Polariton lasing vs. photon lasing in a semiconductor microcavity

Abstract

Nearly one decade after the first observation of Bose-Einstein condensation in atom vapors and realization of matter-wave (atom) lasers, similar concepts have been demonstrated recently for polaritons: half-matter, half-light quasiparticles in semiconductor microcavities. The half-light nature of polaritons makes polariton lasers promising as a new source of coherent and nonclassical light with extremely low threshold energy. The half-matter nature makes polariton lasers a unique test bed for many-body theories and cavity quantum electrodynamics. In this article, we present a series of experimental studies of a polariton laser, exploring its properties as a relatively dense degenerate Bose gas and comparing it to a photon laser achieved in the same structure. The polaritons have an effective mass that is twice the cavity photon effective mass, yet seven orders of magnitude less than the hydrogen atom mass; hence, they can potentially condense at temperatures seven orders of magnitude higher than those required for atom Bose-Einstein condensations. Accompanying the phase transition, a polariton laser emits coherent light but at a threshold carrier density two orders of magnitude lower than that needed for a normal photon laser in a same structure. It also is shown that, beyond threshold, the polariton population splits to a thermal equilibrium Bose-Einstein distribution at in-plane wave number k parallel > 0 and a nonequilibrium condensate at k parallel approximately 0, with a chemical potential approaching to zero. The spatial distributions and polarization characteristics of polaritons also are discussed as unique signatures of a polariton laser.

Fig. 1.

Number of LPs and cavity photons per mode vs. injected carrier density for a polariton laser in scheme I (triangles) and a photon laser in scheme II (circles), respectively. The gray zone marks the population inversion densities from band edge to 15 meV above the band edge.

Fig. 2.

Comparison of the measured and calculated dispersion curves. (a–c) Measured LP dispersion curves (circles) and calculated cavity photon (dotted line), unshifted LP (dashed-dotted line), and blue-shifted LP (dashed line) dispersion curves in scheme I, P_th = 300 W/cm². Origin of the cavity photon dispersion is artificially shifted for comparison. (d) Measured (diamonds) and calculated (dotted line) cavity photon dispersion curves in scheme II, P′_th = 2 KW/cm².

Fig. 3.

Momentum space distribution of LPs. (a) The measured LP population per state vs. k_∥ (stars), compared with BE (solid line) and Maxwell–Boltzmann (dotted line) distribution functions at pump rates P/P_th = 1.5 and P/P_th = 0.6 (Inset). At P/P_th = 0.6, the fitted BE and Maxwell–Boltzmann distribution curves almost overlap. (b) The dimensionless chemical potential α vs. pump rate P/P_th and the fitted effective LP temperature T_LP vs. pump rate (Inset). The dashed lines are a guide for the eye.

Fig. 4.

Turn-on time τ_on of the emission at k_∥ > 0 vs. pump rate P/P_th (triangles) compared to the LP lifetimes at k_∥ = 0 and k_∥ = 0.1 k₀ (dashed-dotted lines), where τ_on is defined as the delay of the maximum of the emission relative to the pump. It is derived from the time-domain spectral measurement after deconvolution of pump spectrum from the emission spectra. The dashed line is a guide for the eye.

Fig. 5.

Spatial profiles of LPs at P/P_th = 0.8 (a) and P/P_th = 1 (b).

Fig. 6.

The spatial profiles of LPs (a) and lasing cavity mode (b) at 1.4 times the threshold pump powers. (c) The expansion of the spot-size vs. pump rate for the polariton laser (circles) and the photon laser (stars). The latter fits well the transportless model described by Eq. 2 (dashed line) assuming a pump spot size of 23 μm.

Fig. 7.

Polarization properties of LP emission. Emission intensity of LPs near k_∥ = 0 vs. pump power under circularly polarized pump (a) and linearly polarized pump (b). The two circular-polarization components of the emission and the their total intensities are plotted. (c) The circular degree of polarization vs. pump power with circularly polarized (triangles) and linearly polarized (circles) pumps.