Studying entanglement growth in quantum dynamics provides both insight into the underlying microscopic processes and information about the complexity of the quantum states, which is related to the efficiency of simulations on classical computers. Recently, experiments with trapped ions, polar molecules, and Rydberg excitations have provided new opportunities to observe dynamics with long-range interactions. We explore nonequilibrium coherent dynamics after a quantum quench in such systems, identifying qualitatively different behavior as the exponent of algebraically decaying spin-spin interactions in a transverse Ising chain is varied. Computing the buildup of bipartite entanglement as well as mutual information between distant spins, we identify linear growth of entanglement entropy corresponding to propagation of quasiparticles for shorter-range interactions, with the maximum rate of growth occurring when the Hamiltonian parameters match those for the quantum phase transition. Counterintuitively, the growth of bipartite entanglement for long-range interactions is only logarithmic for most regimes, i.e., substantially slower than for shorter-range interactions. Experiments with trapped ions allow for the realization of this system with a tunable interaction range, and we show that the different phenomena are robust for finite system sizes and in the presence of noise. These results can act as a direct guide for the generation of large-scale entanglement in such experiments, towards a regime where the entanglement growth can render existing classical simulations inefficient.

We report an experiment in which an atomic excitation is localized to a spatial width that is a factor of 8 smaller than the wavelength of the incident light. The experiment utilizes the sensitivity of the dark state of electromagnetically induced transparency (EIT) to the intensity of the coupling laser beam. A standing-wave coupling laser with a sinusoidally varying intensity yields tightly confined Raman excitations during the EIT process. The excitations, located near the nodes of the intensity profile, have a width of 100 nm. The experiment is performed using ultracold ${}^{87}\mathrm{Rb}$ atoms trapped in an optical dipole trap, and atomic localization is achieved with EIT pulses that are approximately 100 ns long. To probe subwavelength atom localization, we have developed a technique that can measure the width of the atomic excitations with nanometer spatial resolution.

In this work, we describe a scheme to execute all-optical control of the routing or switching of photonic information where, by optically controlling the internal quantum state of a individual scatterer coupled to two independent cavity modes, one can dynamically and rapidly modulate the intermode coupling. This allows all-optical modulation of intercavity couplings via ac Stark or shuffle (stimulated Raman adiabatic passage) control of the scatterer’s internal states, and from this modulation, we show that we can perform all-optical switching and all-optical routing with near-unit switching contrast and with high bandwidth.

We create squeezed light by exploiting the quantum nature of the mechanical interaction between laser light and a membrane mechanical resonator embedded in an optical cavity. The radiation-pressure shot noise (fluctuating optical force from quantum laser amplitude noise) induces resonator motion well above that of thermally driven motion. This motion imprints a phase shift on the laser light, hence correlating the amplitude and phase noise, a consequence of which is optical squeezing. We experimentally demonstrate strong and continuous optomechanical squeezing of $1.7\pm 0.2\mathrm{dB}$ below the shot-noise level. The peak level of squeezing measured near the mechanical resonance is well described by a model whose parameters are independently calibrated and that includes thermal motion of the membrane with no other classical noise sources.

We introduce a promising new platform for Majorana zero modes and various spintronics applications based on gate-defined wires in HgTe quantum wells. Because of the Dirac-like band structure for HgTe, the physics of such systems differs markedly from that of conventional quantum wires. Most strikingly, we show that the subband parameters for gate-defined HgTe wires exhibit exquisite tunability: Modest gate voltage variation allows one to modulate the Rashba spin-orbit energies from zero up to about 30 K, and the effective $g$ factors from zero up to giant values exceeding 600. The large achievable spin-orbit coupling and $g$ factors together allow one to access Majorana modes in this setting at exceptionally low magnetic fields while maintaining robustness against disorder. As an additional benefit, gate-defined wires (in HgTe or other settings) should greatly facilitate the fabrication of networks for refined transport experiments used to detect Majoranas, as well as the realization of non-Abelian statistics and quantum information devices.

