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Journal of Physics Conference Series

A dynamical probe of superfluidity in one-dimension: The adiabatic quantum pump

R. Citro

Published Dec 14, 2012• 0 citations
Publisher

Abstract

Quantum pumping as a dynamical probe of the superfluid response of a one-dimensional (1D) quantum fluid is discussed. It is shown that a spatially periodic potential, oscillating adiabatically in time with frequency ω 0 , acts as a quantum pump inducing a continuous momentum current from broken spatiotemporal symmetries of the driven potential. The momentum current generated by the pump is strongly affected by the interactions. It has a power-law dependence on the frequency and the temperature with the exponent determined by the interaction. It depends on the phase difference between two umklapp terms of the drive, providing indication for the effect of quantum phase slips on the decay of superflow. Application of the results in understanding the superfluid properties of helium confined in nanometer-size pores or of laser-cooled atoms is briefly discussed.

DOI
10.1088/1742-6596/391/1/012142

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Quantum pumping as a dynamical probe of the superfluid response of a one-dimensional (1D) quantum fluid is discussed. It is shown that a spatially periodic potential, oscillating adiabatically in time with frequency ω 0 , acts as a quantum pump inducing a continuous momentum current from broken spatiotemporal symmetries of the driven potential. The momentum current generated by the pump is strongly affected by the interactions. It has a power-law dependence on the frequency and the temperature with the exponent determined by the interaction. It depends on the phase difference between two umklapp terms of the drive, providing indication for the effect of quantum phase slips on the decay of superflow. Application of the results in understanding the superfluid properties of helium confined in nanometer-size pores or of laser-cooled atoms is briefly discussed.
Quantum pumping in an interacting one-dimensional Bose-Einstein condensate is analyzed. It is shown that a spatially periodic potential, oscillating adiabatically in time with frequency ${\ensuremath{\omega}}_{0}$, acts as a quantum pump inducing an atom current from broken spatiotemporal symmetries of the driven potential. The current generated by the pump is strongly affected by the interactions. It has a power-law dependence on the frequency with the exponent determined by the interaction, while the coupling to the pump affects the amplitudes. It depends on the phase difference between two umklapp terms of the drive, providing evidence for the full quantum character of the boson transport. The results suggest the realization of a quantum pump with laser-cooled atoms.
A theory accounting for the dynamical aspects of the superfluid response of one dimensional (1D) quantum fluids is reported. In long 1D systems, the onset of superfluidity is related to the dynamical suppression of quantum phase slips at low temperatures. The effect of this suppression as a function of frequency and temperature is discussed within the framework of the experimentally relevant momentum response function. Applications of these results to the understanding of the superfluid properties of helium confined in 1D pores with nanometer diameter, dislocations in solid 4He, and ultracold atomic gases are also briefly discussed.
We study the decay of superflow of a one-dimensional (1D) superfluid in the presence of a periodic potential. In 1D, superflow at zero temperature can decay via quantum nucleation of phase slips even when the flow velocity is much smaller than the critical velocity predicted by mean-field theories. Applying the instanton method to the O(2) quantum rotor model, we calculate the nucleation rate of quantum phase slips $\ensuremath{\Gamma}$. When the flow momentum ppp is small, we find that the nucleation rate per unit length increases algebraically with ppp as $\ensuremath{\Gamma}/L\ensuremath{\propto}{p}^{2K\ensuremath{-}2}$, where LLL is the system size and KKK is the Tomonaga-Luttinger parameter. Based on the relation between the nucleation rate and the quantum superfluid-insulator transition, we present a unified explanation on the scaling formulas of the nucleation rate for periodic, disorder, and single-barrier potentials. Using the time-evolving block decimation method, we compute the exact quantum dynamics of the superflow decay in the 1D Bose-Hubbard model at unit filling. From the numerical analyses, we show that the scaling formula is valid for the case of the Bose-Hubbard model, which can quantitatively describe Bose gases in optical lattices.
We study charge and spin pumping in an interacting one-dimensional wire. We show that a spatially periodic potential modulated in space and time acts as a quantum pump, inducing a dc--current component at zero bias. The current generated by the pump is strongly affected by the interactions. It has a power-law dependence on the frequency or temperature, with the exponent determined by the interaction in the wire, while the coupling to the pump affects the amplitudes only. We also show that pure spinpumping can be achieved without the presence of a magnetic field.
Quantum phase slips are the primary excitations in one-dimensional superfluids and superconductors at low temperatures but their existence in ultracold quantum gases has not been demonstrated yet. We now study experimentally the nucleation rate of phase slips in one-dimensional superfluids realized with ultracold quantum gases, flowing along a periodic potential. We observe a crossover between a regime of temperature-dependent dissipation at small velocity and interaction and a second regime of velocity-dependent dissipation at larger velocity and interaction. This behavior is consistent with the predicted crossover from thermally-assisted quantum phase slips to purely quantum phase slips.
Motivated by the search for an experimentally realizable high density and strongly interacting one-dimensional quantum liquid, we have performed quantum Monte Carlo simulations of bosonic helium-4 confined inside a nanopore with cylindrical symmetry. By implementing two numerical estimators of superfluidity corresponding to capillary flow and the rotating bucket experiment, we have simultaneously measured the finite size and temperature superfluid response of 4{}^{4}4He to the longitudinal and rotational motion of the walls of a nanopore. Within the two-fluid model, the portion of the normal liquid dragged along with the boundaries is dependent on the type of motion, and the resulting anisotropic superfluid density plateaus far below unity at T=0.5KT=0.5\phantom{\rule{0.16em}{0ex}}\text{K}T=0.5K. The origin of the saturation is uncovered by computing the spatial distribution of superfluidity, with only the core of the nanopore exhibiting any evidence of phase coherence. The superfluid core displays a scaling behavior consistent with Luttinger liquid theory, thereby providing an experimental test for the emergence of a one-dimensional quantum liquid.