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

TL;DR

This paper investigates how quantum diffusion-induced dissipation causes long-wavelength instabilities and singularities in one-dimensional condensates, leading to the formation of dissipative solitons and dynamic depletion regions.

Contribution

It introduces a dispersive KPZ-like equation for nearly-uniform condensates with quantum diffusion loss, revealing finite-time singularities and novel dissipative solitons.

Findings

Long-wavelength density fluctuations cause rapid depletion regions.

Singularities develop in finite time in the dispersive KPZ equation.

Wavefronts are described by dissipative solitons with no lossless analog.

Abstract

Dissipative systems can 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 $k\to 0$. 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 condensate -- a 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.