Generalizing the prior work of P. W. Anderson and E. R. Huggins, we show that a “detailed Josephson-Anderson relation” holds for drag on a finite body held at rest in a classical incompressible fluid flowing with velocity $\mathbf{V}$. The relation asserts an exact equality between the instantaneous power consumption by the drag $-\mathbf{F}·\mathbf{V}$ and the vorticity flux across the potential mass current $-(1/2)\int dJ\int {\epsilon }_{ijk}{\mathrm{\Sigma }}_{ij}d{\ell }_k$. Here, ${\mathrm{\Sigma }}_{ij}$ is the flux in the $i$th coordinate direction of the conserved $j$th component of vorticity, and the line integrals over $\mathbf{\ell }$ are taken along streamlines of the potential-flow solution ${\mathbf{u}}_{\varphi }=\mathbf{\nabla }\varphi$ of the ideal Euler equation, carrying mass flux $dJ=\rho {\mathbf{u}}_{\varphi }·d\mathbf{A}$. Drag and dissipation are thus associated with the motion of vorticity relative to this background ideal potential flow solving Euler’s equation. The results generalize the theories of M. J. Lighthill for flow past a body and, in particular, the steady-state relation $(1/2){\epsilon }_{ijk}⟨{\mathrm{\Sigma }}_{jk}⟩={\partial }_i⟨h⟩$, where $h=p+(1/2)|\mathbf{u}{|}^2$ is the generalized enthalpy or total pressure, extends Lighthill’s theory of vorticity generation at solid walls into the interior of the flow. We use these results to explain drag on the body in terms of vortex dynamics, unifying the theories for classical fluids and for quantum superfluids. The results offer a new solution to the “d’Alembert paradox” at infinite Reynolds numbers, provide an explanation for a long-standing puzzle about the experimental conditions required for anomalous turbulent energy dissipation, and imply the necessary and sufficient conditions for turbulent drag reduction.

Fluid dynamics is one of the cornerstones of modern physics and has recently found applications in the transport of electrons in solids. In most solids, electron transport is dominated by extrinsic factors, such as sample geometry and scattering from impurities. However, in the hydrodynamic regime, Coulomb interactions transform the electron motion from independent particles to the collective motion of a viscous “electron fluid.” The fluid viscosity is an intrinsic property of the electron system, determined solely by the electron-electron interactions. Resolving the universal intrinsic viscosity is challenging, as it affects the resistance only through interactions with the sample boundaries, whose roughness not only is unknown but also varies from device to device. Here, we eliminate all unknown parameters by fabricating samples with smooth sidewalls to achieve the perfect slip boundary condition, which has been elusive in both molecular fluids and electronic systems. We engineer the device geometry to create viscous dissipation and reveal the true intrinsic hydrodynamic properties of a 2D system. We observe a clear transition from ballistic to hydrodynamic electron motion, driven by both temperature and magnetic field. We directly measure the viscosity and electron-electron scattering lifetime (the Fermi quasiparticle lifetime) over a wide temperature range without fitting parameters and show they have a strong dependence on electron density that cannot be explained by conventional theories based on the random phase approximation.

Mechanical oscillators have been demonstrated with very high quality factors over a wide range of frequencies. They also couple to a wide variety of fields and forces, making them ideal as sensors. The realization of a mechanically based quantum bit could therefore provide an important new platform for quantum computation and sensing. Here, we show that by coupling one of the flexural modes of a suspended carbon nanotube to the charge states of a double quantum dot defined in the nanotube, it is possible to induce sufficient anharmonicity in the mechanical oscillator so that the coupled system can be used as a mechanical quantum bit. However, these results can only be achieved when the device enters the ultrastrong coupling regime. We discuss the conditions for the anharmonicity to appear, and we show that the Hamiltonian can be mapped onto an anharmonic oscillator, allowing us to work out the energy level structure and find how decoherence from the quantum dot and the mechanical oscillator is inherited by the qubit. Remarkably, the dephasing due to the quantum dot is expected to be reduced by several orders of magnitude in the coupled system. We outline qubit control, readout protocols, the realization of a CNOT gate by coupling two qubits to a microwave cavity, and finally how the qubit can be used as a static-force quantum sensor.

