Theory of Terahertz Spectroscopy and Fluctuation Modes in Polariton Lasers

Abstract

Semiconductor microcavities are among the most widely used laser technologies today. They can exhibit various macroscopic quantum phenomena, including Bose-Einstein condensation (BEC) of polaritons, Bardeen-Cooper-Schrieffer (BCS) states of polaritons, and photon lasing (lasing with negligible Coulombic exciton effects). These states have primarily been studied by measurement of the laser emission, while driven fluctuations of the order parameter are also an important tool for characterization. However, optical-probe spectroscopy of microcavities is constrained by the wavelength-selective distributed Bragg reflectors (DBRs), which typically form the end faces of the cavity. Terahertz radiation is little affected by the DBRs, and therefore THz spectroscopy can effectively probe the lasing system. In this dissertation, we construct and explain the microscopic theory of this continuous wave (CW) optical-pump THz-probe spectroscopy of quasi-two-dimensional (2D) semiconductor media, which include gallium arsenide (GaAs) quantum wells (QWs). We analyze the spectrum of spatially uniform fluctuation modes in the linear electromagnetic response of a semiconductor laser. With the condensate formed by composite particles, comprised of electrons, holes, and cavity light field photons, the set of zero-momentum single-frequency fluctuations contain both continua of single-particle electron-hole modes; and discrete-energy collective modes, which constitute coherent oscillations of all electronic states in the two bands. The quasiparticle excitations of the electron-hole system together determine the spectroscopic observables, such as the THz conductivity. The eigenmode spectra confirm that the interactions between the two bands induce their splitting, into an effective set of four bands, with the new intraband gap referred to as the BCS gap. The BCS gap is a signature of a macroscopic quantum state, and in the semiconductor laser is determined by the Coulomb interaction between charge carriers and the coupling between the carriers and the cavity light field. For the first time, our work has shown that the magnitude of the BCS gap can be measured with the linear THz response. We have also discovered that for a range of small but nonzero values of the order parameter (spontaneously emerging effective Rabi frequency), the BCS gap is absent from the mode spectra. In this gapless excitation region of the parameter domain, the 3 transition continua, rather than being wholly separate in the 2D mode frequency and decay rate space, intersect at exceptional points (EPs). As the laser is an open, pumped, and dissipative system, this regime may be considered a nonequilibrium analog of gapless superconductivity. For larger values of the BCS gap, we have predicted new collective oscillation modes in semiconductor lasers, which may be analogous to Bardasis-Schrieffer modes in superconductors. These “BaSh” modes, when they appear, dominate the observable response, and at the highest excitation levels may be unstable. For sufficiently small plasma damping, spectral regions of terahertz gain may be possible. Describing an archetype of nonequilibrium, highly-correlated systems, our theory of terahertz spectroscopy in polariton lasers illuminates new connections between superconductivity and optics.