Quantum dark solitons in ultracold one-dimensional Bose and Fermi gases

Abstract

Solitons are ubiquitous phenomena that appear, among others, in the description of tsunami waves, fiber-optic communication and ultracold atomic gases. The latter systems turned out to be an excellent playground for investigations of matter-wave solitons in a quantum world. This tutorial provides a general overview of the ultracold contact interacting Bose and Fermi systems in a one-dimensional space that can be described by the renowned Lieb–Liniger and Yang–Gaudin models. Both the quantum many-body systems are exactly solvable by means of the Bethe ansatz technique, granting us a possibility for investigations of quantum nature of solitonic excitations. We discuss in details a specific class of quantum many-body excited eigenstates called yrast states and show that they are strictly related to quantum dark solitons in the both considered Bose and Fermi systems.

Drag-induced dynamical formation of dark solitons in Bose mixture on a ring

“…In the absence of drag, i.e., for g d = 0, Eqs. (1) become independent and support both bright and dark soliton solutions that for PBC can be expressed analytically in terms of Jacobi functions [84][85][86][87][88]. A stationary bright soliton in ring geometry (PBC) form spontaneously in the ground state when g α < g c = −π 2 /Lm α .…”

“…Similar many-body excitations correspond to dark solitons also in the presence of open boundary conditions [108]. For an overview see [88]. Here, we study whether current-current drag interactions can lead to yrast excitations, inducing formation of dark solitons.…”

“…A stationary bright soliton in ring geometry (PBC) form spontaneously in the ground state when g α < g c = −π 2 /Lm α . On the other hand, dark solitons are collective excitations characterized by density notches accompanied by phase slips in phase distribution ϕ and appear for any g α > 0 [88,89]. For finite rings, i.e., L < ∞, a single dark soliton always propagates with some finite velocity because the phase cyclicity condition, ϕ(L) − ϕ(0) = 2πW where the winding number W ∈ Z, requires a nonzero phase gradient to be satisfied in the presence of a solitonic phase slip.…”

Beyond Gross-Pitaevskii equation for 1D gas: quasiparticles and solitons

“…There has been a lot of effort devoted to understanding better this relation [6-14, 52, 52-55]. It has been pointed out that the GPE soliton emerges in the high order correlation function computed for the type-II excitation [9,10,55,56]. The other observation points that the solitonic shape appears also in the single-body reduced density matrix evaluated in the appropriate superpositions of the type-II excitations [8,[11][12][13]54].…”

Many-body molecule formation at a domain wall in a one-dimensional strongly interacting ultracold Fermi gas

“…1(f). Such a behavior can be tracked back to a system interacting via only contact potential undergoing an interaction quench from an infinitely repulsive Tonks-Girardeau (TG) gas [63,64] to an excited super-Tonks-Girardeau (sTG) gaslike state of infinitely attractive atoms [65,66]. The initial state we consider can be decomposed into few lowest TG eigenstates due to the spatial separation between atoms, while γ < γ crit provides an effective strong attraction, despite large g 1D .…”