The realization of quantum networks critically depends on establishing efficient, coherent light-matter interfaces. Optically active spins in diamond have emerged as promising quantum nodes based on their spin-selective optical transitions, long-lived spin ground states, and potential for integration with nanophotonics. Tin-vacancy (${\mathrm{SnV}}^{-}$) centers in diamond are of particular interest because they exhibit narrow-linewidth emission in nanostructures and possess long spin coherence times at temperatures above 1 K. However, a nanophotonic interface for ${\mathrm{SnV}}^{-}$ centers has not yet been realized. Here, we report cavity enhancement of the emission of ${\mathrm{SnV}}^{-}$ centers in diamond. We integrate ${\mathrm{SnV}}^{-}$ centers into one-dimensional photonic crystal resonators and observe a 40-fold increase in emission intensity. The Purcell factor of the coupled system is 25, resulting in a channeling of the majority of photons (90%) into the cavity mode. Our results pave the way for the creation of efficient, scalable spin-photon interfaces based on ${\mathrm{SnV}}^{-}$ centers in diamond.

The two main classes of liquid-crystal (LC) phases of rodlike molecules are nematics, where the rods align in the same direction (the nematic director $\mathbf{n}$), and smectics, where the rods not only are aligned but also form layers. The electro-optic effects in LC devices that are a backbone in today’s display industry mainly use the Fréedericksz transition, which is the bulk reorientation of a surface-anchored nematic by an electric field. Conventional (uniaxial) smectics do not present a Fréedericksz transition, because, due to their layered structure, the director reorientation would distort the layers, which would cost too much energy. In a worldwide ongoing effort to extend the variety of LC compounds suitable for applications in the display industry, bent-shaped molecules have recently raised much attention, since they present multiple new LC phases with unusual properties. In this paper, we report on a structural and electro-optic study of the LC phases of a bent-shaped dimer. On cooling from the isotropic liquid, this compound shows a usual nematic ($N$), a twist-bend nematic ($N_{\mathrm{TB}}$), and a biaxial smectic-$A$ phase ($\mathrm{Sm}{A}_b$). Quite surprisingly, contrary to usual smectics, $\mathrm{Sm}{A}_b$ presents a remarkable electro-optic response, with low ($<4\mathrm{V}$) voltage threshold, no reorganization of the smectic layers, and low ($<1\mathrm{ms}$) response time (i.e., 30 times faster than the $N$ phase at higher temperature). We interpret this unexpected electro-optic effect as a Fréedericksz transition affecting the secondary director $\mathbf{m}$ of the $\mathrm{Sm}{A}_b$, and we model it by analogy with the usual Fréedericksz transition of the $\mathbf{n}$ director of the uniaxial $N$ phase. Indeed, a Fréedericksz transition affecting only $\mathbf{m}$ in this biaxial fluid smectic does not alter its layered structure and costs little energy. From the point of view of applications, thanks to its low relaxation time, this “biaxial” Fréedericksz transition could be exploited in electro-optic devices that require fast switching.

The physical realization of ${\mathbb{Z}}_2$ topological order as encountered in the paradigmatic toric code has proven to be an elusive goal. We predict that this phase of matter can be realized in a two-dimensional array of Rydberg atoms placed on the ruby lattice, at specific values of the Rydberg blockade radius. First, we show that the blockade model—also known as a “$PXP$” model—realizes a monomer-dimer model on the kagome lattice with a single-site kinetic term. This model can be interpreted as a ${\mathbb{Z}}_2$ gauge theory whose dynamics is generated by monomer fluctuations. We obtain its phase diagram using the numerical density matrix renormalization group method and find a topological quantum liquid (TQL) as evidenced by multiple measures including (i) a continuous transition between two featureless phases, (ii) a topological entanglement entropy of $\ln 2$ as measured in various geometries, (iii) degenerate topological ground states, and (iv) the expected modular matrix from ground state overlap. Next, we show that the TQL persists upon including realistic, algebraically decaying van der Waals interactions $V(r)\sim 1/r^6$ for a choice of lattice parameters. Moreover, we can directly access topological loop operators, including the Fredenhagen-Marcu order parameter. We show how these can be measured experimentally using a dynamic protocol, providing a “smoking gun” experimental signature of the TQL phase. Finally, we show how to trap an emergent anyon and realize different topological boundary conditions, and we discuss the implications for exploring fault-tolerant quantum memories.

