Dynamics and Bloch oscillations of mobile impurities in one-dimensional quantum liquids

M. Schecter; D. M. Gangardt; A. Kamenev

doi:10.1016/j.aop.2011.10.001

Dynamics and Bloch oscillations of mobile impurities in one-dimensional quantum liquids

M. Schecter, D. M. Gangardt, A. Kamenev

Physics and Astronomy (Twin Cities)

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71 Scopus citations

Abstract

We study the dynamics of a mobile impurity moving in a one-dimensional quantum liquid. Such an impurity induces a strong, non-linear depletion of the liquid around it. The dispersion relation of the combined object, called depleton, is a periodic function of its momentum with the period 2πn, where n is the mean density of the liquid. In the adiabatic approximation, a constant external force acting on the impurity leads to the Bloch oscillations of the impurity around a fixed position. Dynamically, such oscillations are accompanied by the radiation of energy in the form of phonons. The ensuing energy loss results in the uniform drift of the oscillation center. We derive exact results for the radiation-induced mobility as well as the thermal friction force in terms of the equilibrium dispersion relation of the dressed impurity (depleton). These results show that there is a wide range of external forces where the (drifted) Bloch oscillations exist and may be observed experimentally.

Original language	English (US)
Pages (from-to)	639-670
Number of pages	32
Journal	Annals of Physics
Volume	327
Issue number	3
DOIs	https://doi.org/10.1016/j.aop.2011.10.001
State	Published - Mar 2012

Bibliographical note

Funding Information:
We are indebted to L. Glazman, A. Lamacraft, M. Zvonarev, I. Lerner and J.M.F. Gunn for illuminating discussions. We also extend our gratitude to K. Matveev who pointed out an erroneous numerical factor in the thermal friction in the original version. MS and AK were supported by DOE contract DE-FG02-08ER46482 . DMG acknowledges the support by EPSRC Advanced Fellowship EP/D072514/1 . DMG and AK are thankful to Abdus Salam ICTP in Trieste for hospitality at the early stages of this work.

Keywords

1d quantum liquids
Bloch oscillations
Mobile impurity
Non-equilibrium transport
Superfluidity
Ultracold atoms

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N2 - We study the dynamics of a mobile impurity moving in a one-dimensional quantum liquid. Such an impurity induces a strong, non-linear depletion of the liquid around it. The dispersion relation of the combined object, called depleton, is a periodic function of its momentum with the period 2πn, where n is the mean density of the liquid. In the adiabatic approximation, a constant external force acting on the impurity leads to the Bloch oscillations of the impurity around a fixed position. Dynamically, such oscillations are accompanied by the radiation of energy in the form of phonons. The ensuing energy loss results in the uniform drift of the oscillation center. We derive exact results for the radiation-induced mobility as well as the thermal friction force in terms of the equilibrium dispersion relation of the dressed impurity (depleton). These results show that there is a wide range of external forces where the (drifted) Bloch oscillations exist and may be observed experimentally.

AB - We study the dynamics of a mobile impurity moving in a one-dimensional quantum liquid. Such an impurity induces a strong, non-linear depletion of the liquid around it. The dispersion relation of the combined object, called depleton, is a periodic function of its momentum with the period 2πn, where n is the mean density of the liquid. In the adiabatic approximation, a constant external force acting on the impurity leads to the Bloch oscillations of the impurity around a fixed position. Dynamically, such oscillations are accompanied by the radiation of energy in the form of phonons. The ensuing energy loss results in the uniform drift of the oscillation center. We derive exact results for the radiation-induced mobility as well as the thermal friction force in terms of the equilibrium dispersion relation of the dressed impurity (depleton). These results show that there is a wide range of external forces where the (drifted) Bloch oscillations exist and may be observed experimentally.

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KW - Ultracold atoms

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Dynamics and Bloch oscillations of mobile impurities in one-dimensional quantum liquids

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Bibliographical note

Keywords

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