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arXiv:0812.0207 · Physical Review B

Entanglement of photons due to nonlinear optical response of quantum wells

Mikhail Erementchouk, Michael Niklaus Leuenberger

Published May 6, 2010• 6 citations
arXivHTMLPDF

Abstract

We study photons entangling in the short-time response of a quantum well excited by a short intense pulse. At the time scales, where the biexciton effect is not yet pronounced, the Pauli principle is responsible for many-body correlations among excitons, giving rise to the production of entangled photons with a yield $\ensuremath{\sim}{10}^{\ensuremath{-}2}$. The quantum-field theoretical two-particle density matrix in second quantization is used to calculate the entanglement for arbitrary emission angles of the entangled pairs of photons. At the time scales, where the heavy-light hole splitting is resolved, the resonances corresponding to different two-exciton states develop, which allow for a simple kinematic theory relating the states of the outgoing photons with the respective two-exciton states. The resonant response can be expected at symmetric emission angles for resonances with the heavy-heavy and light-light two-exciton states with remarkably nontrivial dependence of entanglement on the emission angles and on the ellipticity parameters of the excitation. We show that the emitted entangled two-photon states are always in a triplet state.

DOI
10.1103/physrevb.81.195308

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We investigate the spectral properties of the excitonic nonlinear response in a GaAs quantum-well sample containing wells of different thicknesses. We observe both the heavy-hole biexciton and the light-hole biexciton in the transient four-wave mixing spectrum and estimate their binding energy dependence on well width. For moderate excitation densities the signal for negative delay at the heavy-hole exciton and biexciton resonances is due to two-photon transitions to the biexciton states through the exciton states. The temporal behavior of the transient four-wave mixing signal from the heavy-hole exciton resonance is strongly dependent on the spectral position of the laser. We show that this effect is due to interference phenomena and to excitation-induced dephasing.
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We demonstrate the presence of strong exciton-exciton correlations in GaAs-AlGaAs multiple quantum wells by using the polarization selection rules for four-wave mixing and a test that was originally designed to distinguish between quantum beats and polarization interference. We show that, when the four-wave-mixing signal is produced by two pulses that have the same circular polarization, dynamic beating behavior is observed at the heavy-hole-light-hole frequency that provides evidence of Coulomb-induced correlations that go beyond those expected from the semiconductor Bloch equations in the Hartree-Fock approximation and beyond the local field corrections used in simple phenomenological models. Moreover, this behavior cannot be explained by invoking biexcitonic effects. We demonstrate that this dynamic excitonic coupling can be explained in terms of a competition between quantum-beat-like and polarization-interference-like behavior, and we show that such behavior can be used to place quantitative limits on the coupling strength. In addition, we use a simple phenomenological model to show that excitation-induced-dephasing can produce such correlations.
We study the coherent time-resolved response of a semiconductor microcavity excited by an ultrashort light pulse. The cavity contains embedded quantum wells and quantum well excitons are strongly coupled to cavity photons. Two experimental situations are examined. We describe a linear regime when the exciting light pulse is weak. Further, a low-temperature pump-and-probe experiment in a nonlinear regime is analyzed, with a cw pump beam circularly polarized opposite to a weak ultrashort probe pulse in conditions yielding a bipolariton-mediated optical Stark effect. In both cases we examine the response of a single quantum well and contrast it with that of several quantum wells. In the latter case light is coupled only to a symmetric linear combination (bright exciton) of excitonic states in individual quantum wells. We find distinctive fingerprints of other linear combinations of exciton states (dark excitons). In the linear regime, in addition to a pattern of Rabi oscillations between the two polariton states, additional beating frequencies appear, related to dark states. In the nonlinear case, the bipolariton formalism outlined by Ivanov et al. [Phys. Rev. B 52, 11 017 (1995)] allows one to deduce a similar additional beating frequency and a splitting of bipolariton frequencies related to their dark or bright state character. This work identifies the effect of the microcavity parameters on its coherent response and determines the experimental conditions in which the influence of dark states may be observed.
The paper presents a description of two-pair correlations in an electron-hole system in laser-excited direct-gap semiconductors in terms of the exciton-boson formalism. The dependence of the states of quasi-particles on their angular momentum orientation is properly taken into account following group theory rules. It is shown for the example of heavy hole excitons in GaAs quantum wells that Coulomb two-exciton correlations include effective repulsion between excitons with nonzero total momenta and effective attraction between excitons with zero total momenta. They generate exciton and biexciton nonlinearities, respectively, in the exciton-biexciton system. The Heisenberg equations of motion derived are applied to four-wave mixing in the coherent mode. Two components of Coulomb two-exciton correlations were found to generate coherent four-wave mixing either separately, one at the cocircular and the other at the perpendicular-linear polarization of applied pulses, or jointly at parallel-linear polarization. General equations are obtained for the amplitude of four-wave mixing signals with time resolution in these polarization configurations, which, in the limit of ultranarrow pulses, reduce to analytic functions of time and excitation and sample parameters. These equations are used to analyze signal characteristics in every polarization configuration. The results give a correct picture of biexciton effects and the polarization dependence of coherent four-wave mixing in GaAs quantum wells.
Semiconductor quantum dots are among the best sources of on-demand entangled photon pairs. The degree of entanglement, however, is generally limited by the fine structure splitting of exciton states. In this paper, we theoretically investigate the generation of polarization-entangled photon pairs under two-photon excitation and cavity-assisted two-photon emission, both in the weak and strong cavity coupling regimes. We demonstrate and clarify that cavity coupling together with an excitation pulse reduces the degree of entanglement in three different ways. First, in a strong coupling regime, the cavity introduces the unequal ac-Stark shift of horizontally and vertically polarized exciton states, which results in the effective splitting of exciton states. Second, it induces the cross-coupling between the exciton states even in the weak coupling regime, causing the creation of unfavorable two-photon states. Finally, higher excited states of the cavity modes also contribute to the reduction of entanglement. Therefore, in the setting considered here, cavity coupling, which is generally required for the efficient collection of emitted photons, degrades the entanglement both in weak and strong coupling regimes.