Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1710.10439

Generalized Josephson relation for conserved charges in multi-component bosons

Yi-Cai Zhang
View original source ↗Read source document ↗Export metadata ↓

Abstract

The Josephson relation is generalized for conserved charges in multi-component bosons. With linear response theory, a formula for derivation of generalized superfluid density is given. When there are several conserved charges, the superfluid density is generally a second order tensor in internal spin space. When the rank of Green's function matrix is one, Josephson relation is given explicitly with phase operator method. For two-component bosons, with quantum field theory, we show a generalized Hugenholtz-Pines relation hold and existence of two gapless phonons. When the interactions are $U(2)$ invariant, we show there is a gapless quadratic dispersion excitation no matter how strong the interactions are. The corresponding generalized Josephson relation is expressed with Green's function matrix elements.

Explore related subjects

cond-mat.quant-gas

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Yi-Cai Zhang. 2017-11-04. Generalized Josephson relation for conserved charges in multi-component bosons. https://doi.org/10.1103/physreva.98.033611

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Exact quantum geometry from sublattice symmetry: Closed-form solution of the quarter-flux Harper-Hofstadter model

Quantum geometry has emerged as a guiding principle across atomic and condensed-matter physics, shaping the topological responses of Bloch bands and the stability of the correlated phases they host. Sublattice symmetry, though common among bipartite lattice models, has not yet been exploited to obtain closed-form quantum geometry in multiband systems. For this purpose, we derive a general expression for the QGT of sublattice-symmetric systems in terms of contributions from the individual sublattice sectors, and show that this symmetry renders the Bloch Hamiltonian of a paradigmatic four-band model, the quarter-flux Harper-Hofstadter model, anti-block-diagonal, analytically yielding the spectrum, eigenstates, and full quantum geometric tensor (QGT), including the Berry curvature and quantum metric, for all four bands. The model, describing charged particles on a two-dimensional square lattice subjected to a uniform magnetic field, has recently been realized experimentally with ultracold atoms, photons, and superconducting circuits. Finally, we evaluate fractional-Chern-insulator stability criteria analytically and quantify the lowest band of the quarter-flux Harper-Hofstadter model to be a nearly ideal Chern band. Our approach opens a route for studying also the quantum geometry of other sublattice-symmetric multiband systems.

cond-mat.quant-gas↗
arXiv2026

Limit of Spin Squeezing in Finite Temperature Bose-Einstein Condensates

We show that, at finite temperature, the maximum spin squeezing achievable using interactions in Bose-Einstein condensates has a finite limit when the atom number $N\to \infty$ at fixed density and interaction strength. We calculate the limit of the squeezing parameter for a spatially homogeneous system and show that it is bounded from above by the initial non-condensed fraction.

cond-mat.quant-gas↗
arXiv2026

Quantum fields in a cold atomic simulator: relaxation and phase locking in tunnel-coupled 1D bosonic quasi-condensates

We consider a prime example of simulating interacting relativistic QFT with cold atoms: the realisation of the sine-Gordon model by tunnel-coupled quasi-1D Bose gases. While experiments have shown that it can realise the sine-Gordon model in equilibrium, studies of non-equilibrium dynamics have revealed phase-locking behaviour that contrasts with predictions from sine-Gordon field theory. Here, we examine a one-dimensional field-theoretic model of the system and find that the phase-locking behaviour can be understood in terms of the longitudinal harmonic trap, and that the additional degrees of freedom observed in the experiment do not appear to play a significant role. Therefore, the experimental setup provides a good simulator of the sine-Gordon quantum field theory, even out of equilibrium, if the inhomogeneous background induced by the trap is taken into account. Furthermore, our results support the idea that modifying the longitudinal trap to a box shape should result in agreement with standard sine-Gordon dynamics. The main remaining open issues are accounting for 3D corrections and modelling the effect of the boundaries.

cond-mat.quant-gas↗