Supersolids are a fundamental quantum phase of matter where the global phase and translational symmetries are spontaneously broken. The recently discovered supersolidity in quantum gases of strongly magnetic atoms gives the opportunity to explore in depth how superfluidity and crystalline order are mixed in this fascinating phase. The dipolar supersolid is usually created from a Bose-Einstein condensate, i.e., a standard superfluid, crossing a quantum phase transition that is related to the crystallization transitions of ordinary matter. In this work, we assess experimentally and theoretically the character of the superfluid-supersolid quantum phase transition. We find that one-row supersolids can have already two types of phase transitions, discontinuous and continuous, that are reminiscent of the first- and second-order transitions predicted in the thermodynamic limit in 2D and 1D, respectively. The dimensional crossover is peculiar to supersolids, is controlled via the transverse confinement and the atom number, and can be justified on the general ground of the Landau theory of phase transitions. The quasiadiabatic crossing of a continuous phase transition opens new directions of investigation for supersolids.

Driving a many-body system out of equilibrium induces phenomena such as the emergence and decay of transient states, which can manifest itself as pattern and domain formation. The understanding of these phenomena expands the scope of established thermodynamics into the out-of-equilibrium domain. Here, we experimentally and theoretically study the out-of-equilibrium dynamics of a bosonic lattice model subjected to a strong dc field, realized as ultracold atoms in a strongly tilted triangular optical lattice. We observe the emergence of pronounced density-wave patterns—which spontaneously break the underlying lattice symmetry—using a novel single-shot imaging technique with two-dimensional single-site resolution in three-dimensional systems, which also resolves the domain structure. Our study suggests that the short-time dynamics arises from resonant pair tunneling processes within an effective description of the tilted Hubbard model. More broadly, we establish the far out-of-equilibrium regime of lattice models subjected to a strong dc field, as an exemplary and paradigmatic scenario for transient pattern formation.

We consider a two-dimensional quantum memory of qubits on a torus which encode the extended Fibonacci string-net code and devise strategies for error correction when those qubits are subjected to depolarizing noise. Building on the concept of tube algebras, we construct a set of measurements and of quantum gates which map arbitrary qubit errors to the string-net subspace and allow for the characterization of the resulting error syndrome in terms of doubled Fibonacci anyons. Tensor network techniques then allow us to quantitatively study the action of Pauli noise on the string-net subspace. We perform Monte Carlo simulations of error correction in this Fibonacci code and compare the performance of several decoders. For the case of a fixed-rate sampling depolarizing noise model, we find an error correction threshold of 4.7% using a clustering decoder.

One manifestation of quantum chaos is a random-matrix-like fine-grained energy spectrum. Prior to the inverse level spacing time, random matrix theory predicts a “ramp” of increasing variance in the connected part of the spectral form factor. However, in realistic quantum chaotic systems, the finite-time dynamics of the spectral form factor is much richer, with the pure random matrix ramp appearing only at sufficiently late time. In this article, we present a hydrodynamic theory of the connected spectral form factor prior to the inverse level spacing time. We first derive a general formula for the spectral form factor of a system with almost-conserved sectors in terms of return probabilities and spectral form factors within each sector. Next we argue that the theory of fluctuating hydrodynamics can be adapted from the usual Schwinger-Keldysh contour to the periodic time setting needed for the spectral form factor, and we show explicitly that the general formula is recovered in the case of energy diffusion. We also initiate a study of interaction effects in this modified hydrodynamic framework and show how the Thouless time defined as the time required for the spectral form factor to approach the pure random matrix result is controlled by the slow hydrodynamics modes. We then extend the formalism to Floquet systems, where a ramp is expected but with a different coefficient, and we derive a crossover formula from the Hamiltonian ramp to the Floquet ramp when the Floquet drive is weak. Taken together, these results establish an effective field theory of chaotic spectral correlations which predicts the random matrix ramp at late time and computes corrections to it at earlier times.

We observe the emission of bunches of $k\ge 1$ photons by a circuit made of a microwave resonator in series with a voltage-biased tunable Josephson junction. The bunches are emitted at specific values $V_k$ of the bias voltage, for which each Cooper pair tunneling across the junction creates exactly $k$ photons in the resonator. The latter is a microfabricated spiral coil which resonates and leaks photons at 4.4 GHz in a measurement line. Its characteristic impedance of $1.97\mathrm{k}\mathrm{\Omega }$ is high enough to reach a strong junction-resonator coupling and a bright emission of the $k$-photon bunches. We show that a rotating-wave approximation treatment of the system accounts quantitatively for the observed radiation intensity, from $k=1$ to 6, and over 3 orders of magnitude when varying the Josephson energy $E_J$. We also measure the second-order correlation function of the radiated microwave to determine its Fano factor $F_k$, which in the low $E_J$ limit confirms with $F_k\simeq k$ the emission of $k$-photon bunches. At larger $E_J$, a more complex behavior is observed in quantitative agreement with numerical simulations.

