Broken Time Translation Symmetry Research Articles

Relaxation dynamics and dissipative phase transition in quantum oscillators with period tripling

Period tripling in driven quantum oscillators reveals unique features absent for linear and parametric drive, but generic for all higher-order resonances. Here, we focus at zero temperature on the relaxation dynamics towards a stationary state starting initially from a domain around a classical fixed point in phase space. Beyond a certain threshold for the driving strength, the long-time dynamics is governed by a single time constant that sets the rate for switching between different states with broken time translation symmetry. By analyzing the lowest eigenvalues of the corresponding time evolution generator for the dissipative dynamics, we find that near the threshold the gap between these eigenvalues nearly closes. The closing becomes complete for a vanishing quantum parameter. We demonstrate that this behavior, reminiscent of a quantum phase transition, is associated with a transition from a stationary state which is localized in phase space to a delocalized one. We further show, that switching between domains of classical fixed points happens via quantum activation, however, with rates that differ from those obtained by a standard semiclassical treatment. As period tripling has been explored with superconducting circuits mainly in the quasi-classical regime recently, our findings may trigger new activities towards the deep quantum realm.

Interaction-induced time-symmetry breaking in driven quantum oscillators

We study parametrically driven quantum oscillators and show that, even for weak coupling between the oscillators, they can exhibit various many-body states with broken time-translation symmetry. In the quantum-coherent regime, the symmetry breaking occurs via a nonequilibrium quantum phase transition. For dissipative oscillators, the main effect of the weak coupling is to make the switching rate of an oscillator between its period-2 states dependent on the states of other oscillators. This allows mapping the oscillators onto a system of coupled spins. Away from the bifurcation parameter values where the period-2 states emerge, the stationary state corresponds to having a microscopic current in the spin system, in the presence of disorder. In the vicinity of the bifurcation point or for identical oscillators, the stationary state can be mapped on that of the Ising model with an effective temperature $\propto \hbar$, for low temperature. Closer to the bifurcation point the coupling can not be considered weak and the system maps onto coupled overdamped Brownian particles performing quantum diffusion in a potential landscape.

Algebraic Time Crystallization in a Two-Dimensional Superfluid

Time crystallization is a hallmark of superfluidity, indicative of the fundamental fact that along with breaking the global U(1) symmetry, superfluids also break time-translation symmetry. While the standard discussion of the time crystallization phenomenon is based on the notion of the global phase and genuine condensate, for the superfluidity to take place in two dimensions an algebraic (topological) order is sufficient. We find that the absence of long-range order in a finite-temperature two-dimensional superfluid translates into in an algebraic time crystallization caused by the temporal phase correlations. The exponent controlling the algebraic decay is a universal function of the superfluid-stiffness-to-temperature ratio; this exponent can be also seen in the power-law singularity of the Fourier spectrum of the AC Josephson current. We elaborate on subtleties involved in defining the phenomenon of time crystallization in both classical-filed and all-quantum cases and propose an experimental protocol in which the broken time translation symmetry---more precisely, temporal correlations of the relative phase, with all possible finite-size, dimensional, and quantum effects included---can be observed without permanently keeping two superfluids in a contact.

ALGEBRAIC TIME CRYSTALLIZATION IN A TWO-DIMENSIONAL SUPERFLUID

Time crystallization is a hallmark of superfluidity, indicative of the fundamental fact that along with breaking the global U(1) symmetry, superfluids also break time-translation symmetry. While the standard discussion of the time crystallization phenomenon is based on the notion of the global phase and genuine condensate, for the superfluidity to take place in two dimensions an algebraic (topological) order is sufficient. We find that the absence of long-range order in a finite-temperature two-dimensional superfluid translates into in an algebraic time crystallization caused by the temporal phase correlations. The exponent controlling the algebraic decay is a universal function of the superfluid-stiffness-to-temperature ratio; this exponent can be also seen in the power-law singularity of the Fourier spectrum of the AC Josephson current. We elaborate on subtleties involved in defining the phenomenon of time crystallization in both classical-filed and all-quantum cases and propose an experimental protocol in which the broken time translation symmetry---more precisely, temporal correlations of the relative phase, with all possible finite-size, dimensional, and quantum effects included---can be observed without permanently keeping two superfluids in a contact.

The quantum phase-transitions of water

It is shown that hexagonal ices and steam are macroscopically quantum condensates, with continuous spacetime-translation symmetry, whereas liquid water is a quantum fluid with broken time-translation symmetry. Fusion and vaporization are quantum phase-transitions. The heat capacities, the latent heats, the phase-transition temperatures, the critical temperature, the molar volume expansion of ice relative to water, as well as neutron scattering data and dielectric measurements are explained. The phase-transition mechanisms along with the key role of quantum interferences and that of Hartley-Shannon's entropy are enlightened. The notions of chemical bond and force-field are questioned.

Time crystals

Physicists have come up with the mind-boggling concept of a time crystal. This intriguing proposal, which is based on the notion of broken time-translation symmetry, might open up a whole new field of research.

Broken Time Translation Symmetry as a Model for Quantum State Reduction

The symmetries that govern the laws of nature can be spontaneously broken, enabling the occurrence of ordered states. Crystals arise from the breaking of translation symmetry, magnets from broken spin rotation symmetry and massive particles break a phase rotation symmetry. Time translation symmetry can be spontaneously broken in exactly the same way. The order associated with this form of spontaneous symmetry breaking is characterised by the emergence of quantum state reduction: systems which spontaneously break time translation symmetry act as ideal measurement machines. In this review the breaking of time translation symmetry is first compared to that of other symmetries such as spatial translations and rotations. It is then discussed how broken time translation symmetry gives rise to the process of quantum state reduction and how it generates a pointer basis, Born’s rule, etc. After a comparison between this model and alternative approaches to the problem of quantum state reduction, the experimental implications and possible tests of broken time translation symmetry in realistic experimental settings are discussed.