We study the stability of quasinormal modes (QNM) in asymptotically flat black hole spacetimes by means of a pseudospectrum analysis. The construction of the Schwarzschild QNM pseudospectrum reveals the following: (i) the stability of the slowest-decaying QNM under perturbations respecting the asymptotic structure, reassessing the instability of the fundamental QNM discussed by Nollert [H. P. Nollert, About the Significance of Quasinormal Modes of Black Holes, Phys. Rev. D 53, 4397 (1996)] as an “infrared” effect; (ii) the instability of all overtones under small-scale (“ultraviolet”) perturbations of sufficiently high frequency, which migrate towards universal QNM branches along pseudospectra boundaries, shedding light on Nollert’s pioneer work and Nollert and Price’s analysis [H. P. Nollert and R. H. Price, Quantifying Excitations of Quasinormal Mode Systems, J. Math. Phys. (N.Y.) 40, 980 (1999)]. Methodologically, a compactified hyperboloidal approach to QNMs is adopted to cast QNMs in terms of the spectral problem of a non-self-adjoint operator. In this setting, spectral (in)stability is naturally addressed through the pseudospectrum notion that we construct numerically via Chebyshev spectral methods and foster in gravitational physics. After illustrating the approach with the Pöschl-Teller potential, we address the Schwarzschild black hole case, where QNM (in)stabilities are physically relevant in the context of black hole spectroscopy in gravitational-wave physics and, conceivably, as probes into fundamental high-frequency spacetime fluctuations at the Planck scale.

Reaction-diffusion waves have long been used to describe the growth and spread of populations undergoing a spatial range expansion. Such waves are generally classed as either pulled, where the dynamics are driven by the very tip of the front and stochastic fluctuations are high, or pushed, where cooperation in growth or dispersal results in a bulk-driven wave in which fluctuations are suppressed. These concepts have been well studied experimentally in populations where the cooperation leads to a density-dependent growth rate. By contrast, relatively little is known about experimental populations that exhibit density-dependent dispersal. Using bacteriophage T7 as a test organism, we present novel experimental measurements that demonstrate that the diffusion of phage T7, in a lawn of host E. coli, is hindered by steric interactions with host bacteria cells. The coupling between host density, phage dispersal, and cell lysis caused by viral infection results in an effective density-dependent diffusion coefficient akin to cooperative behavior. Using a system of reaction-diffusion equations, we show that this effect can result in a transition from a pulled to pushed expansion. Moreover, we find that a second, independent density-dependent effect on phage dispersal spontaneously emerges as a result of the viral incubation period, during which, phage is trapped inside the host unable to disperse. Additional stochastic agent-based simulations reveal that lysis time dramatically affects the rate of diversity loss in viral expansions. Taken together, our results indicate both that bacteriophage can be used as a controllable laboratory population to investigate the impact of density-dependent dispersal on evolution, and that the genetic diversity and adaptability of expanding viral populations could be much greater than is currently assumed.

Multimode optical fibers (MMFs) have gained renewed interest in the past decade, emerging as a way to boost optical communication data rates in the context of an expected saturation of current single-mode fiber-based networks. They are also attractive for endoscopic applications, offering the possibility to achieve a similar information content as multicore fibers, but with a much smaller footprint, thus reducing the invasiveness of endoscopic procedures. However, these advances are hindered by the unavoidable presence of disorder that affects the propagation of light in MMFs and limits their practical applications. We introduce here a general framework to study and avoid the effect of disorder in wave-based systems and demonstrate its application for multimode fibers. We experimentally find an almost complete set of optical channels that are resilient to disorder induced by strong deformations. These deformation principal modes are obtained by only exploiting measurements for weak perturbations harnessing the generalized Wigner-Smith operator. We explain this effect by demonstrating that, even for a high level of disorder, the propagation of light in MMFs can be characterized by just a few key properties. These results are made possible thanks to a precise and fast estimation of the modal transmission matrix of the fiber which relies on a model-based optimization using deep learning frameworks.

Metasurfaces have been enabling the miniaturization and integration of complex optical functionalities within an ultrathin platform by engineering the scattering features of localized modes. However, these efforts have mostly been limited to the manipulation of externally produced coherent light, e.g., from a laser. In parallel, the past two decades have seen the development of structured surfaces that emit partially coherent radiation via thermally populated, spatially extended (nonlocal) modes. However, the control over thermally emitted light is severely limited compared to optical metasurfaces, and even basic functionalities such as unidirectional emission to an arbitrary angle and polarization remain elusive. Here, we derive the necessary conditions to achieve full control over thermally emitted light, pointing to the need for simultaneously tailoring local and nonlocal scattering features across the structure. Based on these findings, we introduce a platform for thermal metasurfaces based on quasibound states in the continuum that satisfies these requirements and completes the program of compactification of optical systems by enabling a full degree of control of partially coherent light emission from structured thin films, including unidirectional emission of circularly polarized light, focusing, and control of spatial and temporal coherence, as well as wave-front control with designer spin and angular orbital momenta.

