Suppressed Electron-Hole Exchange Spin Flip in Cavity Polaritons

Abstract

We consider theoretically the spin relaxation of exciton-polaritons in semiconductor microcavities in the strong coupling regime. The dominant quantum well exciton polarization relaxation mechanism is typically due to the long-range intra-exciton electron-hole exchange. We estimate perturbatively the corresponding contribution for the lower polaritons as a function of the elastic scattering time in analogy to the Dyakonov-Perel model for electron spin relaxation. We find a strong suppression of the polariton spin flip rate due to the electron-hole exchange with respect to the quantum well exciton case.Semiconductor microcavities have attracted much interest, as in these systems the lightmatter interaction between the Fabry-Perot-like photon mode of the cavity and the exciton resonance of a suitably chosen semiconductor quantum well can be controlled and tailored. In particular, in the regime of strong coupling when such exciton-photon interaction is larger than the exciton and photon mode broadenings, the eigenmodes of the system are a doublet of cavity polaritons separated by the Rabi splitting (typically about 5 meV) [1]. Such modes represent coherent superpositions of exciton and cavity photon modes and their properties are related, but distinct, from those of the bare parent modes. The scattering processes (elastic as well as inelastic) are affected by the strong coupling in a non-trivial way and are very different from those in a bare quantum well. In general, they depend on the exciton-cavity detuning and the Rabi splitting.In this context, we have theoretically addressed the open question of the spin relaxation of cavity polaritons and its relation to the well known [2] bare quantum well exciton spin relaxation. In general, spin flip processes are crucial for the coherent control of the polarization in ultrafast spectroscopy and also as a potential source of dephasing of the optically active excitations, i.e. increasing their homogeneous linewidth. The heavy hole quantum well exciton manifold includes four spin states (nearly degenerate, only split by the short-range exchange interaction): the two optically active states j1i ¼ j3=2; À1=2i, jÀ1i ¼ jÀ3=2; 1=2i, and the two inactive ones j2i ¼ j3=2; 1=2i, jÀ2i ¼ jÀ3=2; À1=2i. The luminescence polarization decay proceeds via two channels: a direct relaxation with simultaneous electron and hole spin flip, and an indirect one with sequential single particle spin flips. The direct relaxation between the optical active states is driven mainly by the long-range intra-exciton electron-hole exchange interaction [2]. Different experiments by different groups indicate that this is the leading exci-# WILEY-

Exciton Spin Dynamics in Semiconductor Quantum Wells

“…Because of the very small overlap between the electron and hole wavefunction, the spin relaxation mechanism induced by the exchange interaction between the electron and the hole does not play a significant role in contrast to type I QWs (see sections 1.1.2, 1.3.4). However the strong localization of the carrier wavefunction at the QW interface will (i) modify drastically the exciton fine structure and (ii) yield very long electron spin relaxation times (≈ a few tens of ns) compared to type I QWs [64]. It has been shown that the symmetry of the system is reduced form D 2d to C 2v and [51,58,63].…”

Coherent spin dynamics of polaritons in semiconductor microcavities

“…It is based on the simultaneous flip of electron and hole spins and takes into account the electron-hole exchange, the long-range part being the dominant contribution. We generalize this result in the polariton picture [18,19]. This leads to 1…”

“…For δ < 0, the polariton population is concentrated around k ≈ k p states in the k-space, as the acoustic phonon scattering is quenched due to the low polariton density of state for k k p . An evaluation of each factor of equation ( 10) leads to a spin relaxation time T s1 at least three ordersof magnitude longer than the bare exciton one [18,19], which is mainly due to the weakness of the exchange matrix element which is proportional to the small wavevector k p . This is in good agreement with the observed relaxation quenching.…”