Nonequilibrium phase transitions exist in damped-driven open quantum systems when the continuous tuning of an external parameter leads to a transition between two robust steady states. In second-order transitions this change is abrupt at a critical point, whereas in first-order transitions the two phases can coexist in a critical hysteresis domain. Here, we report the observation of a first-order dissipative quantum phase transition in a driven circuit quantum electrodynamics system. It takes place when the photon blockade of the driven cavity-atom system is broken by increasing the drive power. The observed experimental signature is a bimodal phase space distribution with varying weights controlled by the drive strength. Our measurements show an improved stabilization of the classical attractors up to the millisecond range when the size of the quantum system is increased from one to three artificial atoms. The formation of such robust pointer states could be used for new quantum measurement schemes or to investigate multiphoton phases of finite-size, nonlinear, open quantum systems.

Quantum correlations between imprecision and backaction are a hallmark of continuous linear measurements. Here, we study how measurement-based feedback can be used to improve the visibility of quantum correlations due to the interaction of a laser field with a nanomechanical oscillator. Backaction imparted by the meter laser, due to radiation-pressure quantum fluctuations, gives rise to correlations between its phase and amplitude quadratures. These quantum correlations are observed in the experiment both as squeezing of the meter field fluctuations below the vacuum level in a homodyne measurement and as sideband asymmetry in a heterodyne measurement, demonstrating the common origin of both phenomena. We show that quantum feedback, i.e., feedback that suppresses measurement backaction, can be used to increase the visibility of the sideband asymmetry ratio. In contrast, by operating the feedback loop in the regime of noise squashing, where the in-loop photocurrent variance is reduced below the vacuum level, the visibility of the sideband asymmetry is reduced. This is due to backaction arising from vacuum noise in the homodyne detector. These experiments demonstrate the possibility, as well as the fundamental limits, of measurement-based feedback as a tool to manipulate quantum correlations.

Understanding the general principles underlying strongly interacting quantum states out of equilibrium is one of the most important tasks of current theoretical physics. With experiments accessing the intricate dynamics of many-body quantum systems, it is paramount to develop powerful methods that encode the emergent physics. Up to now, the strong dichotomy observed between integrable and nonintegrable evolutions made an overarching theory difficult to build, especially for transport phenomena where space-time profiles are drastically different. We present a novel framework for studying transport in integrable systems: hydrodynamics with infinitely many conservation laws. This bridges the conceptual gap between integrable and nonintegrable quantum dynamics, and gives powerful tools for accurate studies of space-time profiles. We apply it to the description of energy transport between heat baths, and provide a full description of the current-carrying nonequilibrium steady state and the transition regions in a family of models including the Lieb-Liniger model of interacting Bose gases, realized in experiments.

We experimentally and theoretically investigate the quantum trajectories of jointly monitored transmon qubits embedded in spatially separated microwave cavities. Using nearly quantum-noise-limited superconducting amplifiers and an optimized setup to reduce signal loss between cavities, we can efficiently track measurement-induced entanglement generation as a continuous process for single realizations of the experiment. The quantum trajectories of transmon qubits naturally split into low and high entanglement classes. The distribution of concurrence is found at any given time, and we explore the dynamics of entanglement creation in the state space. The distribution exhibits a sharp cutoff in the high concurrence limit, defining a maximal concurrence boundary. The most-likely paths of the qubits’ trajectories are also investigated, resulting in three probable paths, gradually projecting the system to two even subspaces and an odd subspace, conforming to a “half-parity” measurement. We also investigate the most-likely time for the individual trajectories to reach their most entangled state, and we find that there are two solutions for the local maximum, corresponding to the low and high entanglement routes. The theoretical predictions show excellent agreement with the experimental entangled-qubit trajectory data.

One major change of the future revision of the International System of Units is a new definition of the ampere based on the elementary charge $e$. Replacing the former definition based on Ampère’s force law will allow one to fully benefit from quantum physics to realize the ampere. However, a quantum realization of the ampere from $e$, accurate to within ${10}^{-8}$ in relative value and fulfilling traceability needs, is still missing despite the many efforts made for the development of single-electron tunneling devices. Starting again with Ohm’s law, applied here in a quantum circuit combining the quantum Hall resistance and Josephson voltage standards with a superconducting cryogenic amplifier, we report on a practical and universal programmable quantum current generator. We demonstrate that currents generated in the milliampere range are accurately quantized in terms of $e{f}_{\mathrm{J}}$ ($f_{\mathrm{J}}$ is the Josephson frequency) with measurement uncertainty of ${10}^{-8}$. This new quantum current source, which is able to deliver such accurate currents down to the microampere range, can greatly improve the current measurement traceability, as demonstrated with the calibrations of digital ammeters. In addition, it opens the way to further developments in metrology and in fundamental physics, such as a quantum multimeter or new accurate comparisons to single-electron pumps.

