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We study the quantum evolution of 1D Bose gases immediately after several variants of high-energy quenches, both experimentally and theoretically. Using the advantages conveyed by the relative simplicity of these nearly integrable many-body systems, we are able to differentiate the behavior of two distinct but often temporally overlapping processes, hydrodynamization and local prethermalization. There is a universal character to our findings, which can be applied to the short-time behavior of any interacting many-body quantum system after a sudden high-energy quench. We specifically discuss its potential relevance to heavy-ion collisions., Comment: 17 pages, 18 figures

Hydrodynamics accurately describes relativistic heavy-ion collision experiments well before local thermal equilibrium is established. This unexpectedly rapid onset of hydrodynamics -- which takes place on the fastest available timescale -- is called hydrodynamization. It occurs when an interacting quantum system is quenched with an energy density that is much greater than its initial energy density. During hydrodynamization, energy gets redistributed across very different energy scales. Hydrodynamization precedes local equilibration among momentum modes, which is local prethermalization to a generalized Gibbs ensemble in nearly integrable systems or local thermalization in non-integrable systems. Many theories of quantum dynamics postulate local (pre)thermalization, but the associated timescale has not been quantitatively studied. Here we use an array of 1D Bose gases to directly observe both hydrodynamization and local prethermalization. After we apply a Bragg scattering pulse, hydrodynamization is evident in the fast redistribution of energy among distant momentum modes, which occurs on timescales associated with the Bragg peak energies. Local prethermalization can be seen in the slower redistribution of occupation among nearby momentum modes. We find that the time scale for local prethermalization in our system is inversely proportional to the momenta involved. During hydrodynamization and local prethermalization, existing theories cannot quantitatively model our experiment. Exact theoretical calculations in the Tonks-Girardeau limit show qualitatively similar features., Comment: 28 pages, 4 main figures, 8 extended data figures

We propose a way to measure the qubit state of an arbitrary sub-ensemble of atoms in an array without significantly disturbing the quantum information in the unmeasured atoms. The idea is to first site-selectively transfer atoms out of the qubit basis so that one of the two states at a time is put into an auxiliary state. Electromagnetically induced transparency (EIT) light will then protect most states while detection light is scattered from atoms in the auxiliary state, which is made immune to the EIT protection by angular momentum selection rules and carefully chosen light polarization. The two states will be measured in turn, after which it is possible to recool and return the atoms to a qubit state. These measurements can be the basis of quantum error correction., Comment: 14 pages, 16 figures

The dynamics of strongly interacting many-body quantum systems are notoriously complex and difficult to simulate. A new theory, generalized hydrodynamics (GHD), promises to efficiently accomplish such simulations for nearly-integrable systems. It predicts the evolution of the distribution of rapidities, which are the momenta of the quasiparticles in integrable systems. GHD was recently tested experimentally for weakly interacting atoms, but its applicability to strongly interacting systems has not been experimentally established. Here we test GHD with bundles of one-dimensional (1D) Bose gases by performing large trap quenches in both the strong and intermediate coupling regimes. We measure the evolving distribution of rapidities, and find that theory and experiment agree well over dozens of trap oscillations, for average dimensionless coupling strengths that range from 0.3 to 9.3. By also measuring momentum distributions, we gain experimental access to the interaction energy and thus to how the quasiparticles themselves evolve. The accuracy of GHD demonstrated here confirms its wide applicability to the simulation of nearly-integrable quantum dynamical systems. Future experimental studies are needed to explore GHD in spin chains, as well as the crossover between GHD and regular hydrodynamics in the presence of stronger integrability breaking perturbations., Comment: 21 pages, 4 main text figures, 10 extended data figures

Quantum simulators are a promising technology on the spectrum of quantum devices from specialized quantum experiments to universal quantum computers. These quantum devices utilize entanglement and many-particle behaviors to explore and solve hard scientific, engineering, and computational problems. Rapid development over the last two decades has produced more than 300 quantum simulators in operation worldwide using a wide variety of experimental platforms. Recent advances in several physical architectures promise a golden age of quantum simulators ranging from highly optimized special purpose simulators to flexible programmable devices. These developments have enabled a convergence of ideas drawn from fundamental physics, computer science, and device engineering. They have strong potential to address problems of societal importance, ranging from understanding vital chemical processes, to enabling the design of new materials with enhanced performance, to solving complex computational problems. It is the position of the community, as represented by participants of the NSF workshop on "Programmable Quantum Simulators," that investment in a national quantum simulator program is a high priority in order to accelerate the progress in this field and to result in the first practical applications of quantum machines. Such a program should address two areas of emphasis: (1) support for creating quantum simulator prototypes usable by the broader scientific community, complementary to the present universal quantum computer effort in industry; and (2) support for fundamental research carried out by a blend of multi-investigator, multi-disciplinary collaborations with resources for quantum simulator software, hardware, and education., Comment: 41 pages -- references and acknowledgments added in v2

