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Physical Review A

Goldstone mode of optical parametric oscillators in planar semiconductor microcavities in the strong-coupling regime

Michiel Wouters, Iacopo Carusotto

Published Oct 9, 2007• 79 citations
Publisher

Abstract

We propose an experimental setup to probe the low-lying excitation modes of a parametrically oscillating planar cavity, in particular the soft Goldstone mode which appears as a consequence of the spontaneously broken $\text{U}(1)$ symmetry of signal-idler phase rotations. A strong and narrow peak corresponding to the Goldstone mode is identified in the transmission spectrum of a weak probe beam incident on the cavity. When the $\text{U}(1)$ symmetry is explicitly broken by an additional laser beam pinning the signal-idler phase, a gap opens in the dispersion and the Goldstone peak is dramatically suppressed. Quantitative predictions are given for the case of semiconductor planar cavities in the strong exciton-photon coupling regime.

DOI
10.1103/physreva.76.043807

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The statistic of parametric photon emission in a one-dimensional semiconductor microcavity optical parametric oscillator is reported. We perform photon-counting experiments on signal and idler beams by means of a Hanbury Brown and Twiss setup for studying the second-order coherence. Under pulsed laser excitation at normal incidence, energy-degenerate signal and idler beams are emitted in a mirror-symmetric configuration and share the same excitonic/photonic composition. Moreover the two emissions share the same intensity and the same coherence properties. We show that the bunching visibility [i.e., the value of ${g}^{(2)}(\ensuremath{\tau}=0)$] changes across the parametric threshold and it is associated both to different spectral composition of the emission and to the buildup of coherence at high injection. Nevertheless, different from conventional optical parametric oscillators, a full coherence is never recovered.
We investigate the appearance of spontaneous coherence in the parametric emission from planar semiconductor microcavities in the strong coupling regime. Calculations are performed by means of a quantum Monte Carlo technique based on the Wigner representation of the coupled exciton and cavity-photon fields. The numerical results are interpreted in terms of a nonequilibrium phase transition occurring at the parametric oscillation threshold: below the threshold, the signal emission is incoherent, and both the first and the second-order coherence functions have a finite correlation length which becomes macroscopic as the threshold is approached. Above the threshold, the emission is instead phase coherent over the whole two-dimensional sample and intensity fluctuations are suppressed. Similar calculations for quasi-one-dimensional microcavities show that in this case the phase coherence of the signal emission has a finite extension even above the threshold, while intensity fluctuations are suppressed.
We report on the optical response of a semiconductor microcavity featuring a strong exciton–photon coupling. The weak excitation regime is investigated experimentally by means of time-resolved transmission and four-wave mixing experiments. The influence of electronic disorder on the coherent exciton–photon dynamics is discussed in terms of the solutions of the Maxwell-Bloch equations. The high excitation regime is investigated by using transient sub-picosecond pump–probe experiments. Optical amplification of the probe beam (up to a factor of five), as well as a fundamental change of the optical spectra, have been found close to and above the exciton saturation density. The observed oscillations are corresponding to the Rabi frequency of the excitons in the pump field.
Recently, cavity quantum electrodynamic (QED) effects in semiconductor microcavities have been of considerable interest since, in the weak-coupling regime they play an important role in selectively increasing spontaneous emission into the lasing mode of vertical-cavity surface-emitting lasers (VCSEL’s) [1,2], enabling low-threshold, high speed, and high efficiency. In a strong-coupling regime, the normal modes of the coupled system are superpositions of the exciton and cavity modes. Hence the impulsively excited system will evolve in time with the energy oscillating between the exciton and cavity modes. This is known as a vacuum-Rabi oscillation (VRO), with a frequency of Ω=d¯⋅E¯/@@h, where d¯ is the transition dipole moment of atoms and E¯ the vacuum-field strength. Of course, VRO are observable only when the cavity lifetime and exciton dephasing time are long enough compared to VRO period. Recently, Weisbuch et al. [3] have reported an observation of the normal-mode vacuum Rabi splitting in 2-D-exciton/planar-DBR microcavities. The observed splittings were as large as 6 meV in reflection and transmission spectra, implying 690-fs vacuum Rabi oscillations.
Abstract We report the observation of optical bistability in a semiconductor microcavity pumped at the “magic angle” above the parametric oscillation threshold. Experimental evidence is given in the form of a hysteresis cycle of the nonlinear emission as a function of the pump intensity. A model analogous to those developped for triply resonant Optical Parametric Oscillators (OPO) is in good agreement with the experimental findings. In the second part, we study the potential application of the parametric oscillation regime to quantum optics. The quantum correlations between the emitted “signal” and “idler” beams are computed. We show that very strong quantum correlations between the signal and idler polaritons can be achieved. However the quantum effects in the outgoing light fields are strongly reduced due to the large mismatch in the coupling of the signal and idler polaritons to the external photons. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
The threshold of triply resonant optical parametric oscillation in a semiconductor microcavity in the strong coupling regime is investigated. Because of the third-order nature of the excitonic nonlinearity, a variety of different behaviors is observed thanks to the interplay of parametric oscillation and optical bistability effects. The behavior of the signal amplitude and of the quantum fluctuations in approaching the threshold has been characterized as a function of the pump, signal, and idler frequencies.