Bose-Hubbard ground state: Extended Bogoliubov and variational methods compared with time-evolving block decimation

Danshita, Ippei; Naidon, Pascal

doi:10.1103/physreva.79.043601

Cited by 22 publications

(25 citation statements)

References 45 publications

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“…Also, increasing the filling factor at a fixed lattice size, but keeping the effective mean-field interaction νU/J fixed, causes an increase in the soliton lifetime. Since the effective strength of quantum fluctuations is quantified by U/(2νJ) in the 1D BHH [58,59], these trends clearly indicate that the soliton decay shown above is due to quantum fluctuations. A plot of these trends can be found in Fig.…”

Section: Quantum Soliton Engineeringmentioning

confidence: 94%

“…However, the substantial amount of quantum depletion and quantum entanglement present as predicted by our full quantum TEBD simulations suggests that such a theory based on noninteracting Bogoliubov quasiparticles would inevitably be inapplicable. On a related note, breakdown of BDG theory when applied to ground state properties of the 1D BHH is known to occur for interaction strengths as low as U/J 0.2 [59].…”

Section: Bogoliubov Analysismentioning

confidence: 99%

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Quantum many-body dynamics of dark solitons in optical lattices

et al. 2009

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We present a fully quantum many-body treatment of dark solitons formed by ultracold bosonic atoms in one-dimensional optical lattices. Using time-evolving block decimation to simulate the single-band Bose-Hubbard Hamiltonian, we consider the quantum dynamics of density and phase engineered dark solitons as well as the quantum evolution of mean-field dark solitons injected into the quantum model. The former approach directly models how one may create quantum entangled dark solitons in experiment. While we have already presented results regarding the latter approach elsewhere [Phys. Rev. Lett. 103, 140403 (2009)], we expand upon those results in this work. In both cases, quantum fluctuations cause the dark soliton to fill in and may induce an inelasticity in soliton-soliton collisions. Comparisons are made to the Bogoliubov theory which predicts depletion into an anomalous mode that fills in the soliton. Our many-body treatment allows us to go beyond the Bogoliubov approximation and calculate explicitly the dynamics of the system's natural orbitals.

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Section: Quantum Soliton Engineeringmentioning

confidence: 94%

Section: Bogoliubov Analysismentioning

confidence: 99%

Quantum many-body dynamics of dark solitons in optical lattices

et al. 2009

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“…To deal with the quantum dynamics of superflow of the 1D BHM Eq. (33), we use the TEBD method [33] for a periodic boundary condition [34], which allows us to accurately compute the time evolution of many-body wave functions in 1D quantum lattice systems. It has been shown in our previous work that TEBD is applicable to the problem of superflow dynamics associated with quantum phase slips [39].…”

Section: Tebd Analyses Of the Bose-hubbard Modelmentioning

confidence: 99%

Quantum phase slips in one-dimensional superfluids in a periodic potential

Danshita

Polkovnikov

2012

Phys. Rev. A

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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 Γ. When the flow momentum p is small, we find that the nucleation rate per unit length increases algebraically with p as Γ/L ∝ p 2K−2 , where L is the system size and K 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 formulae 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.

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“…For example, the self-consistent mean-field approximation [24][25][26][27][28][29] describes well the uniform Bose systems with any strong atomic interactions. But the region of applicability of this approximation can be limited for Bose atoms in a lattice at zero temperature in the vicinity of the superfluid-insulator phase transition [30].…”

Section: Introductionmentioning

confidence: 99%

Bose systems in spatially random or time-varying potentials

2009

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Bose systems, subject to the action of external random potentials, are considered. For describing the system properties, under the action of spatially random potentials of arbitrary strength, the stochastic mean-field approximation is employed. When the strength of disorder increases, the extended Bose-Einstein condensate fragments into spatially disconnected regions, forming a granular condensate. Increasing the strength of disorder even more transforms the granular condensate into the normal glass. The influence of time-dependent external potentials is also discussed. Fastly varying temporal potentials, to some extent, imitate the action of spatially random potentials. In particular, strong time-alternating potential can induce the appearance of a nonequilibrium granular condensate.

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Bose-Hubbard ground state: Extended Bogoliubov and variational methods compared with time-evolving block decimation

Cited by 22 publications

References 45 publications

Quantum many-body dynamics of dark solitons in optical lattices

Quantum many-body dynamics of dark solitons in optical lattices

Quantum phase slips in one-dimensional superfluids in a periodic potential

Bose systems in spatially random or time-varying potentials

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