitters, employing a general theoretical framework for open cavity-QED systems, which is valid across all light-matter interaction regimes and preserves gauge invariance within truncated Hilbert spaces. Furthermore, we study the influence of the emitter-environment interaction on the spectral properties of the system. Specifically, when each emitter interacts independently with its own reservoir, we observe the emergence of an emission peak at the cavity's resonant frequency for even values of NNN. Our analysis also clarifies the evolution of the system as the number of emitters increases, ultimately converging toward an equivalent system composed of two interacting single-mode bosonic fields.
The spectrum of spontaneously emitted photons from an atom interacting with a single cavity mode depends on the relative sizes of the mode coupling constant and the cavity loss rate. If the coupling constant is not too large, perturbation theory can he used to show that the atomic linewidth is either increased (enhanced spontaneous emission) or decreased (inhibited spontaneous emission) by the presence of the cavity. When the coupling constant is so large that perturbation theory cannot be used, the spontaneous- emission spectrum forms a doublet, with peaks located at the normal-mode frequencies for the coupled-dipole and cavity-mode oscillators (the so-called "vacuum" Rabi splitting).
The authors have investigated the spectrum of the emitted light by a single atom interacting with a single mode of the radiation in an ideal cavity via the intensity-dependent coupling (the Jaynes-Cummings model with intensity-dependent coupling see B. Buck, Phys. Lett., vol.A81, p.132 (1981)). From the authors' results it follows that in the resonant case the two-peaked structure of the spectrum associated with the vacuum-field Rabi splitting is preserved for any initial state of the radiation field (e.g. number state, thermal state, coherent state and the squeezed vacuum) with an arbitrary average number of photons.