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Nonlinear Optics

Observation of Quantum Coherence in the Nonlinear Emission of Semiconductor Microcavity Polaritons

Hui Deng, Gregor Weihs, Charles Santori, Jacqueline Bloch, Y. Yamamoto

Published Jan 1, 2002• 0 citations
Publisher

Abstract

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.

DOI
10.1364/nlo.2002.fa1

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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.
A phase transition from a classical thermal mixed state to a quantum-mechanical pure state of exciton polaritons is observed in a GaAs multiple quantum-well microcavity from the decrease of the second-order coherence function. Supporting evidence is obtained from the observation of a nonlinear threshold behavior in the pump-intensity dependence of the emission, a polariton-like dispersion relation above threshold, and a decrease of the relaxation time into the lower polariton state. The condensation of microcavity exciton polaritons is confirmed.
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 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.
Second-order time correlations of polaritons have been measured across the condensation threshold in a CdTe microcavity. The onset of Bose-Einstein condensation is marked by the disappearance of photon bunching, demonstrating the transition from a thermal-like state to a coherent state. Coherence is, however, degraded with increasing polariton density, most probably as a result of self-interaction within the condensate and scatterings with noncondensed excitons and polaritons. Such behavior clearly differentiates polariton Bose condensation from photon lasing.
Summary form only given. Semiconductor microcavities can be engineered to produce strong coupling between photons and quantum well excitons leading to the formation of new eigenstates called polaritons. Due to their peculiar dispersion, enabling non-equilibrium Bose-Einstein condensation [1], and their straightforward experimental accessibility, microcavity polaritons have gained considerable interest in recent years. Polariton states can be selectively populated by choosing the excitation angle and the wavelength of the excitation laser. After a lifetime of a few picoseconds the polariton decays and a photon is emitted from the cavity, carrying the complete information on the underlying polariton state. Several theoretical works [2-3] suggest that polariton-polariton interactions can be a source of non-classical photon correlations, producing photon pairs that are entangled in either the energy, the polarization, or the momentum degree of freedom. One appeal of such a system is that many parameters such as the polariton-polariton interaction strength are tunable [4] and multipartite entangled states can be created in a single device [5]. However, due to the lack of high-quality samples, experimental realisations of these schemes have been elusive so far. In this contribution, we will discuss some of our experimental work on the statistics of polariton-polariton parametric scattering. Excited polaritons can scatter in a four-wave mixing process into signal and idler states lying on a figure-eight shaped curve in k-space, where phase-matching is fulfilled. We make use of a sample with ultra narrow exciton resonances, which allows for the generation and detection of correlated light. We present our measurements of the second order correlation functions using time-correlated photon counting. We discuss in detail, how polariton quantum correlations depend on a number of experimental parameters, such as phase space location and excitation density and find that the results can be understood in the framework of the well known Bogoliubov theory for 2D Bose gases utilised for microcavity polaritons [6]. We find bunching below the parametric threshold and a slow buildup of coherence above the threshold similar to the quantum statistics of a non-degenerate optical parametric oscillator, which is well known for its nonclassical properties [7]. We discuss in particular the influence of strong background processes on the observed photon statistics.