New trends in quantum integrability: recent experiments with ultracold atoms

Guan, Xi-Wen; He, Peng

doi:10.1088/1361-6633/ac95a9

Cited by 15 publications

(3 citation statements)

References 257 publications

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“…Furthermore, we have compared our results with that obtained from the ABACUS and SCE, and observed their discrepancies from our calculations and the nonlinear TLL theory, indicating that the Gaussian used in the ABACUS is unnecessary at a large system size. Our work offers a reliable approach to the correlation properties merely emergent in thermodynamic limit, and manifests the FFA itself as a benchmark of the state-of-art ultra-cold atom experiments in near future [64][65][66].…”

Section: Discussionmentioning

confidence: 87%

Exact results of dynamical structure factor of Lieb–Liniger model

Run-Tian

Song

Chen

et al. 2023

J. Phys. A: Math. Theor.

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The dynamical structure factor (DSF) represents a measure of dynamical density-density correlations in a quantum many-body system.Due to the complexity of many-body correlations and quantum fluctuations in a system of an infinitely large Hilbert space, such kind of dynamical correlations often impose a big theoretical challenge. For one dimensional (1D) quantum many-body systems, qualitative predictions of dynamical response functions are usually carried out by using the Tomonaga-Luttinger liquid (TLL) theory. In this scenario, a precise evaluation of the DSF for a 1D quantum system with arbitrary interaction strength remains a formidable task. In this paper, we use the form factor approach based on algebraic Bethe ansatz theory to calculate precisely the DSF of Lieb-Liniger model with an arbitrary interaction strength at a large scale of particle number. We find that the DSF for a system as large as 2000 particles enables us to depict precisely its line-shape from which the power-law singularity with corresponding exponents in the vicinities of spectral thresholds naturally emerge. It should be noted that, the advantage of our algorithm promises an access to the threshold behavior of dynamical correlation functions, further confirming the validity of nonlinear TLL theory besides Kitanine {\em et. al.} 2012 {\em J. Stat. Mech.} P09001. Finally we discuss a comparison of results with the results from the ABACUS method by J.-S. Caux 2009 {\em J. Math. Phys.} {\bf 50} 095214 as well as from the strongly coupling expansion by Brand and Cherny 2005 {\em Phys. Rev.} A {\bf 72} 033619.

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Section: Discussionmentioning

confidence: 87%

Exact results of dynamical structure factor of Lieb–Liniger model

Run-Tian

Song

Chen

et al. 2023

J. Phys. A: Math. Theor.

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“…Among these applications, ultracold chemistry is closely related to laser-cooled atoms or molecules [14,15]. Along this direction, one-dimensional ultracold atoms/molecules, which are formed by a tight confinement with a wave guide [16], play a crucial role due to their relatively simple theoretical model with rich physics [17].…”

Section: Introductionmentioning

confidence: 99%

Disassociation of a one-dimensional cold molecule via quantum scattering

Li,

Song,

Song

et al. 2023

Commun. Theor. Phys.

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Motivated by the recent experimental developments in ultracold molecules and atoms, we propose a simple theoretical model to address the disassociation, reflection, and transmission probability of a one-dimensional cold molecule via quantum scattering. First, we show the Born approximation results in the weak interaction regime. Then, by employing the Lippmann–Schwinger equation, we give the numerical solution and investigate the disassociation’s dependence on the injection momentum and the interaction strengths. We find that the maximum disassociation rate has a limit when increasing the interaction strengths and injection momentum. We expect that our model can be realized in experiments in the near future.

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“…In the last two decades, a growing interest in lowdimensional quantum many-body systems has stimulated tremendous success in both theoretical and experimental developments of quantum physics [1][2][3][4][5]. In contrast to Landau's quasi-particles emergent from condensed matter problems of higher dimensions [6,7], the bosonic collective excitations [8,9] take over the main role of low-energy physics for the one-dimensional (1D) strongly correlated systems.…”

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confidence: 99%

One-body dynamical correlation function of Lieb-Liniger model at finite temperature

Song¹,

Chen²,

Guan³

et al. 2022

Preprint

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The dynamical correlated properties of one-dimensional (1D) Bose gases provide profound understanding of novel physics emergent from collective excitations, for instance the breakdown of off-diagonal long-range order, and the establishment of Tomonaga-Luttinger liquid (TLL) theory. However, due to the non-perturbative nature of 1D many-body systems, the exact evaluation of correlation functions is notoriously difficult. Here by means of form factor approach based on algebraic Bethe ansatz and numerics, we present a thorough study on the one-body dynamical correlation function (1BDCF) of the Lieb-Liniger model at finite temperature. The influence of thermal fluctuation and dynamical interaction on the behavior of 1BDCF has been demonstrated and analyzed from various perspectives, including the spectral distribution, the line-shape of 1BDCF, and the static correlations etc. The static correlation properties, i.e. the momentum distribution and one body density matrix are shown in good agreement with the TLL prediction.

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New trends in quantum integrability: recent experiments with ultracold atoms

Cited by 15 publications

References 257 publications

Exact results of dynamical structure factor of Lieb–Liniger model

Exact results of dynamical structure factor of Lieb–Liniger model

Disassociation of a one-dimensional cold molecule via quantum scattering

One-body dynamical correlation function of Lieb-Liniger model at finite temperature

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