In quantum many-body systems with local interactions, quantum information and entanglement cannot spread outside of a linear light cone, which expands at an emergent velocity analogous to the speed of light. Local operations at sufficiently separated spacetime points approximately commute—given a many-body state $|\psi ⟩$, ${\mathcal{O}}_x(t){\mathcal{O}}_y|\psi ⟩\approx {\mathcal{O}}_y{\mathcal{O}}_x(t)|\psi ⟩$ with arbitrarily small errors—so long as $|x-y|\gtrsim vt$, where $v$ is finite. Yet, most nonrelativistic physical systems realized in nature have long-range interactions: Two degrees of freedom separated by a distance $r$ interact with potential energy $V(r)\propto 1/r^{\alpha }$. In systems with long-range interactions, we rigorously establish a hierarchy of linear light cones: At the same $\alpha$, some quantum information processing tasks are constrained by a linear light cone, while others are not. In one spatial dimension, this linear light cone exists for every many-body state $|\psi ⟩$ when $\alpha >3$ (Lieb-Robinson light cone); for a typical state $|\psi ⟩$ chosen uniformly at random from the Hilbert space when $\alpha >\frac{5}{2}$ (Frobenius light cone); and for every state of a noninteracting system when $\alpha >2$ (free light cone). These bounds apply to time-dependent systems and are optimal up to subalgebraic improvements. Our theorems regarding the Lieb-Robinson and free light cones—and their tightness—also generalize to arbitrary dimensions. We discuss the implications of our bounds on the growth of connected correlators and of topological order, the clustering of correlations in gapped systems, and the digital simulation of systems with long-range interactions. In addition, we show that universal quantum state transfer, as well as many-body quantum chaos, is bounded by the Frobenius light cone and, therefore, is poorly constrained by all Lieb-Robinson bounds.

We introduce a new boundary condition which renders the flux-insertion argument for the Lieb-Schultz-Mattis-type theorems in two or higher dimensions free from the specific choice of system sizes. It also enables a formulation of the Lieb-Schultz-Mattis-type theorems in arbitrary dimensions in terms of the anomaly in field theories in $1+1$ dimensions with a bulk correspondence as a BF theory in $2+1$ dimensions. Furthermore, we apply the anomaly-based formulation to the constraints on a half-filled spinless fermion on a square lattice with $\pi$ flux, utilizing a time-reversal, magnetic translations and an on-site internal $\mathrm{U}(N)$ symmetries. This demonstrates the role of the time-reversal anomaly on the ingappabilities of a lattice model. Moreover, by our new boundary condition, we show that the many-body Chern number of this lattice model is nonvanishing as $N$ mod $2N$ in the presence of $\mathrm{U}(N)$ and magnetic translations. This can be a general mechanism of anomaly-based constraints on quantized Hall conductance, which generally depends on high-energy physics, from field theory.

Heisenberg exchange coupling between neighboring electron spins in semiconductor quantum dots provides a powerful tool for quantum information processing and simulation. Although so far unrealized, extended Heisenberg spin chains can enable long-distance quantum information transfer and the generation of nonequilibrium quantum states. In this work, we implement simultaneous, coherent exchange coupling between all nearest-neighbor pairs of spins in a quadruple quantum dot. The main challenge in implementing simultaneous exchange couplings is the nonlinear and nonlocal dependence of the exchange couplings on gate voltages. Through a combination of electrostatic simulation and theoretical modeling, we show that this challenge arises primarily due to lateral shifts of the quantum dots during gate pulses. Building on this insight, we develop two models that can be used to predict the confinement gate voltages for a desired set of exchange couplings. Although the model parameters depend on the number of exchange couplings desired (suggesting that effects in addition to lateral wave-function shifts are important), the models are sufficient to enable simultaneous and independent control of all three exchange couplings in a quadruple quantum dot. We demonstrate two-, three-, and four-spin exchange oscillations, and our data agree with simulations.

