Nucleation in Finite Topological Systems During Continuous Metastable Quantum Phase Transitions

Fialko, O.; Delattre, Marie-Coralie; Brand, Joachim; Kolovsky, Andrey R.

doi:10.1103/physrevlett.108.250402

Cited by 33 publications

(43 citation statements)

References 31 publications

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“…References [52,53] first identified the energy-momentum dispersion relation of dark solitons with Lieb's type-II branch in the weak coupling limit, which was later extended to multi-soliton solutions [51,54,55]. Reference [56] further strengthened the connection by establishing how the localized dark solitons of mean-field theories (and experimental observations) emerge from a superposition of the translationally invariant yrast states. Syrwid and Sacha went on to demonstrate that localized density depressions typical of dark solitons emerge at random positions from the translationally invariant yrast states under a single-shot measurement procedure, where the position of the atoms is detected one-by-one [57].…”

Section: Introductionmentioning

confidence: 99%

“…They are part of the set of yrast states, which refers to the lowest energy state at given momentum 2 . By now there is mounting evidence for the association of the yrast excitations of the Lieb-Liniger model to dark solitons known to exist in the 3D BEC and found mathematically in the nonlinear Schrödinger equation [51][52][53][54][55][56][57][58][59][60]. References [52,53] first identified the energy-momentum dispersion relation of dark solitons with Lieb's type-II branch in the weak coupling limit, which was later extended to multi-soliton solutions [51,54,55].…”

Section: Introductionmentioning

confidence: 99%

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

Shamailov¹,

Brand²

2016

New J. Phys.

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Yrast states are the lowest energy states at given non-zero momentum and provide a natural extension of the concept of dark solitons to strongly interacting one-dimensional quantum gases. Here we study the yrast states of the balanced spin-1 2 Fermi gas with attractive delta-function interactions in onedimension with the exactly solvable Yang-Gaudin model. The corresponding Bethe-ansatz equations are solved for finite particle number and in the thermodynamic limit. Properties corresponding to the soliton-like nature of the yrast excitations are calculated including the missing particle number, phase step, and inertial and physical masses. The inertial to physical mass ratio, which is related to the frequency of oscillations in a trapped gas, is found to be unity in the limits of strong and weak attraction and falls to »0.78 in the crossover regime. This result is contrasted by one-dimensional mean field theory, which predicts a divergent mass ratio in the weakly attractive limit. By means of an exact mapping our results also predict the existence and properties of dark-soliton-like excitations in the super Tonks-Girardeau gas. The prospects for experimental observations are briefly discussed. I P trap 2where w trap is the frequency of the harmonic trapping potential. The mass ratio m I /m P is a non-trivial characteristic of the underlying many-body physics of the medium. For (tightly confined) atomic BECs the ratio

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Shamailov¹,

Brand²

2016

New J. Phys.

Self Cite

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“…A two orbital approximation as in [30] does not qualify as a minimal model for a superfluid circuit, but it captures one essential ingredient: as a parameter is varied a fixed-point can undergo a bifurcation. Specifically a vortex-state can bifurcate into solitons.…”

Section: Discussionmentioning

confidence: 99%

“…The phase-space of the ring model was studied within a two-orbital approximation [30]. However, such an approximation is not a valid minimal model by itself.…”

Section: Introductionmentioning

confidence: 99%

Triangular Bose-Hubbard trimer as a minimal model for a superfluid circuit

2014

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The triangular Bose-Hubbard trimer is topologically the minimal model for a BEC superfluid circuit. As a dynamical system of two coupled freedoms it has mixed phase-space with chaotic dynamics. We employ a semiclassical perspective to study triangular trimer physics beyond the conventional picture of the superfluid-to-insulator transition. From the analysis of the PeierlsNabarro energy landscape, we deduce the various regimes in the (Ω, u) parameter-space, where u is the interaction, and Ω is the superfluid rotation-velocity. We thus characterize the superfluidstability and chaoticity of the many-body eigenstates throughout the Hilbert space.

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“…We refer to the M = 2 system as the "dimer" or as a bosonics Josephson junction. We refer to the M = 3 system as the "trimer" [2,3] or as a minimal model for a superfluid circuit [4][5][6][7][8]. In the latter case there appears in the BHH an additional dimensionless parameter Φ that reflects the rotation frequency of the device.…”

Section: Introductionmentioning

confidence: 99%

Stability and stabilization of unstable condensates

Cohen¹

2015

Phys. Scr.

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It is possible to condense a macroscopic number of bosons into a single mode. Adding interactions the question arises whether the condensate is stable. For repulsive interaction the answer is positive with regard to the ground-state, but what about a condensation in an excited mode? We discuss some results that have been obtained for a 2-mode bosonic Josephson junction, and for a 3-mode minimal-model of a superfluid circuit. Additionally we mention the possibility to stabilize an unstable condensate by introducing periodic or noisy driving into the system: this is due to the Kapitza and the Zeno effects.

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Nucleation in Finite Topological Systems During Continuous Metastable Quantum Phase Transitions

Cited by 33 publications

References 31 publications

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

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

Triangular Bose-Hubbard trimer as a minimal model for a superfluid circuit

Stability and stabilization of unstable condensates

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