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Localized states and interaction-induced delocalization in Bose gases with quenched disorder

G. M. Falco, Thomas Nattermann, V. L. Pokrovsky

Published Jan 1, 2009• 11 citations
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Abstract

Very diluted Bose gas placed into a disordered environment falls into a fragmented localized state.At some critical density the repulsion between particles overcomes the disorder.The gas transits into a coherent superfluid state.In this article the geometrical and energetic characteristics of the localized state at zero temperature and the critical density at which the quantum phase transition from the localized to the superfluid state proceeds are found.

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Localized states and interaction-induced delocalization in Bose gases with quenched disorder

G. M. Falco, T. Nattermann, V. L. Pokrovsky

Very diluted Bose gas placed into a disordered environment falls into a fragmented localized state. At some critical density the repulsion between particles overcomes the disorder. The gas transits into a coherent superfluid state. In this article the geometrical and energetic characteristics of the localized state at zero temperature and the critical density at which the quantum phase transition from the localized to the superfluid state proceeds are found.

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Weakly interacting Bose gas in a random environment

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The localization-disorder paradigm is analyzed for a specific system of weakly repulsive Bose gas at zero temperature placed into a quenched random potential. We show that at low average density or weak enough interaction the particles fill deep potential wells of the random potential whose radius and depth depend on the characteristics of the random potential and the interacting gas. The localized state is the random singlet with no long-range phase correlation. At a critical density the quantum phase transition to the coherent superfluid state proceeds. We calculate the critical density in terms of the geometrical characteristics of the noise and the gas. In a finite system the ground state becomes nonergodic at very low density. For atoms in traps four different regimes are found; only one of it is superfluid. The theory is extended to lower (one and two) dimensions. Its quantitative predictions can be checked in experiments with ultracold atomic gases and other Bose systems.

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Interaction-Localization Paradigm: Bose Gas in a random Environment

V. L. Pokrovsky, G. M. Falco, Thomas Nattermann +2 more

The localization‐disorder paradigm is analyzed for a specific system of weakly repulsive Bose gas at zero temperature placed into a quenched random potential. We show that, at low average density or weak enough interaction the particles fill deep potential wells of the random potential whose radius and depth depend on the characteristics of the random potential and the interacting gas. The localized state is the random singlet with no long‐range phase correlation. At a critical density the quantum phase transition to the coherent superfluid state proceeds. We calculate the critical density in terms of the geometrical characteristics of the noise and the gas. In a finite system the ground state becomes non‐ergodic at very low density. For atoms in traps four different regimes are found, only one of it is superfluid. The theory is extended to lower (1 and 2) dimensions. Its quantitative predictions can be checked in experiments with ultracold atomic gases and other Bose‐systems.This article is an extended version of a presentation delivered by one of the authors (V.L.P.) at a Conference on Modern Trends in Theoretical Physics dedicated to the Lev Landau Centenary (Chernogolovka, Russia, June 2008).

AIP conference proceedings•Jan 1, 2009•0 citations

ORDER VIA NONLINEARITY IN RANDOMLY CONFINED BOSE GASES

Robert Graham, Axel Pelster

A Hartree–Fock mean-field theory of a weakly interacting Bose-gas in a quenched white noise disorder potential is presented. A direct continuous transition from the normal gas to a localized Bose-glass phase is found which has localized short-lived excitations with a gapless density of states and vanishing superfluid density. The critical temperature of this transition is as for an ideal gas undergoing Bose–Einstein condensation. Increasing the particle-number density a first-order transition from the localized state to a superfluid phase perturbed by disorder is found. At intermediate number densities both phases can coexist.

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Quantum Phase Transition in a Low-Dimensional Weakly Interacting Bose Gas

