Spontaneous symmetry breaking occurs in a physical system whenever the ground state does not share the symmetry of the underlying theory, e.g., the Hamiltonian. This mechanism gives rise to massless Nambu-Goldstone modes and massive Anderson-Higgs modes. These modes provide a fundamental understanding of matter in the Universe and appear as collective phase or amplitude excitations of an order parameter in a many-body system. The amplitude excitation plays a crucial role in determining the critical exponents governing universal nonequilibrium dynamics in the Kibble-Zurek mechanism (KZM). Here, we characterize the amplitude excitations in a spin-1 condensate and measure the energy gap for different phases of the quantum phase transition. At the quantum critical point of the transition, finite-size effects lead to a nonzero gap. Our measurements are consistent with this prediction, and furthermore, we demonstrate an adiabatic quench through the phase transition, which is forbidden at the mean field level. This work paves the way toward generating entanglement through an adiabatic phase transition.

In brane cosmology, the Big Bang is hypothesized to occur by the annihilation of the brane–anti-brane pair in a collision, where the branes are three-dimensional objects in a higher-dimensional Universe. Spontaneous symmetry breaking accompanied by the formation of lower-dimensional topological defects, e.g. cosmic strings, is triggered by the so-called ‘tachyon condensation’, where the existence of tachyons is attributable to the instability of the brane–anti-brane system. Here, we discuss the closest analogue of the tachyon condensation in atomic Bose–Einstein condensates. We consider annihilation of domain walls, namely branes, in strongly segregated two-component condensates, where one component is sandwiched by two domains of the other component. In this system, the process of the brane annihilation can be projected effectively as ferromagnetic ordering dynamics onto a two-dimensional space. Based on this correspondence, three-dimensional formation of vortices from a domain-wall annihilation is considered to be a kink formation due to spontaneous symmetry breaking in the two-dimensional space. We also discuss a mechanism to create a ‘vorton’ when the sandwiched component has a vortex string bridged between the branes. We hope that this study motivates experimental researches to realize this exotic phenomenon of spontaneous symmetry breaking in superfluid systems.

Abstract We consider the homogeneous Bose gas in the three-dimensional unit torus, where N particles interact via a two-body potential of the form $$N^{-1} v(x)$$ N - 1 v ( x ) . The system is studied at inverse temperatures of order $$N^{-2/3}$$ N - 2 / 3 , which corresponds to the temperature scale of the Bose–Einstein condensation phase transition. We show that spontaneous U (1) symmetry breaking occurs if and only if the system exhibits Bose–Einstein condensation in the sense that the one-particle density matrix of the Gibbs state has a macroscopic eigenvalue.

A phase transition describes the sudden change of state of a physical system, such as melting or freezing. Quantum gases provide the opportunity to establish a direct link between experiments and generic models that capture the underlying physics. The Dicke model describes a collective matter–light interaction and has been predicted to show an intriguing quantum phase transition. Here we realize the Dicke quantum phase transition in an open system formed by a Bose–Einstein condensate coupled to an optical cavity, and observe the emergence of a self-organized supersolid phase. The phase transition is driven by infinitely long-range interactions between the condensed atoms, induced by two-photon processes involving the cavity mode and a pump field. We show that the phase transition is described by the Dicke Hamiltonian, including counter-rotating coupling terms, and that the supersolid phase is associated with a spontaneously broken spatial symmetry. The boundary of the phase transition is mapped out in quantitative agreement with the Dicke model. Our results should facilitate studies of quantum gases with long-range interactions and provide access to novel quantum phases. The Dicke model describes a collective interaction between matter and light and has been predicted to show an intriguing quantum phase transition. A team from ETH Zurich now reports the realization of the Dicke quantum phase transition in an open system formed by a Bose–Einstein condensate (BEC) coupled to an

It is known that stable 2D solitons of the semi-vortex (SV) and mixed-mode (MM) types are maintained by the interplay of the cubic attractive nonlinearity and spin-orbit coupling (SOC) in binary Bose-Einstein condensates. We introduce a double-layer system, in which two binary condensates, stabilized by the SOC, are linearly coupled by tunneling. By means of the numerical methods, it is found that symmetric two-layer solitons undergo the spontaneous-symmetry-breaking (SSB) bifurcation of the subcritical type. The bifurcation produces families of asymmetric 2D solitons, which exist up to the value of the total norm equal to the norm of the Townes solitons, above which the collapse occurs. This situation terminates at a critical value of the inter-layer coupling, beyond which the SSB bifurcation is absent, as the collapse sets in earlier. Symmetric 2D solitons that are destabilized by the SSB demonstrate dynamical symmetry breaking, in combination with intrinsic oscillations of the solitons, or transition to the collapse, if the soliton's norm is sufficiently large. Asymmetric MMs produced by the SSB instability start spontaneous drift, in addition to the intrinsic vibrations. Consideration of moving 2D solitons is a nontrivial problem because SOC breaks the Galilean invariance. It is found that the system supports moving MMs up to a critical value of the velocity, beyond which they undergo delocalization.

Spontaneous Circulation in Ground-State Spinor Dipolar Bose-Einstein Condensates We report on a study of the spin-1 ferromagnetic Bose-Einstein condensate with magnetic dipole-dipole interactions. By solving the non-local Gross-Pitaevskii equations for this system, we find three ground-state phases. Moreover, we show that a substantial orbital angular momentum accompanied by chiral symmetry breaking emerges spontaneously in a certain parameter regime. We predict that all these phases can be observed in the spin-1 $^{87}$Rb condensate by changing the number of atoms or the trap frequency. Published as: Phys. Rev. Lett. 97, 130404 (2006) DOI: 10.1103/PhysRevLett.97.130404 arXiv categories: cond-mat.other

In this paper we consider Bose-Einstein condensates (BECs) in one-, two- and three-dimension lattice potentials. The key argument for the explanation of the transition from Superfluidity phase to Mott-Insulator phase is suggested to be the spontaneous symmetry breaking effect which occurs for critical values of the ratio between the on-site interaction term and the hopping matrix element. Such an effect can be directly seen in the Gross-Pitaevskii equation with double-well potentials and it also explains the different behavior between one-dimensional models and two/three-dimensional models.