Coherent states and phase transitions in a high-density exciton system

Leonid V. Keldysh

Guillermo A. Guirales, Boris A. Rodríguez, Herbert Vinck Posada

Recently, the two-dimensional nanocavity exciton-polariton system confined in semiconductor nanocavities has emerged as a promising alternative of BoseEinstein Condensate (BEC). The strong quantum correlations presents in this system, make it an unique candidate for studying entanglement and quantum phase transitions —qualitative changes in the ground state properties—. In this work, we review previous evidence, obtained by us, in the phase transitions of a finite exciton-polariton system. First, by using a BCS wave function to compute the ground state energy of N excitons without the photonic field, a crossover from the high-density electron-hole phase to the BCS excitonic phase is found, at a density which is roughly four times the close-packing density of excitons. Second, by means of a self-consistent procedure with a trial function composed of a coherent photon field and a BCS function for the electron-hole pairs, we obtain the scaling of the critical temperature with the number of polaritons. Using the method proposed originally by Olliver and Zurek, and subsequently developed by Bo Li and Zhi-Xi Wang , we calculate the discord for a generalized density operator, proposed by Blaizot

Eliezer Estrecho, Tingge Gao, Nataliya Bobrovska +9 more

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.

Leonid V. Keldysh

S. Brazovskiǐ, Natasha Kirova

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.

Leonid V. Keldysh