High-momentum tail in the Tonks gas under harmonic confinement

Minguzzi, Anna; Vignolo, Patrizia; Tosi, M. P.

doi:10.1016/s0375-9601(02)00042-7

Cited by 104 publications

(139 citation statements)

References 17 publications

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“…Furthermore, the momentum distribution, still having a strong peak at k = 0, spreads to higher k values, revealing a universal decay ∝ k −4 in the asymptotic regime [67] due to the short-range contact interaction. Finally, exemplary one-and two-body reduced density matrices for the harmonic case can be found in Refs.…”

Section: B Strong Interactionsmentioning

confidence: 96%

Ground-state properties of ultracold trapped bosons with an immersed ionic impurity

2014

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We consider a trapped atomic ensemble of interacting bosons in the presence of a single trapped ion in a quasi-one-dimensional geometry. Our study is carried out by means of the newly developed multilayer-multiconfiguration time-dependent Hartree method for bosons, a numerical exact approach to simulate quantum many-body dynamics. In particular, we are interested in the scenario by which the ion is so strongly trapped that its motion can be effectively neglected. This enables us to focus on the atomic ensemble only. With the development of a model potential for the atom-ion interaction, we are able to numerically obtain the exact many-body ground state of the atomic ensemble in the presence of an ion. We analyze the influence of the atom number and the atom-atom interaction on the ground state properties. Interestingly, for weakly interacting atoms, we find that the ion impedes the transition from the ideal gas behavior to the Thomas-Fermi limit. Furthermore, we show that this effect can be exploited to infer the presence of the ion both in the momentum distribution of the atomic cloud and by observing the interference fringes occurring during an expansion of the quantum gas. In the strong interacting regime, the ion modifies the fragmentation process in dependence of the atom number parity which allows a clear identification of the latter in expansion experiments. Hence, we propose in both regimes experimentally viable strategies to assess the impact of the ion on the many-body state of the atomic gas. This study serves as the first building block for systematically investigating the many-body physics of such hybrid system.

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Section: B Strong Interactionsmentioning

confidence: 96%

Ground-state properties of ultracold trapped bosons with an immersed ionic impurity

2014

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“…The presence of a universal Tan's contact is a robust feature related to the interaction form only, but its value is expected to be influenced by the type of confinement the Fermi gas is subjected to, as it is indeed the case for bosons [24][25][26]. Its value for strongly interacting, homogeneous, two-component Fermi gas has been calculated both in three [27] and in one dimension [28]; for a multi-component mixture, the Bethe Ansatz exact solution [8,9,[29][30][31] has been exploited to extract a strongcoupling expansion in the thermodynamic limit [32,33].…”

Section: Introductionmentioning

confidence: 99%

High-momentum tails as magnetic-structure probes for strongly correlatedSU(κ)fermionic mixtures in one-dimensional traps

et al. 2016

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A universal k −4 decay of the large-momentum tails of the momentum distribution, fixed by Tan's contact coefficients, constitutes a direct signature of strong correlations in a short-range interacting quantum gas. Here we consider a repulsive multicomponent Fermi gas under harmonic confinement, as in the experiment of Pagano et al. [Nat. Phys. 10, 198 (2014)], realizing a gas with tunable SU (κ) symmetry. We exploit an exact solution at infinite repulsion to show a direct correspondence between the value of the Tan's contact for each of the κ components of the gas and the Young tableaux for the SN permutation symmetry group identifying the magnetic structure of the groundstate. This opens a route for the experimental determination of magnetic configurations in cold atomic gases, employing only standard (spin-resolved) time-of-flight techniques. Combining the exact result with matrix-product-states simulations, we obtain the Tan's contact at all values of repulsive interactions. We show that a local density approximation (LDA) on the Bethe-Ansatz equation of state for the homogeneous mixture is in excellent agreement with the results for the harmonically confined gas. At strong interactions, the LDA predicts a scaling behavior of the Tan's contact. This provides a useful analytical expression for the dependence on the number of fermions, number of components and on interaction strength. Moreover, using a virial approach, we study the Tan's contact behaviour at large temperatures and in the limit of infinite interactions and we show that it increases with the temperature and the number of components. At zero temperature, we predict that the weight of the momentum distribution tails increases with interaction strength and the number of components if the population per component is kept constant. This latter property was experimentally observed in Ref. [Nat. Phys. 10, 198 (2014)].