Remarkably, complex assemblies of superconducting wires, electrodes, and Josephson junctions are compactly described by a handful of collective phase degrees of freedom that behave like quantum particles in a potential. Almost all these circuits operate in the regime where quantum phase fluctuations are small—the associated flux is smaller than the superconducting flux quantum—although entering the regime of large fluctuations would have profound implications for metrology and qubit protection. The difficulty arises from the apparent need for circuit impedances vastly exceeding the resistance quantum. Independently, exotic circuit elements that require Cooper pairs to form pairs in order to tunnel have been developed to encode and topologically protect quantum information. In this work, we demonstrate that pairing Cooper pairs magnifies the phase fluctuations of the circuit ground state. We measure a tenfold suppression of flux sensitivity of the first transition energy only, implying a twofold increase in the vacuum phase fluctuations and showing that the ground state is delocalized over several Josephson wells.

Nuclear spins interact weakly with their environment and therefore exhibit long coherence times. This has led to their use as memory qubits in quantum information platforms, where they are controlled via electromagnetic waves. Scaling up such platforms comes with challenges in terms of power efficiency, as well as cross-talk between devices. Here, we demonstrate coherent control of a single nuclear spin using surface acoustic waves. We use mechanically driven Ramsey and spin-echo sequences to show that the nuclear spin retains its excellent coherence properties. We estimate that this approach requires 2–3 orders of magnitude less power than more conventional control methods. Furthermore, this technique is scalable because of the possibility of guiding acoustic waves and reduced cross-talk between different acoustic channels. This work demonstrates the use of mechanical waves for complex quantum control sequences, offers an advantageous alternative to the standard electromagnetic control of nuclear spins, and opens prospects for incorporating nuclear spins in mechanically interfaced hybrid quantum architectures.

We investigate the collective decay dynamics of atoms with a generic multilevel structure (angular momenta $F\leftrightarrow F^{\prime }$) coupled to two light modes of different polarization inside a cavity. In contrast to two-level atoms, we find that multilevel atoms can harbor eigenstates that are perfectly dark to cavity decay even within the subspace of permutationally symmetric states (collective Dicke manifold). The dark states arise from destructive interference between different internal transitions and are shown to be entangled. Remarkably, the superradiant decay of multilevel atoms can end up stuck in one of these dark states, where a macroscopic fraction of the atoms remains excited. This opens the door to the preparation of entangled dark states of matter through collective dissipation that are useful for quantum sensing and quantum simulation. Our predictions should be readily observable in current optical cavity experiments with alkaline-earth atoms or Raman-dressed transitions.

Understanding and protecting the coherence of individual quantum systems is a central challenge in quantum science and technology. Over the past decades, a rich variety of methods to extend coherence have been developed. A complementary approach is to look for naturally occurring systems that are inherently protected against decoherence. Here, we show that pairs of identical nuclear spins in solids form intrinsically long-lived qubits. We study three carbon-13 pairs in diamond and realize high-fidelity measurements of their quantum states using a single nitrogen-vacancy center in their vicinity. We then reveal that the spin pairs are robust to external perturbations due to a combination of three phenomena: a decoherence-free subspace, a clock transition, and a variant on motional narrowing. The resulting inhomogeneous dephasing time is $T_2^{*}=1.9(3)\min$, the longest reported for individually controlled qubits. Finally, we develop complete control and realize an entangled state between two spin pairs through projective parity measurements. These long-lived qubits are abundantly present in diamond and other solids and provide new opportunities for ancilla-enhanced quantum sensing and for robust memory qubits for quantum networks.

We characterize the variational power of quantum circuit tensor networks in the representation of physical many-body ground states. Such tensor networks are formed by replacing the dense block unitaries and isometries in standard tensor networks by local quantum circuits. We explore both quantum circuit matrix product states and the quantum circuit multiscale entanglement renormalization Ansatz, and introduce an adaptive method to optimize the resulting circuits to high fidelity with more than ${10}^4$ parameters. We benchmark their expressiveness against standard tensor networks, as well as other common circuit architectures, for the 1D and 2D Heisenberg and 1D Fermi-Hubbard models. We find quantum circuit tensor networks to be substantially more expressive than other quantum circuits for these problems, and that they can even be more compact than standard tensor networks. Extrapolating to circuit depths which can no longer be emulated classically, this suggests a region of advantage in quantum expressiveness in the representation of physical ground states.

