We introduce a new class of states for bosonic quantum fields which extend tensor network states to the continuum and generalize continuous matrix product states to spatial dimensions $d\ge 2$. By construction, they are Euclidean invariant and are genuine continuum limits of discrete tensor network states. Admitting both a functional integral and an operator representation, they share the important properties of their discrete counterparts: expressiveness, invariance under gauge transformations, simple rescaling flow, and compact expressions for the $N$-point functions of local observables. While we discuss mostly the continuous tensor network states extending projected entangled-pair states, we propose a generalization bearing similarities with the continuum multiscale entanglement renormalization ansatz.

We present a theoretical method to generate a highly accurate time-independent Hamiltonian governing the finite-time behavior of a time-periodic system. The method exploits infinitesimal unitary transformation steps, from which renormalization-group–like flow equations are derived to produce the effective Hamiltonian. Our tractable method has a range of validity reaching into frequency—and drive strength—regimes that are usually inaccessible via high-frequency $\omega$ expansions in the parameter $h/\omega$, where $h$ is the upper limit for the strength of local interactions. We demonstrate exact properties of our approach on a simple toy model and test an approximate version of it on both interacting and noninteracting many-body Hamiltonians, where it offers an improvement over the more well-known Magnus expansion and other high-frequency expansions. For the interacting models, we compare our approximate results to those found via exact diagonalization. While the approximation generally performs better globally than other high-frequency approximations, the improvement is especially pronounced in the regime of lower frequencies and strong external driving. This regime is of special interest because of its proximity to the resonant regime where the effect of a periodic drive is the most dramatic. Our results open a new route towards identifying novel nonequilibrium regimes and behaviors in driven quantum many-particle systems.

Transformation of light carrying spin angular momentum (SAM) to optical field vortices carrying orbital angular momentum (OAM) has been of wide interest in recent years. The interactions between two optical fields, each carrying one of those degrees of freedom, and furthermore, the transfer of the resulting angular momentum product to matter are seldom discussed. Here, we measure the interaction between 3D light carrying axial SAM and 2D plasmon-polariton vortices carrying high-order transverse OAM. The interaction is mediated by two-photon absorption within a gold surface, imprinting the resulting angular-momentum mixing into matter by excitation of electrons that are photo-emitted into vacuum. Interestingly, the spatial distribution of the emitted electrons carries the signature of a subtraction of the spin from the orbit angular momenta. We show experimentally and theoretically that the absorptive nature of this interaction leads to both single and double photon-plasmon angular momentum mixing processes by one- and two- photon interactions. Our results demonstrate high order angular momenta light-matter interactions, provide a glimpse into specific electronic excitation routes, and may be applied in future electronic sources and coherent control.

The quantum coherence of electronic quasiparticles underpins many of the emerging transport properties of conductors at small scales. Novel electronic implementations of quantum optics devices are now available with perspectives such as “flying-qubit” manipulations. However, electronic quantum interferences in conductors remained up to now limited to propagation paths shorter than $30\mu \mathrm{m}$ independent of the material. Here we demonstrate strong electronic quantum interferences after a propagation along two 0.1-mm-long pathways in a circuit. Interferences of visibility as high as 80% and 40% are observed on electronic analogues of the Mach-Zehnder interferometer of, respectively, $24\text{−}\mu \mathrm{m}$ and 0.1-mm arm length, consistently corresponding to a 0.25-mm electronic phase coherence length. While such devices perform best in the integer quantum Hall regime at filling factor 2, the electronic interferences are restricted by the Coulomb interaction between copropagating edge channels. We overcome this limitation by closing the inner channel in micron-scale loops of frozen internal degrees of freedom combined with a loop-closing strategy providing an essential isolation from the environment.

Silicon quantum dots are considered an excellent platform for spin qubits, partly due to their weak spin-orbit interaction. However, the sharp interfaces in the heterostructures induce a small but significant spin-orbit interaction that degrades the performance of the qubits or, when understood and controlled, could be used as a powerful resource. To understand how to control this interaction, we build a detailed profile of the spin-orbit interaction of a silicon metal-oxide-semiconductor double quantum-dot system. We probe the derivative of the Stark shift, $g$-factor and $g$-factor difference for two single-electron quantum-dot qubits as a function of external magnetic field and find that they are dominated by spin-orbit interactions originating from the vector potential, consistent with recent theoretical predictions. Conversely, by populating the double dot with two electrons, we probe the mixing of singlet and spin-polarized triplet states during electron tunneling, which we conclude is dominated by momentum-term spin-orbit interactions that vary from 1.85 MHz up to 27.5 MHz depending on the magnetic field orientation. Finally, we exploit the tunability of the derivative of the Stark shift of one of the dots to reduce its sensitivity to electric noise and observe an 80% increase in $T_2^{*}$. We conclude that the tuning of the spin-orbit interaction will be crucial for scalable quantum computing in silicon and that the optimal setting will depend on the exact mode of qubit operations used.