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“…In contrast, the momentum distributions showed a pronounced temperature dependence, and, to the best of our knowledge, have been unexplained by theory to date. Previous work on the momentum properties of the 1D Bose gas has focused on limiting cases [12,13,15].Here we investigate the momentum properties of the 1D Bose gas and their application to thermometry through measurements of the system kinetic energy. Our methods provide a reliable foundation for accurate thermometry in all regimes of a 1D Bose gas with repulsive interactions, including the strongly correlated regime.…”

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confidence: 99%

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confidence: 99%

Yang-Yang thermometry and momentum distribution of a trapped one-dimensional Bose gas

et al. 2012

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We describe the use of the exact Yang-Yang solutions for the one-dimensional Bose gas to enable accurate kinetic-energy thermometry based on the root-mean-square width of an experimentally measured momentum distribution. Furthermore, we use the stochastic projected Gross-Pitaevskii theory to provide a quantitative description of the full momentum distribution measurements of Van Amerongen et al. [Phys. Rev. Lett. 100, 090402 (2008)]. We find the fitted temperatures from the stochastic projected Gross-Pitaevskii approach are in excellent agreement with those determined by Yang-Yang kinetic-energy thermometry. Ultracold gases offer a unique opportunity to study fundamental problems in quantum many-body physics, allowing experimental observations to be compared directly with microscopic theories. An area of significant recent interest has been the measurement of thermodynamic relations [1][2][3]. The one-dimensional (1D) Bose gas with repulsive interactions has emerged as a paradigm system because exact solutions are available for both eigenstates [4] and thermodynamic quantities [5] (see Ref.[6] and references therein). Furthermore, this system exhibits a surprisingly rich variety of regimes [7,8] connected by broad crossovers. Most studies of the 1D Bose gas have focused on the position-space distributions [3,[8][9][10] and local correlations [7,8,[11][12][13][14], which can be directly obtained from the exact theories.A recent experiment by Van Amerongen et al.[10] measured the position and momentum distributions of a trapped 1D Bose gas throughout the crossover from an ideal gas to the quasicondensate regime. The position-space measurements were compared with the Yang-Yang (YY) thermodynamic solutions [5] within the local density approximation (LDA), and showed smooth behavior throughout the crossover. In contrast, the momentum distributions showed a pronounced temperature dependence, and, to the best of our knowledge, have been unexplained by theory to date. Previous work on the momentum properties of the 1D Bose gas has focused on limiting cases [12,13,15].Here we investigate the momentum properties of the 1D Bose gas and their application to thermometry through measurements of the system kinetic energy. Our methods provide a reliable foundation for accurate thermometry in all regimes of a 1D Bose gas with repulsive interactions, including the strongly correlated regime. This approach is reminiscent of molecular dynamics calculations, where the average kinetic energy per particle is a direct measure of the temperature [16].First, we use the exact YY thermodynamic formalism [5] to calculate the root-mean-square (rms) width of the momentum distribution, which is equivalent to determining the average kinetic energy per particle. In combination with * Current address: SRON, Netherlands Institute for Space Research, Utrecht, The Netherlands.the LDA for trapped (nonuniform) quasi-1D systems, we show how the YY kinetic energy results can be applied to accurate thermometry for a broad range of conditions that are re...

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High-momentum tail in the Tonks gas under harmonic confinement

Cited by 104 publications

References 17 publications

Ground-state properties of ultracold trapped bosons with an immersed ionic impurity

Ground-state properties of ultracold trapped bosons with an immersed ionic impurity

High-momentum tails as magnetic-structure probes for strongly correlatedSU(κ)fermionic mixtures in one-dimensional traps

Yang-Yang thermometry and momentum distribution of a trapped one-dimensional Bose gas

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