Tan relations in one dimension

Barth, Marcus; Zwerger, W.

doi:10.1016/j.aop.2011.05.010

Cited by 157 publications

(247 citation statements)

References 58 publications

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“…By contrast, the DE momentum distribution n DE (k) appears to retain the Lorentzianlike character expected for the LL model at nonzero but small temperatures, such that quantum-degeneracy effects remain significant. We note also that the coefficient lim k→∞ k 4 n(k) of the high-momentum tail (i.e., the Tan contact [111,114,115]) in the DE is always larger than that in the CE. In the case of γ = 1 this coefficient is larger in the DE as compared to the CE by a factor of approximately two, and its value in the DE exceeds that in the CE by an increasingly large factor as γ increases, being more than an order of magnitude larger in the case of γ = 100.…”

Section: A Momentum Distributionmentioning

confidence: 99%

Relaxation dynamics of the Lieb-Liniger gas following an interaction quench: A coordinate Bethe-ansatz analysis

et al. 2015

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We investigate the relaxation dynamics of the integrable Lieb-Liniger model of contact-interacting bosons in one dimension following a sudden quench of the collisional interaction strength. The system is initially prepared in its noninteracting ground state and the interaction strength is then abruptly switched to a positive value, corresponding to repulsive interactions between the bosons. We calculate equal-time correlation functions of the nonequilibrium Bose field for small systems of up to five particles via symbolic evaluation of coordinate Bethe-ansatz expressions for operator matrix elements between Lieb-Liniger eigenstates. We characterize the relaxation of the system by comparing the time-evolving correlation functions following the quench to the equilibrium correlations predicted by the diagonal ensemble and relate the behavior of these correlations to that of the quantum fidelity between the many-body wave function and the initial state of the system. Our results for the asymptotic scaling of local second-order correlations with increasing interaction strength agree with the predictions of recent generalized thermodynamic Bethe-ansatz calculations. By contrast, third-order correlations obtained within our approach exhibit a markedly different power-law dependence on the interaction strength as the Tonks-Girardeau limit of infinitely strong interactions is approached.

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Section: A Momentum Distributionmentioning

confidence: 99%

Relaxation dynamics of the Lieb-Liniger gas following an interaction quench: A coordinate Bethe-ansatz analysis

et al. 2015

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“…For temperatures higher than ∆E the whole manifold is thermally populated, and the state of the system is described as an incoherent mixture with various symmetry components. For this high-temperature regime we estimate the Tan's contact for the gas using a thermodynamic form of the Tan's relation [23,27,28],…”

Section: Symmetry Spectroscopymentioning

confidence: 99%

“…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]. However, despite many cold atomic experimental setups are still based on a harmonic confinement [1,2], a few facts are known to date for the correspondent fermionic momentum distribution, besides the smearing of the Fermi sphere due to the inhomogeneous density of the atomic cloud.…”

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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“…Efimov bound states also play a role in the recent exploration of the unitarity limit, where the so-called Tan relations can be used to deduce properties of bulk many-body systems from basic knowledge of few-body quantities (Tan 2008a, Tan 2008b, Tan 2008c, Braaten & Platter 2008, Combescot et al 2009, Barth & Zwerger 2011, Pricoupenko 2011, Valiente et al 2011, Langmack et al 2012, Valiente 2012, Hofmann 2012, Valiente et al 2012, Werner & Castin 2012a. It turns out that macroscopic observables such as the momentum distribution of a two-component Fermi system with |a| → ∞ are universal and depend on only one parameter called the contact, C , Kuhnle et al 2010.…”

Section: New Directionsmentioning

confidence: 99%

Comparing and contrasting nuclei and cold atomic gases

Zinner¹,

Jensen²

2013

J. Phys. G: Nucl. Part. Phys.

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Abstract. The experimental revolution in ultracold atomic gas physics over the past decades have brought tremendous amounts of new insight to the world of degenerate quantum systems. Here we compare and constrast the developments of cold atomic gases with the physics of nuclei since many concepts, techniques, and nomenclatures are common to both fields. However, nuclei are finite systems with interactions that are typically much more complicated than those of ultracold atomic gases. The simularities and differences must therefore be carefully addressed for a meaningful comparison and to facilitate fruitful crossdisciplinary activity. We first consider condensates of bosonic and paired systems of fermionic particles with the mean-field description but take great care to point out potential problems in the limit of small particle numbers. Along the way we review some of the basic results of BEC and BCS theory, as well as the BCS-BEC crossover and the Fermi gas in the unitarity limit, all within the context of ultracold atoms. Subsequently, we consider the specific example of an atomic Fermi gas from a nuclear physics perspective, comparing degrees of freedom, interactions, and relevant length and energy scales of cold atoms and nuclei. Next we address some attempts in nuclear physics to transfer the concepts of condensates in nuclei that can in principle be built from bosonic alpha-particle constituents. We also consider Efimov physics, a prime example of nuclear physics transfered to cold atoms, and consider which systems are more likely to show interesting bound state spectra. Finally, we address some recent studies of the BCS-BEC crossover in light nuclei and compare them to the concepts used in ultracold atomic gases. While many-body concepts such as BEC or BCS states are applicable in both subfields, we find that the interactions and finite particle numbers in nuclei can obscure the clear meaning they have in cold atoms. On the other hand, universal results from atomic physics should have impact in certain limits of the nuclear domain. In particular, with advances in the trapping of few-body atomic systems we expect a more direct exchange of ideas and results.

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Tan relations in one dimension

Cited by 157 publications

References 58 publications

Relaxation dynamics of the Lieb-Liniger gas following an interaction quench: A coordinate Bethe-ansatz analysis

Relaxation dynamics of the Lieb-Liniger gas following an interaction quench: A coordinate Bethe-ansatz analysis

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

Comparing and contrasting nuclei and cold atomic gases

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