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Register a new userNon-local propagation of correlations in long-range interacting quantum systems
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The maximum speed with which information can propagate in a quantum many-body system directly affects how quickly disparate parts of the system can become correlated and how difficult the system will be to describe numerically. For systems with only short-range interactions, Lieb and Robinson derived a constant-velocity bound that limits correlations to within a linear effective light cone. However, little is known about the propagation speed in systems with long-range interactions, since the best long-range bound is too loose to give the correct light-cone shape for any known spin model and since analytic solutions rarely exist. In this work, we experimentally determine the spatial and time-dependent correlations of a far-from-equilibrium quantum many-body system evolving under a long-range Ising- or XY-model Hamiltonian. For several different interaction ranges, we extract the shape of the light cone and measure the velocity with which correlations propagate through the system. In many cases we find increasing propagation velocities, which violate the Lieb-Robinson prediction, and in one instance cannot be explained by any existing theory. Our results demonstrate that even modestly-sized quantum simulators are well-poised for studying complicated many-body systems that are intractable to classical computation.
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The non-equilibrium response of a quantum many-body system defines its fundamental transport properties and how initially localized quantum information spreads. However, for long-range-interacting quantum systems little is known. We address this issue by analyzing a local quantum quench in the long-range Ising model in a transverse field, where interactions decay as a variable power-law with distance $propto r^{-alpha}$, $alpha>0$. Using complementary numerical and analytical techniques, we identify three dynamical regimes: short-range-like with an emerging light cone for $alpha>2$; weakly long-range for $1<alpha<2$ without a clear light cone but with a finite propagation speed of almost all excitations; and fully non-local for $alpha<1$ with instantaneous transmission of correlations. This last regime breaks generalized Lieb--Robinson bounds and thus locality. Numerical calculation of the entanglement spectrum demonstrates that the usual picture of propagating quasi-particles remains valid, allowing an intuitive interpretation of our findings via divergences of quasi-particle velocities. Our results may be tested in state-of-the-art trapped-ion experiments.
The presence of non-local and long-range interactions in quantum systems induces several peculiar features in their equilibrium and out-of-equilibrium behavior. In current experimental platforms control parameters such as interaction range, temperature, density and dimension can be changed. The existence of universal scaling regimes, where diverse physical systems and observables display quantitative agreement, generates a common framework, where the efforts of different research communities can be -- in some cases rigorously -- connected. Still, the application of this general framework to particular experimental realisations requires the identification of the regimes where the universality phenomenon is expected to appear. In the present review we summarise the recent investigations of many-body quantum systems with long-range interactions, which are currently realised in Rydberg atom arrays, dipolar systems, trapped ion setups and cold atoms in cavity experiments. Our main aim is to present and identify the common and (mostly) universal features induced by long-range interactions in the behaviour of quantum many-body systems. We will discuss both the case of very strong non-local couplings, i.e. the non-additive regime, and the one in which energy is extensive, but nevertheless low-energy, long wavelength properties are altered with respect to the short-range limit. Cases of competition with other local effects in the above mentioned setups are also reviewed.
We unveil a mechanism for generating oscillations with arbitrary multiplets of the period of a given external drive, in long-range interacting quantum many-particle spin systems. These oscillations break discrete time translation symmetry as in time crystals, but they are understood via two intertwined stroboscopic effects similar to the aliasing resulting from video taping a single fast rotating helicopter blade. The first effect is similar to a single blade appearing as multiple blades due to a frame rate that is in resonance with the frequency of the helicopter blades rotation; the second is akin to the optical appearance of the helicopter blades moving in reverse direction. Analogously to other dynamically stabilized states in interacting quantum many-body systems, this stroboscopic aliasing is robust to detuning and excursions from a chosen set of driving parameters, and it offers a novel route for engineering dynamical $n$-tuplets in long-range quantum simulators, with potential applications to spin squeezing generation and entangled state preparation.
We analyze the dynamics of periodically-driven (Floquet) Hamiltonians with short- and long-range interactions, finding clear evidence for a thermalization time, $tau^*$, that increases exponentially with the drive frequency. We observe this behavior, both in systems with short-ranged interactions, where our results are consistent with rigorous bounds, and in systems with long-range interactions, where such bounds do not exist at present. Using a combination of heating and entanglement dynamics, we explicitly extract the effective energy scale controlling the rate of thermalization. Finally, we demonstrate that for times shorter than $tau^*$, the dynamics of the system is well-approximated by evolution under a time-independent Hamiltonian $D_{mathrm{eff}}$, for both short- and long-range interacting systems.
The recent observation of the dynamical Casimir effect in a modulated superconducting waveguide, coronating thirty years of world-wide research, empowered the quantum technology community with a powerful tool to create entangled photons on-chip. In this work we show how, going beyond the single waveguide paradigm using a scalable array, it is possible to create multipartite nonclassical states, with the possibility to control the long-range quantum correlations of the emitted photons. In particular, our finite-temperature theory shows how maximally entangled $NOON$ states can be engineered in a realistic setup. The results here presented open the way to new kinds of quantum fluids of light, arising from modulated vacuum fluctuations in linear systems.
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