The extension of many-body quantum dynamics to the nonunitary domain has led to a series of exciting developments, including new out-of-equilibrium entanglement phases and phase transitions. We show how a duality transformation between space and time, on one hand, and unitarity and nonunitarity, on the other, can be used to realize steady-state phases of nonunitary dynamics that exhibit a rich variety of behavior in their entanglement scaling with subsystem size—from logarithmic to extensive to fractal. We show how these outcomes in nonunitary circuits (that are “spacetime dual” to unitary circuits) relate to the growth of entanglement in time in the corresponding unitary circuits, and how they differ, through an exact mapping to a problem of unitary evolution with boundary decoherence, in which information gets “radiated away” from one edge of the system. In spacetime duals of chaotic unitary circuits, this mapping allows us to analytically derive a nonthermal volume-law entangled phase with a universal logarithmic correction to the entropy, previously observed in unitary-measurement dynamics. Notably, we also find robust steady-state phases with fractal entanglement scaling, $S(\ell )\sim {\ell }^{\alpha }$ with tunable $0<\alpha <1$ for subsystems of size $\ell$ in one dimension. We present an experimental protocol for preparing these novel steady states with only a vanishing density of postselected measurements via a type of “teleportation” between spacelike and timelike slices of quantum circuits.

Ultracold atomic gas provides a useful tool to explore many-body physics. One of the recent additions to this experimental toolbox is Floquet engineering, where periodic modulation of the Hamiltonian allows the creation of effective potentials that do not exist otherwise. When subject to external modulations, however, generic interacting many-body systems absorb energy, thus posing a heating problem that may impair the usefulness of this method. For discrete systems with bounded local energy, an exponentially suppressed heating rate with driving frequency has been observed previously, leaving the system in a prethermal state for exceedingly long durations. However, for systems in continuous space, the situation remains unclear. Here, we show that Floquet engineering can be applied to a strongly interacting degenerate Fermi gas held in a flat boxlike potential without inducing excessive heating on experimentally relevant timescales. The driving eliminates the effect of a spin-dependent potential originating from the simultaneous magnetic levitation of two different spin states. We calculate the heating rate and obtain a power-law suppression with the drive frequency. To further test the many-body behavior of the driven gas, we measure both the pair-condensation fraction at unitarity and the contact parameter across the BEC-BCS crossover. At low driving frequencies, the condensate fraction is reduced by the time-dependent force, but at higher frequencies, it revives and attains an even higher value than without driving. Our results are promising for future exploration of exotic many-body phases of a bulk strongly interacting Fermi gas with dynamically engineered Hamiltonians.

Quantum processing architectures that include multiple qubit modalities offer compelling strategies for high-fidelity operations and readout, quantum error correction, and a path for scaling to large system sizes. Such hybrid architectures have been realized for leading platforms, including superconducting circuits and trapped ions. Recently, a new approach for constructing large, coherent quantum processors has emerged based on arrays of individually trapped neutral atoms. However, these demonstrations have been limited to arrays of a single atomic element where the identical nature of the atoms makes crosstalk-free control and nondemolition readout of a large number of atomic qubits challenging. Here we introduce a dual-element atom array with individual control of single rubidium and cesium atoms. We demonstrate their independent placement in arrays with up to 512 trapping sites and observe negligible crosstalk between the two elements. Furthermore, by continuously reloading one atomic element while maintaining an array of the other, we demonstrate a new continuous operation mode for atom arrays without any off-time. Our results enable avenues for auxiliary-qubit-assisted quantum protocols such as quantum nondemolition measurements and quantum error correction, as well as continuously operating quantum processors and sensors.

The presence of noise or the interaction with an environment can radically change the dynamics of observables of an otherwise isolated quantum system. We derive a bound on the speed with which observables of open quantum systems evolve. This speed limit is divided into Mandelstam and Tamm’s original time-energy uncertainty relation and a time-information uncertainty relation recently derived for classical systems, and both are generalized to open quantum systems. By isolating the coherent and incoherent contributions to the system dynamics, we derive both lower and upper bounds on the speed of evolution. We prove that the latter provide tighter limits on the speed of observables than previously known quantum speed limits and that a preferred basis of speed operators serves to completely characterize the observables that saturate the speed limits. We use this construction to bound the effect of incoherent dynamics on the evolution of an observable and to find the Hamiltonian that gives the maximum coherent speedup to the evolution of an observable.