We introduce a near-term experimental platform for realizing an associative memory. It can simultaneously store many memories by using spinful bosons coupled to a degenerate multimode optical cavity. The associative memory is realized by a confocal cavity QED neural network, with the modes serving as the synapses, connecting a network of superradiant atomic spin ensembles,which serve as the neurons. Memories are encoded in the connectivity matrix between the spins and can be accessed through the input and output of patterns of light. Each aspect of the scheme is based on recently demonstrated technology using a confocal cavity and Bose-condensed atoms. Our scheme has two conceptually novel elements. First, it introduces a new form of random spin system that interpolates between a ferromagnetic and a spin glass regime as a physical parameter is tuned—the positions of ensembles within the cavity. Second, and more importantly, the spins relax via deterministic steepest-descent dynamics rather than Glauber dynamics. We show that this nonequilibrium quantum-optical scheme has significant advantages for associative memory over Glauber dynamics: These dynamics can enhance the network’s ability to store and recall memories beyond that of the standard Hopfield model. Surprisingly, the cavity QED dynamics can retrieve memories even when the system is in the spin glass phase. Thus, the experimental platform provides a novel physical instantiation of associative memories and spin glasses as well as provides an unusual form of relaxational dynamics that is conducive to memory recall even in regimes where it was thought to be impossible.

Variational quantum circuits (VQCs) built upon noisy intermediate-scale quantum (NISQ) hardware, in conjunction with classical processing, constitute a promising architecture for quantum simulations, classical optimization, and machine learning. However, the required VQC depth to demonstrate a quantum advantage over classical schemes is beyond the reach of available NISQ devices. Supervised learning assisted by an entangled sensor network (SLAEN) is a distinct paradigm that harnesses VQCs trained by classical machine-learning algorithms to tailor multipartite entanglement shared by sensors for solving practically useful data-processing problems. Here, we report the first experimental demonstration of SLAEN and show an entanglement-enabled reduction in the error probability for classification of multidimensional radio-frequency signals. Our work paves a new route for quantum-enhanced data processing and its applications in the NISQ era.

We induce strong nonlocal interactions in a 2D Fermi gas in an optical lattice using Rydberg dressing. The system is approximately described by a $t-V$ model on a square lattice where the fermions experience isotropic nearest-neighbor interactions and are free to hop only along one direction. We measure the interactions using many-body Ramsey interferometry and study the lifetime of the gas in the presence of tunneling, finding that tunneling does not reduce the lifetime. To probe the interplay of nonlocal interactions with tunneling, we investigate the short-time-relaxation dynamics of charge-density waves in the gas. We find that strong nearest-neighbor interactions slow down the relaxation. Our work opens the door for quantum simulations of systems with strong nonlocal interactions such as extended Fermi-Hubbard models.

We report the observation of subradiance in dense ensembles of cold ${}^{87}\mathrm{Rb}$ atoms operating near Dicke’s regime of a large number of atoms in a volume with dimensions smaller than the transition wavelength. We validate that the atom number is the only cooperativity parameter governing subradiance. We probe the dynamics in the many-body regime and support the picture that multiply excited subradiant states are built as a superposition of singly excited states that decay independently. Moreover, we implement an experimental procedure to release the excitation stored in the long-lived modes in a pulse of light. This technique is a first step towards the realization of tailored light storing based on subradiance.

All clocks, in some form or another, use the evolution of nature toward higher entropy states to quantify the passage of time. Because of the statistical nature of the second law and corresponding entropy flows, fluctuations fundamentally limit the performance of any clock. This suggests a deep relation between the increase in entropy and the quality of clock ticks. Indeed, minimal models for autonomous clocks in the quantum realm revealed that a linear relation can be derived, where for a limited regime every bit of entropy linearly increases the accuracy of quantum clocks. But can such a linear relation persist as we move toward a more classical system? We answer this in the affirmative by presenting the first experimental investigation of this thermodynamic relation in a nanoscale clock. We stochastically drive a nanometer-thick membrane and read out its displacement with a radio-frequency cavity, allowing us to identify the ticks of a clock. We show theoretically that the maximum possible accuracy for this classical clock is proportional to the entropy created per tick, similar to the known limit for a weakly coupled quantum clock but with a different proportionality constant. We measure both the accuracy and the entropy. Once nonthermal noise is accounted for, we find that there is a linear relation between accuracy and entropy and that the clock operates within an order of magnitude of the theoretical bound.

