Dynamics Of Spontaneous Symmetry Breaking Research Articles

Dynamics of spontaneous symmetry breaking in a space-time crystal

We present the theory of spontaneous symmetry breaking (SSB) of discrete time translations as recently realized in the space-time crystals of an atomic Bose-Einstein condensate. The non-equilibrium physics related to such a driven-dissipative system is discussed in both the Langevin as well as the Fokker-Planck formulation. We consider a semi-classical and a fully quantum approach, depending on the dissipation being either frequency independent or linearly dependent on frequency, respectively. For both cases, the Langevin equation and Fokker-Planck equation are derived, and the resulting equilibrium distribution is studied. We also study the time evolution of the space-time crystal and focus in particular on its formation and the associated dynamics of the spontaneous breaking of a Z2 symmetry out of the symmetry unbroken phase, i.e., the equilibrium Bose-Einstein condensate before the periodic drive is turned on. Finally, we compare our results with experiments and conclude that our theory provides a solid foundation for the observations.

Nonequilibrium dynamics of spontaneous symmetry breaking into a hidden state of charge-density wave

Nonequilibrium phase transitions play a pivotal role in broad physical contexts, from condensed matter to cosmology. Tracking the formation of nonequilibrium phases in condensed matter requires a resolution of the long-range cooperativity on ultra-short timescales. Here, we study the spontaneous transformation of a charge-density wave in CeTe3 from a stripe order into a bi-directional state inaccessible thermodynamically but is induced by intense laser pulses. With ≈100 fs resolution coherent electron diffraction, we capture the entire course of this transformation and show self-organization that defines a nonthermal critical point, unveiling the nonequilibrium energy landscape. We discuss the generation of instabilities by a swift interaction quench that changes the system symmetry preference, and the phase ordering dynamics orchestrated over a nonadiabatic timescale to allow new order parameter fluctuations to gain long-range correlations. Remarkably, the subsequent thermalization locks the remnants of the transient order into longer-lived topological defects for more than 2 ns.

Jitter of condensation time and dynamics of spontaneous symmetry breaking in a gas of microcavity polaritons

We investigate the statistics of microcavity polariton Bose-Einstein condensation by measuring photoluminescence dynamics from a GaAs microcavity excited by single laser excitation pulses. We directly observe fluctuations (jitter) of the polariton condensation onset time and model them using a master equation for the occupancy probabilities. The jitter of the condensation onset time is an inherent property of the condensate formation and its magnitude is approximately equal to the rise time of the condensate density. We investigate temporal correlations between the emission of condensate in opposite circular or linear polarizations by measuring the second-order correlation function $g^{(2)}(t_1,t_2)$. Polariton condensation is accompanied by spontaneous symmetry breaking revealed by the occurrence of random (i.e., varying from pulse to pulse) circular and linear polarizations of the condensate emission. The degree of circular polarization generally changes its sign in the course of condensate decay, in contrast to the degree of linear polarization.

Kibble-Zurek dynamics in an array of coupled binary Bose condensates

Universal dynamics of spontaneous symmetry breaking is central to understanding the universal behavior of spontaneous defect formation in various systems from the early universe, condensed-matter systems to ultracold atomic systems. We explore the universal real-time dynamics in an array of coupled binary atomic Bose-Einstein condensates in optical lattices, which undergo a spontaneous symmetry breaking from the symmetric Rabi oscillation to the broken-symmetry self-trapping. In addition to Goldstone modes, there exist gapped Higgs modes whose excitation gap vanishes at the critical point. In the slow passage through the critical point, we analytically find that the symmetry-breaking dynamics obeys the Kibble-Zurek mechanism. From the scalings of bifurcation delay and domain formation, we numerically extract two Kibble-Zurek exponents, and , which give the static correlation-length critical exponent ν and the dynamic critical exponent z. Our approach provides an efficient way for the simultaneous determination of the critical exponents ν and z for a continuous phase transition.

Critical dynamics of spontaneous symmetry breaking in a homogeneous Bose gas

Kibble-Zurek theory models the dynamics of spontaneous symmetry breaking, which plays an important role in a wide variety of physical contexts, ranging from cosmology to superconductors. We explored these dynamics in a homogeneous system by thermally quenching an atomic gas with short-range interactions through the Bose-Einstein phase transition. Using homodyne matter-wave interferometry to measure first-order correlation functions, we verified the central quantitative prediction of the Kibble-Zurek theory, namely the homogeneous-system power-law scaling of the coherence length with the quench rate. Moreover, we directly confirmed its underlying hypothesis, the freezing of the correlation length near the transition. Our measurements agree with a beyond-mean-field theory and support the expectation that the dynamical critical exponent for this universality class is z = 3/2.

Symmetry breaking and fluctuations within stochastic mean-field dynamics: Importance of initial quantum fluctuations

Dynamics of spontaneous symmetry breaking and fluctuations in the Lipkin-Meshkov-Glick model are investigated in a stochastic mean-field approach. Different from the standard mean-field, in the stochastic approach, initial state fluctuations, are incorporated. In weak coupling, the approach perfectly reproduces the exact quantal dynamics. On the other hand, for increasing coupling strength, above the symmetry breaking threshold, the approach provides description of gross properties (i.e. time averaged behavior) of the exact quantal evolution.

Tachyonic instability and dynamics of spontaneous symmetry breaking

Spontaneous symmetry breaking usually occurs due to the tachyonic (spinodal) instability of a scalar field near the top of its effective potential at $\ensuremath{\varphi}=0.$ Naively, one might expect the field $\ensuremath{\varphi}$ to fall from the top of the effective potential and then experience a long stage of oscillations with amplitude $O(v)$ near the minimum of the effective potential at $\ensuremath{\varphi}=v$ until it gives its energy to particles produced during these oscillations. However, it was recently found that the tachyonic instability rapidly converts most of the potential energy $V(0)$ into the energy of colliding classical waves of the scalar field. This conversion, which was called ``tachyonic preheating,'' is so efficient that symmetry breaking typically completes within a single oscillation of the field distribution as it rolls towards the minimum of its effective potential [G. Felder et al., Phys. Rev. Lett. 87, 011601 (2001)]. In this paper we give a detailed description of tachyonic preheating and show that the dynamics of this process crucially depends on the shape of the effective potential near its maximum. In the simplest models where $V(\ensuremath{\varphi})\ensuremath{\sim}\ensuremath{-}{m}^{2}{\ensuremath{\varphi}}^{2}/2$ near the maximum, the process occurs solely due to the tachyonic instability, whereas in the theories $\ensuremath{-}\ensuremath{\lambda}{\ensuremath{\varphi}}^{n}$ with $n>2$ one encounters a combination of the effects of tunneling, tachyonic instability and bubble wall collisions.

Dynamics of symmetry breaking and tachyonic preheating.

We reconsider the old problem of the dynamics of spontaneous symmetry breaking (SSB) using 3D lattice simulations. We develop a theory of tachyonic preheating, which occurs due to the spinodal instability of the scalar field. Tachyonic preheating is so efficient that SSB typically completes within a single oscillation as the field rolls towards the minimum of its effective potential. We show that, contrary to previous expectations, preheating in hybrid inflation is typically tachyonic. Our results may also be relevant for the theory of the formation of topological defects and of disoriented chiral condensates in heavy ion collisions.

Dynamics of spontaneous symmetry breaking in the Weinberg-Salam theory

We argue that the existence of fundamental scalar fields constitutes a serious flaw of the Weinberg-Salam theory. A possible scheme without such fields is described. The symmetry breaking is induced by a new strongly interacting sector whose natural scale is of the order of a few TeV.