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arXiv:cond-mat/0607297 · Physical Review Letters

Melting of Discrete Vortices via Quantum Fluctuations

Chaohong Lee, Tristram J. Alexander, Yuri S. Kivshar

Published Nov 1, 2006• 41 citations
arXivHTMLPDF

Abstract

We consider nonlinear boson states with a nontrivial phase structure in the three-site Bose-Hubbard ring, quantum discrete vortices (or q vortices), and study their "melting" under the action of quantum fluctuations. We calculate the spatial correlations in the ground states to show the superfluid-insulator crossover and analyze the fidelity between the exact and variational ground states to explore the validity of the classical analysis. We examine the phase coherence and the effect of quantum fluctuations on q vortices and reveal that the breakdown of these coherent structures through quantum fluctuations accompanies the superfluid-insulator crossover.

DOI
10.1103/physrevlett.97.180408

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We consider nonlinear boson states with a nontrivial phase structure in the three-site Bose-Hubbard ring, quantum discrete vortices (or q vortices), and study their "melting" under the action of quantum fluctuations. We calculate the spatial correlations in the ground states to show the superfluid-insulator crossover and analyze the fidelity between the exact and variational ground states to explore the validity of the classical analysis. We examine the phase coherence and the effect of quantum fluctuations on q vortices and reveal that the breakdown of these coherent structures through quantum fluctuations accompanies the superfluid-insulator crossover.
Quantum fluctuations play a pivotal role in determining the ground state properties and phase transitions of ultra-cold bosonic systems. This study presents a comprehensive theoretical investigation of fluctuation effects beyond mean-field theory in dilute Bose gases, examining their impact on the superfluid–Mott insulator transition, quantum droplet formation, and critical phenomena. Beginning with the Gross–Pitaevskii mean-field framework , we systematically incorporate quantum corrections through Bogoliubov theory, yielding the Lee–Huang–Yang (LHY) energy correction scaling as . The quantum depletion quantifies the fraction of atoms driven from the condensate by zero-point fluctuations. For the Bose–Hubbard model , quantum Monte Carlo simulations establish the superfluid–Mott insulator critical point at , shifted 15% from the mean-field prediction. Critical exponents and confirm 3D XY universality. Quantum droplets in binary mixtures are stabilized by the repulsive LHY correction against mean-field collapse, with equilibrium densities matching experimental observations in K mixtures. Finite-size scaling analysis and the Ginzburg criterion delineate regimes where fluctuation effects dominate. All theoretical predictions are validated against precision measurements in ultracold atomic gases.
The Cluster Mean Field theory calculation is extended for finite temperatures to study the combined effect of quantum and thermal fluctuations on various phases arising in the spin-1 Bose Hubbard model. This investigation finds that the polar nature of the superfluid phase persists, and the density of bosons with spin component σ = 0 increases with the temperature. The phase diagram is obtained and compared with that of the single-site mean-field theory. Compressibility shows a signature of divergence at the transition from the polar superfluid phase to the normal bose liquid phase. Small thermal fluctuations are sufficient to destroy the anti-ferromagnetic, maximally entangled odd density Mott insulator phase, whereas large thermal fluctuations are needed to break the singlet formed in the even density Mott insulator phase. However, in both the cases, the insulators melt to normal bose liquid at the same temperature.
In this work we study quantum signatures of charge flipping vortices, found in the classical discrete nonlinear Schrödinger trimer, by use of the Bose-Hubbard model. We are able to identify such signatures in the quantum energy eigenstates, for instance when comparing the site amplitudes of the classical charge flipping vortices with the probability distribution over different particle configurations. It is also discussed how to construct quantum states that correspond to the classical charge flipping vortices and which effects can lead to deviations between the classical and quantum dynamics. We also examine properties of certain coherent states: classical-like quantum states that can be used to derive the classical model. Several quantum signatures are identified when studying the dynamics of these coherent states, for example, when comparing the average number of particles on a site with the classical site amplitude, when comparing the quantum and classical currents and topological charge, and when studying the evolution of the quantum probability amplitudes. The flipping of the quantum currents are found to be an especially robust feature of these states.
Abstract Quantum coherence and phase transitions are studied in a finite one‐dimensional Bose–Hubbard model using exact diagonalization under thermal fluctuations, a Stark potential, and disorder. The condensate fraction, superfluid fraction, visibility, number fluctuations, and the ‐norm of coherence are computed to characterize the Mott insulator–superfluid transition. Although finite‐size effects prevent a sharp transition, ground‐state properties reveal signatures of quantum criticality. Thermal fluctuations can enhance coherence via tunneling, a Stark potential promotes localization, and disorder suppresses global superfluidity while preserving local coherence. These results highlight how disorder, tilt, and temperature reshape coherence and offer insights for quantum simulation and strongly correlated phases. For systems up to six sites with unit filling, a spectral analysis is also performed through the metric mean gap ratio (MGR). However, limited statistics due to the small system size and computational constraints prevent a complete characterization of quantum chaos, yielding only approximate signatures.
Recent experiments on strongly interacting bosons in optical lattices have revealed the coexistence of spatially separated Mott-insulating and number-fluctuating phases. We explore the condensate properties of the number fluctuating phase trapped between the Mott-insulating regions and derive the associated collective-mode structure. We discuss the crossover of the interlayer properties between two- and three-dimensional behavior as a function of the lattice parameters and estimate the critical temperatures for the transition from the normal to superfluid state.
We develop a unified field-theoretical description of the Bose-Hubbard model that captures low-energy dynamics across the insulator-to-superfluid transition. We show that commonly used cumulant expansions about the Mott ground state fail in the superfluid phase not only quantitatively but also fundamentally, because they impose an incorrect canonical structure. Expanding instead about the appropriate mean-field saddle point, we derive an effective action in which the dynamics of fluctuations are governed by a Berry-phase term, giving rise to an emergent magnetic field in the associated oscillator description. This field encodes particle-hole symmetry breaking in both the Mott-insulator phase and the superfluid, and vanishes at the point where a pure Goldstone mode emerges. The resulting effective hydrodynamic theory admits a speed of sound that approaches the Bogoliubov limit in the weakly interacting regime, demonstrating consistency across the entire phase diagram, from the Mott-insulator to the deep superfluid regime. While the total density remains continuous within mean-field theory, we find that quantum fluctuations generate a discontinuous contribution at the quantum phase transition, which vanishes at the tip of the Mott lobe.