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Physical Review A

Local-field correction in the strong-coupling regime

Tran Minh Hien, Ho Trung Dung, Dirk‐Gunnar Welsch

Published Apr 18, 2011• 7 citations
Publisher

Abstract

The influence of the local-field correction on the strong atom-field coupling regime are investigated using the real-cavity model. The atom is positioned at the center of a multilayer sphere. Three types of mirrors are considered: perfectly reflecting, Lorentz band gap, and Bragg-distributed ones, with special emphasis on experimental practicability. In particular, the influence of the local field on the spectral resonance lines, the Rabi oscillation frequency and decay rate, and the condition indicating the occurrence of the strong-coupling regime are studied in detail. It is shown that the local-field correction gives rise to a structureless plateau in the density of states of the electromagnetic field. The level of the plateau rises with increasing material density and/or absorption, which may eventually destroy the strong-coupling regime. The effect of the local field is especially pronounced at high-material densities due to direct energy transfer from the guest atom to the medium. At lower material density and/or absorption, variation of the material density does not seem to affect much the strong-coupling regime, except for a small shift in the resonance frequency.

DOI
10.1103/physreva.83.043820

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Physical Review A•Jul 1, 1990•20 citations
The influence of the local-field correction on the strong atom-field coupling regime are investigated using the real-cavity model. The atom is positioned at the center of a multilayer sphere. Three types of mirrors are considered: perfectly reflecting, Lorentz band gap, and Bragg-distributed ones, with special emphasis on experimental practicability. In particular, the influence of the local field on the spectral resonance lines, the Rabi oscillation frequency and decay rate, and the condition indicating the occurrence of the strong-coupling regime are studied in detail. It is shown that the local-field correction gives rise to a structureless plateau in the density of states of the electromagnetic field. The level of the plateau rises with increasing material density and/or absorption, which may eventually destroy the strong-coupling regime. The effect of the local field is especially pronounced at high-material densities due to direct energy transfer from the guest atom to the medium. At lower material density and/or absorption, variation of the material density does not seem to affect much the strong-coupling regime, except for a small shift in the resonance frequency.
A formalism for studying spontaneous decay of an excited two-level atom in the presence of dispersing and absorbing dielectric bodies is developed. An integral equation, which is suitable for numerical solution, is derived for the atomic upper-state-probability amplitude. The emission pattern and the power spectrum of the emitted light are expressed in terms of the Green tensor of the dielectric-matter formation, including absorption and dispersion. The theory is applied to the spontaneous decay of an excited atom at the center of a three-layered spherical cavity, with the cavity wall being modeled by a band-gap dielectric of Lorentz type. Both weak and strong coupling are studied, the latter with a special emphasis on cases where the atomic transition is (i) in the normal-dispersion zone near the medium resonance, and (ii) in the anomalous-dispersion zone associated with the band gap. In a single-resonance approximation, conditions of the appearance of Rabi oscillations and closed solutions to the evolution of the atomic state population are derived, which are in good agreement with the exact numerical results.
Spontaneous decay of an excited atom near a dispersing and absorbing microsphere of given complex permittivity that satisfies the Kramers-Kronig relations is studied, with special emphasis on a Drude-Lorentz permittivity. Both the whispering gallery field resonances below the band gap (for a dielectric sphere) and the surface-guided field resonances inside the gap (for a dielectric or a metallic sphere) are considered. Since the decay rate mimics the spectral density of the sphere-assisted ground-state fluctuation of the radiation field, the strengths and widths of the field resonances essentially determine the feasible enhancement of spontaneous decay. In particular, strong enhancement can be observed for transition frequencies within the interval in which the surface-guided field resonances strongly overlap. When material absorption becomes significant, then the highly structured emission pattern that can be observed when radiative losses dominate, reduces to that of a strongly absorbing mirror. Accordingly, nonradiative decay becomes dominant. In particular, if the distance between the atom and the surface of the microsphere is small enough, the decay becomes purely nonradiative.
