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arXiv:1210.6906 · Physical Review Letters

Coherence Expansion and Polariton Condensate Formation in a Semiconductor Microcavity

V. V. Belykh, Nikolai N. Sibeldin, V. D. Kulakovskiĭ, Михаил Михайлович Глазов, Marina A. Semina, Christian Schneider, Sven Höfling, Martin Kamp, A. Forchel

Published Mar 26, 2013• 52 citations
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Abstract

The dynamics of the expansion of the first order spatial coherence g(1) for a polariton system in a high-Q GaAs microcavity was investigated on the basis of Young's double slit experiment under 3 ps pulse excitation at the conditions of polariton Bose-Einstein condensation. It was found that in the process of condensate formation the coherence expands with a constant velocity of about 10(8) cm/s. The measured coherence is smaller than that in a thermal equilibrium system during the growth of condensate density and well exceeds it at the end of condensate decay. The onset of spatial coherence is governed by polariton relaxation while condensate amplitude and phase fluctuations are not suppressed.

DOI
10.1103/physrevlett.110.137402

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The dynamics of the expansion of the first order spatial coherence g(1) for a polariton system in a high-Q GaAs microcavity was investigated on the basis of Young's double slit experiment under 3 ps pulse excitation at the conditions of polariton Bose-Einstein condensation. It was found that in the process of condensate formation the coherence expands with a constant velocity of about 10(8) cm/s. The measured coherence is smaller than that in a thermal equilibrium system during the growth of condensate density and well exceeds it at the end of condensate decay. The onset of spatial coherence is governed by polariton relaxation while condensate amplitude and phase fluctuations are not suppressed.
The fascination of macroscopic quantum coherence formed in a degenerate Bose gas drives the worldwide work on atomic Bose-Einstein condensates. Semiconductor polaritons1 are another promising system to explore the physics of degenerate Bose gases in a stronger interaction regime. It is also a system easily produced and probed through optical methods. In this work we present the first observation of the onset of a quantum coherence formed out of an initially thermal population of polaritons in a microcavity quantum well system. The quantum coherence is measured by a time domain second order coherence g(2)(0) of the light emitted from the polaritons. Second and higher order coherence functions are crucial in quantum optics to distinguish among various pure states of light, such as coherent state or squeezed state, from classical thermal light2. They have been measured indirectly in the spatial domain for atomic BECs3,4. In our system, with supporting evidence from measurements of the input-output, dispersion, and time evolution of the emission, the phase transition was identified by a decrease of g(2)(0) ≈2, the value for a thermal state, toward g(2)(0) ≈1 for a coherent state. This is a direct evidence of the formation of a macroscopic quantum coherence in the lower polariton ground state.
Second-order time correlation measurements with a temporal resolution better than 3 ps were performed on a CdTe microcavity where spontaneous Bose-Einstein condensation is observed. After the laser pulse, the nonresonantly excited thermal polariton population relaxes into a coherent polariton condensate. Photon statistics of the light emitted by the microcavity evidences a clear phase transition from the thermal state to a coherent state, which occurs within 3.2 ps after the onset of stimulated scattering. Following this very fast transition, we show that the emission possesses a very high coherence that persists for more than 100 ps after the build-up of the condensate.
Bose-Einstein condensate of exciton polaritons in a semiconductor microcavity is a macroscopically populated coherent quantum state subject to concurrent pumping and decay. Debates about the fundamental nature of the condensed phase in this open quantum system still persist. Here, we gain a new insight into the spontaneous condensation process by imaging long-lifetime exciton polaritons in a high-quality inorganic microcavity in the single-shot optical excitation regime, without averaging over multiple condensate realisations. In this highly non-stationary regime, a condensate is strongly influenced by the `hot' incoherent reservoir, and reservoir depletion is critical for the transition to the ground energy and momentum state. Condensates formed by more photonic exciton polaritons exhibit dramatic reservoir-induced density filamentation and shot-to-shot fluctuations. In contrast, condensates of more excitonic quasiparticles display smooth density and are second-order coherent. Our observations show that the single-shot measurements offer a unique opportunity to study formation of macroscopic phase coherence during a quantum phase transition in a solid state system.
The demonstration of coherent polariton emission from a CdTe microcavity structure [1] has provided a new system for the study of condensate physics. Unlike atomic condensates, the microcavity system is not in equilibrium; the polariton life-time in the cavity is only ∼ 2ps, so the population has to be maintained by pumping. This raises interesting questions about how the properties of such a non-equilibrium condensate differ from those of an equilibrium system. Recent experimental measurements of the first (g(1)) and second (g(2)) order correlation functions of the emitted light have shown that the decay times of both are ∼ 100−200ps, much longer than the cavity life-time. In this work, we present a theroetical treatment which provides a quantitative explanation of these results, and shows that the ultimate cause of the coherence decay is interactions between polaritons in the condensate. The microcavity polariton condensate is a mesoscopic quantum system, consisting of N ∼ 102 po-laritons within the finite size excitation spot. As a result, number fluctuations of ∼ N 1 2 are expected. For a finite equilibrium condensate of interacting particles, it is straight forward to show that the decay
We have created polaritons in a harmonic potential trap analogous to atoms in optical traps. The trap can be loaded by creating polaritons 50 micrometers from its center that are allowed to drift into the trap. When the density of polaritons exceeds a critical threshold, we observe a number of signatures of Bose-Einstein condensation: spectral and spatial narrowing, a peak at zero momentum in the momentum distribution, first-order coherence, and spontaneous linear polarization of the light emission. The polaritons, which are eigenstates of the light-matter system in a microcavity, remain in the strong coupling regime while going through this dynamical phase transition.
We adopt a kinetic theory of polariton non-equilibrium Bose-Einstein condensation, to describe the formation of off-diagonal long-range order. The theory accounts properly for the dominant role of quantum fluctuations in the condensate. In realistic situations with optical excitation at high energy, it predicts a significant depletion of the condensate caused by long-wavelength fluctuations. As a consequence, the one-body density matrix in space displays a partially suppressed long-range order and a pronounced dependence on the finite size of the system.