We develop a general stochastic thermodynamics of RLC electrical networks built on top of a graph-theoretical representation of the dynamics commonly used by engineers. The network is (i) open, as it contains resistors and current and voltage sources, (ii) nonisothermal, as resistors may be at different temperatures, and (iii) driven, as circuit elements may be subjected to external parametric driving. The proper description of the heat dissipated in each resistor requires care within the white-noise idealization as it depends on the network topology. Our theory provides the basis to design circuits-based thermal machines, as we illustrate by designing a refrigerator using a simple driven circuit. We also derive exact results for the low-temperature regime in which the quantum nature of the electrical noise must be taken into account. We do so using a semiclassical approach, which can be shown to coincide with a fully quantum treatment of linear circuits for which canonical quantization is possible. We use this approach to generalize the Landauer-Büttiker formula for energy currents to arbitrary time-dependent driving protocols.

Quantum metrology is a powerful tool for explorations of fundamental physical phenomena and applications in material science and biochemical analysis. While in principle the sensitivity can be improved by increasing the density of sensing particles, in practice this improvement is severely hindered by interactions between them. Here, using a dense ensemble of interacting electronic spins in diamond, we demonstrate a novel approach to quantum metrology to surpass such limitations. It is based on a new method of robust quantum control, which allows us to simultaneously suppress the undesired effects associated with spin-spin interactions, disorder, and control imperfections, enabling a fivefold enhancement in coherence time compared to state-of-the-art control sequences. Combined with optimal spin state initialization and readout directions, this allows us to achieve an ac magnetic field sensitivity well beyond the previous limit imposed by interactions, opening a new regime of high-sensitivity solid-state ensemble magnetometers.

We introduce a new approach for the robust control of quantum dynamics of strongly interacting many-body systems. Our approach involves the design of periodic global control pulse sequences to engineer desired target Hamiltonians that are robust against disorder, unwanted interactions, and pulse imperfections. It utilizes a matrix representation of the Hamiltonian engineering protocol based on time-domain transformations of the Pauli spin operator along the quantization axis. This representation allows us to derive a concise set of algebraic conditions on the sequence matrix to engineer robust target Hamiltonians, enabling the simple yet systematic design of pulse sequences. We show that this approach provides an efficient framework to (i) treat any secular many-body Hamiltonian and engineer it into a desired form, (ii) target dominant disorder and interaction characteristics of a given system, (iii) achieve robustness against imperfections, (iv) provide optimal sequence length within given constraints, and (v) substantially accelerate numerical searches of pulse sequences. Using this systematic approach, we develop novel sets of pulse sequences for the protection of quantum coherence, optimal quantum sensing, and quantum simulation. Finally, we experimentally demonstrate the robust operation of these sequences in a system with the most general interaction form.

We propose a novel one-way quantum repeater architecture based on photonic tree-cluster states. Encoding a qubit in a photonic tree cluster protects the information from transmission loss and enables long-range quantum communication through a chain of repeater stations. As opposed to conventional approaches that are limited by the two-way communication time, the overall transmission rate of the current quantum repeater protocol is determined by the local processing time enabling very high communication rates. We further show that such a repeater can be constructed with as little as two stationary qubits and one quantum emitter per repeater station, which significantly increases the experimental feasibility. We discuss potential implementations with diamond defect centers and semiconductor quantum dots efficiently coupled to photonic nanostructures and outline how such systems may be integrated into repeater stations.