Prethermalization has been extensively studied in systems close to integrability. We propose a more general, yet conceptually simpler, setup for this phenomenon. We consider a—possibly nonintegrable—reference dynamics, weakly perturbed so that the perturbation breaks at least one conservation law of the reference dynamics. We argue then that the evolution of the system proceeds via intermediate (generalized) equilibrium states of the reference dynamics. The motion on the manifold of equilibrium states is governed by an autonomous equation, flowing towards global equilibrium in a time of order $g^{-2}$, where $g$ is the perturbation strength. We also describe the leading correction to the time-dependent reference equilibrium state, which is, in general, of order $g$. The theory is well confirmed in numerical calculations of model Hamiltonians, for which we use a numerical linked cluster expansion and full exact diagonalization.

Dipolar coupling plays a fundamental role in the interaction between electrically or magnetically polarized species such as magnetic atoms and dipolar molecules in a gas or dipolar excitons in the solid state. Unlike Coulomb or contactlike interactions found in many atomic, molecular, and condensed-matter systems, this interaction is long-ranged and highly anisotropic, as it changes from repulsive to attractive depending on the relative positions and orientation of the dipoles. Because of this unique property, many exotic, symmetry-breaking collective states have been recently predicted for cold dipolar gases, but only a few have been experimentally detected and only in dilute atomic dipolar Bose-Einstein condensates. Here, we report on the first observation of attractive dipolar coupling between excitonic dipoles using a new design of stacked semiconductor bilayers. We show that the presence of a dipolar exciton fluid in one bilayer modifies the spatial distribution and increases the binding energy of excitonic dipoles in a vertically remote layer. The binding energy changes are explained using a many-body polaron model describing the deformation of the exciton cloud due to its interaction with a remote dipolar exciton. The surprising nonmonotonic dependence on the cloud density indicates the important role of dipolar correlations, which is unique to dense, strongly interacting dipolar solid-state systems. Our concept provides a route for the realization of dipolar lattices with strong anisotropic interactions in semiconductor systems, which open the way for the observation of theoretically predicted new and exotic collective phases, as well as for engineering and sensing their collective excitations.

Nitrogen-vacancy (NV) centers in diamond are appealing nanoscale quantum sensors for temperature, strain, electric fields, and, most notably, magnetic fields. However, the cryogenic temperatures required for low-noise single-shot readout that have enabled the most sensitive NV magnetometry reported to date are impractical for key applications, e.g., biological sensing. Overcoming the noisy readout at room temperature has until now demanded the repeated collection of fluorescent photons, which increases the time cost of the procedure, thus reducing its sensitivity. Here, we show how machine learning can process the noisy readout of a single NV center at room temperature, requiring on average only one photon per algorithm step, to sense magnetic-field strength with a precision comparable to those reported for cryogenic experiments. Analyzing large datasets from NV centers in bulk diamond, we report absolute sensitivities of $60\mathrm{nT}{\mathrm{s}}^{1/2}$ including initialization, readout, and computational overheads. We show that dephasing times can be simultaneously estimated and that time-dependent fields can be dynamically tracked at room temperature. Our results dramatically increase the practicality of early-term single-spin sensors.

Single-photon generation is an important proof of the underlying quantum nature of a physical process and a ubiquitous tool for scientific exploration, with applications ranging from spectroscopy and metrology to quantum computing. In the microwave regime, emission of antibunched radiation has so far relied on coherent control of Josephson qubits requiring precisely calibrated microwave pulses. In this work, we experimentally demonstrate the operation of a bright on-demand source of quantum microwave radiation driven by a simple dc voltage bias across a Josephson junction. Our source is based on photon emission into a microwave resonator through inelastic Cooper pair tunneling regulated by a high-impedance $RC$ circuit preventing simultaneous tunnel events. It is characterized by its normalized second-order correlation function of $g^{(2)}(0)\approx 0.43$ corresponding to antibunching in the single-photon regime. Our device can be triggered, and its in situ tunable emission rate exceeds those obtained with current microwave single-photon sources by more than 1 order of magnitude.

