Charles E. Creffield

The Sachdev-Ye-Kitaev (SYK) model has attracted widespread attention due to its relevance to diverse areas of physics, such as high temperature superconductivity, black holes, and quantum chaos. The model is, however, extremely challenging to realize experimentally. In this work, we show how a particular form of Floquet engineering, termed ``kinetic driving'', effectively eliminates single-particle processes and creates quasi-random all-to-all interactions when applied to models of Hubbard type. For the specific case of the Bose-Hubbard model, we explicitly verify that the driven system indeed reproduces SYK physics by direct comparison of the spectral form factor and out-of-time ordered correlation functions (OTOCs). Our findings indicate that a cold-atom realization of kinetic driving -- achieved through modulation of hopping amplitudes in an optical lattice -- offers a practical and accurate platform for quantum simulation of the SYK model.

Tilted lattice potentials with periodic driving play a crucial role in the study of artificial gauge fields and topological phases with ultracold quantum gases. However, driving-induced heating and the growth of phonon modes restrict their use for probing interacting many-body states. Here, we experimentally investigate phonon modes and interaction-driven instabilities of superfluids in the lowest band of a shaken optical lattice. We identify stable and unstable parameter regions and provide a general resonance condition. In contrast to the high-frequency approximation of a Floquet description, we use the micromotion of the superfluids to analyze the growth of phonon modes from slow- to fast-driving frequencies. The model describes phonon excitations in both resonantly and nonresonantly driven systems, with or without a tilted potential. Our observations enable the prediction of stable parameter regimes for quantum-simulation experiments aimed at studying driven systems with strong interactions over extended time scales. Published by the American Physical Society 2024

We study the spectral statistics of a one-dimensional Bose–Hubbard model subjected to kinetic driving; a form of Floquet engineering where the kinetic energy is periodically driven in time with a zero time-average. As the amplitude of the driving is increased, the ground state of the resulting flat-band system passes from the Mott insulator regime to an exotic superfluid. We show that this transition is accompanied by a change in the system’s spectral statistics from Poisson to GOE-type. Remarkably, and unlike in the conventional Bose–Hubbard model which we use as a benchmark, the details of the GOE statistics are sensitive to the parity of both the particle number and the lattice sites. We show how this effect arises from a hidden symmetry of the Hamiltonian produced by this form of Floquet driving.

We experimentally investigate the stability of a quantum gas with repulsive interactions in an optical one-dimensional lattice subjected to periodic driving. Excitations of the gas in the lowest lattice band are analyzed across the complete stability diagram, from slow to fast driving frequencies and from weak to strong driving strengths. To interpret our results, we expand the established analysis based on parametric instabilities to include modulational instabilities. Extending the concept of modulational instabilities from static to periodically driven systems provides a convenient mapping of the stability in a static system to the cases of slow and fast driving. At intermediate driving frequencies, we observe an interesting competition between modulational and parametric instabilities. We experimentally confirm the existence of both types of instabilities in driven systems and probe their properties. Our results allow us to predict stable and unstable parameter regions for the minimization of heating in future applications of Floquet driving.

The duration of bidirectional transfer protocols in 1D topological models usually scales exponentially with distance. In this work, we propose transfer protocols in multidomain SSH chains and Creutz ladders that lose the exponential dependence, greatly speeding up the process with respect to their single-domain counterparts, reducing the accumulation of errors and drastically increasing their performance, even in the presence of symmetry-breaking disorder. We also investigate how to harness the localization properties of the Creutz ladder---with two localized modes per domain wall---to choose the two states along the ladder that will be swapped during the transfer protocol, without disturbing the states located in the intermediate walls between them. This provides a 1D network with all-to-all connectivity that can be helpful for quantum information purposes.

We investigate theoretically the superfluidity of a one-dimensional boson system whose hopping energy is periodically modulated with a zero time average, which results in the suppression of first-order single-particle hopping processes. The dynamics of this Floquet-engineered flat-band system is entirely driven by correlations and described by exotic Hamiltonian and current operators. We employ exact diagonalization and compare our results with those of the conventional, undriven Bose–Hubbard system. We focus on the two main manifestations of superfluidity, the Hess-Fairbank effect and the metastability of supercurrents, with explicit inclusion of an impurity when relevant. Among the novel superfluid features, we highlight the presence of a cat-like ground state, with branches that have opposite crystal momentum but carry the same flux-dependent current, and the essential role of the interference between the collective components of the ground-state wave function. Calculation of the dynamic form factor reveals the presence of an acoustic mode that guarantees superfluidity in the thermodynamic limit.

We study a gas of interacting ultracold bosons held in a parabolic trap in the presence of an optical lattice potential. Treating the system as a discretized Gross-Pitaevskii model, we show how Floquet engineering, by rapidly “shaking” the lattice, allows the ground state of the system to be converted into a train of bright solitons by inverting the sign of the hopping energy. We study how the number of solitons produced depends on the system's nonlinearity and the curvature of the trap, show how the technique can be applied in both the high- and low-driving-frequency regimes, and demonstrate the phenomenon's stability against noise. We conclude that the Floquet approach is a useful and stable method of preparing solitons in cold-atom systems.

We study the expansion of a one-dimensional boson gas by initialising it in a small region of a chain, and then suddenly allowing it to expand into the remainder of the chain. We consider three initial ground-state configurations: the Mott insulator, the conventional superfluid, whose momentum density is sharply peaked at zero momentum, and the cat-like state with momentum peaks at ±π/2, produced by kinetic driving, the latter being a particular case of a flat-band system. In turn, we consider three types of expansion: spectroscopic (with interactions tuned to zero), dynamic (with standard short-range repulsive interactions), and under kinetic driving. The numerical calculations are exact. We compute the momentum and real-space one-particle densities, as well as the two-particle momentum correlations. We find that the spectroscopic time-of-flight experiment reflects the initial momentum distribution except for the larger number of momentum states and at high momenta. For the dynamic expansion starting from an insulator, we recover the non-equilibrium quasi-condensation into momenta ±π/2, provide a physical explanation in terms of interacting bosons that is confirmed by the numerical simulation, and note the existence of nontrivial correlations in the momentum distribution. Under kinetic driving the expansion is comparatively slow, but we conjecture that at high densities it will be much faster. We compare various measures of the two-particle momentum correlations, noting that some of them tend to conceal the possible cat-like structure of a many-body state.