We observe dynamical fermionization, where the momentum distribution of a Tonks-Girardeau (T-G) gas of strongly interacting bosons in 1D evolves from bosonic to fermionic after its axial confinement is removed. The asymptotic momentum distribution after expansion in 1D is the distribution of rapidities, which are the conserved quantities associated with many-body integrable systems. Rapidities have not previously been measured in any interacting many-body quantum system. Our measurements agree well with T-G gas theory. We also study momentum evolution after the trap depth is suddenly changed to a new non-zero value. We observe the predicted bosonic-fermionic oscillations and see deviations from the theory outside of the T-G gas limit.

We study the loss of atoms in quantum Newton's cradles (QNCs) with a range of average energies and transverse confinements. We find that the three-body collision rate in one-dimension is strongly energy dependent, as predicted by a strictly 1D theory. We adapt the theory to atoms in waveguides, then using detailed momentum measurements to infer all the collisions that occur, we compare the observed loss to the adapted theory and find that they agree well.

We demonstrate qubit state measurement for ~160 Cesium atoms in a 3D optical lattice based on coherent spatial splitting of the atoms' wavefunctions. The measurement fidelity is 0.9994, essentially independent of the number of qubits measured. The detection scheme is reminiscent of the Stern-Gerlach experiment, but carried out in light traps. The measurement causes no loss, which allows us to demonstrate re-initialization of the 3D qubit array after state measurement, including the replacement of an atom lost to a background gas collision., Comment: 25 pages, 4 figures, Methods section, 3 supplementary figures

We demonstrate highly filled 3D arrays of neutral atoms by moving individual atoms in a 3D optical lattice. Starting from a randomly half-filled 5x5x5 optical lattice of Cesium atoms, a sorting algorithm calculates and implements a sequence of high fidelity targeted state flips and state dependent motion steps to fill a sub-lattice in real time. We achieve a filling fraction of ~97% and a perfect filling rate of 30%. With 89% of the atoms cooled to the 3D vibrational ground state, the sorting procedure reduces the configurational entropy by a factor of 8 and the total system entropy by a factor of 2.44. The sorting process is analogous to a Maxwell's demon., Comment: 19 pages, 4 figures, Methods section, 2 extended data figures

We explore ways to use the ability to measure the populations of individual magnetic sublevels to improve the sensitivity of magnetic field measurements and measurements of atomic electric dipole moments (EDMs). When atoms are initialized in the $m=0$ magnetic sublevel, the shot-noise-limited uncertainty of these measurements is $1/\sqrt{2F(F+1)}$ smaller than that of a Larmor precession measurement. When the populations in the even (or odd) magnetic sublevels are combined, we show that these measurements are independent of the tensor Stark shift and the second order Zeeman shift. We discuss the complicating effect of a transverse magnetic field and show that when the ratio of the tensor Stark shift to the transverse magnetic field is sufficiently large, an EDM measurement with atoms initialized in the superposition of the stretched states can reach the optimal sensitivity.

Although the quality of quantum bits (qubits) and quantum gates has been steadily improving, the available quantity of qubits has increased quite slowly. To address this important issue in quantum computing, we have demonstrated arbitrary single qubit gates based on targeted phase shifts, an approach that can be applied to atom, ion or other atom-like systems. These gates are highly insensitive to addressing beam imperfections and have little crosstalk, allowing for a dramatic scaling up of qubit number. We have performed gates in series on 48 individually targeted sites in a 40% full $5\times 5\times 5$ 3D array created by an optical lattice. Using randomized benchmarking, we demonstrate an average gate fidelity of 0.9962(16), with an average crosstalk fidelity of 0.9979(2)., Comment: 8 pages, 4 figures and 1 table, supplementary material included

We demonstrate arbitrary coherent addressing of individual neutral atoms in a $5\times 5\times 5$ array formed by an optical lattice. Addressing is accomplished using rapidly reconfigurable crossed laser beams to selectively ac Stark shift target atoms, so that only target atoms are resonant with state-changing microwaves. The effect of these targeted single qubit gates on the quantum information stored in non-targeted atoms is smaller than $3\times 10^{-3}$ in state fidelity. This is an important step along the path of converting the scalability promise of neutral atoms into reality., Comment: 11 pages, 4 figures, supplemental material included

