Singularities in nearly-uniform 1D condensates due to quantum diffusion

Abstract

Dissipative systems often exhibit wavelength-dependent loss rates. One prominent example is Rydberg polaritons formed by electromagnetically-induced transparency, which have long been a leading candidate for studying the physics of interacting photons and also hold promise as a platform for quantum information. In this system, dissipation is in the form of quantum diffusion, i.e., proportional to k 2 (k being the wavevector) and vanishing at long wavelengths as k → 0. Here, we show that one-dimensional condensates subject to this type of loss are unstable to long-wavelength density fluctuations in an unusual manner: after a prolonged period in which the condensate appears to relax to a uniform state, local depleted regions quickly form and spread ballistically throughout the system. We connect this behavior to the leading-order equation for the nearly-uniform condensatea dispersive analogue to the Kardar-Parisi-Zhang (KPZ) equation-which develops singularities in finite time. Furthermore, we show that the wavefronts of the depleted regions are described by purely dissipative solitons within a pair of hydrodynamic equations, with no counterpart in lossless condensates. We close by discussing conditions under which such singularities and the resulting solitons can be physically realized.

Universality class of Ising critical states with long-range losses

“…Softening such gap and allowing the noise spectrum to scale down to zero at small momenta, is the route for instances of driven-open criticality without thermal counterpart. In quadratic fermionic models [47,48] or interacting quan-tum wires [49][50][51], dissipation with non-local support in real space acting on neighboring sites in a correlated fashion [52], has been employed to achieve non-equilibrium quantum criticality. Such dissipation induces a structured noise spectrum in momentum space, that is vanishing in the infrared, and which exposes a set of modes which are asymptotically decoupled, for q → 0, from the decohering and thermalizing effect of the environment.…”