A particle in an Anderson-localized system, if launched in any direction, should, on average, return to its starting point and stay there. Despite the central role played by Anderson localization in the modern understanding of condensed matter, this “quantum boomerang” effect, an essential feature of the localized state, was only recently theoretically predicted. We report the experimental observation of the quantum boomerang effect. Using a degenerate gas and a phase-shifted pair of optical lattices, we not only confirm the predicted dependence of the boomerang effect on Floquet gauge but also elucidate the crucial role of initial-state symmetries. Highlighting the key role of localization, we observe that as stochastic kicking destroys dynamical localization, the quantum boomerang effect also disappears. Measured dynamics are in agreement with numerical models and with predictions of an analytical theory we present which clarifies the connection between time-reversal symmetry and boomerang dynamics. These results showcase a unique experimental probe of the underlying quantum nature of Anderson localized matter.

We describe a qubit linearly coupled to a heat bath, either directly or via a cavity. The main focus of the paper is on calorimetric detection in a realistic circuit, specifically a solid-state qubit coupled to a resistor as an absorber. The bath in the model is formed of oscillators initially in the ground state with a distribution of energies and coupling strengths. A direct numerical solution of the Schrödinger equation for the full system including up to ${10}^6$ oscillators in the bath verifies the expected decay process. We address quantitatively the question of separation of the qubit and bath by adding a cavity in between which by detuning allows one to adjust the decay rate into a convenient regime for detection purposes. Most importantly, we propose splitting a quantum to two uncoupled baths and performing a cross-correlation measurement of their temperatures. This technique enhances significantly the signal-to-noise ratio of the calorimeter.

Coherent feedback stabilizes a system toward a target state without the need of a measurement, thus avoiding the quantum backaction inherent to measurements. Here, we employ optical coherent feedback to remotely cool a nanomechanical membrane using atomic spins as a controller. Direct manipulation of the atoms allows us to tune from strong coupling to an overdamped regime. Making use of the full coherent control offered by our system, we perform spin-membrane state swaps combined with stroboscopic spin pumping to cool the membrane in a room-temperature environment to $T=216\mathrm{mK}$ (${\overline{n}}_m=2.3\times {10}^3\mathrm{phonons}$) in $200\mu \mathrm{s}$. We furthermore observe and study the effects of delayed feedback on the cooling performance. Starting from a cryogenically precooled membrane, this method would enable cooling of the mechanical oscillator close to its quantum mechanical ground state and the preparation of nonclassical states.

The spectral form factor (SFF), characterizing statistics of energy eigenvalues, is a key diagnostic of many-body quantum chaos. In addition, partial spectral form factors (PSFFs) can be defined which refer to subsystems of the many-body system. They provide unique insights into energy eigenstate statistics of many-body systems, as we show in an analysis on the basis of random matrix theory and of the eigenstate thermalization hypothesis. We propose a protocol that allows the measurement of the SFF and PSFFs in quantum many-body spin models, within the framework of randomized measurements. Aimed to probe dynamical properties of quantum many-body systems, our scheme employs statistical correlations of local random operations which are applied at different times in a single experiment. Our protocol provides a unified test bed to probe many-body quantum chaotic behavior, thermalization, and many-body localization in closed quantum systems which we illustrate with numerical simulations for Hamiltonian and Floquet many-body spin systems.

We revisit the dissipative approach to producing and stabilizing spin-squeezed states of an ensemble of $N$ two-level systems, providing a detailed analysis of two surprising yet generic features of such protocols. The first is a macroscopic sensitivity of the steady state to whether $N$ is even or odd. We discuss how this effect can be avoided (if the goal is parity-insensitive squeezing) or could be exploited as a new kind of sensing modality to detect the addition or removal of a single spin. The second effect is an anomalous emergent long timescale and a “prethermalized” regime that occurs for even weak single-spin dephasing. This effect allows one to have strong spin squeezing over a long transient time even though the level of spin squeezing in the steady state is very small. We also discuss a general hybrid-systems approach for implementing dissipative spin squeezing that does not require squeezed input light or complex multilevel atoms, but instead makes use of bosonic reservoir-engineering ideas. Our protocol is compatible with a variety of platforms, including trapped ions, nitrogen-vacancy defect spins coupled to diamond optomechanical crystals, and spin ensembles coupled to superconducting microwave circuits.

Deterministic photon-photon gates enable the controlled generation of entanglement between mobile carriers of quantum information. Such gates have thus far been exclusively realized in the optical domain and by relying on postselection. Here, we present a nonpostselected, deterministic, photon-photon gate in the microwave frequency range realized using superconducting circuits. We emit photonic qubits from a source chip and route those qubits to a gate chip with which we realize a universal gate set by combining controlled absorption and reemission with single-qubit gates and qubit-photon controlled-phase gates. We measure quantum process fidelities of 75% for single- and of 57% for two-qubit gates, limited mainly by radiation loss and decoherence. This universal gate set has a wide range of potential applications in superconducting quantum networks.