By combining theory and experiments, we demonstrate that dipolar quantum gases of both ${}^{166}\mathrm{Er}$ and ${}^{164}\mathrm{Dy}$ support a state with supersolid properties, where a spontaneous density modulation and a global phase coherence coexist. This paradoxical state occurs in a well-defined parameter range, separating the phases of a regular Bose-Einstein condensate and of an insulating droplet array, and is rooted in the roton mode softening, on the one side, and in the stabilization driven by quantum fluctuations, on the other side. Here, we identify the parameter regime for each of the three phases. In the experiment, we rely on a detailed analysis of the interference patterns resulting from the free expansion of the gas, quantifying both its density modulation and its global phase coherence. Reaching the phases via a slow interaction tuning, starting from a stable condensate, we observe that ${}^{166}\mathrm{Er}$ and ${}^{164}\mathrm{Dy}$ exhibit a striking difference in the lifetime of the supersolid properties, due to the different atom loss rates in the two systems. Indeed, while in ${}^{166}\mathrm{Er}$ the supersolid behavior survives only a few tens of milliseconds, we observe coherent density modulations for more than 150 ms in ${}^{164}\mathrm{Dy}$. Building on this long lifetime, we demonstrate an alternative path to reach the supersolid regime, relying solely on evaporative cooling starting from a thermal gas.

We study the spreading of initially local operators under unitary time evolution in a one-dimensional random quantum circuit model that is constrained to conserve a $U(1)$ charge and also the dipole moment of this charge. These constraints are motivated by the quantum dynamics of fracton phases. We discover that the charge remains localized at its initial position, providing a crisp example of a nonergodic dynamical phase of random circuit dynamics. This localization can be understood as a consequence of the return properties of low-dimensional random walks, through a mechanism reminiscent of weak localization, but insensitive to dephasing. The charge dynamics is well described by a system of coupled hydrodynamic equations, which makes several nontrivial predictions that are all in good agreement with numerics in one dimension. Importantly, these equations also predict localization in two-dimensional fractonic random circuits. We further find that the immobile fractonic charge emits nonconserved operators, whose spreading is governed by exponents that are distinct from those observed in nonfractonic circuits. These nonstandard exponents are also explained by our coupled hydrodynamic equations. Where entanglement properties are concerned, we find that fractonic operators exhibit a short time linear growth of observable entanglement with saturation to an area law, as well as a subthermal volume law for operator entanglement. The entanglement spectrum is found to follow semi-Poisson statistics, similar to eigenstates of many-body localized systems. The nonergodic phenomenology is found to persist to initial conditions containing nonzero density of dipolar or fractonic charge, including states near the sector of maximal charge. Our work implies that low-dimensional fracton systems should preserve forever a memory of their initial conditions in local observables under noisy quantum dynamics, thereby constituting ideal memories. It also implies that one- and two-dimensional fracton systems should realize true many-body localization (MBL) under Hamiltonian dynamics, even in the absence of disorder, with the obstructions to MBL in translation-invariant systems and in spatial dimensions greater than one being evaded by the nature of the mechanism responsible for localization. We also suggest a possible route to new nonergodic phases in high dimensions.

Quantum simulations with ultracold atoms typically create atomic wave functions with structures at optical length scales, where direct imaging suffers from the diffraction limit. In analogy to advances in optical microscopy for biological applications, we use a nonlinear atomic response to surpass the diffraction limit. Exploiting quantum interference, we demonstrate imaging with superresolution of $\lambda /50$ and excellent temporal resolution of 500 ns. We characterize our microscope’s performance by measuring the ensemble-averaged probability density of atoms within the unit cells of an optical lattice and observe the dynamics of atoms excited into motion. This approach can be readily applied to image any atomic or molecular system, as long as it hosts a three-level system.

Superresolution microscopy has revolutionized the fields of chemistry and biology by resolving features at the molecular level. In atomic physics, such a scheme can be applied to resolve the atomic density distribution beyond the diffraction limit and to perform quantum control. Here we demonstrate superresolution imaging based on the nonlinear response of atoms to an optical pumping pulse. With this technique, the atomic density distribution can be imaged with a full-width-at-half-maximum resolution of 32(4) nm and a localization precision below 500 pm. The short optical pumping pulse of $1.4\mu \mathrm{s}$ enables us to resolve fast atomic dynamics within a single lattice site. A by-product of our scheme is the emergence of moiré patterns on the atomic cloud, which we show to be immensely magnified images of the atomic density in the lattice.

We derive a quantum limit to the sensitivity of laser interferometric gravitational-wave detectors from optical-loss-induced dissipation, analogous to the sensitivity limit from the mechanical dissipation. It applies universally to different interferometer configurations and cannot be surpassed unless the optical properties of the interferometer are improved. This result provides an answer to the long-standing question of how far we can push the detector sensitivity given the state-of-the-art optics.

We explore, both experimentally and theoretically, the response of an elongated Bose-Einstein condensate to modulated interactions. We identify two distinct regimes differing in modulation frequency and modulation strength. Longitudinal surface waves are generated either resonantly or parametrically for modulation frequencies near the radial trap frequency or twice the trap frequency, respectively. The dispersion of these waves, the latter being a Faraday wave, is well reproduced by a mean-field theory that accounts for the 3D nature of the elongated condensate. In contrast, in the regime of lower modulation frequencies, we find that no clear resonances occur, but with an increased modulation strength, the condensate forms an irregular granulated distribution that is outside the scope of a mean-field approach. We find that the granulated condensate is characterized by large quantum fluctuations and correlations, which are well described with single-shot simulations obtained from wave functions computed by a beyond-mean-field theory at zero temperature, the multiconfigurational time-dependent Hartree for bosons method.