Ultracold atomic gases have revolutionized the study of non-equilibrium dynamics in quantum many-body systems. Many counterintuitive non-equilibrium effects have been observed, such as suppressed thermalization in a one-dimensional (1D) gas, the formation of repulsive self-bound dimers, and identical behaviors for attractive and repulsive interactions. Here, we observe the expansion of a bundle of ultracold 1D Bose gases in a flat-bottomed optical lattice potential. By combining in situ measurements with photoassociation, we follow the spatial dynamics of singly, doubly, and triply occupied lattice sites. The system sheds interaction energy by dissolving some doublons and triplons. Some singlons quantum distill out of the doublon center, while others remain confined. Our Gutzwiller mean-field model captures these experimental features in a physically clear way. These experiments might be used to study thermalization in systems with particle losses or the evolution of quantum entanglement, or if applied to fermions, to prepare very low entropy states., Comment: 22 pages, 8 figures

We theoretically study how excitations due to spontaneous emission and trap fluctuations combine with elastic collisions to change the momentum distribution of a trapped non-degenerate one-dimensional (1D) Bose gas. Using calculated collisional relaxation rates, we first present a semi-analytical model for the momentum distribution evolution to get insight into the main processes responsible for the system dynamics. We then present a Monte-Carlo simulation that includes features that cannot be handled analytically, and compare its results to experimental data. These calculations provide a baseline for how integrable 1D Bose gases evolve due to heating processes in the absence of diffractive collisions that might thermalize the gases.

We demonstrate Babinet's principle by the absorption of high intensity light from dense clouds of ultracold atoms. Images of the diffracted light are directly related to the spatial distribution of atoms. The advantages of employing Babinet's principle as an imaging technique are that it is easy to implement and the detected signal is large. We discuss the regimes of applicability of this technique as well as its limitations., Comment: 4 pages, 2 figures

We describe theoretical models for the recent experimental observation of Macroscopic Quantum Self-Trapping (MQST) in the transverse dynamics of an ultracold bosonic gas in a 2D lattice. The pure mean-field model based on the solution of coupled nonlinear equations fails to reproduce the experimental observations. It greatly overestimates the initial expansion rates at short times and predicts a slower expansion rate of the cloud at longer times. It also predicts the formation of a hole surrounded by a steep square fort-like barrier which was not observed in the experiment. An improved theoretical description based on a simplified Truncated Wigner Approximation (TWA), which adds phase and number fluctuations in the initial conditions, pushes the theoretical results closer to the experimental observations but fails to quantitatively reproduce them. An explanation of the delayed expansion as a consequence of a new type of self-trapping mechanism, where quantum correlations suppress tunneling even when there are no density gradients, is discussed and supported by numerical time-dependent Density Matrix Renormalization Group (t-DMRG) calculations performed in a simplified two coupled tubes set-up.

We study the transverse expansion of arrays of ultracold $^{87}$Rb atoms weakly confined in tubes created by a 2D optical lattice, and observe that transverse expansion is delayed because of mutual atom interactions. A mean-field model of a coupled array shows that atoms become localized within a roughly square fort-like self-trapping barrier with time-evolving edges. But the observed dynamics is poorly described by the mean-field model. Theoretical introduction of random phase fluctuations among tubes improves the agreement with experiment, but does not correctly predict the density at which the atoms start to expand with larger lattice depths. Our results suggest a new type of self-trapping, where quantum correlations suppress tunneling even when there are no density gradients.

We demonstrate 3D microwave projection sideband cooling of trapped, neutral atoms. The technique employs state-dependent potentials that enable microwave photons to drive vibration-number reducing transitions. The particular cooling sequence we employ uses minimal spontaneous emission, and works even for relatively weakly bound atoms. We cool 76% of atoms to their 3D vibrational ground states in a site-resolvable 3D optical lattice., Comment: 5 pages, 4 figures, Supplemental Material included. To appear in Physical Review Letters

We numerically calculate the reliability with which one can optically determine the presence or absence of an individual scatterer in a randomly occupied 3D array of well-localized, coherently radiating scatterers. The reliability depends in a complicated way on the ratio of lattice spacing to wavelength and the numerical aperture of the imaging system. The behavior can be qualitatively understood by considering the dependence of Bragg scattering modes on lattice spacing. These results are of interest for atomic implementations of quantum information processing.

We present a scheme for correcting qubit loss error while quantum computing with neutral atoms in an addressable optical lattice. The qubit loss is first detected using a quantum non-demolition measurement and then transformed into a standard qubit error by inserting a new atom in the vacated lattice site. The logical qubit, encoded here into four physical qubits with the Grassl-Beth-Pellizzari code, is reconstructed via a sequence of one projective measurement, two single-qubit gates, and three controlled-NOT operations. No ancillary qubits are required. Both quantum non-demolition and projective measurements are implemented using a cavity QED system which can also detect a general leakage error and thus allow qubit loss to be corrected within the same framework. The scheme can also be applied in quantum computation with trapped ions or with photons., Comment: 5 pages, 3 figures