Nonlocal pair correlations in the one-dimensional Bose gas at finite temperature

We investigate the sensitivity with which the temperature and the chemical potential characterizing quantum gases can be measured. We calculate the corresponding quantum Fisher information matrices for both fermionic and bosonic gases. For the latter, particular attention is devoted to the situation close to the Bose-Einstein condensation transition, which we examine not only for the standard scenario in three dimensions, but also for generalized condensation in lower dimensions, where the bosons condense in a subspace of Hilbert space instead of a unique ground state, as well as condensation at fixed volume or fixed pressure. We show that Bose Einstein condensation can lead to sub-shot noise sensitivity for the measurement of the chemical potential. We also examine the influence of interactions on the sensitivity in three different models, and show that mean-field and contact interactions deteriorate the sensitivity but only slightly for experimentally accessible weak interactions.

Section: Contact Interactionmentioning

confidence: 99%

“…The quantum degenerate gas with small interactions, √ γ τ 1, is close to the ideal bosonic gas. Therefore, the g (2) function was derived in [108] within perturbation theory in the coupling constant c:…”

Section: Contact Interactionmentioning

confidence: 99%

Precision measurements of temperature and chemical potential of quantum gases

Marzolino¹,

Braun²

2013

“…First-order corrections can then be effectively described using perturbation theory, and the reduced temperature τ = T (n 1 +n 2 ) 2 allows one to distinguish between the decoherent quantum regime (DQ) for √ γ τ 1 and the DC regime with τ max{1,γ 2 } [48, 49,55]. We use Feynman diagrams to express the perturbed Gibbs free energy.…”

Section: Decoherent Regimesmentioning

confidence: 99%

Equilibrium thermodynamic properties of interacting two-component bosons in one dimension

Klauser

Caux

2011

Equilibrium thermodynamic properties of interacting two-component bosons in one dimensionKlauser, A.M.; Caux, J.S. General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. Download date: 12 May 2018PHYSICAL REVIEW A 84, 033604 (2011) The interplay of quantum statistics, interactions, and temperature is studied within the framework of the bosonic two-component theory with repulsive delta-function interaction in one dimension. We numerically solve the thermodynamic Bethe ansatz and obtain the equation of state as a function of temperature and of the interaction strength, the relative chemical potential, and either the total chemical potential or a fixed number of particles, allowing quantification of the full crossover behavior of the system between its low-temperature ferromagnetic and high-temperature unpolarized regime, and from the low coupling decoherent regime to the fermionization regime at high interaction. Equilibrium thermodynamic properties of interacting two-component bosons in one dimension

“…There is a reach literature devoted to both the first order [21,22] and the second order correlations [23][24][25][26] of the 1D or quasi-one-dimensional systems. A number of different approximate formulas for the second order correlation function in various regimes of the system parameters and temperatures are available.…”

mentioning

confidence: 99%

Density fluctuations in a quasi-one-dimensional Bose gas as observed in free expansion

Gawryluk¹,

Gajda²,

Brewczyk

2015

We study, within a framework of the classical fields approximation, the density correlations of a weakly interacting expanding Bose gas for the whole range of temperatures across the Bose-Einstein condensation threshold. We focus on elongated quasi-one-dimensional systems where there is a huge discrepancy between the existing theory and experimental results (A. Perrin et al., Nature Phys. 8, 195 (2012)). We find that the density correlation function is not reduced for temperatures below the critical one as it is predicted for the ideal gas or for a weakly interacting system within the Bogoliubov approximation. This behavior of the density correlations agrees with the above mentioned experiment with the elongated system. Although the system was much larger then studied here we believe that the behavior of the density correlation function found there is quite generic. Our theoretical studies indicate also large density fluctuations in the trap in the quasicondensate regime where only phase fluctuations were expected. We argue that the enhanced density fluctuations can originate in the presence of interactions in the system, or more precisely in the existence of spontaneous dark solitons in the elongated gas at thermal equilibrium.Correlations are the essence of any many body systems. In particular, the quantum features of the system are manifested by some unusual correlations. The first order coherence is the basic criterion used as the definition of a Bose-Einstein condensate. And indeed, very soon after observation of trapped atomic condensates the first order coherence of such systems, manifesting itself in the ability to produce the interference fringes in a two-slit experiment, had been proven [1] experimentally. Higher order correlations leading to atom bunching were established from collisions and three-body losses [2]. Although the Glauber coherence theory introduced to characterize correlations of quantum electromagnetic field is well established now, the issue of coherence of a matter field is still under intensive investigation.A Bose-Einstein condensate is a matter wave analogue of a coherent light. A very important question is how far this analogy can be pursuit. The first difference is that atoms exist in a Fock states only: the states which are the eigenstates of the particle number operator. As a consequence, the coherent state of a matter field, understood as the exact analogue of the coherent electromagnetic field, does not exist. On the other hand, the atomic field can exhibit a higher order coherence too. The coherence ought to be understood here as the ability to produce the interference patterns not only in a single-particle detection schemes, but also in a simultaneous detection of larger number of atoms. Although the phase of a number state can be arbitrary, the Fock states can interfere in a single realization of the system [3] when no averaging over global phase is performed. Therefore higher order coherence of atomic condensates, as can be observed in a single realization of the system,...