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arXiv:1012.3048 · Physical Review Letters

Weakly Interacting Bose Gas in the One-Dimensional Limit

P. Krüger, Sebastian Hofferberth, I. E. Mazets, Igor Lesanovsky, Jörg Schmiedmayer

Published Dec 28, 2010• 75 citations
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Abstract

We prepare a chemically and thermally one-dimensional (1D) quantum degenerate Bose gas in a single microtrap. We introduce a new interferometric method to distinguish the quasicondensate fraction of the gas from the thermal cloud at finite temperature. We reach temperatures down to $kT\ensuremath{\approx}0.5\ensuremath{\hbar}{\ensuremath{\omega}}_{\ensuremath{\perp}}$ (transverse oscillator eigenfrequency ${\ensuremath{\omega}}_{\ensuremath{\perp}}$) when collisional thermalization slows down as expected in 1D. At the lowest temperatures the transverse-momentum distribution exhibits a residual dependence on the line density ${n}_{1\mathrm{D}}$, characteristic for 1D systems. For very low densities the approach to the transverse single-particle ground state is linear in ${n}_{1\mathrm{D}}$.

DOI
10.1103/physrevlett.105.265302

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We prepare a chemically and thermally one-dimensional (1D) quantum degenerate Bose gas in a single microtrap. We introduce a new interferometric method to distinguish the quasicondensate fraction of the gas from the thermal cloud at finite temperature. We reach temperatures down to kT\ensuremath≈0.5\ensuremathℏ\ensuremathω\ensuremath⊥kT\ensuremath{\approx}0.5\ensuremath{\hbar}{\ensuremath{\omega}}_{\ensuremath{\perp}}kT\ensuremath≈0.5\ensuremathℏ\ensuremathω\ensuremath⊥​ (transverse oscillator eigenfrequency \ensuremathω\ensuremath⊥{\ensuremath{\omega}}_{\ensuremath{\perp}}\ensuremathω\ensuremath⊥​) when collisional thermalization slows down as expected in 1D. At the lowest temperatures the transverse-momentum distribution exhibits a residual dependence on the line density n1D{n}_{1\mathrm{D}}n1D​, characteristic for 1D systems. For very low densities the approach to the transverse single-particle ground state is linear in n1D{n}_{1\mathrm{D}}n1D​.
We study the nonequilibrium dynamics of the quantum Newton's cradle in a one-dimensional (1D) Bose gas in the weakly interacting quasicondensate regime. This is the opposite regime to the original quantum Newton's cradle experiment of [Kinoshita et al., Nature 440, 900 (2006)], which was realized in the strongly interacting 1D Bose gas. Using finite temperature ccc-field methods, we calculate the characteristic relaxation rates to the final equilibrium state. Hence, we identify the different dynamical regimes of the system in the parameter space that characterizes the strength of interatomic interactions, the initial temperature, and the magnitude of the Bragg momentum used to initiate the collisional oscillations of the cradle. In all parameter regimes, we find that the system relaxes to a final equilibrium state for which the momentum distribution is consistent with a thermal distribution. For sufficiently large initial Bragg momentum, the system can undergo hundreds of repeated collisional oscillations before reaching the final thermal equilibrium. The corresponding thermalization timescales can reach tens of seconds, which is an order of magnitude smaller than in the strongly interacting regime.
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To finalize information about the accuracy of the classical field approach for the one-dimensional (1D) Bose gas, the lowest-temperature quasicondensate is studied by comparing the extended Bogoliubov model of Mora and Castin [Mora and Castin, Phys. Rev. A 67, 053615 (2003)] to its classical field analog. The parameters for which the physics is well described by matter waves are now presented for all 1D regimes and, concurrently, the optimal cutoff that best matches all observables together is also provided. This cutoff rises strongly with density when the chemical potential is higher than the thermal energy to account for kinetic energy. As a consequence, clouds that reach this coldest quantum fluctuating regime are better described using a trap basis than plane waves. This contrasts with higher-temperature clouds for which the basis choice is less important. In passing, estimates for chemical potential, density fluctuations, and kinetic and interaction energy in the low-temperature quasicondensate are obtained up to several leading terms.
We investigate the momentum distribution of weakly interacting one-dimensional (1D) Bose gases at thermal equilibrium both experimentally and theoretically. Momentum distribution of 1D Bose gases is measured using a focusing technique, whose resolution we improve via a guiding scheme. The momentum distribution compares very well with quantum Monte Carlo calculations for the Lieb-Liniger model at finite temperature, allowing for an accurate thermometry of the gas that agrees with (and improves upon) the thermometry based on in situ density fluctuation measurements. The quasicondensation crossover is investigated via two different experimental parameter sets, corresponding to the two different sides of the crossover. Classical field theory is expected to correctly describe the quasicondensation crossover of weakly interacting gases. We derive the condition of validity of the classical field theory, and find that, in typical experiments, interactions are too strong for this theory to be accurate. This is confirmed by a comparison between the classical field predictions and the numerically exact quantum Monte Carlo calculations.
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We report on the realization of a trapped one-dimensional Bose gas and its characterization by means of measuring its lowest lying collective excitations. The quantum degenerate Bose gas is prepared in a 2D optical lattice, and we find the ratio of the frequencies of the lowest compressional (breathing) mode and the dipole mode to be (omega(B)/omega(D))(2) approximately 3.1, in accordance with the Lieb-Liniger and mean-field theory. For a thermal gas we measure (omega(B)/omega(D))(2) approximately 4. By heating the quantum degenerate gas, we have studied the transition between the two regimes. For the lowest number of particles attainable in the experiment the kinetic energy of the system is similar to the interaction energy, and we enter the strongly interacting regime.