We study how useful random states are for quantum metrology, i.e., whether they surpass the classical limits imposed on precision in the canonical phase sensing scenario. First, we prove that random pure states drawn from the Hilbert space of distinguishable particles typically do not lead to superclassical scaling of precision even when allowing for local unitary optimization. Conversely, we show that random pure states from the symmetric subspace typically achieve the optimal Heisenberg scaling without the need for local unitary optimization. Surprisingly, the Heisenberg scaling is observed for random isospectral states of arbitrarily low purity and preserved under loss of a fixed number of particles. Moreover, we prove that for pure states, a standard photon-counting interferometric measurement suffices to typically achieve resolution following the Heisenberg scaling for all values of the phase at the same time. Finally, we demonstrate that metrologically useful states can be prepared with short random optical circuits generated from three types of beam splitters and a single nonlinear (Kerr-like) transformation.

In contrast to classical empty space, the quantum vacuum fundamentally alters the properties of embedded particles. This paradigm shift allows one to explain the discovery of the celebrated Lamb shift in the spectrum of the hydrogen atom. Here, we engineer a synthetic vacuum, building on the unique properties of ultracold atomic gas mixtures, offering the ability to switch between empty space and quantum vacuum. Using high-precision spectroscopy, we observe the phononic Lamb shift, an intriguing many-body effect originally conjectured in the context of solid-state physics. We find good agreement with theoretical predictions based on the Fröhlich model. Our observations establish this experimental platform as a new tool for precision benchmarking of open theoretical challenges, especially in the regime of strong coupling between the particles and the quantum vacuum.

In a joint experimental and theoretical effort, we report on the formation of a macrodroplet state in an ultracold bosonic gas of erbium atoms with strong dipolar interactions. By precise tuning of the $s$-wave scattering length below the so-called dipolar length, we observe a smooth crossover of the ground state from a dilute Bose-Einstein condensate to a dense macrodroplet state of more than $2\times {10}^4\mathrm{atoms}$. Based on the study of collective excitations and loss features, we prove that quantum fluctuations stabilize the ultracold gas far beyond the instability threshold imposed by mean-field interactions. Finally, we perform expansion measurements, showing that although self-bound solutions are prevented by losses, the interplay between quantum stabilization and losses results in a minimal time-of-flight expansion velocity at a finite scattering length.

A major signature of quantum mechanics beyond classical physics is coherence, the existence of superposition states. The recently developed resource theory of quantum coherence allows the formalization of incoherent operations—those operations which cannot create coherence. We identify the set of operations which additionally do not use coherence. These are such that coherence cannot be exploited by a classical observer, who measures incoherent properties of the system, to go beyond classical dynamics. We give a physical interpretation in terms of interferometry and prove a dilation theorem, showing how these operations can always be constructed by the system interacting, in an incoherent way, with an ancilla. Such a physical justification is not known for the incoherent operations; thus, our results lead to a physically well-motivated resource theory of coherence. Next, we investigate the implications for coherence in multipartite systems. We show that quantum correlations can be defined naturally with respect to a fixed basis, providing a link between coherence and quantum discord. We demonstrate the interplay between these two quantities in the operations that we study and suggest implications for the theory of quantum discord by relating these operations to those which cannot create discord.

Strongly driving a two-level quantum system with light leads to a ladder of Floquet states separated by the photon energy. Nanoscale quantum devices allow the interplay of confined electrons, phonons, and photons to be studied under strong driving conditions. Here, we show that a single electron in a periodically driven double quantum dot functions as a “Floquet gain medium,” where population imbalances in the double quantum dot Floquet quasienergy levels lead to an intricate pattern of gain and loss features in the cavity response. We further measure a large intracavity photon number $n_c$ in the absence of a cavity drive field, due to equilibration in the Floquet picture. Our device operates in the absence of a dc current—one and the same electron is repeatedly driven to the excited state to generate population inversion. These results pave the way to future studies of nonclassical light and thermalization of driven quantum systems.

