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arXiv:2209.09132 · Proceedings of the National Academy of Sciences

Experimental observation of curved light-cones in a quantum field simulator

Mohammadamin Tajik, Marek Gluza, Nicolas Sebe, Philipp Schüttelkopf, Federica Cataldini, João Sabino, Frederik Møller, Si-Cong Ji, Sebastian Erne, Giacomo Guarnieri, Spyros Sotiriadis, Jens Eisert, Jörg Schmiedmayer

Published May 15, 2023• 35 citations
arXivHTMLPDF

Abstract

We investigate signal propagation in a quantum field simulator of the Klein-Gordon model realized by two strongly coupled parallel one-dimensional quasi-condensates. By measuring local phononic fields after a quench, we observe the propagation of correlations along sharp light-cone fronts. If the local atomic density is inhomogeneous, these propagation fronts are curved. For sharp edges, the propagation fronts are reflected at the system's boundaries. By extracting the space-dependent variation of the front velocity from the data, we find agreement with theoretical predictions based on curved geodesics of an inhomogeneous metric. This work extends the range of quantum simulations of nonequilibrium field dynamics in general space-time metrics.

DOI
10.1073/pnas.2301287120

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We investigate signal propagation in a quantum field simulator of the Klein-Gordon model realized by two strongly coupled parallel one-dimensional quasi-condensates. By measuring local phononic fields after a quench, we observe the propagation of correlations along sharp light-cone fronts. If the local atomic density is inhomogeneous, these propagation fronts are curved. For sharp edges, the propagation fronts are reflected at the system's boundaries. By extracting the space-dependent variation of the front velocity from the data, we find agreement with theoretical predictions based on curved geodesics of an inhomogeneous metric. This work extends the range of quantum simulations of nonequilibrium field dynamics in general space-time metrics.
The light-cone spreading of entanglement and correlation is a fundamental and ubiquitous feature of homogeneous extended quantum systems. Here we point out that a class of inhomogenous Luttinger liquids (those with a uniform Luttinger parameter K K ) at low energy display the universal phenomenon of curved light cones: gapless excitations propagate along the null geodesics of the metric ds^2 = dx^2 - v(x)^2 dt^2 d s 2 = d x 2 − v ( x ) 2 d t 2 , with v(x) v ( x ) being the calculable spatial dependent velocity induced by the inhomogeneity. We confirm our findings with explicit analytic and numerical calculations both in- and out-of-equilibrium for a Tonks-Girardeau gas in a harmonic potential and in lattice systems with artificially tuned hamiltonian density.
We investigate the dynamical spreading of correlations in many-body quantum systems with competing short- and global-range couplings. We monitor the nonequilibrium dynamics of the correlations following a quench, showing that for strong short-range couplings the propagation of correlations is dominated at short and intermediate distances by a causal, light-cone dynamics, resembling the purely short-range quantum systems. However, the interplay of short- and global-range couplings leads to a crossover between space-time regions in which the light cone persists to regions where a supersonic, distance-independent spreading of the correlations occurs. We identify the important ingredients needed for capturing the supersonic spreading and demonstrate our findings in systems of interacting bosonic atoms, in which the global-range coupling is realized by a coupling to a cavity light field or atomic long-range interactions, respectively. We show that our results hold in both one and two dimensions and in the presence of dissipation. Furthermore, we characterize the short-time power-law scaling of the distance-independent growth of the density-density correlations.
We digitally simulate quantum many-body dynamics in emergent curved backgrounds using 80 superconducting qubits on IBM Heron processors. By engineering spatially varying couplings in the spin-12\frac1221​ XXZ chain, consistent with the low-energy description of the model in terms of an inhomogeneous Tomonaga-Luttinger liquid, we realize excitations that follow geodesics of an effective metric inherited from the underlying spatial deformation. Following quenches from Néel and few-spin-flip states, we observe curved light-cone propagation, horizon-induced freezing in the local magnetization, and position-dependent oscillation frequencies set by the engineered spatial deformation. Despite strong spatial inhomogeneity, unequal-time correlators reveal ballistic quasiparticle propagation in the spin chain. These results establish large-scale digital quantum processors as a flexible platform for detailed and controlled exploration of many-body dynamics in tunable and synthetic curved spacetimes.
We study the spreading of density-density correlations in Bose-Hubbard models after a quench of the interaction strength, using time-dependent variational Monte Carlo simulations. It gives access to unprecedented long propagation times and to dimensions higher than one. In both one and two dimensions, we find ballistic light-cone spreading of correlations and extract accurate values of the light-cone velocity in the superfluid regime. We show that the spreading of correlations is generally supersonic, with a light-cone propagating faster than sound modes but slower than the maximum group velocity of density excitations, except at the Mott transition, where all the characteristic velocities are equal. Further, we show that in two dimensions the correlation spreading is highly anisotropic and presents nontrivial interference effects.
We study the light-cone and front dynamics of a single-particle continuous time extended quantum walk on a one-dimensional lattice with finite range hopping. We show that, in general, for an initially localized state, propagating wave fronts can be characterized as ordinary or extremal fronts with the latter exhibiting an anomalous subdiffusive scaling behavior in the front region. We investigate the dynamical global and local scaling properties of the cumulative probability distribution function for the extended walk with nearest- and next-nearest-neighbor hopping using analytical and numerical methods. The global scaling shows the existence of a ``causal light-cone'' corresponding to excitations traveling with a velocity smaller than a maximal ``light velocity.'' Maximal fronts moving with fixed light velocity bound the causal cone. The front regions spread with time subdiffusively exhibiting a local Airy scaling which leads to an internal staircase structure. At a certain critical next-nearest-neighbor hopping strength, there is a transition from a phase with one `causal cone' to a phase with two nested `causal cones' and the existence of an internal staircase structure in the corresponding cumulative distribution profiles. We also connect the study to that in spin chain systems and indicate that a single-particle quantum walk on the one-dimensional lattice already captures the many-body physics of a spin chain system. In particular, we suggest that the time evolution of a single-particle quantum walk on the one-dimensional lattice with an initially localized state is equivalent to the time evolution of a domain-wall initial state in a corresponding spin chain system.
We investigate the properties of the condensates of cold atoms at zero temperature in the tunable binary Bose-Einstein condensate system with a Rabi transition between atomic hyperfine states. We use this system to examine the effect of quantum fluctuations in a tunable quantum gas on phonon propagation. We show that the system can be represented by a coupled two-field model of a gapless phonon and a gapped mode, which are analogous to the Goldstone and Higgs particles in particle physics. We then further trace out the gapped modes to give an effective purely phononic theory using closed-time-path formalism. In particular, we are interested in the sound cone fluctuations due to the variation of the speed-of-sound acoustic metric, induced by quantum fluctuations of the gapped modes. These fluctuations can be interpreted as inducing a stochastic space-time, and thus are regarded as analogue phenomena of light cone fluctuations presumably arising from quantum gravity effects. The effects of fluctuations can be displayed in the variation in the travel time of sound waves. We suggest the relevant experiments to discuss the possibility of experimental observations.