The efficient simulation of quantum systems is a primary motivating factor for developing controllable quantum machines. For addressing systems with underlying bosonic structure, it is advantageous to utilize a naturally bosonic platform. Optical photons passing through linear networks may be configured to perform quantum simulation tasks, but the efficient preparation and detection of multiphoton quantum states of light in linear optical systems are challenging. Here, we experimentally implement a boson sampling protocol for simulating molecular vibronic spectra [J. Huh et al., Nat. Photonics 9, 615 (2015)] in a two-mode superconducting device. In addition to enacting the requisite set of Gaussian operations across both modes, we fulfill the scalability requirement by demonstrating, for the first time in any platform, a high-fidelity single-shot photon number resolving detection scheme capable of resolving up to 15 photons per mode. Furthermore, we exercise the capability of synthesizing non-Gaussian input states to simulate spectra of molecular ensembles in vibrational excited states. We show the reprogrammability of our implementation by extracting the spectra of photoelectron processes in ${\mathrm{H}}_2\mathrm{O}$, ${\mathrm{O}}_3$, ${\mathrm{NO}}_2$, and ${\mathrm{SO}}_2$. The capabilities highlighted in this work establish the superconducting architecture as a promising platform for bosonic simulations, and by combining them with tools such as Kerr interactions and engineered dissipation, enable the simulation of a wider class of bosonic systems.

The precise engineering of quantum states, a basic prerequisite for technologies such as quantum-enhanced sensing or quantum computing, becomes more challenging with increasing dimension of the system Hilbert space. Standard preparation techniques then require a large number of operations or slow adiabatic evolution and give access to only a limited set of states. Here, we use quantum optimal control theory to overcome this problem and derive shaped radio-frequency pulses to experimentally navigate the Stark manifold of a Rydberg atom. We demonstrate that optimal control, beyond improving the fidelity of an existing protocol, also enables us to accurately generate a nonclassical superposition state that cannot be prepared with reasonable fidelity using standard techniques. Optimal control thus substantially enlarges the range of accessible states. Our joint experimental and theoretical work establishes quantum optimal control as a key tool for quantum engineering in complex Hilbert spaces.

Using the deterministic, on-demand generation of two entangled phonons, we demonstrate a quantum eraser protocol in a phononic interferometer where the which-path information can be heralded during the interference process. Omitting the heralding step yields a clear interference pattern in the interfering half-quanta pathways; including the heralding step suppresses this pattern. If we erase the heralded information after the interference has been measured, the interference pattern is recovered, thereby implementing a delayed-choice quantum erasure. The test is implemented using a closed surface acoustic wave communication channel into which one superconducting qubit can emit itinerant phonons that the same or a second qubit can later recapture. If the first qubit releases only half of a phonon, the system follows a superposition of paths during the phonon propagation: either an itinerant phonon is in the channel or the first qubit remains in its excited state. These two paths are made to constructively or destructively interfere by changing the relative phase of the two intermediate states, resulting in a phase-dependent modulation of the first qubit’s final state, following interaction with the half-phonon. A heralding mechanism is added to this construct, entangling a heralding phonon with the signaling phonon. The first qubit emits a phonon herald conditioned on the qubit being in its excited state, with no signaling phonon, and the second qubit catches this heralding phonon, storing which-path information which can either be read out, destroying the signaling phonon’s self-interference, or erased.

Quantum computing and quantum simulation can be implemented by concatenation of one- and two-qubit gates and interactions. For most physical implementations, however, it may be advantageous to explore state components and interactions that depart from this universal paradigm and offer faster or more robust access to more advanced operations on the system. In this article, we show that adiabatic passage along the dark eigenstate of excitation exchange interactions can be used to implement fast multiqubit Toffoli (${\mathrm{C}}_k$-NOT) and fan-out (C-${\text{NOT}}^k$) gates. This mechanism can be realized by simultaneous excitation of atoms to Rydberg levels, featuring resonant exchange interaction. Our theoretical estimates and numerical simulations show that these multiqubit Rydberg gates are possible with errors below 1% for up to 20 qubits. The excitation exchange mechanism is ubiquitous across experimental platforms, and we show that similar multiqubit gates can be implemented in superconducting circuits.