High-gain amplifiers of electromagnetic signals operating near the quantum limit are crucial for quantum information systems and ultrasensitive quantum measurements. However, the existing techniques have a limited gain-bandwidth product and only operate with weak input signals. Here, we demonstrate a two-port optomechanical scheme for amplification and routing of microwave signals, a system that simultaneously performs high-gain amplification and frequency conversion in the quantum regime. Our amplifier, implemented in a two-cavity microwave optomechanical device, shows 41 dB of gain and has a high dynamic range, handling input signals up to ${10}^{13}$ photons per second, 3 orders of magnitude more than corresponding Josephson parametric amplifiers. We show that although the active medium, the mechanical resonator, is at a high temperature far from the quantum limit, only 4.6 quanta of noise is added to the input signal. Our method can be readily applied to a wide variety of optomechanical systems, including hybrid optical-microwave systems, creating a universal hub for signals at the quantum level.

We investigate the connection between recent results in quantum thermodynamics and fluctuation relations by adopting a fully quantum mechanical description of thermodynamics. By including a work system whose energy is allowed to fluctuate, we derive a set of equalities that all thermodynamical transitions have to satisfy. This extends the condition for maps to be Gibbs preserving to the case of fluctuating work, providing a more general characterization of maps commonly used in the information theoretic approach to thermodynamics. For final states, block diagonal in the energy basis, this set of equalities is a necessary and sufficient condition for a thermodynamical state transition to be possible. The conditions serve as a parent equation that can be used to derive a number of results. These include writing the second law of thermodynamics as an equality featuring a fine-grained notion of the free energy. It also yields a generalization of the Jarzynski fluctuation theorem which holds for arbitrary initial states, and under the most general manipulations allowed by the laws of quantum mechanics. Furthermore, we show that each of these relations can be seen as the quasiclassical limit of three fully quantum identities. This allows us to consider the free energy as an operator, and allows one to obtain more general and fully quantum fluctuation relations from the information theoretic approach to quantum thermodynamics.

If the second law of thermodynamics forbids a transition from one state to another, then it is still possible to make the transition happen by using a sufficient amount of work. But if we do not have access to this amount of work, can the transition happen probabilistically? In the thermodynamic limit, this probability tends to zero, but here we find that for finite-sized and quantum systems it can be finite. We compute the maximum probability of a transition or a thermodynamical fluctuation from any initial state to any final state and show that this maximum can be achieved for any final state that is block diagonal in the energy eigenbasis. We also find upper and lower bounds on this transition probability, in terms of the work of transition. As a by-product, we introduce a finite set of thermodynamical monotones related to the thermomajorization criteria which governs state transitions and compute the work of transition in terms of them. The trade-off between the probability of a transition and any partial work added to aid in that transition is also considered. Our results have applications in entanglement theory, and we find the amount of entanglement required (or gained) when transforming one pure entangled state into any other.

There are two general requirements to harness the computational power of quantum mechanics: the ability to manipulate the evolution of an isolated system and the ability to faithfully extract information from it. Quantum error correction and simulation often make a more exacting demand: the ability to perform nondestructive measurements of specific correlations within that system. We realize such measurements by employing a protocol adapted from Nigg and Girvin [Phys. Rev. Lett. 110, 243604 (2013)], enabling real-time selection of arbitrary register-wide Pauli operators. Our implementation consists of a simple circuit quantum electrodynamics module of four highly coherent 3D transmon qubits, collectively coupled to a high-$Q$ superconducting microwave cavity. As a demonstration, we enact all seven nontrivial subset-parity measurements on our three-qubit register. For each, we fully characterize the realized measurement by analyzing the detector (observable operators) via quantum detector tomography and by analyzing the quantum backaction via conditioned process tomography. No single quantity completely encapsulates the performance of a measurement, and standard figures of merit have not yet emerged. Accordingly, we consider several new fidelity measures for both the detector and the complete measurement process. We measure all of these quantities and report high fidelities, indicating that we are measuring the desired quantities precisely and that the measurements are highly nondemolition. We further show that both results are improved significantly by an additional error-heralding measurement. The analyses we present here form a useful basis for the future characterization and validation of quantum measurements, anticipating the demands of emerging quantum technologies.

Entangling two remote quantum systems that never interact directly is an essential primitive in quantum information science and forms the basis for the modular architecture of quantum computing. When protocols to generate these remote entangled pairs rely on using traveling single-photon states as carriers of quantum information, they can be made robust to photon losses, unlike schemes that rely on continuous variable states. However, efficiently detecting single photons is challenging in the domain of superconducting quantum circuits because of the low energy of microwave quanta. Here, we report the realization of a robust form of concurrent remote entanglement based on a novel microwave photon detector implemented in the superconducting circuit quantum electrodynamics platform of quantum information. Remote entangled pairs with a fidelity of $0.57\pm 0.01$ are generated at 200 Hz. Our experiment opens the way for the implementation of the modular architecture of quantum computation with superconducting qubits.