We study theoretically and experimentally the emergence of supersolid properties in a dipolar Bose-Einstein condensate. The theory reveals a ground state phase diagram with three distinct regimes—a regular Bose-Einstein condensate and incoherent and coherent arrays of quantum droplets. The coherent droplets are connected by a background condensate, which leads—in addition to the periodic density modulation—to a robust phase coherence throughout the whole system. We further theoretically demonstrate that we are able to dynamically approach the ground state in our experiment and that its lifetime is limited only by three-body losses. Experimentally we probe and confirm the signatures of the phase diagram by observing the in situ density modulation as well as the phase coherence using matter wave interference.

We experimentally investigate the effects of parametric instabilities on the short-time heating process of periodically driven bosons in 2D optical lattices with a continuous transverse (tube) degree of freedom. We analyze three types of periodic drives: (i) linear along the $x$-lattice direction only, (ii) linear along the lattice diagonal, and (iii) circular in the lattice plane. In all cases, we demonstrate that the Bose-Einstein condensate (BEC) decay is dominated by the emergence of unstable Bogoliubov modes, rather than scattering in higher Floquet bands, in agreement with recent theoretical predictions. The observed BEC depletion rates are much higher when shaking along both the $x$ and $y$ directions, as opposed to only $x$ or only $y$. We also report an explosion of the decay rates at large drive amplitudes and suggest a phenomenological description beyond the Bogoliubov theory. In this strongly coupled regime, circular drives heat faster than diagonal drives, which illustrates the nontrivial dependence of the heating on the choice of drive.

We analyze state preparation within a restricted space of local control parameters between adiabatically connected states of control Hamiltonians. We formulate a conjecture that the time integral of energy fluctuations over the protocol duration is bounded from below by the geodesic length set by the quantum geometric tensor. The conjecture implies a geometric lower bound for the quantum speed limit (QSL). We prove the conjecture for arbitrary, sufficiently slow protocols using adiabatic perturbation theory and show that the bound is saturated by geodesic protocols, which keep the energy variance constant along the trajectory. Our conjecture implies that any optimal unit-fidelity protocol, even those that drive the system far from equilibrium, are fundamentally constrained by the quantum geometry of adiabatic evolution. When the control space includes all possible couplings, spanning the full Hilbert space, we recover the well-known Mandelstam-Tamm bound. However, using only accessible local controls to anneal in complex models such as glasses or to target individual excited states in quantum chaotic systems, the geometric bound for the quantum speed limit can be exponentially large in the system size due to a diverging geodesic length. We validate our conjecture both analytically by constructing counter-diabatic and fast-forward protocols for a three-level system, and numerically in nonintegrable spin chains and a nonlocal SYK model.

In topological insulators doped with magnetic ions, spin-orbit coupling and ferromagnetism give rise to the quantum anomalous Hall effect. Here, we show that in $s$-wave superconductors with strong spin-orbit coupling, magnetic impurity ions can generate topological vortices in the absence of external magnetic fields. Such vortices, dubbed quantum anomalous vortices, support robust Majorana zero-energy modes when superconductivity is induced in the topological surface states. We demonstrate that the zero-energy bound states observed in Fe(Te,Se) superconductors are possible realizations of the Majorana zero modes in quantum anomalous vortices produced by the interstitial magnetic Fe. The quantum anomalous vortex matter not only advances fundamental understandings of topological defect excitations of Cooper pairing but also provides new and advantageous platforms for manipulating Majorana zero modes in quantum computing.

Qubits strongly coupled to a photonic crystal give rise to qubit-photon dressed bound states. These bound states, comprising the qubits and spatially localized photonic modes induced around the qubits, are the basis for many exotic physical scenarios. The localization of these states changes with qubit detuning from the photonic crystal band edge, offering an avenue of in situ control of bound-state interaction. Here, we present experimental results from a device with two transmon qubits coupled to a superconducting microwave photonic crystal and realize tunable on-site and interbound state interactions. We observe a fourth-order two-photon virtual process between bound states indicating strong coupling between the photonic crystal and transmon qubits. Because of their localization-dependent interaction, these states offer the ability to realize one-dimensional chains of bound states with tunable and potentially long-range interactions that preserve the qubits’ spatial organization. The widely tunable, strong, and robust interactions demonstrated with this system are promising benchmarks towards realizing larger, more complex systems that use bound states to build and study quantum spin models.