We describe an explicit statistical model of local hidden variables that reproduces the predictions of quantum mechanics for the ideal Franson experiment and sheds light on the physical mechanisms that might be involved in the actual experiment. The crux of our model is the spontaneous breaking of the time-translation gauge symmetry by the hidden configurations of the pairs of photons locked in time and energy involved in the experiment, which acquire a non-zero geometric phase through certain cyclic transformations.
Franson interferometry is a well-known quantum measurement technique for probing photon-pair frequency correlations that is often used to certify time-energy entanglement. We demonstrate the complementary technique in the time basis, called conjugate-Franson interferometry, that measures photon-pair arrival-time correlations, thus providing a valuable addition to the quantum toolbox. We obtain a conjugate-Franson interference visibility of $96\pm 1$% without background subtraction for entangled photon pairs generated by spontaneous parametric down-conversion. Our measured result surpasses the …
We show that an ultra-cold atomic cloud bouncing on an oscillating mirror can reveal spontaneous breaking of a discrete time translation symmetry. In many-body simulations we illustrate the process of the symmetry breaking that can be induced by atomic losses or by a measurement of particle positions. The results pave the way for understanding and realization of the time crystal idea where crystalline structures form in the time domain due to spontaneous breaking of continuous time translation symmetry.
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 br…
In analogy to spontaneous breaking of continuous space translation symmetry in the process of space crystal formation, it was proposed that spontaneous breaking of continuous time translation symmetry could lead to time crystal formation. In other words, a time-independent system prepared in the energy ground state is expected to reveal periodic motion under infinitely weak perturbation. In the case of the system proposed originally by Frank Wilczek, spontaneous breaking of time translation symmetry can not be observed if one starts with the ground state. We point out that the symmetry breakin…
A discrete time crystal is a phase unique to nonequilibrium systems, where discrete time translation symmetry is spontaneously broken. Most of conventional time crystals proposed so far rely on spontaneous breaking of on-site symmetries and their corresponding on-site symmetry operations. In this Letter, we propose a new time crystal dubbed "spatial-translation-induced discrete time crystal (STI-DTC)", which is realized by spatial translation and its symmetry breaking. Owing to the properties of spatial translation, in this new time crystal, various time crystal orders can emerge only by chang…
In a periodically driven (Floquet) system, there is the possibility for new phases of matter, not present in stationary systems, protected by discrete time-translation symmetry. This includes topological phases protected in part by time-translation symmetry, as well as phases distinguished by the spontaneous breaking of this symmetry, dubbed "Floquet time crystals". We show that such phases of matter can exist in the pre-thermal regime of periodically-driven systems, which exists generically for sufficiently large drive frequency, thereby eliminating the need for integrability or strong quench…
The possibility of Spontaneous Symmetry Breaking in momentum space in a generic Lifshitz scalar model - a non-relativistic scalar field theory with higher spatial derivative terms - has been studied. We show that the minimum energy state, the ground state, has a lattice structure, where the translation invariance of the continuum theory is reduced to a discrete translation symmetry. The scale of translation symmetry breaking (or induced lattice spacing) is proportional to the inverse of the momentum of the condensate particle. The crystalline ground state is stable under excitations below a ce…
In the last years we have proposed the use of the mechanism of spontaneous symmetry breaking with the purpose of generating perfect quadrature squeezing. Here we review previous work dealing with spatial (translational and rotational) symmetries, both on optical parametric oscillators and four-wave mixing cavities, as well as present new results. We then extend the phenomenon to the polarization state of the signal field, hence introducing spontaneous polarization symmetry breaking. Finally we propose a Jaynes-Cummings model in which the phenomenon can be investigated at the single-photon-pair…
Between space crystals and amorphous materials there exists a third class of aperiodic structures which lack translational symmetry but reveal long-range order. They are dubbed quasi-crystals and their formation, similarly as the formation of space crystals, is related to spontaneous breaking of translational symmetry of underlying Hamiltonians. Here, we investigate spontaneous emergence of quasi-crystals in periodically driven systems. We consider a quantum many-body system which is driven by a harmonically oscillating force and show that interactions between particles result in spontaneous s…
The Lorentz symmetry and the space and time translational symmetry are fundamental symmetries of nature. Crystals are the manifestation of the continuous space translational symmetry being spontaneously broken into a discrete one. We argue that, following the space translational symmetry, the continuous Lorentz symmetry should also be broken into a discrete one, which further implies that the continuous time translational symmetry is broken into a discrete one. We deduce all the possible discrete Lorentz and discrete time translational symmetries in 1+1-dimensional spacetime, and show how to b…
Under conventional Legendre transformation, systems with a non-convex Lagrangian will result in a multi-valued Hamiltonian as a function of conjugate momentum. This causes problems such as non-unitary time evolution of quantum state and non-determined motion of classical particles, and is physically unacceptable. In this work, we propose a new construction of single-valued Hamiltonian by applying Legendre-Fenchel transformation, which is a mathematically rigorous generalization of conventional Legendre transformation, valid for non-convex Lagrangian systems, but not yet widely known to the phy…
Time crystals are physical systems whose time translation symmetry is spontaneously broken. Although the spontaneous breaking of continuous time-translation symmetry in static systems is proved impossible for the equilibrium state, the discrete time-translation symmetry in periodically driven (Floquet) systems is allowed to be spontaneously broken, resulting in the so-called Floquet or discrete time crystals. While most works so far searching for time crystals focus on the symmetry breaking process and the possible stabilising mechanisms, the many-body physics from the interplay of symmetry-br…
We define what it means for time translation symmetry to be spontaneously broken in a quantum system, and show with analytical arguments and numerical simulations that this occurs in a large class of many-body-localized driven systems with discrete time-translation symmetry.
