Instability-induced formation and nonequilibrium dynamics of phase defects in polariton condensates

Abstract

We study, theoretically and numerically, the onset and development of modulational instability in an incoherently pumped spatially homogeneous polariton condensate. Within the framework of mean-field theory, we identify regimes of modulational instability in two cases: 1) Strong feedback between the condensate and reservoir, which may occur in scalar condensates, and 2) Parametric scattering in the presence of polarization splitting in spinor condensates. In both cases we investigate the instability induced textures in space and time including non-equilibrium dynamics of phase dislocations and vortices. In particular we discuss the mechanism of vortex destabilization and formation of spiraling waves. We also identify the presence of topological defects, which take the form of half-vortex pairs in the spinor case, giving an "eyelet" structure in intensity and dipole type structure in the spin polarization. In the modulationally stable parameter domains, we observe formation of the phase defects in the process of condensate formation from an initially spatially incoherent low-density state. In analogy to the Kibble-Zurek type scaling for nonequilibrium phase transitions, we find that the defect density scales with the pumping rate.

Kibble-Zurek Mechanism in Topologically Nontrivial Zigzag Chains of Polariton Micropillars

“…This stability requires the interactions in the condensate to be smaller than the TE-TM splitting [48]. It allows to detect such objects in cw experiments, being advantageous with respect to the previous proposals of the KZM studies with polaritons [14,15], requiring single-pulse experiments. Fig.3 shows the results of simulations based on the numerical solution of the equation (4) with a homogeneous reservoir potential (σ = ∞) and interactions [48].…”

“…Because of the finite polariton lifetime, polariton condensation can be an out-of-equilibrium process driven by the condensation kinetics rather than by thermodynamics [12,13]. As previously pointed out [14,15], the establishment of a steady state by non-resonant pumping in an initially empty system cannot be an adiabatic process and is therefore equivalent to a quenching of the parameters of the system, leading to the appearance of topological defects.Another class of systems which possess topologically protected states are periodic lattices with topologically non-trivial band structures characterized by non-zero Chern numbers, or Zak phase, depending on their dimensionality. The most well-known examples of such systems are the topological insulators [16], Kitaev chains supporting topologically protected Majorana states [17] and dimer chains [18].…”

“…Because of the finite polariton lifetime, polariton condensation can be an out-of-equilibrium process driven by the condensation kinetics rather than by thermodynamics [12,13]. As previously pointed out [14,15], the establishment of a steady state by non-resonant pumping in an initially empty system cannot be an adiabatic process and is therefore equivalent to a quenching of the parameters of the system, leading to the appearance of topological defects.…”

Bosonic lasers: The state of the art (Review Article)

“…Mechanisms of electrically controlled bistability were also demonstrated [72] and several theoretical mechanisms of bistability with incoherent excitation remain open [40,73,74].…”

“…The resulting coherent state of polaritons is well described by a nonlinear Schrödinger equation (also known as a Gross-Pitaevskii equation), modified to account for gain and loss in the system [30]. Theoretical studies revealed that this equation supports a variety of spatially nontrivial structures, including: vortices and vortex lattices [31,32]; solitons [33][34][35][36][37]; and various other patterns [38][39][40].…”