We derive general evolution equations describing the ensemble-average quantum dynamics generated by disordered Hamiltonians. The disorder average affects the coherence of the evolution and can be accounted for by suitably tailored effective coupling agents and associated rates that encode the specific statistical properties of the Hamiltonian’s eigenvectors and eigenvalues, respectively. Spectral disorder and isotropically disordered eigenvector distributions are considered as paradigmatic test cases.

We describe the creation of a long-lived spin-orbit-coupled gas of quantum degenerate atoms using the most magnetic fermionic element, dysprosium. Spin-orbit coupling arises from a synthetic gauge field created by the adiabatic following of degenerate dressed states composed of optically coupled components of an atomic spin. Because of dysprosium’s large electronic orbital angular momentum and large magnetic moment, the lifetime of the gas is limited not by spontaneous emission from the light-matter coupling, as for gases of alkali-metal atoms, but by dipolar relaxation of the spin. This relaxation is suppressed at large magnetic fields due to Fermi statistics. We observe lifetimes up to 400 ms, which exceeds that of spin-orbit-coupled fermionic alkali atoms by a factor of 10–100 and is close to the value obtained from a theoretical model. Elastic dipolar interactions are also observed to influence the Rabi evolution of the spin, revealing an interacting fermionic system. The long lifetime of this weakly interacting spin-orbit-coupled degenerate Fermi gas will facilitate the study of quantum many-body phenomena manifest at longer time scales, with exciting implications for the exploration of exotic topological quantum liquids.

Realizing systems that support robust, controlled interactions between individual photons is an exciting frontier of nonlinear optics. To this end, one approach that has emerged recently is to leverage atomic interactions to create strong and spatially nonlocal interactions between photons. In particular, effective photonic interactions have been successfully created via interactions between atoms excited to Rydberg levels. Here, we investigate an alternative approach, in which atomic interactions arise via their common coupling to photonic crystal waveguides. This technique takes advantage of the ability to separately tailor the strength and range of interactions via the dispersion engineering of the structure itself, which can lead to qualitatively new types of phenomena. For example, much of the work on photon-photon interactions relies on the linear optical effect of electromagnetically induced transparency, in combination with the use of interactions to shift optical pulses into or out of the associated transparency window. Here, we identify a large new class of “correlated transparency windows,” in which photonic states of a certain number and shape selectively propagate through the system. Through this technique, we show that molecular bound states of photon pairs can be created.

We introduce a scheme for preparation, manipulation, and read out of Majorana zero modes in semiconducting wires with mesoscopic superconducting islands. Our approach synthesizes recent advances in materials growth with tools commonly used in quantum-dot experiments, including gate control of tunnel barriers and Coulomb effects, charge sensing, and charge pumping. We outline a sequence of milestones interpolating between zero-mode detection and quantum computing that includes (1) detection of fusion rules for non-Abelian anyons using either proximal charge sensors or pumped current, (2) validation of a prototype topological qubit, and (3) demonstration of non-Abelian statistics by braiding in a branched geometry. The first two milestones require only a single wire with two islands, and additionally enable sensitive measurements of the system’s excitation gap, quasiparticle poisoning rates, residual Majorana zero-mode splittings, and topological-qubit coherence times. These pre-braiding experiments can be adapted to other manipulation and read out schemes as well.

Quantum annealing (QA) has been proposed as a quantum enhanced optimization heuristic exploiting tunneling. Here, we demonstrate how finite-range tunneling can provide considerable computational advantage. For a crafted problem designed to have tall and narrow energy barriers separating local minima, the D-Wave 2X quantum annealer achieves significant runtime advantages relative to simulated annealing (SA). For instances with 945 variables, this results in a time-to-99%-success-probability that is $\sim 10^8$ times faster than SA running on a single processor core. We also compare physical QA with the quantum Monte Carlo algorithm, an algorithm that emulates quantum tunneling on classical processors. We observe a substantial constant overhead against physical QA: D-Wave 2X again runs up to $\sim 10^8$ times faster than an optimized implementation of the quantum Monte Carlo algorithm on a single core. We note that there exist heuristic classical algorithms that can solve most instances of Chimera structured problems in a time scale comparable to the D-Wave 2X. However, it is well known that such solvers will become ineffective for sufficiently dense connectivity graphs. To investigate whether finite-range tunneling will also confer an advantage for problems of practical interest, we conduct numerical studies on binary optimization problems that cannot yet be represented on quantum hardware. For random instances of the number partitioning problem, we find numerically that algorithms designed to simulate QA scale better than SA. We discuss the implications of these findings for the design of next-generation quantum annealers.