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arXiv:1201.5015 · Physical Review A

Spatiotemporal fermionization of strongly interacting one-dimensional bosons

Vera Guarrera, Dominik Muth, Ralf Labouvie, Andreas Vogler, Giovanni Barontini, Michael Fleischhauer, Herwig Ott

Published Aug 2, 2012• 25 citations
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Abstract

Building on the recent experimental achievements obtained with scanning electron microscopy on ultracold atoms, we study one-dimensional Bose gases in the crossover between the weakly (quasicondensate) and the strongly interacting (Tonks-Girardeau) regime. We measure the temporal two-particle correlation function and compare it with calculations performed using the time-evolving block decimation algorithm. More pronounced antibunching is observed when entering the more strongly interacting regime. Even though this mimics the onset of a fermionic behavior, we highlight that the exact and simple duality between one-dimensional bosons and fermions does not hold when such a dynamical response is probed. The onset of fermionization is also reflected in the density distribution, which we measure in situ to extract the relevant parameters and to identify the different regimes. Our results show agreement between experiment and theory and give insight into the dynamics of strongly correlated many-body systems.

DOI
10.1103/physreva.86.021601

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Building on the recent experimental achievements obtained with scanning electron microscopy on ultracold atoms, we study one-dimensional Bose gases in the crossover between the weakly (quasicondensate) and the strongly interacting (Tonks-Girardeau) regime. We measure the temporal two-particle correlation function and compare it with calculations performed using the time-evolving block decimation algorithm. More pronounced antibunching is observed when entering the more strongly interacting regime. Even though this mimics the onset of a fermionic behavior, we highlight that the exact and simple duality between one-dimensional bosons and fermions does not hold when such a dynamical response is probed. The onset of fermionization is also reflected in the density distribution, which we measure in situ to extract the relevant parameters and to identify the different regimes. Our results show agreement between experiment and theory and give insight into the dynamics of strongly correlated many-body systems.
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.
Ultracold bosonic and fermionic quantum gases confined to quasi-one-dimensional (1D) geometry are promising candidates for probing fundamental concepts of Luttinger liquid (LL) physics. They can also be exploited for devising applications in quantum information processing and precision measurements. Here, we focus on 1D dipolar Bose gases, where evidence of super-strong coupling behavior has been demonstrated by analyzing the low-energy static and dynamical structures of the fluid at zero temperature by a combined reptation quantum Monte Carlo (RQMC) and bosonization approach. Fingerprints of LL behavior emerge in the whole crossover from the already strongly interacting Tonks–Girardeau at low density to a dipolar density wave regime at high density. We have also shown that a LL framework can be effectively set up and utilized to describe this strongly correlated crossover physics in the case of confined 1D geometries after using the results for the homogeneous system in LL hydrodynamic equations within a local density approximation. This leads to the prediction of observable quantities such as the frequencies of the collective modes of the trapped dipolar gas under the more realistic conditions that could be found in ongoing experiments. The present paper provides a description of the theoretical framework in which the above results have been worked out, making available all the detailed derivations of the hydrodynamic Luttinger equations for the inhomogeneous trapped gas and of the correlation functions for the homogeneous system.
A strongly correlated Luttinger-liquid behavior is found to emerge well beyond the Tonks-Girardeau (TG) regime in a one-dimensional Bose gas with dipolar repulsions at T=0T=0T=0, persisting for a wide range of densities. After combining reptation quantum Monte Carlo and bosonization techniques, we provide a unifying theory of the underlying crossover physics, evolving from the TG gas at low density into a classical quasiordered state at high density. The density dependent Luttinger parameters extracted from the numerical data provide all that is needed to determine the low-energy behavior from analytical expressions. Our quantitative predictions, in the whole crossover, for measurable quantities such as the structure factor and the momentum distribution, are estimated to be accessible in underway experiments with ultracold polar molecules.
We study the dynamics of a one-dimensional Bose gas after a sudden change of the interaction strength from zero to a finite value using the numerical time-evolving block decimation (TEBD) algorithm. It is shown that despite the integrability of the system, local quantities such as the two-particle correlation g (2) ( x , x ) attain steady-state values in a short characteristic time inversely proportional to the Tonks parameter γ and the square of the density. The asymptotic values are very close to those of a finite temperature grand canonical ensemble, with a local temperature corresponding to the initial energy and density. Non-local density–density correlations, however, approach a steady state on a much larger time scale determined by the finite propagation velocity of oscillatory correlation waves.
Dynamical fermionization refers to the phenomenon in Tonks-Girardeau gases where, upon release from harmonic confinement, the gases' momentum density profile evolves asymptotically to that of an ideal Fermi gas in the initial trap. This phenomenon has been demonstrated theoretically in hardcore and anyonic Tonks-Girardeau gases and was recently experimentally observed in a strongly interacting Bose gas. We extend this study to a one-dimensional spinor gas of arbitrary spin in the strongly interacting regime and analytically prove that the total momentum distribution after the harmonic trap is turned off approaches that of a spinless ideal Fermi gas, while the asymptotic momentum distribution of each spin component takes the same shape of the initial real space density profile of that spin component. Our work demonstrates the rich physics arising from the interplay between the spin and the charge degrees of freedom in a spinor system.
This dissertation serves as a summary of my Ph.D. work numerically studying equilibrium and non-equilibrium properties of strongly-interacting one-dimensional (1D) boson systems. This work is motivated by the fact that 1D systems are realizable and highly controllable with ultracold atoms in optical lattice and atom chip experiments. We apply a recent worm algorithmic Monte Carlo approach developed for 1D continuous systems to study their equilibrium properties, both with and without an underlying lattice. We also apply an exact lattice approach based on the Bose-Fermi mapping to check our Monte Carlo results in the Tonks-Girardeau limit, and more importantly, to study far-from-equilibrium expansion dynamics of the systems. We first study the scaling of one-particle correlations of the harmonically trapped Lieb-Liniger gas with changing temperature and interaction strength. Based on the universal behaviors of the density and momentum profiles, we are able to determine the effective parameters needed to fully characterize the system. We also find that the Tonks-Girardeau limit at low temperatures is the ideal regime for the experimental observation of the 1/k41/k^41/k4 momentum tail. An extra periodic lattice can drive the transition from superfluid to Mott insulator states. Exact and complete phase diagrams for such transitions are available only in the weak interacting and deep lattice limit, in which the system can be described using one-band Bose-Hubbard model. Beyond this limit, we use the worm algorithm in continuous space to map out the phase diagrams at various interaction strengths. We compare our phase diagrams with one-band Bose-Hubbard predictions and identify the regime where the one-band description breaks down. We introduce an inverse confined scattering solution to obtain effective Hubbard parameters, with which the Bose-Hubbard model provides correct results for strong interactions and deep lattices at unit filling. In addition to the equilibrium properties, we also study the expansion dynamics of ultracold atoms in the hard-core limit. Experimentally, this is usually achieved by turning off confining potentials and letting atoms expand in optical lattices. Theoretical studies from initial ground states predicted the occurrence of fermionization of the momentum distribution after long expansion times. In addition, quasicondensation at finite momenta emerges when expanding from Mott insulating domains. Here, we develop a finite-temperature extension of the lattice approach for dynamics. We find the dynamical ferminoization of the momentum distributions at all temperatures. For expansion from initial Mott domains, we observe enhanced correlations reminiscent of dynamical quasicondensation. Surprisingly, we find the systems appear to cool down during the melting of the Mott domains. We use an emergent local Hamiltonian to understand these emergent phenomena.