We report the analogue simulation of an ergodiclocalized junction by using an array of 12 coupled superconducting qubits. To perform the simulation, we fabricated a superconducting quantum processor that is divided into two domains: a driven domain representing an ergodic system, while the second is localized under the effect of disorder. Due to the overlap between localized and delocalized states, for small disorder there is a proximity effect and localization is destroyed. To experimentally investigate this, we prepare a microwave excitation in the driven domain and explore how deep it can penetrate the disordered region by probing its dynamics. Furthermore, we performed an ensemble average over 50 realizations of disorder, which clearly shows the proximity effect. Our work opens a new avenue to build quantum simulators of driven-disordered systems with applications in condensed matter physics and material science
Quantum phases of matter have many relevant applications in quantum computation and quantum information processing. Current experimental feasibilities in diverse platforms allow us to couple two or more subsystems in different phases. In this letter, we investigate the situation where one couples two domains of a periodically-driven spin chain where one of them is ergodic while the other is fully localized. By combining tools of both graph and Floquet theory, we show that the localized domain remains stable for strong disorder, but as this disorder decreases the localized domain becomes ergodi…
We study the quantum dynamics of Josephson junction arrays. We find isolated groups of low-entanglement eigenstates, that persist even when the Josephson interaction is strong enough to destroy the organization of the spectrum in multiplets, and a perturbative description is no longer possible. These eigenstates provide a weak ergodicity breaking, and are reminiscent of the quantum scars. Due to the presence of these eigenstates, initializing with a charge-density-wave state, the system does not thermalize and the charge-density-wave order persists for long times. Considering global ergodicity…
We consider a Bose-Josephson junction (BJJ) formed by a binary mixture of ultracold atoms to investigate the manifestation of coherent collective dynamics on ergodicity and quantum scars, unfolding the connection between them. By tuning the inter- and intra-species interaction, we demonstrate a rich variety of Josephson dynamics and transitions between them, which plays a crucial role in controlling the overall ergodic behavior. The signature of underlying classicality is revealed from the entanglement spectrum, which also elucidates the formation of quantum scars of unstable steady states and…
By means of a Floquet analysis, we study the quantum dynamics of a fully connected Lipkin-Ising ferromagnet in a periodically driven transverse field showing that thermalization in the steady state is intimately connected to properties of the $N\to \infty$ classical Hamiltonian dynamics. When the dynamics is ergodic, the Floquet spectrum obeys a Wigner-Dyson statistics and the system satisfies the eigenstate thermalization hypothesis (ETH): Independently of the initial state, local observables relax to the $T=\infty$ thermal value, and Floquet states are delocalized in the Hilbert space. On th…
We experimentally study a periodically driven many-body localized system realized by interacting fermions in a one-dimensional quasi-disordered optical lattice. By preparing the system in a far-from-equilibrium state and monitoring the remains of an imprinted density pattern, we identify a localized phase at high drive frequencies and an ergodic phase at low ones. These two distinct phases are separated by a dynamical phase transition which depends on both the drive frequency and the drive strength. Our observations are quantitatively supported by numerical simulations and are directly connect…
According to the second law of thermodynamics the total entropy of a system is increased during almost any dynamical process. The positivity of the specific heat implies that the entropy increase is associated with heating. This is generally true both at the single particle level, like in the Fermi acceleration mechanism of charged particles reflected by magnetic mirrors, and for complex systems in everyday devices. Notable exceptions are known in noninteracting systems of particles moving in periodic potentials. Here the phenomenon of dynamical localization can prevent heating beyond certain …
General relation is derived which expresses the fidelity of quantum dynamics, measuring the stability of time evolution to small static variation in the hamiltonian, in terms of ergodicity of an observable generating the perturbation as defined by its time correlation function. Fidelity for ergodic dynamics is predicted to decay exponentially on time-scale proportional to delta^(-2) where delta is the strength of perturbation, whereas faster, typically gaussian decay on shorter time scale proportional to delta^(-1) is predicted for integrable, or generally non-ergodic dynamics. This surprising…
We study the thermally fluctuating state of a bi-layer cuprate superconductor under the periodic action of a staggered field oscillating at optical frequencies. This analysis distills essential elements of the recently discovered phenomenon of light enhanced coherence in YBa$_2$Cu$_3$O$_{6+x}$, which was achieved by periodically driving infrared active apical oxygen distortions. The effect of a staggered periodic perturbation is studied using a Langevin and Fokker-Planck description of driven, coupled Josephson junctions, which represent two neighboring pairs of layers and their two plasmons. …
The Floquet-Magnus expansion is a useful tool to calculate an effective Hamiltonian for periodically driven systems. In this study, we investigate the convergence of the expansion for a one-body nonlinear system in a continuous space, a driven anharmonic oscillator. In this model, all eigenstates of the time evolution operator are found to be localized in energy space, and the expectation value of the energy is bounded from above. We first propose a general procedure to estimate the radius of convergence of the Floquet-Magnus expansion for periodically driven systems with an unbounded energy s…
We demonstrate that the counting statistics of currents in periodically driven ergodic stochastic systems can show sharp changes of some of its properties in response to continuous changes of the driving protocol. To describe this effect, we introduce a new topological phase factor in evolution of the moment generating function which is akin to the topological geometric phase in evolution of a periodically driven quantum mechanical system with time-reversal symmetry. This phase leads to the prediction of a sign change for the difference of the probabilities to find even and odd number particle…
