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Register a new userObservation of a dissipative time crystal
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The formation of a phase of matter can be associated with the spontaneous breaking of a symmetry. For crystallization, this broken symmetry is the spatial translation symmetry, as the atoms spontaneously localize in a periodic fashion. In analogy to spatial crystals, the spontaneous breaking of temporal translation symmetry results in the formation of time crystals. While recent and on-going experiments on driven isolated systems aim to minimize dissipative processes, as it is an undesired source of decay, well-designed dissipation has been put forth as a constitutive ingredient in the formation of dissipative time crystals (DTCs). Here, we present the first experimental realisation of a DTC, implemented in an atom-cavity system. Its defining feature is a period doubled switching between distinct chequerboard density wave patterns, induced by controlled cavity-dissipation and cavity-mediated interactions. We demonstrate the robustness of this phase against system parameter changes and temporal perturbations of the driving. Our work provides a framework for realising phases of matter with spatiotemporal order in presence of dissipation. We note that this is the natural environment of matter, and therefore shapes its physical phenomena profoundly, making its study imperative.
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Time crystals are a phase of matter, for which the discrete time symmetry of the driving Hamiltonian is spontaneously broken. The breaking of discrete time symmetry has been observed in several experiments in driven spin systems. Here, we show the observation of a space-time crystal using ultra-cold atoms, where the periodic structure in both space and time are directly visible in the experimental images. The underlying physics in our superfluid can be described ab initio and allows for a clear identification of the mechanism that causes the spontaneous symmetry breaking. Our results pave the way for the usage of space-time crystals for the discovery of novel nonequilibrium phases of matter.
We propose the dynamical stabilization of a nonequilibrium order in a driven dissipative system comprised an atomic Bose-Einstein condensate inside a high finesse optical cavity, pumped with an optical standing wave operating in the regime of anomalous dispersion. When the amplitude of the pump field is modulated close to twice the characteristic limit-cycle frequency of the unmodulated system, a stable subharmonic response is found. The dynamical phase diagram shows that this subharmonic response occurs in a region expanded with respect to that where stable limit-cycle dynamics occurs for the unmodulated system. In turning on the modulation we tune the atom-cavity system from a continuous to a discrete time crystal.
Open physical systems with balanced loss and gain, described by non-Hermitian parity-time ($mathcal{PT}$) reflection symmetric Hamiltonians, exhibit a transition which could engenders modes that exponentially decay or grow with time and thus spontaneously breaks the $mathcal{PT}$-symmetry. Such $mathcal{PT}$-symmetry breaking transitions have attracted many interests because of their extraordinary behaviors and functionalities absent in closed systems. Here we report on the observation of $mathcal{PT}$-symmetry breaking transitions by engineering time-periodic dissipation and coupling, which are realized through state-dependent atom loss in an optical dipole trap of ultracold $^6$Li atoms. Comparing with a single transition appearing for static dissipation, the time-periodic counterpart undergoes $mathcal{PT}$-symmetry breaking and restoring transitions at vanishingly small dissipation strength in both single and multiphoton transition domains, revealing rich phase structures associated to a Floquet open system. The results enable ultracold atoms to be a versatile tool for studying $mathcal{PT}$-symmetric quantum systems.
We investigate the dynamics of fermionic atoms in a high-finesse optical resonator after a sudden switch on of the coupling between the atoms and the cavity. The atoms are additionally confined by optical lattices to a ladder geometry. The tunneling mechanism on a rung of a ladder is induced by a cavity assisted Raman process. At long times after the quantum quench the arising steady state can carry a chiral current. In this work we employ exact diagonalization techniques on small system sizes to study the dissipative attractor dynamics after the quench towards the steady state and deviations of the properties of the steady state from predictions obtained by adiabatically eliminating the cavity mode.
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.
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