In numerical simulations, spontaneously broken symmetry is often detected by computing two-point correlation functions of the appropriate local order parameter. This approach, however, computes the square of the local order parameter, and so when it is small, very large system sizes at high precisions are required to obtain reliable results. Alternatively, one can pin the order by introducing a local symmetry-breaking field and then measure the induced local order parameter infinitely far from the pinning center. The method is tested here at length for the Hubbard model on honeycomb lattice, within the realm of the projective auxiliary-field quantum Monte Carlo algorithm. With our enhanced resolution, we find a direct and continuous quantum phase transition between the semimetallic and the insulating antiferromagnetic states with increase of the interaction. The single-particle gap, measured in units of Hubbard $U$, tracks the staggered magnetization. An excellent data collapse is obtained by finite-size scaling, with the values of the critical exponents in accord with the Gross-Neveu universality class of the transition.

Multipartite entanglement of large numbers of physically distinct linear resonators is of both fundamental and applied interest, but there have been no feasible proposals to date for achieving it. At the same time, the Bose-Hubbard model with attractive interactions (ABH) is theoretically known to have a phase transition from the superfluid phase to a highly entangled nonlocal superposition, but observation of this phase transition has remained out of experimental reach. In this theoretical work, we jointly address these two problems by (1) proposing an experimentally accessible quantum simulation of the ABH phase transition in an array of tunably coupled superconducting circuit microwave resonators and (2) incorporating the simulation into a highly scalable protocol that takes as input any microwave-resonator state with negligible occupation of number states $|0⟩$ and $|1⟩$ and nonlocally superposes it across the whole array of resonators. The large-scale multipartite entanglement produced by the protocol is of the $W$ type, which is well known for its robustness. The protocol utilizes the ABH phase transition to generate the multipartite entanglement of all of the resonators in parallel, and is therefore deterministic and permits an increase in resonator number without any increase in protocol complexity; the number of resonators is limited instead by system characteristics such as resonator-frequency disorder and inter-resonator coupling strength. Only one local and two global controls are required for the protocol. We numerically demonstrate the protocol with realistic system parameters and estimate that current experimental capabilities can realize the protocol with high fidelity for greater than 40 resonators. Because superconducting-circuit microwave resonators are capable of interfacing with other devices and platforms such as mechanical resonators and (potentially) optical fields, this proposal provides a route toward large-scale $W$-type entanglement in those systems as well.

Strongly correlated fractional quantum Hall liquids support fractional excitations, which can be understood in terms of adiabatic flux insertion arguments. A second route to fractionalization is through the coupling of weakly interacting electrons to topologically nontrivial backgrounds such as in polyacetylene. Here, we demonstrate that electronic fractionalization combining features of both these mechanisms occurs in noncoplanar itinerant magnetic systems, where integer quantum Hall physics arises from the coupling of electrons to the magnetic background. The topologically stable magnetic vortices in such systems carry fractional (in general, irrational) electronic quantum numbers and exhibit Abelian anyonic statistics. We analyze the properties of these topological defects by mapping the distortions of the magnetic texture onto effective non-Abelian vector potentials. We support our analytical results with extensive numerical calculations.

Device-independent quantum key distribution (DIQKD) is a formalism that supersedes traditional quantum key distribution, as its security does not rely on any detailed modeling of the internal working of the devices. This strong form of security is only possible using devices producing correlations that violate a Bell inequality. Full security proofs of DIQKD have recently been reported, but they tolerate zero or small amounts of noise and are restricted to protocols based on specific Bell inequalities. Here, we provide a security proof of DIQKD that is both more efficient and noise resistant, and also more general, as it applies to protocols based on arbitrary Bell inequalities and can be adapted to cover supraquantum eavesdroppers limited by the no-signaling principle only. It is formulated, however, in the bounded-quantum-storage model, where an upper bound on the adversary’s quantum memory is a priori known. This condition is not a limitation at present, since the best existing quantum memories have very short coherence times.

Device-independent quantum key distribution (DIQKD) in its current design requires a violation of a Bell’s inequality between two parties, Alice and Bob, who are connected by a quantum channel. However, in reality, quantum channels are lossy and current DIQKD protocols are thus vulnerable to attacks exploiting the detection loophole of the Bell test. Here, we propose a novel approach to DIQKD that overcomes this limitation. In particular, we propose a protocol where the Bell test is performed entirely on two casually independent devices situated in Alice’s laboratory. As a result, the detection loophole caused by the losses in the channel is avoided.

