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Register a new userMapping as a probe for heating suppression in periodically driven quantum many-body systems
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Experiments on periodically driven quantum systems have effectively realized quasi-Hamiltonians, in the sense of Floquet theory, that are otherwise inaccessible in static condensed matter systems. Although the Floquet quasi-Hamiltonians are time-independent, however, these continuously driven systems can still suffer from heating due to a secular growth in the expectation value of the time-dependent physical Hamiltonian. Here we use an exact space-time mapping to construct a class of many-body systems with rapid periodic driving which we nonetheless prove to be completely free of heating, by mapping them exactly onto time-independent systems. The absence of heating despite the periodic driving occurs in these cases of harmonically trapped dilute Bose gas because the driving is a certain periodic but anharmonic modulation of the gass two-body contact interaction, at a particular frequency. Although we prove that the absence of heating is exact within full quantum many-body theory, we then use mean-field theory to simulate Floquet heating spectroscopy and compute the heating rate when the driving frequency is varied away from the critical value for zero heating. In both weakly and strongly non-linear regimes, the heating rate as a function of driving frequency appears to show a number of Fano resonances, suggesting that the exactly proven absence of heating at the critical frequency may be explained in terms of destructive interferences between excitation modes.
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We investigate multi-photon interband excitation processes in an optical lattice that is driven periodically in time by a modulation of the lattice depth. Assuming the system to be prepared in the lowest band, we compute the excitation spectrum numerically. Moreover, we estimate the effective coupling parameters for resonant interband excitation processes analytically, employing degenerate perturbation theory in Floquet space. We find that below a threshold driving strength, interband excitations are suppressed exponentially with respect to the inverse driving frequency. For sufficiently low frequencies, this leads to a rather sudden onset of interband heating, once the driving strength reaches the threshold. We argue that this behavior is rather generic and should also be found in lattice systems that are driven by other forms of periodic forcing. Our results are relevant for Floquet engineering, where a lattice system is driven periodically in time in order to endow it with novel properties like the emergence of a strong artificial magnetic field or a topological band structure. In this context, interband excitation processes correspond to detrimental heating.
We study a two-level impurity coupled locally to a quantum gas on an optical lattice. For state-dependent interactions between the impurity and the gas, we show that its evolution encodes information on the local excitation spectrum of gas at the coupling site. Based on this, we design a nondestructive method to probe the systems excitations in a broad range of energies by measuring the state of the probe using standard atom optics methods. We illustrate our findings with numerical simulations for quantum lattice systems, including realistic dephasing noise on the quantum probe, and discuss practical limits on the probe dephasing rate to fully resolve both regular and chaotic spectra.
We propose a method to obtain optimal protocols for adiabatic ground-state preparation near the adiabatic limit, extending earlier ideas from [D. A. Sivak and G. E. Crooks, Phys. Rev. Lett. 108, 190602 (2012)] to quantum non-dissipative systems. The space of controllable parameters of isolated quantum many-body systems is endowed with a Riemannian quantum metric structure, which can be exploited when such systems are driven adiabatically. Here, we use this metric structure to construct optimal protocols in order to accomplish the task of adiabatic ground-state preparation in a fixed amount of time. Such optimal protocols are shown to be geodesics on the parameter manifold, maximizing the local fidelity. Physically, such protocols minimize the average energy fluctuations along the path. Our findings are illustrated on the Landau-Zener model and the anisotropic XY spin chain. In both cases we show that geodesic protocols drastically improve the final fidelity. Moreover, this happens even if one crosses a critical point, where the adiabatic perturbation theory fails.
We review the recent developments and the current status in the field of quantum-gas cavity QED. Since the first experimental demonstration of atomic self-ordering in a system composed of a Bose-Einstein condensate coupled to a quantized electromagnetic mode of a high-$Q$ optical cavity, the field has rapidly evolved over the past decade. The composite quantum-gas--cavity systems offer the opportunity to implement, simulate, and experimentally test fundamental solid-state Hamiltonians, as well as to realize non-equilibrium many-body phenomena beyond conventional condensed-matter scenarios. This hinges on the unique possibility to design and control in open quantum environments photon-induced tunable-range interaction potentials for the atoms using tailored pump lasers and dynamic cavity fields. Notable examples range from Hubbard-like models with long-range interactions exhibiting a lattice-supersolid phase, over emergent magnetic orderings and quasicrystalline symmetries, to the appearance of dynamic gauge potentials and non-equilibrium topological phases. Experiments have managed to load spin-polarized as well as spinful quantum gases into various cavity geometries and engineer versatile tunable-range atomic interactions. This led to the experimental observation of spontaneous discrete and continuous symmetry breaking with the appearance of soft-modes as well as supersolidity, density and spin self-ordering, dynamic spin-orbit coupling, and non-equilibrium dynamical self-ordered phases among others. In addition, quantum-gas--cavity setups offer new platforms for quantum-enhanced measurements. In this review, starting from an introduction to basic models, we pedagogically summarize a broad range of theoretical developments and put them in perspective with the current and near future state-of-art experiments.
The single-particle density is the most basic quantity that can be calculated from a given many-body wave function. It provides the probability to find a particle at a given position when the average over many realizations of an experiment is taken. However, the outcome of single experimental shots of ultracold atom experiments is determined by the $N$-particle probability density. This difference can lead to surprising results. For example, independent Bose-Einstein condensates (BECs) with definite particle numbers form interference fringes even though no fringes would be expected based on the single-particle density [1-4]. By drawing random deviates from the $N$-particle probability density single experimental shots can be simulated from first principles [1, 3, 5]. However, obtaining expressions for the $N$-particle probability density of realistic time-dependent many-body systems has so far been elusive. Here, we show how single experimental shots of general ultracold bosonic systems can be simulated based on numerical solutions of the many-body Schrodinger equation. We show how full counting distributions of observables involving any number of particles can be obtained and how correlation functions of any order can be evaluated. As examples we show the appearance of interference fringes in interacting independent BECs, fluctuations in the collisions of strongly attractive BECs, the appearance of randomly fluctuating vortices in rotating systems and the center of mass fluctuations of attractive BECs in a harmonic trap. The method described is broadly applicable to bosonic many-body systems whose phenomenology is driven by information beyond what is typically available in low-order correlation functions.
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