Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userScaling properties of the Tans contact: embedding pairs and correlation effect in the Tonks limit
221
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We study the Tans contact of a one dimensional quantum gas of N repulsive identical bosons confined in a harmonic trap at finite temperature. This canonical ensemble framework corresponds to the experimental conditions, the number of particles being fixed for each experimental sequence. We show that, in the strongly interacting regime, the contact rescaled by the contact at the Tonks-Girardeau limit is an universal function of two parameters, the rescaled interaction strength and temperature. This means that all pair and correlation effects in the Tans contact are embedded in the Tans contact in the Tonks-Girardeau limit.
rate research
Read More
We show that the contact parameter of N harmonically-trapped interacting 1D bosons at zero temperature can be analytically and accurately obtained by a simple rescaling of the exact two-boson solution, and that N-body effects can be almost factorized. The small deviations observed between our analytical results and DMRG calculations are more pronounced when the interaction energy is maximal (i.e. at intermediate interaction strengths) but they remain bounded by the large-N local-density approximation obtained from the Lieb-Liniger equation of state stemming from the Bethe Ansatz. The rescaled two-body solution is so close to the exact ones, that is possible, within a simple expression interpolating the rescaled two-boson result to the local-density, to obtain N-boson contact and ground state energy functions in very good agreement with DMRG calculations. Our results suggest a change of paradigm in the study of interacting quantum systems, giving to the contact parameter a more fundamental role than energy.
We compute the Tans contact of a weakly interacting Bose gas at zero temperature in a cigar-shaped configuration. Using an effective one-dimensional Gross-Pitaeskii equation and Bogoliubov theory, we derive an analytical formula that interpolates between the three-dimensional and the one-dimensional mean-field regimes. In the strictly one-dimensional limit, we compare our results with Lieb-Liniger theory. Our study can be a guide for actual experiments interested in the study of Tans contact in the dimensional crossover.
Tans contact is a quantity that unifies many different properties of a low-temperature gas with short-range interactions, from its momentum distribution to its spatial two-body correlation function. Here, we use a Ramsey interferometric method to realize experimentally the thermodynamic definition of the two-body contact, i.e. the change of the internal energy in a small modification of the scattering length. Our measurements are performed on a uniform two-dimensional Bose gas of $^{87}$Rb atoms across the Berezinskii-Kosterlitz-Thouless superfluid transition. They connect well to the theoretical predictions in the limiting cases of a strongly degenerate fluid and of a normal gas. They also provide the variation of this key quantity in the critical region, where further theoretical efforts are needed to account for our findings.
We study Tans contact, i.e. the coefficient of the high-momentum tails of the momentum distribution at leading order, for an interacting one-dimensional Bose gas subjected to a harmonic confinement. Using a strong-coupling systematic expansion of the ground-state energy of the homogeneous system stemming from the Bethe-Ansatz solution, together with the local-density approximation, we obtain the strong-coupling expansion for Tans contact of the harmonically trapped gas. Also, we use a very accurate conjecture for the ground-state energy of the homogeneous system to obtain an approximate expression for Tans contact for arbitrary interaction strength, thus estimating the accuracy of the strong-coupling expansion. Our results are relevant for ongoing experiments with ultracold atomic gases.
We study the local correlations in the super Tonks-Girardeau gas, a highly excited, strongly correlated state obtained in quasi one-dimensional Bose gases by tuning the scattering length to large negative values using a confinement-induced resonance. Exploiting a connection with a relativistic field theory, we obtain results for the two-body and three-body local correlators at zero and finite temperature. At zero temperature our result for the three-body correlator agrees with the extension of the results of Cheianov et al. [Phys. Rev. A 73, 051604(R) (2006)], obtained for the ground-state of the repulsive Lieb-Liniger gas, to the super Tonks-Girardeau state. At finite temperature we obtain that the three-body correlator has a weak dependence on the temperature up to the degeneracy temperature. We also find that for temperatures larger than the degeneracy temperature the values of the three-body correlator for the super Tonks-Girardeau gas and the corresponding repulsive Lieb-Liniger gas are rather similar even for relatively small couplings.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
