Quantum phase transitions with parity-symmetry breaking and hysteresis

Abstract

Symmetry-breaking quantum phase transitions play a key role in several condensed matter, cosmology and nuclear physics theoretical models [1][2][3] . Its observation in real systems is often hampered by finite temperatures and limited control of the system parameters. In this work we report, for the first time, the experimental observation of the full quantum phase diagram across a transition where the spatial parity symmetry is broken. Our system consists of an ultracold gas with tunable attractive interactions trapped in a spatially symmetric double-well potential. At a critical value of the interaction strength, we observe a continuous quantum phase transition where the gas spontaneously localizes in one well or the other, thus breaking the underlying symmetry of the system. Furthermore, we show the robustness of the asymmetric state against controlled energy mismatch between the two wells. This is the result of hysteresis associated with an additional discontinuous quantum phase transition that we fully characterize. Our results pave the way to the study of quantum critical phenomena at finite temperature 4 , the investigation of macroscopic quantum tunnelling of the order parameter in the hysteretic regime and the production of strongly quantum entangled states at critical points .Parity is a fundamental discrete symmetry of nature 6 conserved by gravitational, electromagnetic and strong interactions 7 . It states the invariance of a physical phenomenon under mirror reflection. Our world is pervaded by robust discrete asymmetries, spanning from the imbalance of matter and antimatter to the homo-chirality of DNA of all living organisms 8 . Their origin and stability is a subject of active debate. Quantum mechanics predicts that asymmetric states can be the result of phase transitions occurring at zero temperature, named in the literature as quantum phase transitions (QPTs) 1,4 . The breaking of a discrete symmetry via a QPT provides also asymmetric states that are particularly robust against external perturbations. Indeed, the order parameter of a continuous-symmetry-breaking QPT can freely (with no energy cost) wander along the valley of a 'mexican hat' Ginzburg-Landau potential (GLP) by coupling with gapless Goldstone modes 9 . In contrast, the order parameter of discrete-symmetry-breaking QPTs is governed by a one-dimensional double-well GLP 10 . The reduced dimensionality suppresses Goldstone excitations, and the order parameter can remain trapped at the bottom of one of the two wells. This provides a robust hysteresis associated with a first-order QPT.Evidence of parity-symmetry breaking has been reported in relativistic heavy-ions collisions 11 and in engineered photonic crystal fibres 12 . Observation of parity-symmetry breaking in a QPT has been reported for neutral atoms coupled to a high-finesse optical cavity 13 . However, this is a strongly dissipative system, with no direct access to the symmetry-breaking mechanism necessary to study the robustness of asymmetric states. In addition, previous the...

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