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Register a new userTans contact in a cigar-shaped dilute Bose gas
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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.
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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 theoretically examine three-well interferometry in Bose-Einstein condensates using adiabatic passage. Specifically, we demonstrate that a fractional coherent transport adiabatic passage protocol enables stable spatial splitting in the presence of nonlinear interactions. A reversal of this protocol produces a coherent recombination of the BEC with a phase-dependent population of the three wells. The effect of nonlinear interactions on the interferometric measurement is quantified and found to lead to an enhancement in sensitivity for moderate interaction strengths.
The dynamics of a weakly interacting Bose gas at low temperatures is close to integrable due to the approximate quadratic nature of the many-body Hamiltonian. While the short-time physics after an abrupt ramp of the interaction constant is dominated by the integrable dynamics, integrability is broken at longer times by higher-order interaction terms in the Bogoliubov Hamiltonian, in particular by Beliaev-Landau scatterings involving three quasiparticles. The two-stage relaxation process is highlighted in the evolution of local observables such as the density-density correlation function: a dephasing mechanism leads the system to a prethermal stage, followed by true thermalization conveyed by quasiparticle collisions. Our results bring the crossover from prethermalization to thermalization within reach of current experiments with ultracold atomic gases.
Using Boltzmanns equation, we study the effect of three-body losses on the momentum distribution of a homogeneous unitary Bose gas in the dilute limit where quantum correlations are negligible. We calculate the momentum distribution of the gas and show that inelastic collisions are quantitatively as important as a second order virial correction.
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