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arXiv:1607.06451 · Physical Review Letters

Space-Time Vortex Driven Crossover and Vortex Turbulence Phase Transition in One-Dimensional Driven Open Condensates

Liang He, Lukas M. Sieberer, Sebastian Diehl

Published Feb 21, 2017• 44 citations
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Abstract

We find a first-order transition driven by the strength of nonequilibrium conditions of one-dimensional driven open condensates. Associated with this transition is a new stable nonequilibrium phase, space-time vortex turbulence, whose vortex density and quasiparticle distribution show strongly nonthermal behavior. Below the transition, we identify a new time scale associated with noise-activated unbound space-time vortices, beyond which, the temporal coherence function changes from a Kardar-Parisi-Zhang-type subexponential to a disordered exponential decay. Experimental realization of the nonequilibrium vortex turbulent phase is facilitated in driven open condensates with a large diffusion rate.

DOI
10.1103/physrevlett.118.085301

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We find a first-order transition driven by the strength of nonequilibrium conditions of one-dimensional driven open condensates. Associated with this transition is a new stable nonequilibrium phase, space-time vortex turbulence, whose vortex density and quasiparticle distribution show strongly nonthermal behavior. Below the transition, we identify a new time scale associated with noise-activated unbound space-time vortices, beyond which, the temporal coherence function changes from a Kardar-Parisi-Zhang-type subexponential to a disordered exponential decay. Experimental realization of the nonequilibrium vortex turbulent phase is facilitated in driven open condensates with a large diffusion rate.
We find a first order transition driven by the strength of non-equilibrium conditions of one-dimensional driven open condensates. Associated with this transition is a new stable non-equilibrium phase, space-time vortex turbulence, whose vortex density and quasiparticle distribution show strongly non-thermal behavior. Below the transition, we identify a new time scale associated with noise activated unbound space-time vortices, beyond which the temporal coherence function changes from a Kardar-Parisi-Zhang type subexponential to a disordered exponential decay. Experimental realization of the non-equilibrium vortex turbulent phase is facilitated in driven open condensates with a large diffusion rate.
We theoretically investigate the time dependence of the first-order coherence function for a one-dimensional driven dissipative nonequilibrium condensate. Simulations on the generalized Gross-Pitaevskii equation show that the characteristic time scale of exponential decay agrees with the linearized Bogoliubov theory in the regime of large interaction energy. For very weak interactions, the temporal correlation deviates from the linear theory, and instead respects the dynamic scaling of the Kardar-Parisi-Zhang universality class. This nonlinear dynamics is found to be quantitatively captured by a noisy Kuramoto-Sivashinsky equation for the phase dynamics.
We study the emergence of distinctly subdiffusive scaling in the vicinity of an anomalous nonthermal fixed point, which reflects spatio-temporally self-similar scaling dynamics, in a quasi-two-dimensional Bose gas in the superfluid phase. In this regime, the far-from-equilibrium dynamics is governed by ensembles of quantum vortices. Mutual annihilation of vortices and antivortices drives coarsening, leading to the observed scaling behavior and an algebraically growing mean inter-defect distance over time. Introducing dipolar interactions provides additional control over the anisotropy and long-range character of the interactions. This control, combined with various parameter regimes and initial conditions, allows us to explore the universality of the subdiffusive scaling near the anomalous nonthermal fixed point. Scaling exponents are extracted from occupation-number spectra, the temporal evolution of inter-defect distances, and the decay of the total vortex number. At late times, compressible excitations of the background condensate grow due to ongoing vortex-antivortex annihilation, resulting in a crossover toward diffusion-type scaling near the Gaussian nonthermal fixed point. The observed temporal scaling depends only weakly on the strength and anisotropy of the dipolar interactions, demonstrating the universality of both anomalous and diffusion-type nonthermal fixed points. Nevertheless, the dipolar case exhibits qualitatively distinct vortex-clustering behavior. In contrast to non-dipolar gases, roton excitations in anisotropic, dipolar interactions appear to suppress same-sign vortex clustering, favoring the formation of vortex dipoles and maximizing the separation between vortices of equal sign. For pure contact interaction, we additionally observe spatial scaling characteristics consistent with Kraichnan--Kolmogorov turbulence. During a universal interval, in which the characteristic length scale associated with the inter-defect distance exhibits subdiffusive power-law growth, the moments of the superfluid velocity circulation around a square contour scale as predicted from classical turbulence theory. Higher-order moments of the velocity circulation reveal intermittent deviations, which are found to be consistent with values measured in fully developed classical turbulence. Notably, the subdiffusive coarsening clearly deviates from values known in classical systems. Collectively, these results provide strong evidence for the universality of the subdiffusive scaling near the anomalous nonthermal fixed point and establish a direct connection to decaying quantum turbulence cascades, highlighting the relevance of nonthermal fixed points in turbulence theory.
We present a theoretical analysis of spatial correlations in a one-dimensional driven-dissipative nonequilibrium condensate. Starting from a stochastic generalized Gross-Pitaevskii equation, we derive a noisy Kuramoto-Sivashinsky equation for the phase dynamics. For sufficiently strong interactions, the coherence decays exponentially in close analogy to the equilibrium Bose gas. When interactions are small on a scale set by the nonequilibrium condition, we find through numerical simulations a crossover between a Gaussian and exponential decay with peculiar scaling of the coherence length on the fluid density and noise strength.
Critical dynamics of an ultracold Bose gas far from equilibrium is studied in two spatial dimensions. Superfluid turbulence is created by quenching the equilibrium state close to zero temperature. Instead of immediately rethermalizing, the system approaches a meta-stable transient state, characterized as a nonthermal fixed point. A focus is set on the vortex density and vortex-antivortex correlations which characterize the evolution towards the nonthermal fixed point and the departure to final (quasi-)condensation. Two distinct power-law regimes in the vortex-density decay are found and discussed in terms of a vortex unbinding process and a kinetic description of vortex scattering. A possible relation to decaying turbulence in classical fluids is pointed out. By comparing the results to equilibrium studies of a two-dimensional Bose gas, an intuitive understanding of the location of the nonthermal fixed point in a reduced phase space is developed.
We investigate the steady state phase diagram of two-component driven open condensates (DOCs) in one dimension. We identify a miscible–immiscible transition which is predominantly driven by gapped density fluctuations and occurs upon increasing the inter-component dissipative coupling. Below the transition in the miscible phase, we find the effective long wavelength dynamics to be described by a two-component Kardar–Parisi–Zhang (KPZ) equation that belongs to the nonequilibrium universality class of the one-dimensional single-component KPZ equation at generic choices of parameters. Our results are relevant for different experimental realizations for two-component DOCs in exciton–polariton systems.