Displaced squeezed number states of the phonon field in polar semiconductors

Abstract

Considering that the Fröhlich continuum model of polarons, in the static approximation, describes the electron-phonon interaction in polar semiconductors, and that the Hamiltonian of the generalized parametric oscillator represents the ion vibrations, we have studied a way of producing phonon-displaced squeezed number states. By the use of the evolution operator method, the exact wave function as well as the probability density are obtained. In order to see explicitly the wave function's squeezing property, we have given the analytical forms of the variances ⌬q and ⌬p. Dealing with the radiative recombination process, which occurs at imperfections, we have derived the phonon number distribution. A calculation of Mandel's Q parameter, which accounts for the kind of the distribution, and of the Huang-Rhys factor S, are also presented. An interesting result is obtained when we study the case of a simple driven harmonic oscillator, whose Q parameter imposes the value 0.5 on the factor S, in order to have a Poissonian distribution. Any deviation from this value yields sub-or super-Poissonian distributions which characterize the photoluminescence ͑PL͒ spectrum, as regards the sharpness of the PL lines and the number of phonons involved in the recombination process. With regard to the time dependence of the factor S and of the Hamiltonian representing the ion vibrations, unexpected values ͑in comparison with the time-independent case͒ for the Q parameter can be found. This behavior can affect the number of emitted phonons, defined by the kind of the phonon number distribution.

Interaction of light and semiconductor can generate quantum states required for solid state quantum computing: Entangled, steered and other nonclassical states

“…The possibilities of generation of nonclassical states through the light-semiconductor interaction have already been investigated in Refs. [34][35][36][37][38][39][40][41]. These investigations were partially motivated by the easy availability and a few more advantages of the semiconductor over the usual nonlinear crystals.…”

“…The generation of squeezing and entanglement in nuclear spins were reported in semiconductor quantum dot [35]. Interestingly, phonon-displaced squeezed number state has been extensively investigated in polar semiconductors [36]. In a recent experiment, Zeytino{\breve{g}}lu et al, have established that the direct band gap semiconductor can behave as a nonlinear mirror and produce broadband squeezing [37].…”