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Physical review. B./Physical review. B

Dynamical phase transitions and pattern formation induced by a pulse pumping of excitons to a system near a thermodynamic instability

S. Brazovskiǐ, Natasha Kirova

Published Aug 2, 2016• 4 citations
Publisher

Abstract

We suggest a phenomenological theory of dynamical phase transitions and the subsequent spaciotemporal evolution induced by a short optical pulse in a system which is already prone to a thermodynamic instability. We address the case of pumping to excitons whose density contributes additively to the thermodynamic order parameter like for charge-transfer excitons in electronic charge-ordering transitions. To describe both thermodynamic and dynamical effects on equal footing, we adopt for the phase transition a view of the ``excitonic insulator'' (EI) and suggest a formation of the macroscopic quantum state for the pumped excitons. The double nature of the ensemble of excitons leads to an intricate time evolution: the dynamical transition between number-preserved and phase-locked regimes, macroscopic quantum oscillations from interference between the Bose condensate of excitons, and the ground state of the EI. Modeling for an extended sample shows also stratification in domains of low and high densities which evolve through local dynamical phase transitions and a sequence of domain merges.

DOI
10.1103/physrevb.94.054302

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We suggest a phenomenological theory of dynamical phase transitions and the subsequent spaciotemporal evolution induced by a short optical pulse in a system which is already prone to a thermodynamic instability. We address the case of pumping to excitons whose density contributes additively to the thermodynamic order parameter like for charge-transfer excitons in electronic charge-ordering transitions. To describe both thermodynamic and dynamical effects on equal footing, we adopt for the phase transition a view of the ``excitonic insulator'' (EI) and suggest a formation of the macroscopic quantum state for the pumped excitons. The double nature of the ensemble of excitons leads to an intricate time evolution: the dynamical transition between number-preserved and phase-locked regimes, macroscopic quantum oscillations from interference between the Bose condensate of excitons, and the ground state of the EI. Modeling for an extended sample shows also stratification in domains of low and high densities which evolve through local dynamical phase transitions and a sequence of domain merges.
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.
A dramatic stabilization of a Bose-Einstein condensate in dark spin states of two-dimensional dipolar excitons is predicted, driven by strong particle correlations which are induced by dipole-dipole interactions. This stability persists up to densities high enough to support the formation of a dark quantum liquid, where the transition to a mixed phase of dark and bright states, becomes robust against variations of system parameters and local conditions. This stabilized behavior is in accordance with puzzling recent observations of a stable dark quantum liquid. In a remarkable similarity to these observations, a model describing the dynamics of such coupled dark and bright condensates with external pumping and variable particle occupation numbers predicts a dynamical step-like dependence of the exciton density on the external pump power or on temperature. The two turning points mark the onsets of the dark and the mixed dark-bright condensates. This unique condensate dynamics demonstrates the possibility of observing new unexpected collective phenomena in coupled condensed Bose systems, where the particle number is not a conserved quantity.
The formation of a dense Bose-Einstein condensate in dark spin states of two-dimensional dipolar excitons is shown to be driven by a dynamical transition to the long-lived dark states. The condensate is stabilized by strong dipole-dipole interactions up to densities high enough for a dark quantum liquid to form. The persistence of dark condensation was observed in recent experiments. A model describing the non-equilibrium dynamics of externally driven coupled dark and bright condensates reproduces the step-like dependence of the exciton density on the pump power or on temperature. This unique condensate dynamics demonstrates the possibility of observing new unexpected collective phenomena in coupled condensed Bose systems, where the particle number is not conserved.
Strongly interacting bosons display a rich variety of quantum phases, the study of which has so far been focused in the dilute regime, at a fixed number of particles. Here we demonstrate the formation of a dense Bose-Einstein condensate in a long-lived dark spin state of 2D dipolar excitons. A dark condensate of weakly interacting excitons is very fragile, being unstable against a coherent coupling of dark and bright spin states. Remarkably, we find that strong dipole-dipole interactions stabilize the dark condensate. As a result, the dark phase persists up to densities high enough for a dark quantum liquid to form. The striking experimental observation of a step-like dependence of the exciton density on the pump power is reproduced quantitatively by a model describing the nonequilibrium dynamics of driven coupled dark and bright condensates. This unique behavior marks a dynamical condensation to dark states with lifetimes as long as a millisecond, followed by a brightening transition at high densities.
We investigate the condition for the photoinduced enhancement of an excitonic order in a two-orbital Hubbard model, which has been theoretically proposed in our previous work [Phys. Rev. B 97, 115105 (2018)], and analyze it from the viewpoint of the Rabi oscillation. Within the mean-field approximation, we simulate real-time dynamics of an excitonic insulator with a direct gap, where the pair condensation in the initial state is of BEC nature and the photoexcitation is introduced by electric dipole transitions. We first discuss that in the atomic limit our model is reduced to a two-level system that undergoes the Rabi oscillation, so that for single cycle pulses physical quantities after the photoirradiation are essentially determined by the ratio of the Rabi frequency to the pump-light frequency. Then, it is shown that this picture holds even in the case of nonzero transfer integrals where each one-particle state exhibits the Rabi oscillation leading to the enhancement of the excitonic order. We demonstrate that effects of electron-phonon interactions do not alter the results qualitatively. We also examine many-body dynamics by the exact diagonalization method on small clusters, which strongly suggests that our mechanism for the enhancement of the excitonic order survives even when quantum fluctuations are taken into account.