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arXiv:2306.02202 · Physical review. B./Physical review. B

Tunable Bose-Einstein condensation and rotonlike excitation spectra with dipolar exciton-polaritons in crossed fields

Timofey V. Maximov, I. L. Kurbakov, Nina S. Voronova, Yu. E. Lozovik

Published Nov 13, 2023• 3 citations
arXivHTMLPDF

Abstract

We develop the many-body theory of dipolar exciton-polaritons in an optical microcavity in crossed out-of-plane electric and in-plane magnetic fields. Even for relatively weak fields, we reveal the existence of two minima in the bare lower-polariton dispersion, which give rise to the tunable transition between the polariton Bose-Einstein condensate and that of excitons, produced by the competition between these minima. We predict that such dipolar condensate exhibits a roton-maxon character of the excitation spectrum, never before observed for polaritons. We show that upon the transition between the two condensation regimes, the weak correlations in the polariton gas give way to the intermediate interparticle correlations characteristic for excitons, and that the transition is accompanied by a sharp quenching of photoluminescence as the lifetime is increased by several orders of magnitude. While in the polariton regime, the luminescence peak corresponding to the condensate is shifted to a nonzero angle. The angular dependence of the two-photon decay time in the Hanbury Brown and Twiss experiment is calculated and used as a tool to evidence the formation of the macroscopically coherent state. Our proposal opens opportunities towards manipulating the superfluid properties and extended-range dipole-dipole correlations of exciton-polariton condensates.