Luca Fontanesi

This thesis is devoted to the study of the effect of disorder on low-dimensional weakly interacting Bose gases. In particular, the disorder triggers a quantum phase transition in one dimension at zero temperature that is investigated here through the study of the long-range behaviour of the one-body density matrix. An algebraic spatial decay of the coherence marks the quasicondensate, whereas, in the case of strong disorder, an exponential decay is recovered and it characterizes the insulating Bose-glass phase. This analysis is performed using an extended Bogoliubov theory to treat low dimensional Bose gases within a density-phase approach. A systematic numerical study allowed to draw the phase diagram of 1D weakly interacting bosons. The phase boundary obeys two different power laws between interaction and disorder strength depending on the regime of the gas where the transition occurs. These relations can be explained by means of scaling arguments valid in the white noise limit and in the Thomas-Fermi regime of the Bose gas. The phase transition to a quasicondensed phase comes along with the onset of superfluidity: the inspection of the superfluid fraction of the gas is consistent with these predictions for the boundary. The finite temperature case and the scenario in two dimensions are briefly discussed. The quantum phase transition is caused by low-energy phase fluctuations that destroy the quasi-long-range order characterizing the uniform system. Within the approach presented here, the phase fluctuations are identified as the low-lying Bogoliubov modes. Their properties have been investigated in detail to understand which changes trigger the phase transition and we found that the transition to the insulating phase is accompanied by a diverging density of states and a localization length, measured through the inverse participation ratio, that diverges as a power-law with power – 1 for vanishing energy. The fragmentation of the gas is also studied: this notion is very often associated with the onset of the insulating phase. The characterization of the density fragmentation is performed by analyzing the probability distribution of the density. A density profile is defined as fragmented when the probability distribution at vanishing density is finite or divergent and this happens for a gas in the Bose-glass phase. On the contrary, the superfluid phase is characterized by a zero limiting probability of having vanishing densities. This definition is derived analytically, and confirmed by a numerical study. This fragmentation criterion is particularly suited for detecting the phase transition in experiments: when a harmonic trap is included, the transition to the insulating phase can be extracted from the statistics of the local density distribution.

•Jan 1, 2011•1 citation

Dilute Bose gas with correlated disorder: a path integral Monte Carlo study

Sebastiano Pilati, S Giorgini, M Modugno +1 more

We investigate the thermodynamic properties of a dilute Bose gas in a correlated random potential using exact path integral Monte Carlo methods. The study is carried out in continuous space and disorder is produced in the simulations by a three-dimensional (3D) speckle pattern with tunable intensity and correlation length. We calculate the shift of the superfluid transition temperature due to disorder and we highlight the role of quantum localization by comparing the critical chemical potential with the classical percolation threshold. The equation of state of the gas is determined in the regime of strong disorder, where superfluidity is suppressed and the normal phase exists down to very low temperatures. We find a T 2 dependence of the energy in agreement with the expected behavior in the Bose glass phase. We also discuss the major role played by the disorder correlation length and we make contact with a Hartree–Fock mean-field approach that holds if the correlation length is very large. The density profiles are analyzed as a function of temperature and interaction strength. Effects of localization and the depletion of the order parameter are emphasized in the comparison between local condensate and total density. At very low temperature, we find that the energy and the particle distribution of the gas are very well described by the T =0 Gross–Pitaevskii theory, even in the regime of very strong disorder.