The prototypical system constituted by a two-level atom interacting with a quantized single-mode electromagnetic field is described by the quantum Rabi model (QRM). The QRM is potentially valid at any light-matter interaction regime, ranging from the weak (where the decay rates exceeds the coupling rate) to the deep strong coupling (where the interaction rate exceeds the bare transition frequencies of the subsystems). However, when reaching the ultrastrong coupling regime, several theoretical issues may prevent the correct description of the observable dynamics of such a system: (i) the standard quantum optics master equation fails to correctly describe the interaction of this system with the reservoirs; (ii) the correct output photon rate is no longer proportional to the intracavity photon number; and (iii) they appear to violate gauge invariance. Here, we study the photon flux emission rate of this system under the incoherent excitation of the two-level atom for any light-matter interaction strength and consider different effective temperatures. The dependence of the emission spectra on the coupling strength is the result of the interplay between energy levels, matrix elements of the observables, and the density of states of the reservoirs. Within this approach, we also study the occurrence of light-matter decoupling in the deep strong-coupling regime and show how all of the obtained results are gauge invariant.
One of the proposed platforms in which both quantum and general relativistic effects can become observable is an atom interacting with the electromagnetic field in a gravitational-wave background. The periodic modulation of field modes induced by variations of the spacetime metric modifies the atomic emission spectrum. Notably, the temporal modulation of the mode-frequency induced by a plane gravitational wave can be simulated through modulated boundary conditions, such as moving cavity mirrors. We analyze the impact of this modulation on atom-field interactions in the strong atom-cavity coupling regime, where Rabi oscillations occur. We show analytically that the modulation is resonantly enhanced, leading to measurable imprints in the atomic transition probability. This establishes a realistic and experimentally accessible platform for probing analogue general relativistic effects in quantum optical systems.
After giving a summary of the basic-theoretical concept of quantization of the electromagnetic field in the presence of dispersing and absorbing (macroscopic) bodies, their effect on spontaneous decay of an excited atom is studied. Various configurations such as bulk material, planar half space media, spherical cavities, and microspheres are considered. In particular, the influence of material absorption on the local-field correction, the decay rate, the line shift, and the emission pattern are examined. Further, the interplay between radiative losses and losses due to material absorption is analyzed. Finally, the possibility of generating entangled states of two atoms coupled by a microsphere-assisted field is discussed.
We calculate the effect of the local-field correction (LFC) on the local response at ${\mathrm{\ensuremath{\omega}}}_{\mathit{s}}$ and 2${\mathrm{\ensuremath{\omega}}}_{\mathit{p}}$-${\mathrm{\ensuremath{\omega}}}_{\mathit{s}}$ of a medium consisting of two-level systems when subject to a pump of arbitrary intensity at ${\mathrm{\ensuremath{\omega}}}_{\mathit{p}}$ and a weak probe at ${\mathrm{\ensuremath{\omega}}}_{\mathit{s}}$. The pump is considered strong if its reduced intensity I=${\mathrm{\ensuremath{\omega}}}_{\mathit{R}}^{2}$/${\ensuremath{\gamma}}_{1}$${\ensuremath{\gamma}}_{2}$ is large compared to unity. Here ${\mathrm{\ensuremath{\omega}}}_{\mathit{R}}$ is the Rabi frequency and ${\ensuremath{\gamma}}_{1}$ and ${\ensuremath{\gamma}}_{2}$ are the longitudinal and transverse relaxation rates. In the weak pump case the LFC manifests itself as a fixed or static frequency shift. When the pump is strong, the response is independent of the LFC. At intermediate pump intensities the effect of LFC is dependent on the intensity of the pump. Both line-shift and line-shape distortions are present. The LFC thus gives rise to a shift in the resonance response that varies according to the intensity and frequency of the applied radiation. We call this effect the dynamic Lorentz shift.