Dark-soliton-like excitations in the Yang–Gaudin gas of attractively interacting fermions

Shamailov, Sophie S.; Brand, Joachim

doi:10.1088/1367-2630/18/7/075004

Cited by 26 publications

(60 citation statements)

References 86 publications

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“…As for equations, analogous to the mean field theory GP equation, calculations using them involve the variables µ, V . Equation (25) has been employed to calculate N D in a one-dimensional Fermi gas [10]. Notice that by substituting N D from Eqn (26) into Eqn (13) we obtain, by resorting to the canonical momentum definition (9), the equation which defines the phase jump ∆φ in terms of the derivatives of ǫ(P C , µ).…”

Section: Effective Number Of Particles and Depletion Of Particle Numbermentioning

confidence: 99%

Dynamics of solitary waves in ultracold gases in terms of observable quantities

Pitaevskiĭ¹

2016

Phys.-Usp.

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A variety of solitary waves, such as solitons, vortex rings, solitonic vortices, and more complex entities, have recently been predicted to exist. They can move in superfluid ultracold gases along elongated traps. The theoretical description of this motion requires knowledge of the inertial soliton mass and the effective number of particles in it as functions of the soliton energy. While these functions can be calculated by a microscopic theory, it is also possible to express them directly in terms of observable quantities, such as the order parameter phase jump and the particle number depletion in the soliton. In this article, the corresponding equations are derived in a simple and physically clear way and applied to the recently predicted 'magnetic soliton' in mixtures of Bose gases in various spin states.

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Section: Effective Number Of Particles and Depletion Of Particle Numbermentioning

confidence: 99%

Dynamics of solitary waves in ultracold gases in terms of observable quantities

Pitaevskiĭ¹

2016

Phys.-Usp.

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“…The thermodynamic description reveals that the strongly attractive Yang-Gaudin model is closely related to a strongly interacting gas of bosonic dimers described by the Lieb-Liniger model. That is, the ground state energy of tightly bound pairs of fermions coincides with the energy of the attractive Bose gas, described by the Lieb-Liniger model, which forms a highly excited super Tonks-Girardeau phase [75][76][77][90][91][92][93]. The latter can be described by a system of attractive hard rods [75].…”

Section: Introductionmentioning

confidence: 99%

Emergence of dark soliton signatures in a one-dimensional unpolarized attractive Fermi gas on a ring

2018

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The two-component Fermi gas with contact attractive interactions between different spin components can be described by the Yang-Gaudin model. Applying the Bethe ansatz approach, one finds analytical formulae for the system eigenstates that are uniquely parametrized by the solutions of the corresponding Bethe equations. Recent numerical studies of the so-called yrast eigenstates, i.e. lowest energy eigenstates at a given non-zero total momentum, in the Yang-Gaudin model show that their spectrum resembles yrast dispersion relation of the Lieb-Liniger model which in turn matches the dark soliton dispersion relation obtained within the nonlinear Schrödinger equation. It was shown that such conjecture in the case of the Lieb-Liniger model was not accidental and that dark soliton features emerged in the course of measurement of positions of particles, when the system was initially prepared in an yrast eigenstate. Here, we demonstrate that, starting with yrast eigenstates in the Yang-Gaudin model, the key soliton signatures are revealed by the measurement of pairs of fermions. We study soliton signatures in a wide range of the interaction strength.

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“…The missing particle number N s is closely related to the physical mass defined by equation(3). In fact, for a zero-velocity solitonic vortex[46][47][48]…”

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Asymptotically solvable model for a solitonic vortex in a compressible superfluid

Toikka

Brand

2017

New J. Phys.

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Vortex motion is a complex problem due to the interplay between the short-range physics at the vortex core level and the long-range hydrodynamical effects. Here we show that the hydrodynamic equations of vortex motion in a compressible superfluid can be solved asymptotically in a model 'slab' geometry. Starting from an exact solution for an incompressible fluid, the hydrodynamic equations are solved with a series expansion in a small tunable parameter provided by the ratio of the healing length, characterising the vortex cores, to the slab width. The key dynamical properties of the vortex, the inertial and physical masses, are well defined and renormalizable. They are calculated at leading order beyond the logarithmic accuracy that has limited previous approaches. Subtracting the asymptotic solutions of the universal hydrodynamic problem from experimental observations of vortex motion exposes the physics of the vortex core and provides a window into interesting manybody phenomena that are currently poorly understood including the role of quantum pressure. Our results provide a solid framework for further detailed study of the vortex mass and vortex forces in strongly correlated and exotic superfluids.

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Dark-soliton-like excitations in the Yang–Gaudin gas of attractively interacting fermions

Cited by 26 publications

References 86 publications

Dynamics of solitary waves in ultracold gases in terms of observable quantities

Dynamics of solitary waves in ultracold gases in terms of observable quantities

Emergence of dark soliton signatures in a one-dimensional unpolarized attractive Fermi gas on a ring

Asymptotically solvable model for a solitonic vortex in a compressible superfluid

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