arXiv:1002.3704•New Journal of Physics•Jul 1, 2010•54 citations
Very diluted Bose gas placed into a disordered environment falls into a fragmented localized state.At some critical density the repulsion between particles overcomes the disorder.The gas transits into a coherent superfluid state.In this article the geometrical and energetic characteristics of the localized state at zero temperature and the critical density at which the quantum phase transition from the localized to the superfluid state proceeds are found.
The localization-disorder paradigm is analyzed for a specific system of weakly repulsive Bose gas at zero temperature placed into a quenched random potential. We show that at low average density or weak enough interaction the particles fill deep potential wells of the random potential whose radius and depth depend on the characteristics of the random potential and the interacting gas. The localized state is the random singlet with no long-range phase correlation. At a critical density the quantum phase transition to the coherent superfluid state proceeds. We calculate the critical density in terms of the geometrical characteristics of the noise and the gas. In a finite system the ground state becomes nonergodic at very low density. For atoms in traps four different regimes are found; only one of it is superfluid. The theory is extended to lower (one and two) dimensions. Its quantitative predictions can be checked in experiments with ultracold atomic gases and other Bose systems.
The localization‐disorder paradigm is analyzed for a specific system of weakly repulsive Bose gas at zero temperature placed into a quenched random potential. We show that, at low average density or weak enough interaction the particles fill deep potential wells of the random potential whose radius and depth depend on the characteristics of the random potential and the interacting gas. The localized state is the random singlet with no long‐range phase correlation. At a critical density the quantum phase transition to the coherent superfluid state proceeds. We calculate the critical density in terms of the geometrical characteristics of the noise and the gas. In a finite system the ground state becomes non‐ergodic at very low density. For atoms in traps four different regimes are found, only one of it is superfluid. The theory is extended to lower (1 and 2) dimensions. Its quantitative predictions can be checked in experiments with ultracold atomic gases and other Bose‐systems.This article is an extended version of a presentation delivered by one of the authors (V.L.P.) at a Conference on Modern Trends in Theoretical Physics dedicated to the Lev Landau Centenary (Chernogolovka, Russia, June 2008).
A Hartree–Fock mean-field theory of a weakly interacting Bose-gas in a quenched white noise disorder potential is presented. A direct continuous transition from the normal gas to a localized Bose-glass phase is found which has localized short-lived excitations with a gapless density of states and vanishing superfluid density. The critical temperature of this transition is as for an ideal gas undergoing Bose–Einstein condensation. Increasing the particle-number density a first-order transition from the localized state to a superfluid phase perturbed by disorder is found. At intermediate number densities both phases can coexist.
This thesis is devoted to the study of the effect of disorder on low-dimensional weakly interacting Bose gases. In particular, the disorder triggers a quantum phase transition in one dimension at zero temperature that is investigated here through the study of the long-range behaviour of the one-body density matrix. An algebraic spatial decay of the coherence marks the quasicondensate, whereas, in the case of strong disorder, an exponential decay is recovered and it characterizes the insulating Bose-glass phase. This analysis is performed using an extended Bogoliubov theory to treat low dimensional Bose gases within a density-phase approach. A systematic numerical study allowed to draw the phase diagram of 1D weakly interacting bosons. The phase boundary obeys two different power laws between interaction and disorder strength depending on the regime of the gas where the transition occurs. These relations can be explained by means of scaling arguments valid in the white noise limit and in the Thomas-Fermi regime of the Bose gas. The phase transition to a quasicondensed phase comes along with the onset of superfluidity: the inspection of the superfluid fraction of the gas is consistent with these predictions for the boundary. The finite temperature case and the scenario in two dimensions are briefly discussed. The quantum phase transition is caused by low-energy phase fluctuations that destroy the quasi-long-range order characterizing the uniform system. Within the approach presented here, the phase fluctuations are identified as the low-lying Bogoliubov modes. Their properties have been investigated in detail to understand which changes trigger the phase transition and we found that the transition to the insulating phase is accompanied by a diverging density of states and a localization length, measured through the inverse participation ratio, that diverges as a power-law with power – 1 for vanishing energy. The fragmentation of the gas is also studied: this notion is very often associated with the onset of the insulating phase. The characterization of the density fragmentation is performed by analyzing the probability distribution of the density. A density profile is defined as fragmented when the probability distribution at vanishing density is finite or divergent and this happens for a gas in the Bose-glass phase. On the contrary, the superfluid phase is characterized by a zero limiting probability of having vanishing densities. This definition is derived analytically, and confirmed by a numerical study. This fragmentation criterion is particularly suited for detecting the phase transition in experiments: when a harmonic trap is included, the transition to the insulating phase can be extracted from the statistics of the local density distribution.
We investigate the thermodynamic properties of a dilute Bose gas in a correlated random potential using exact path integral Monte Carlo methods. The study is carried out in continuous space and disorder is produced in the simulations by a three-dimensional (3D) speckle pattern with tunable intensity and correlation length. We calculate the shift of the superfluid transition temperature due to disorder and we highlight the role of quantum localization by comparing the critical chemical potential with the classical percolation threshold. The equation of state of the gas is determined in the regime of strong disorder, where superfluidity is suppressed and the normal phase exists down to very low temperatures. We find a T 2 dependence of the energy in agreement with the expected behavior in the Bose glass phase. We also discuss the major role played by the disorder correlation length and we make contact with a Hartree–Fock mean-field approach that holds if the correlation length is very large. The density profiles are analyzed as a function of temperature and interaction strength. Effects of localization and the depletion of the order parameter are emphasized in the comparison between local condensate and total density. At very low temperature, we find that the energy and the particle distribution of the gas are very well described by the T =0 Gross–Pitaevskii theory, even in the regime of very strong disorder.