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

• Published in: arXiv.org
• Main Authors: Baldwin, C L, Bienias, P, Gorshkov, A V, Gullans, M J, Maghrebi, M
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 12.03.2021
• Subjects: Condensates; Depletion; Diffusion rate; Hydrodynamic equations; Physics - Pattern Formation and Solitons; Physics - Quantum Gases; Physics - Quantum Physics; Polaritons; Quantum phenomena; Singularities; Solitary waves; Wave fronts
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2103.06293

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.