Nuclear magnetic resonance (NMR) spectroscopy is a widely used tool for chemical analysis and molecular structure identification. Because it typically relies on the weak magnetic fields produced by a small thermal nuclear spin polarization, NMR suffers from poor molecule-number sensitivity compared to other analytical techniques. Recently, a new class of NMR sensors based on optically probed nitrogen-vacancy (NV) quantum defects in diamond have allowed molecular spectroscopy from sample volumes several orders of magnitude smaller than the most sensitive inductive detectors. To date, however, NV NMR spectrometers have only been able to observe signals from pure, highly concentrated samples. To overcome this limitation, we introduce a technique that combines picoliter-scale NV NMR with fully integrated Overhauser dynamic nuclear polarization to perform high-resolution spectroscopy on a variety of small molecules in dilute solution, with femtomole sensitivity. Our technique advances the state of the art of mass-limited NMR spectroscopy, opening the door to new applications at the picoliter scale in drug and natural-product discovery, catalysis research, and single-cell studies.

We study in detail the properties of the quantum East model, an interacting quantum spin chain inspired by simple kinetically constrained models of classical glasses. Through a combination of analytics, exact diagonalization, and tensor-network methods, we show the existence of a transition, from a fast to a slow thermalization regime, which manifests itself throughout the spectrum. On the slow side, by exploiting the localization of the ground state and the form of the Hamiltonian, we explicitly construct a large (exponential in size) number of nonthermal states that become exact finite-energy-density eigenstates in the large size limit, as expected for a true phase transition. A “superspin” generalization allows us to find a further large class of area-law states proved to display very slow relaxation. These states retain memory of their initial conditions for extremely long times. Our numerical analysis reveals that the localization properties are not limited to the ground state and that many eigenstates have large overlap with product states and can be approximated well by matrix product states at arbitrary energy densities. The mechanism that induces localization to the ground state, and hence the nonthermal behavior of the system, can be extended to a wide range of models including a number of simple spin chains. We discuss implications of our results for slow thermalization and nonergodicity more generally in disorder-free systems with constraints, and we give numerical evidence that these results may be extended to two-dimensional systems.

Complex molecular structure demands customized solutions to laser cooling by extending its general set of principles and practices. Compared with other laser-cooled molecules, yttrium monoxide (YO) exhibits a large electron-nucleus interaction, resulting in a dominant hyperfine interaction over the electron spin-rotation coupling. The YO ground state is thus comprised of two manifolds of closely spaced states, with one of them possessing a negligible Landé $g$ factor. This unique energy level structure favors dual-frequency dc magneto-optical trapping (MOT) and gray molasses cooling (GMC). We report exceptionally robust cooling of YO at $4\mu \mathrm{K}$ over a wide range of laser intensity, detunings (one- and two-photon), and magnetic field. The magnetic insensitivity enables the spatial compression of the molecular cloud by alternating GMC and MOT under the continuous operation of the quadrupole magnetic field. A combination of these techniques produces a laser-cooled molecular sample with the highest phase space density in free space.

Periodic driving has emerged as a powerful tool in the quest to engineer new and exotic quantum phases. While driven many-body systems are generically expected to absorb energy indefinitely and reach an infinite-temperature state, the rate of heating can be exponentially suppressed when the drive frequency is large compared to the local energy scales of the system—leading to long-lived “prethermal” regimes. In this work, we experimentally study a bosonic cloud of ultracold atoms in a driven optical lattice and identify such a prethermal regime in the Bose-Hubbard model. By measuring the energy absorption of the cloud as the driving frequency is increased, we observe an exponential-in-frequency reduction of the heating rate persisting over more than 2 orders of magnitude. The tunability of the lattice potentials allows us to explore one- and two-dimensional systems in a range of different interacting regimes. Alongside the exponential decrease, the dependence of the heating rate on the frequency displays features characteristic of the phase diagram of the Bose-Hubbard model, whose understanding is additionally supported by numerical simulations in one dimension. Our results show experimental evidence of the phenomenon of Floquet prethermalization and provide insight into the characterization of heating for driven bosonic systems.

We experimentally realize a Peierls phase in the hopping amplitude of excitations carried by Rydberg atoms, and observe the resulting characteristic chiral motion in a minimal setup of three sites. Our demonstration relies on the intrinsic spin-orbit coupling of the dipolar exchange interaction combined with time-reversal symmetry breaking by a homogeneous external magnetic field. Remarkably, the phase of the hopping amplitude between two sites strongly depends on the occupancy of the third site, thus leading to a correlated hopping associated with a density-dependent Peierls phase. We experimentally observe this density-dependent hopping and show that the excitations behave as anyonic particles with a nontrivial phase under exchange. Finally, we confirm the dependence of the Peierls phase on the geometrical arrangement of the Rydberg atoms.

