Vacuum Field Rabi Splitting in a Semiconductor Microcavity

Abstract

We do not intend to give here a background knowledge on vacuum field Rabi splitting. The reader should refer to J.M. Raimond, T. Norris, H. Yokoyama and D.S. Citrin lecture notes. For the sake of completeness we simply remind the reader that the cavity quantum electrodynamics (CQED) treatment of a two level atomic system resonantly coupled to a single photon mode predicts that the eigenstates of the system are no longer the photon and atomic oscillator states but two mixed symmetric and anti symmetric states. The energy separation is $\Delta _{\rm{n}} = \hbar \Omega = {\rm{g}}\sqrt 1 + {\rm{n}}$ where g is a coupling factor that only depends on the dipole matrix element and the cavity volume , and n is the number of photons in the cavity¹. For no incoming photons, a splitting still occurs, which can be regarded as coupling between the atomic oscillator and the vacuum field of the cavity (i.e. in the absence of a driving field). This effect was first called vacuum field Rabi splitting by J. J. Sanchez-Mondragon et al.¹ as it is related to the textbook case of intense field Rabi splitting² which, in the present case, is induced by the zero point field fluctuations in the cavity. If several atomic oscillators are present it can be shown³ that, for the n=0 states, the coupling constant increases as the square root of the number N of atoms ${\text{g}}_{{\text{n = 0}}} ({\text{N}}) = g(1)\sqrt {\text{N}}$. If the system is prepared in a pure atomic oscillator or photon oscillator state, it will oscillate between these two states at the Rabi frequency Ω. In a classical description, the overall system exhibits an anti-crossing behavior when both oscillators are resonant, with the two split modes corresponding to the normal modes of the system⁴. In an atomic transition language, one considers the system as undergoing a coherent evolution with a photon being absorbed by an atom, which subsequently emits a photon with the same energy and wave vector k, the photon being re-absorbed, and so-on. In order to observe a similar effect in a solid we need the equivalent of both atomic and photon oscillators, both of which can be obtained in a monolithic semiconductor structure.