Time crystals are classified as discrete or continuous depending on whether they spontaneously break discrete or continuous time translation symmetry. While discrete time crystals have been extensively studied in periodically driven systems since their recent discovery, the experimental realization of a continuous time crystal is still pending. Here, we report the observation of a limit cycle phase in a continuously pumped dissipative atom-cavity system, which is characterized by emergent oscillations in the intracavity photon number. We observe that the phase of this oscillation is random for…
We show how a large family of interacting nonequilibrium phases of matter can arise from the presence of multiple time-translation symmetries, which occur by quasiperiodically driving an isolated quantum many-body system with two or more incommensurate frequencies. These phases are fundamentally different from those realizable in time-independent or periodically-driven (Floquet) settings. Focusing on high-frequency drives with smooth time-dependence, we rigorously establish general conditions for which these phases are stable in a parametrically long-lived `preheating' regime. We develop a for…
Spontaneous breaking of continuous time translation symmetry into a discrete one is related to time crystal formation. While the phenomenon is not possible in the ground state of a time-independent many-body system, it can occur in an excited eigenstate. Here, we concentrate on bosons on a ring with attractive contact interactions and analyze a quantum quench from the time crystal regime to the non-interacting regime. We show that dynamical quantum phase transitions can be observed where the return probability of the system to the initial state before the quench reveals a non-analytical behavi…
Difficulties around the idea of spontaneous breaking of time translation symmetry in a closed quantum mechanical system are identified, and then overcome in a simple model. The possibility of ordering in imaginary time is also discussed.
Spontaneous symmetry breaking is a universal concept throughout science. For instance, the Landau-Ginzburg paradigm of translational symmetry breaking underlies the classification of nearly all quantum phases of matter and explains the emergence of crystals, insulators, and superconductors. Usually, the consequences of translational invariance are studied in large systems to suppress edge effects which cause undesired symmetry breaking. While this approach works for investigating global properties, studies of local observables and their correlations require access and control of the individual…
Floquet driven systems represent an extremely interesting arena to study out-of-equilibrium phenomena. For instance, they provide realizations of discrete time crystals, where the discrete time translation symmetry of the periodic Hamiltonian is spontaneously broken by a subharmonic response of the system. However, the continuous presence of an external periodic driving is required within the current Floquet paradigm. We propose here the concept of spontaneous many-body Floquet state. This is a state that, in the absence of external periodic driving, self-oscillates like in the presence of a p…
The aim of this paper is to propose a criterion of spontaneous symmetry breaking that makes reference to the properties of pure phases defined by a translationally invariant state. By avoiding any reference to the ground state, at the basis of the standard approach, this criterion applies to a wider class of models. An interesting application is the breaking of time translations. Indeed, we discuss explicit theoretical models which exhibit the prototypical features of quantum time crystals, without the need of a time-dependent Hamiltonian.
Time crystals are proposed states of matter which spontaneously break time translation symmetry. There is no settled definition of such states. We offer a new definition which follows the traditional recipe for Wigner symmetries and order parameters. Supplementing our definition with a few plausible assumptions we find that a) systems with time independent Hamiltonians should not exhibit TTSB while b) the recently studied $π$ spin glass/Floquet time crystal can be viewed as breaking a global internal symmetry and as breaking time translation symmetry as befits its two names.
