Many-body solitonlike states of the bosonic ideal gas

Ołdziejewski, Rafał; Górecki, Wojciech; Pawłowski, Krzysztof; Rza̧żewski, Kazimierz

doi:10.1103/physreva.97.063617

Cited by 14 publications

(25 citation statements)

References 35 publications

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“…The value of r, in this case, equals the characteristic length of the attractive part of van der Waals interactions for dysprosium atoms [80]. We initially set a and ω ⊥ corresponding to the usual situation where the yrast states rather resemble the lowest excitation branch from the Lieb-Liniger model [63,64] and compare their energies (black squares in figure 1(a)) with the Bogoliubov spectrum (black dashed line) given by:…”

Section: Resultsmentioning

confidence: 99%

“…How does the calculated g 2 function correspond to an experimental imaging of particles positions using a CCD camera? Having a many-body wave function of a given eigenstate, in particular the roton state, we can explore a multivariate probability distribution of particles positions in a following way [62,64]. Using Metropolis algorithm we draw N positions from the multi particle probability distribution…”

Section: Resultsmentioning

confidence: 99%

“…x i is randomly placed in accordance with a rotationally uniform distribution [64]. On the other hand, the distances between particles in each configuration are translationally invariant and may reveal any potentially hidden pair correlations for a given eigenstate.Indeed, the probability distribution of the inter particle distances is directly related to the g 2 (x) function.…”

Section: Resultsmentioning

confidence: 99%

“…To fully comprehend the difference between the two types of low-energy excitations we study the probability = á ñ ( )ˆ † P k a a N k k 1 of finding a single-particle moving with momentum k for yrast states with various K. For both weak and strong interactions the type-II yrast states (black markers in figures 1(d) and 2(d)) for > K 1 beside k=0 mainly consists of k=1 states, which is more visible as we increase K. It corresponds to a dominant role of one of the Dicke states (exactly K atoms with k = 1 and N − K with k = 0) in their many-body wave function [63,64], especially for weak interactions. On the other hand, in the rotonic cases (red markers in figures 1(d) and 2(d)) we observe a local maximum of P(k) for k=K rot for the yrast states with K rot , which clearly resembles recently published result by Ferlaino's group [40].…”

Section: Resultsmentioning

confidence: 99%

“…max max , as one would expect for the Bogoliubov excitations [64]. The latter state is important from the fundamental point of view, as representative of an entanglement class [87], and applied side -it can be used to beat the standard quantum limit for the metrological tasks [88].…”

Section: Discussionmentioning

confidence: 95%

See 4 more Smart Citations

Roton in a few-body dipolar system

Ołdziejewski¹,

Górecki²,

Pawłowski³

et al. 2018

New J. Phys.

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We solve numerically exactly the many-body 1D model of bosons interacting via short-range and dipolar forces and moving in the box with periodic boundary conditions. We show that the lowest energy states with fixed total momentum can be smoothly transformed from the typical states of collective character to states resembling single particle excitations. In particular, we identify the celebrated roton state. The smooth transition is realized by simultaneous tuning short-range interactions and adjusting a trap geometry. With our methods we study the weakly interacting regime as well as the regime beyond the range of validity of the Bogoliubov approximation.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 95%

See 3 more Smart Citations

Roton in a few-body dipolar system

Ołdziejewski¹,

Górecki²,

Pawłowski³

et al. 2018

New J. Phys.

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Construction of quantum dark soliton in one-dimensional Bose gas

Kaminishi

Mori

Miyashita

2020

J. Phys. B: At. Mol. Opt. Phys.

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Dark soliton solutions in the one-dimensional classical nonlinear Schrödinger equation has been considered to be related to the yrast states corresponding to the type-II excitations in the Lieb-Liniger model. However, the relation is nontrivial and remains unclear because a dark soliton localized in space breaks the translation symmetry, while yrast states are translationally invariant. In this work, we construct a symmetry-broken quantum soliton state and investigate the relation to the yrast states. By interpreting a quantum dark soliton as a Bose-Einstein condensation to the wave function of a classical dark soliton, we find that the quantum soliton state has a large weight only on the yrast states, which is analytically proved in the free-boson limit and numerically verified in the weak-coupling regime. By extending these results, we derive a parameter-free expression of a quantum soliton state that is written as a superposition of yrast states with Gaussian weights. The density profile of this quantum soliton state excellently agrees to that of the classical dark soliton. The dynamics of a quantum dark soliton is also studied, and it turns out that the density profile of a dark soliton decays, but the decay time increases as the inverse of the coupling constant in the weak-coupling limit.

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

Syrwid

2021

J. Phys. B: At. Mol. Opt. Phys.

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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.

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Many-body solitonlike states of the bosonic ideal gas

Cited by 14 publications

References 35 publications

Roton in a few-body dipolar system

Roton in a few-body dipolar system

Construction of quantum dark soliton in one-dimensional Bose gas

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

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