DOI
10.1103/physrevb.108.195304

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We develop the many-body theory of dipolar exciton-polaritons in an optical microcavity in crossed out-of-plane electric and in-plane magnetic fields. Even for relatively weak fields, we reveal the existence of two minima in the bare lower-polariton dispersion, which give rise to the tunable transition between the polariton Bose-Einstein condensate and that of excitons, produced by the competition between these minima. We predict that such dipolar condensate exhibits a roton-maxon character of the excitation spectrum, never before observed for polaritons. We show that upon the transition between the two condensation regimes, the weak correlations in the polariton gas give way to the intermediate interparticle correlations characteristic for excitons, and that the transition is accompanied by a sharp quenching of photoluminescence as the lifetime is increased by several orders of magnitude. While in the polariton regime, the luminescence peak corresponding to the condensate is shifted to a nonzero angle. The angular dependence of the two-photon decay time in the Hanbury Brown and Twiss experiment is calculated and used as a tool to evidence the formation of the macroscopically coherent state. Our proposal opens opportunities towards manipulating the superfluid properties and extended-range dipole-dipole correlations of exciton-polariton condensates.
We consider quantum phase transitions in a system of bright dipolar excitons which can form bound pairs (dipolar biexcitons). The biexciton energy is tuned from negative to positive values through the scattering threshold. At sufficiently large density an exciton superfluid transforms into a superfluid of biexcitons. With the average relative momenta of excitons in the pairs being beyond the light cone, the transition is accompanied by a reduction of the photoluminescence intensity. Effective magnetic fields due to the long-range exchange splitting of exciton states shift the position of the gap in the elementary excitation spectrum to a circle of degenerate minima in the $\mathbit{k}$ space. Closing the gap results in the formation of exciton stripes polarized linearly along the direction of their translational symmetry. In the biexciton energy vs density phase diagram the novel phase intervenes between the dark biexciton and radiative exciton superfluids. We conclude that formation of a BCS-like biexciton condensate induces correlated alignment of the effective magnetic fields and excitonic spins. We outline important differences in the predicted mechanism from the phenomenon of spin-orbit-coupled Bose-Einstein condensation.
Correlations of the luminescence intensity (the second-order correlation function g (2)(τ)), where τ is the delay time between the photons detected in pairs) under the conditions of the Bose-Einstein condensation (BEC) of dipolar excitons has been studied in a temperature range of 0.45–4.2 K. Photoexcited dipolar excitons have been accumulated in a lateral trap in a GaAs/AlGaAs Schottky diode with a 25-nm wide single quantum well with an electric bias applied across the heterolayers. Two-photon correlations have been measured with the use of a two-beam intensity interferometer with a time resolution of }~0.4 ns according to the well-known classical Hanbury-Brown-Twiss scheme. The photon bunching has been observed at the onset of Bose-Einstein condensation manifested by the appearance of a narrow exciton condensate line in the luminescence spectrum at an increase in the optical pumping (the line width near the threshold is ≲200 μeV). At the same time, the two-photon correlation function itself obeys the super-Poisson distribution, g (2)(τ) > 1, at time scale τc ≲ 1 ns of the system coherence. The photon bunching is absent at a pumping level substantially below the condensation threshold. The effect of bunching also decreases at pumping significantly above the threshold, when the narrow exciton condensate line starts to dominate in the luminescence spectra, and finally disappears with the further increase in the optical excitation. In this region, the distribution of pair photon correlations is a Poisson distribution manifesting the united quantum coherent state of the exciton condensate. Under the same conditions, the first-order spatial correlation function g (1)(r) determined from the interference pattern of the luminescence signals from the spatially separated parts of the condensate at constant pumping remains noticeable at distances of no less than 4 μm. The discovered effect of photon bunching is very sensitive to temperature and decreases by several times with a temperature increase in the range of 0.45–4.2 K. Assuming that the luminescence of the dipolar excitons directly reflects the coherence properties of the gas of interacting excitons, the discovered photon bunching at the onset of condensation, where the fluctuations of the exciton density and, consequently, of the luminescence intensity are most significant, indicates a phase transition in the interacting Bose gas of excitons, which is an independent way of detecting the Bose-Einstein condensation of excitons.
BEC of exciton-polaritons and related effects such as superfluidity1,2, spontaneous symmetry breaking3,4 and quantised vortices5,6 open way to creation of novel light sources7 and optical logic elements8. Remarkable observations of exciton-polariton BEC in microcavities9-12 have been reported in the recent ten years. Very recently, thermalisation and subsequent condensation of cavity photons in a dye-filled microcavity have been observed13. Here we show that BEC of both exciton-polaritons and photons can be created in the same system under different optical excitation conditions. A dynamic phase transition between a photon and a polariton BEC takes place after a single high-power excitation pulse and we find both condensed states in thermal equilibrium with the excited states. At the crossover, photons and polaritons coexist, which results in a decrease in the long-range spatial coherence. Build-up and successive depinning of polarisation is observed at the threshold of both polariton and photon condensation.
The crossover between low and high density regimes of exciton-polariton condensates is examined using a BCS wave-function approach. Our approach is an extension of the BEC-BCS crossover theory for excitons, but includes a cavity photon field. The approach can describe both the low density limit, where the system can be described as a Bose-Einstein condensate (BEC) of exciton-polaritons, and the high density limit, where the system enters a photon-dominated regime. In contrast to the exciton BEC-BCS crossover where the system approaches an electron-hole plasma, the polariton high density limit has strongly correlated electron-hole pairs. At intermediate densities, there is a regime with BCS-like properties, with a peak at nonzero momentum of the singlet pair function. We calculate the expected photoluminescence and give several experimental signatures of the crossover.
We study theoretically the correlation properties of exciton-polaritons in planar microcavities under pulsed excitation. In particular, we analyze the quantum statistics of two pseudo-spin components of an exciton-polariton condensate in the course of its formation. Below the bosonic condensation threshold, the statistics of two components correspond to a chaotic thermal state, while above the threshold, the coherence is built up, and the photons emitted by different spin components of the condensate become anticorrelated. This spin antibunching effect can be evidenced by spin-resolved Hanbury-Brown and Twiss spectroscopy of polariton lasers.
We theoretically investigate the many-body states of exciton polaritons that can be observed by pump-probe spectroscopy in high-Q inorganic microcavities. Here, a weak-probe "spin-down" polariton is introduced into a coherent state of "spin-up" polaritons created by a strong pump. We show that the ↓ impurities become dressed by excitations of the ↑ medium, and that they form new polaronic quasiparticles that feature two-point and three-point many-body quantum correlations that, in the low density regime, arise from coupling to the vacuum biexciton and triexciton states, respectively. In particular, we find that these correlations generate additional branches and avoided crossings in the ↓ optical transmission spectrum that have a characteristic dependence on the ↑-polariton density. Our results thus demonstrate a way to directly observe correlated many-body states in an exciton-polariton system that go beyond classical mean-field theories.