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Quantum stirring as a sensitive probe of 1D superfluidity

R. Citro, Anna Minguzzi, F. W. J. Hekking

Published Feb 7, 2009• 0 citations
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Abstract

We propose quantum stirring with a laser beam as a probe of superfluid behavior for a strongly interacting one-dimensional Bose gas confined to a ring. Within the Luttinger liquid theory framework, we calculate the fraction of stirred particles per period as a function of the stirring velocity, the interaction strength and the coupling between the stirring beam and the bosons. The fraction of stirred particles allows to probe superfluidity of the system. We find that it crosses over at a critical velocity, lower than the sound one, from a characteristic power law at high velocities to a constant at low velocities. Some experimental issues on quantum stirring in ring-trapped condensates are discussed.

Related papers

Quantum stirring in a one-dimensional Bose gas

R. Citro, Anna Minguzzi, F. W. J. Hekking

We propose quantum stirring with a laser beam as a probe of superfluidity in a strongly interacting one-dimensional Bose gas confined to a ring. Within the Luttinger liquid theory framework, we calculate the fraction of stirred particles per period as a function of the stirring velocity, the interaction strength and the coupling between the stirring beam and the bosons. The fraction of stirred particles crosses over at a critical velocity from a constant at low velocities to a characteristic power law at high velocities. The critical velocity depends on the size of the ring and vanishes in the thermodynamic limit. Details of this cross-over depend on the interaction strength and on the coupling between the stirring beam and the bosons. Our results are relevant for ongoing experiments on ring-trapped Bose-Einstein condensates.

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arXiv:0906.2314•Physical Review A•Oct 9, 2009•19 citations
We propose quantum stirring with a laser beam as a probe of superfluid behavior for a strongly interacting one-dimensional Bose gas confined to a ring. Within the Luttinger liquid theory framework, we calculate the fraction of stirred particles per period as a function of the stirring velocity, the interaction strength and the coupling between the stirring beam and the bosons. The fraction of stirred particles allows to probe superfluidity of the system. We find that it crosses over at a critical velocity, lower than the sound one, from a characteristic power law at high velocities to a constant at low velocities. Some experimental issues on quantum stirring in ring-trapped condensates are discussed.
We propose quantum stirring with a laser beam as a probe of superfluidity in a strongly interacting one-dimensional Bose gas confined to a ring. Within the Luttinger liquid theory framework, we calculate the fraction of stirred particles per period as a function of the stirring velocity, the interaction strength and the coupling between the stirring beam and the bosons. The fraction of stirred particles crosses over at a critical velocity from a constant at low velocities to a characteristic power law at high velocities. The critical velocity depends on the size of the ring and vanishes in the thermodynamic limit. Details of this cross-over depend on the interaction strength and on the coupling between the stirring beam and the bosons. Our results are relevant for ongoing experiments on ring-trapped Bose-Einstein condensates.
We propose quantum stirring with a laser beam as a probe of superfluidlike behavior for a strongly interacting one-dimensional Bose gas confined to a ring. Within the Luttinger liquid theory framework, we calculate the fraction of stirred particles per period as a function of the stirring velocity, the interaction strength, and the coupling between the stirring beam and the bosons. We show that the stirred fraction is never zero due to the presence of strong quantum fluctuations in one dimension, implying imperfect superfluid behavior under transport. Some experimental issues on quantum stirring in ring-trapped condensates are discussed.
We investigate the superfluid behavior of a Bose-Einstein condensate of 6Li^{6}\mathrm{Li}6Li molecules. In the experiment by Weimer et al. [Phys. Rev. Lett. 114, 095301 (2015)] a condensate is stirred by a weak, red-detuned laser beam along a circular path around the trap center. The rate of induced heating increases steeply above a velocity vc{v}_{c}vc​, which we define as the critical velocity. Below this velocity, the moving beam creates almost no heating. In this paper, we demonstrate a quantitative understanding of the critical velocity. Using both numerical and analytical methods, we identify the nonzero temperature, the circular motion of the stirrer, and the density profile of the cloud as key factors influencing the magnitude of vc{v}_{c}vc​. A direct comparison to the experimental data shows excellent agreement.
Using a Luttinger-liquid approach we study the quantum fluctuations of a Bose-Josephson junction, consisting of a Bose gas confined to a quasi-one-dimensional ring trap which contains a localized repulsive potential barrier. For an infinite barrier we study the one-particle and two-particle static correlation functions. For the one-body density-matrix we obtain different power-law decays depending on the location of the probe points with respect to the position of the barrier. This quasi-long-range order can be experimentally probed in principle using an interference measurement. The corresponding momentum distribution at small momenta is also shown to be affected by the presence of the barrier and to display the universal power-law behavior expected for an interacting one-dimensional fluid. We also evaluate the particle-density profile, and by comparing with the exact results in the Tonks-Girardeau limit we fix the nonuniversal parameters of the Luttinger-liquid theory. Once the parameters are determined from one-body properties, we evaluate the density-density correlation function, finding a remarkable agreement between the Luttinger-liquid predictions and the exact result in the Tonks-Girardeau limit, even at the length scale of the Friedel-like oscillations which characterize the behavior of the density-density correlation function at intermediate distance. Finally, for a large but finite barrier we use the one-body correlation function to estimate the effect of quantum fluctuations on the renormalization of the barrier height, finding a reduction in the effective Josephson coupling energy, which depends on the length of the ring and on the interaction strength.
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.
We examine the superfluid properties of a one-dimensional (1D) Bose gas in a ring trap based on the model of Lieb and Liniger. While the 1D Bose gas has nonclassical rotational inertia and exhibits quantization of velocities, the metastability of currents depends sensitively on the strength of interactions in the gas: the stronger the interactions, the faster the current decays. It is shown that the Landau critical velocity is zero in the thermodynamic limit due to the first supercurrent state, which has zero energy and finite probability of excitation. We calculate the energy dissipation rate of ring currents in the presence of weak defects, which should be observable on experimental time scales.