The advent of the quantum gas microscope allowed for the in situ probing of ultracold gaseous matter on an unprecedented level of spatial resolution. However, the study of phenomena on ever smaller length scales, as well as the probing of three-dimensional systems, is fundamentally limited by the wavelength of the imaging light for all techniques based on linear optics. Here, we report on a high-resolution ion microscope as a versatile and powerful experimental tool to investigate quantum gases. The instrument clearly resolves atoms in an optical lattice with a spacing of 532 nm over a field of view of 50 sites and offers an extremely large depth of field on the order of at least $70\mu \mathrm{m}$. With a simple model, we extract an upper limit for the achievable resolution of approximately 200 nm from our data. We demonstrate a pulsed operation mode enabling 3D imaging and allowing for the study of ionic impurities and Rydberg physics.

Transforming an initial quantum state into a target state through the fastest possible route—a quantum brachistochrone—is a fundamental challenge for many technologies based on quantum mechanics. In two-level systems, the quantum brachistochrone solutions are long known. These solutions, however, are not applicable to larger systems, especially when the target state cannot be reached through a local transformation. Here, we demonstrate fast coherent transport of an atomic wave packet over a distance of 15 times its size—a paradigmatic case of quantum processes going beyond the two-level system. Our measurements of the transport fidelity reveal the existence of a minimum duration—a quantum speed limit—for the coherent splitting and recombination of matter waves. We obtain physical insight into this limit by relying on a geometric interpretation of quantum state dynamics. These results shed light on a fundamental limit of quantum state dynamics and are expected to find relevant applications in quantum sensing and quantum computing.

Tissue, cell, and nucleus morphology change during tumor progression. In 2D confluent cell cultures, different tissue states, such as fluid (unjammed) and solid (jammed), are correlated with cell shapes. These results do not have to apply a priori to three dimensions. Cancer cell motility requires and corresponds to a fluidization of the tumor tissue on the bulk level. Here, we investigate bulk tissue fluidity in 3D and determine how it correlates with cell and nucleus shape. In patient samples of mamma and cervix carcinoma, we find areas where cells can move or are immobile. We compare 3D cell spheroids composed of cells from a cancerous and a noncancerous cell line. Through bulk mechanical spheroid-fusion experiments and single live-cell tracking, we show that the cancerous sample is fluidized by active cells moving through the tissue. The healthy, epithelial sample with immobile cells behaves more solidlike. 3D segmentations of the samples show that the degree of tissue fluidity correlates with elongated cell and nucleus shapes. This correlation links cell shapes to cell motility and bulk mechanical behavior. We find two active states of matter in solid tumors: an amorphous glasslike state with characteristics of 3D cell jamming and a disordered fluid state. Individual cell and nucleus shape may serve as a marker for metastatic potential to foster personalized cancer treatment.

We present a circuit design composed of two Josephson junctions coupled by a nonreciprocal element, the gyrator, whose ground space is doubly degenerate. The ground states are approximate code words of the Gottesman-Kitaev-Preskill code. We determine the low-energy dynamics of the circuit by working out the equivalence of this system to the problem of a single electron in a crystal, confined to a two-dimensional plane, and subjected to a strong, homogeneous magnetic field. We find that the circuit is naturally protected against the common noise channels in superconducting circuits, such as charge and flux noise, implying that it can be used for passive quantum error correction. We also propose realistic design parameters for an experimental realization, and we describe possible protocols to perform logical one- and two-qubit gates, state preparation, and readout.

It is interesting to observe that all optical materials with a positive refractive index have a value of index that is of order unity. Surprisingly, though, a deep understanding of the mechanisms that lead to this universal behavior seems to be lacking. Moreover, this observation is difficult to reconcile with the fact that a single isolated atom is known to have a giant optical response, as characterized by a resonant scattering cross section that far exceeds its physical size. Here, we theoretically and numerically investigate the evolution of the optical properties of an ensemble of ideal atoms as a function of density, starting from the dilute gas limit, including the effects of multiple scattering and near-field interactions. Interestingly, despite the giant response of an isolated atom, we find that the maximum index does not indefinitely grow with increasing density but rather reaches a limiting value of $n\approx 1.7$. This limit arises purely from electrodynamics, as it occurs at densities far below those where chemical processes become important. We propose an explanation based upon strong-disorder renormalization group theory, in which the near-field interaction combined with random atomic positions results in an inhomogeneous broadening of atomic resonance frequencies. This mechanism ensures that, regardless of the physical atomic density, light at any given frequency only interacts with at most a few near-resonant atoms per cubic wavelength, thus limiting the maximum index attainable. Our work is a promising first step to understand the limits of the refractive index from a bottom-up, atomic physics perspective, and it also introduces the renormalization group as a powerful tool to understand the generally complex problem of multiple scattering of light overall.