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arXiv:cond-mat/0611282 · Physical Review Letters

Quantum Vacuum Radiation Spectra from a Semiconductor Microcavity with a Time-Modulated Vacuum Rabi Frequency

Simone De Liberato, Cristiano Ciuti, Iacopo Carusotto

Published Mar 8, 2007• 246 citations
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Abstract

We develop a general theory of the quantum vacuum radiation generated by an arbitrary time modulation of the vacuum Rabi frequency of an intersubband transition in a doped quantum well system embedded in a planar microcavity. Both nonradiative and radiative losses are included within an input-output quantum Langevin framework. The intensity and the spectral signatures of the extra-cavity emission are characterized versus the modulation properties. For realistic parameters, the photon pair emission is predicted to largely exceed the blackbody radiation in the mid and far infrared. For strong and resonant modulation a parametric oscillation regime is achievable.

DOI
10.1103/physrevlett.98.103602

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We develop a general theory of the quantum vacuum radiation generated by an arbitrary time modulation of the vacuum Rabi frequency of an intersubband transition in a doped quantum well system embedded in a planar microcavity. Both nonradiative and radiative losses are included within an input-output quantum Langevin framework. The intensity and the spectral signatures of the extra-cavity emission are characterized versus the modulation properties. For realistic parameters, the photon pair emission is predicted to largely exceed the blackbody radiation in the mid and far infrared. For strong and resonant modulation a parametric oscillation regime is achievable.
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We present a full quantum theory for the dissipative dynamics of an optical cavity in the ultrastrong light-matter coupling regime, in which the vacuum Rabi frequency is a significant fraction of the active electronic transition frequency and the antiresonant terms of the light-matter coupling play an important role. In particular, our model can be applied to the case of intersubband transitions in doped semiconductor quantum wells embedded in a microcavity. The coupling of the intracavity photonic mode and of the electronic polarization to the external, frequency-dependent, dissipation baths is taken into account by means of quantum Langevin equations in the input-output formalism. In the case of a time-independent vacuum Rabi frequency, exact analytical expressions for the operators are obtained, which allows us to characterize the quantum dissipative response of the cavity to an arbitrary initial condition (vacuum, coherent field, thermal excitation). For a vacuum input in both the photonic and electronic polarization modes, the ground state of the cavity system is a two-mode squeezed vacuum state with a finite population in both photonic and electronic modes. These excitations are, however, virtual and cannot escape from the cavity: for a vacuum input, a vacuum output is found, without any trace of the intracavity squeezing. For a coherent photonic input the linear optical response spectra (reflectivity, absorption, transmission) have been studied, and signatures of the ultrastrong coupling have been identified in the asymmetric and peculiar anticrossing of the polaritonic eigenmodes. Finally, we have calculated the electroluminescence spectra in the case of an incoherent electronic input: the emission intensity in the ultrastrong coupling regime results in being significantly enhanced as compared to the case of an isolated quantum well without a surrounding cavity.
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We present a theory of the quantum vacuum radiation that is generated by a fast modulation of the vacuum Rabi frequency of a single two-level system strongly coupled to a single cavity mode. The dissipative dynamics of the Jaynes-Cummings model in the presence of antirotating-wave terms is described by a generalized master equation including non-Markovian terms. Peculiar spectral properties and significant extracavity quantum vacuum radiation output are predicted for state-of-the-art circuit cavity quantum electrodynamics systems with superconducting qubits.
We calculate the spontaneous-emission characteristics of a quantum-well exciton embedded in the center of a planar microcavity and compare them with the emission characteristics in a single-mode cavity with lateral confinement of the electromagnetic field. The results indicate that because the modal structure of a planar microcavity consists of a spectrally dense continuum, the exciton decays into the cavity continuum with a time constant close to the free-space spontaneous-emission lifetime, even under conditions in which its spectrum displays the vacuum Rabi splitting. This behavior contrasts with the case of cavities with lateral in-plane confinement of the field, in which the vacuum Rabi splitting is the signature of a dramatic modification of the spontaneous-emission lifetime. The technological implications of this difference are discussed.
Exact quantum electrodynamical results are obtained for a semiconductor quantum dot placed inside a microcavity of arbitrary photon leakage ( ), and radiative ( ) and nonradiative ( c ) decay rates. Analytical results are obtained for the density matrix elements. The absorption spectra thus obtained for arbitrary values of , and c exhibit the solid-state analogue of the vacuum Rabi splitting when the system decay parameters are much smaller than the quantum dot-cavity-field coupling parameter. Numerical estimates are made for samples of CdS and GaAs quantum dots of dimensions 19 Å and 56 Å, respectively. The results are in qualitative agreement with the experimental observations.