We present a new approach for deriving exact closed-form solutions for the steady state of a wide class of driven-dissipative nonlinear resonators that is distinct from more common complex-$P$-function methods. Our method generalizes the coherent quantum-absorber approach of Stannigel et al. [New J. Phys. 14, 063014 (2012)] to include nonlinear driving and dissipation and relies crucially on exploiting the Segal-Bargmann representation of Fock space. Our solutions and method reveal a wealth of previously unexplored observable phenomena in these systems, including new generalized photon-blockade and antiblockade effects and an infinite number of new parameter choices that yield quantum bistability.

The creation of delocalized coherent superpositions of quantum systems experiencing different relativistic effects is an important milestone in future research at the interface of gravity and quantum mechanics. This milestone could be achieved by generating a superposition of quantum clocks that follow paths with different gravitational time dilation and investigating the consequences on the interference signal when they are eventually recombined. Light-pulse atom interferometry with elements employed in optical atomic clocks is a promising candidate for that purpose, but it suffers from major challenges including its insensitivity to the gravitational redshift in a uniform field. All of these difficulties can be overcome with the novel scheme presented here, which is based on initializing the clock when the spatially separate superposition has already been generated and performing a doubly differential measurement where the differential phase shift between the two internal states is compared for different initialization times. This scheme can be exploited to test the universality of the gravitational redshift with delocalized coherent superpositions of quantum clocks, and it is argued that its experimental implementation should be feasible with a new generation of 10-meter atomic fountains that will soon become available. Interestingly, the approach also offers significant advantages for more compact setups based on guided interferometry or hybrid configurations. Furthermore, in order to provide a solid foundation for the analysis of the various interferometry schemes and the effects that can be measured with them, a general formalism for a relativistic description of atom interferometry in curved spacetime is developed. It can describe freely falling atoms as well as the effects of external forces and guiding potentials, and it can be applied to a very wide range of situations. As an important ingredient for quantum-clock interferometry, suitable diffraction mechanisms for atoms in internal-state superpositions are investigated too. Finally, the relation of the proposed doubly differential measurement scheme to other experimental approaches and to tests of the universality of free fall is discussed in detail.

Two-dimensional semiconductors provide an ideal platform for exploration of linear exciton and polariton physics, primarily due to large exciton binding energy and strong light-matter coupling. These features, however, generically imply reduced exciton-exciton interactions, hindering the realization of active optical devices such as lasers or parametric oscillators. Here, we show that electrical injection of itinerant electrons into monolayer molybdenum diselenide allows us to overcome this limitation: dynamical screening of exciton-polaritons by electrons leads to the formation of new quasiparticles termed polaron-polaritons that exhibit unexpectedly strong interactions as well as optical amplification by Bose-enhanced polaron-electron scattering. To measure the nonlinear optical response, we carry out time-resolved pump-probe measurements and observe polaron-polariton interaction enhancement by a factor of 50 ($0.5\mu \mathrm{eV}\mu {\mathrm{m}}^2$) as compared to exciton-polaritons. Concurrently, we measure a spectrally integrated transmission gain of the probe field of $\gtrsim 2$ stemming from stimulated scattering of polaron-polaritons. We show theoretically that the nonequilibrium nature of optically excited quasiparticles favors a previously unexplored interaction mechanism stemming from a phase-space filling in the screening cloud, which provides an accurate explanation of the strong repulsive interactions observed experimentally. Our findings show that itinerant electron-exciton interactions provide an invaluable tool for electronic manipulation of optical properties, demonstrate a new mechanism for dramatically enhancing polariton-polariton interactions, and pave the way for realization of nonequilibrium polariton condensates.