Conventionally the mobility edge (ME) separating extended states from localized ones is a central concept in understanding Anderson localization transition. The critical state, being delocalized and non-ergodic, is a third type of fundamental state that is different from both the extended and localized states. Here we study the localization phenomena in a one dimensional periodically kicked quasiperiodic optical Raman lattice by using fractal dimensions. We show a rich phase diagram including the pure extended, critical and localized phases in the high frequency regime, the MEs separating the …
We study the dynamics of microscopic quantum correlations, viz., bipartite entanglement and quantum discord between nearest neighbor sites, in Ising spin chain with a periodically varying external magnetic field along the transverse direction. Quantum correlations exhibit periodic revivals with the driving cycles in the finite-size chain. The time of first revival is proportional to the system size and is inversely proportional to the maximum group velocity of Floquet quasi-particles. On the other hand, the local quantum correlations in the infinite chain may get saturated to non-zero values a…
Using an efficient one and two qubit gate simulator, operating on graphical processing units, we investigate ergodic properties of a quantum Ising spin 1/2 model on a two dimensional lattice, which is periodically driven by a $δ$-pulsed transverse magnetic field. We consider three different dynamical properties: (i) level density and (ii) level spacing distribution of the Floquet quasienergy spectrum, as well as (iii) time-averaged autocorrelation function of components of the magnetization. Varying the parameters of the model, we found transitions between ordered (non ergodic) and quantum cha…
The presence of quantum scars, athermal eigenstates of a many-body Hamiltonian with finite energy density, leads to absence of ergodicity and long-time coherent dynamics in closed quantum systems starting from simple initial states. Such non-ergodic coherent dynamics, where the system does not explore its entire phase space, has been experimentally observed in a chain of ultracold Rydberg atoms. We show, via study of a periodically driven Rydberg chain, that the drive frequency acts as a tuning parameter for several reentrant transitions between ergodic and non-ergodic regimes. The former regi…
We investigate the generation of entanglement through a quantum dot molecule under the influence of vibrational phonon modes in a bias voltage junction. The molecular quantum dot system is realized by coupled quantum dots inside a suspended carbon nanotube. We consider the dynamical entanglement as a function of bias voltage and temperature by taking into account the electron-phonon interaction. In order to generate the robust entanglement between quantum dots and preserve it to reach the maximal achievable amount steadily, we introduce an asymmetric coupling protocol and apply the easy tunabl…
We study the stroboscopic dynamics of a periodically driven finite Rydberg chain with staggered ($Δ$) and time-dependent uniform ($λ(t)$) detuning terms using exact diagonalization (ED). We show that at intermediate drive frequencies ($ω_D$), the presence of a finite $Δ$ results in violation of the eigenstate thermalization hypothesis (ETH) via clustering of Floquet eigenstates. Such clustering is lost at special commensurate drive frequencies for which $\hbar ω_d=n Δ$ ($n \in Z$) leading to restoration of ergodicity. The violation of ETH in these driven finite-sized chains is also evident fro…
We study the dynamical generation of entanglement as a signature of chaos in a system of periodically kicked coupled-tops, where chaos and entanglement arise from the same physical mechanism. The long-time averaged entanglement as a function of the position of an initially localized wave packet very closely correlates with the classical phase space surface of section -- it is nearly uniform in the chaotic sea, and reproduces the detailed structure of the regular islands. The uniform value in the chaotic sea is explained by the random state conjecture. As classically chaotic dynamics take local…
The spontaneous breaking of time-translation symmetry in periodically driven quantum systems leads to a new phase of matter: discrete time crystals (DTC). This phase exhibits collective subharmonic oscillations that depend upon an interplay of non-equilibrium driving, many-body interactions, and the breakdown of ergodicity. However, subharmonic responses are also a well-known feature of classical dynamical systems ranging from predator-prey models to Faraday waves and AC-driven charge density waves. This raises the question of whether these classical phenomena display the same rigidity charact…
By periodically driving a single bosonic Josephson junction (BJJ) with an impurity, a synthetic gauge field is generated in the Fock space of the system. At a critical synthetic gauge flux the ground state undergoes a quantum phase transition which is analogous to the Meissner-Abrikosov-vortex transition found in type-II superconductors with an applied magnetic field. A second quantum phase transition involving attractive interactions between the bosons of the BJJ is shown to enhance the sensitivity of the system to the Meissner-Abrikosov-vortex transition.
We study the effect of many-body quantum interference on the dynamics of coupled periodically kicked systems whose classical dynamics is chaotic and shows an unbounded energy increase. We specifically focus on a $N$ coupled kicked rotors model: we find that the interplay of quantumness and interactions dramatically modifies the system dynamics inducing a transition between energy saturation and unbounded energy increase. We discuss this phenomenon both numerically and analytically, through a mapping onto a $N$-dimensional Anderson model. The thermodynamic limit $N\to\infty$, in particular, alw…
Novel dynamical phases that violate ergodicity have been a subject of extensive research in recent years. A periodically driven system is naively expected to lose all memory of its initial state due to thermalization, yet this can be avoided in the presence of many-body localization. A discrete time crystal represents a driven system whose local observables spontaneously break time translation symmetry and retain memory of the initial state indefinitely. Here we report the observation of a discrete time crystal on a chain consisting of 57 superconducting qubits on a state--of--the--art quantum…
