Communications in Theoretical Physics

Amplitude Squeezing of a Weakly Interacting Bose System with Spontaneous U(1) Symmetry Breaking

Jiao Zhi-Yong, Zhao-Xian Yu, Ji‐Suo Wang

Published Dec 1, 2007• 0 citations

Abstract

We study the quantum fluctuations and the amplitude squeezing of a weakly interacting Bose system with spontaneous U(1) symmetry breaking. It is found that this system can exhibit amplitude squeezing.

DOI: 10.1088/0253-6102/48/6/018

Related papers

Spontaneous U(1) Symmetry Breaking in Coupled Bose System

Ying Wang, Jinrong Xu, Li Chen +1 more

Adding a U(1) symmetry breaking term to Bogoliubov's truncated Hamiltonian H B for a weakly interacting coupled Bose system, by using the mean-field approximation rather than the c-number approximation, we find that, via a Feshbach resonance at zero temperature, the states of the coupled Bose system are generalized SU(1,1) ⊗ SU(1,1) coherent states. The Bose—Einstein condensation occurs in response to the spontaneous U(1) symmetry breaking.

Communications in Theoretical PhysicsJun 1, 20110 citations

Squeezing in the weakly interacting uniform Bose-Einstein condensate

Masudul Haque, Andrei E. Ruckenstein

We investigate the presence of squeezing in the weakly repulsive uniform Bose gas, in both the condensate mode and in the nonzero opposite-momenta mode pairs, using two different variational formulations. We explore the U(1) symmetry breaking and Goldstone's theorem in the context of a squeezed coherent variational wave function and present the associated Ward identity. We show that squeezing of the condensate mode is absent at the mean field Hartree-Fock-Bogoliubov level and emerges as a result of fluctuations about mean field as a finite volume effect, which vanishes in the thermodynamic limit. On the other hand, the squeezing of the excitations about the condensate survives the thermodynamic limit and is interpreted in terms of density-phase variables using a number-conserving formulation of the interacting Bose gas.

arXiv:cond-mat/0602080Physical Review AOct 30, 20066 citations

Scalable Spin Squeezing from Spontaneous Breaking of a Continuous Symmetry

Tommaso Comparin, Fabio Mezzacapo, Martin Robert-De-Saint-Vincent +1 more

Spontaneous symmetry breaking is a property of Hamiltonian equilibrium states which, in the thermodynamic limit, retain a finite average value of an order parameter even after a field coupled to it is adiabatically turned off. In the case of quantum spin models with continuous symmetry, we show that this adiabatic process is also accompanied by the suppression of the fluctuations of the symmetry generator-namely, the collective spin component along an axis of symmetry. In systems of S=1/2 spins or qubits, the combination of the suppression of fluctuations along one direction and of the persistence of transverse magnetization leads to spin squeezing-a much sought-after property of quantum states, both for the purpose of entanglement detection as well as for metrological uses. Focusing on the case of XXZ models spontaneously breaking a U(1) [or even SU(2)] symmetry, we show that the adiabatically prepared states have nearly minimal spin uncertainty; that the minimum phase uncertainty that one can achieve with these states scales as N^{-3/4} with the number of spins N; and that this scaling is attained after an adiabatic preparation time scaling linearly with N. Our findings open the door to the adiabatic preparation of strongly spin-squeezed states in a large variety of quantum many-body devices including, e.g., optical-lattice clocks.

arXiv:2202.08607Physical Review LettersSep 7, 202220 citations

Spontaneous U(1) Symmetry Breaking and Phase Transitions in Rotating Interacting Bose Gases

Wenming Sun

We investigate spontaneous U(1) symmetry breaking and the associated phase transitions in rotating interacting Bose gases. Using a theoretical framework that combines mean-field analysis with rotational dynamics, we analyze how rigid rotation modifies the condensate structure and critical behavior. The study identifies the emergence of Goldstone modes and clarifies their role in the low-energy excitation spectrum. The results provide insight into the interplay between symmetry, rotation, and many-body interactions, contributing to a deeper theoretical understanding of phase structures in Bose systems.

Sep 12, 20250 citations

Spontaneous symmetry breaking under Bose--Einstein condensation

Vyacheslav I. Yukalov

Due to high current interest to Bose-Einstein condensation, the related topics, such as spontaneous gauge symmetry breaking, ergodic decomposition, and particle fluctuations, are intensively discussed in literature. These discussions, unfortunately, involve quite a number of controversies and confusions. The goal of the present brief survey is to clarify some of these confusions, concentrating on the principal points, such as the relationship between the conditions of Bose-Einstein condensation, the Bogolubov method of quasiaverages, spontaneous gauge symmetry breaking, ergodic decomposition, the presumed existence of nonthermodynamic particle fluctuations leading to the so-called ``grand canonical catastrophe", and the requirements for system stability.

arXiv:2606.12606Jun 10, 20260 citations

Broken gauge symmetry in a Bose gas with constant particle number

Alexej Schelle

The interplay between spontaneously broken gauge symmetries and Bose-Einstein condensation has long been controversially discussed in science, since the equation of motions are invariant under phase transformations. Within the present model it is illustrated that spontaneous symmetry breaking appears as a non-local process in position space, but within disjoint subspaces of the underlying Hilbert space. Numerical simulations show that it is the symmetry of the relative phase distribution between condensate and non-condensate quantum fields which is spontaneously broken when passing the critical temperature for Bose-Einstein condensation. Since the total number of gas particles remains constant over time, the global U(1)-gauge symmetry of the system is preserved.

Oct 26, 20140 citations