Recently, several authors have investigated topological phenomena in periodically driven systems of noninteracting particles. These phenomena are identified through analogies between the Floquet spectra of driven systems and the band structures of static Hamiltonians. Intriguingly, these works have revealed phenomena that cannot be characterized by analogy to the topological classification framework for static systems. In particular, in driven systems in two dimensions (2D), robust chiral edge states can appear even though the Chern numbers of all the bulk Floquet bands are zero. Here, we elucidate the crucial distinctions between static and driven 2D systems, and construct a new topological invariant that yields the correct edge-state structure in the driven case. We provide formulations in both the time and frequency domains, which afford additional insight into the origins of the “anomalous” spectra that arise in driven systems. Possibilities for realizing these phenomena in solid-state and cold-atomic systems are discussed.

Parity is a fundamental quantum number used to classify a state of matter. Materials rarely possess ground states with odd parity. We show that the superconducting state in iron-based superconductors is classified as an odd-parity $s$-wave spin-singlet pairing state in a single trilayer $\mathrm{FeAs}/\mathrm{Se}$, the building block of the materials. In a low-energy effective model constructed on the Fe square bipartite lattice, the superconducting order parameter in this state is a combination of an $s$-wave normal pairing between two sublattices and an $s$-wave $\eta$ pairing within the sublattices. The state has a fingerprint with a real-space sign inversion between the top and bottom $\mathrm{As}/\mathrm{Se}$ layers. The results suggest that iron-based superconductors are a new quantum state of matter, and the measurement of the odd parity can help to establish high-temperature superconducting mechanisms.

We report on the stabilization of a microresonator-based optical frequency comb (microcomb) by way of mechanical actuation. These experiments use novel ${\mathrm{CO}}_2$-laser-machined microrod resonators, which are introduced here and feature optical $Q\gtrsim 5\times {10}^8$, less than 1 minute processing time, and tunable geometry. Residual fluctuations of our 32.6 GHz microcomb line spacing reach a stability level of $5\times {10}^{-15}$ for 1 s averaging, thereby highlighting the potential of microcombs to support modern optical-frequency standards. Furthermore, measurements of the line spacing with respect to an independent frequency reference reveal stabilization of different spectral slices of the comb with a $<0.5\mathrm{\text{−}}\mathrm{mHz}$ variation among 140 comb lines spanning 4.5 THz. Together, these results demonstrate an important step in the development of microcombs, namely, that they can be fabricated and precisely controlled with simple and accessible techniques.

Progress in materials science depends on the ability to discover new materials and to obtain and understand their properties. This has recently become particularly apparent for compounds with reduced dimensionality, which often display unexpected physical and chemical properties, making them very attractive for applications in electronics, graphene being so far the most noteworthy example. Here, we report some previously unknown two-dimensional materials and their electronic structure by data mining among crystal structures listed in the International Crystallographic Structural Database, combined with density-functional-theory calculations. As a result, we propose to explore the synthesis of a large group of two-dimensional materials, with properties suggestive of applications in nanoscale devices, and anticipate further studies of electronic and magnetic phenomena in low-dimensional systems.

Nonreciprocal devices perform crucial functions in many low-noise quantum measurements, usually by exploiting magnetic effects. In the proof-of-principle device presented here, on the other hand, two on-chip coupled Josephson parametric converters (JPCs) achieve directionality by exploiting the nonreciprocal phase response of the JPC in the transmission-gain mode. The nonreciprocity of the device is controlled in situ by varying the amplitude and phase difference of two independent microwave pump tones feeding the system. At the desired working point and for a signal frequency of 8.453 GHz, the device achieves a forward power gain of 15 dB within a dynamical bandwidth of 9 MHz, a reverse gain of $-6\mathrm{dB}$, and suppression of the reflected signal by 8 dB. We also find that the amplifier adds a noise equivalent to less than 1.5 photons at the signal frequency (referred back to the input). It can process up to 3 photons at the signal frequency per inverse dynamical bandwidth. With a directional amplifier operating along the principles of this device, qubit and readout preamplifier could be integrated on the same chip.

Charge-density-wave order has been observed in cuprate superconductors whose crystal structure breaks the square symmetry of the ${\mathrm{CuO}}_2$ planes, such as orthorhombic ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_y$ (YBCO), but not so far in cuprates that preserve that symmetry, such as tetragonal ${\mathrm{HgBa}}_2{\mathrm{CuO}}_{4+\delta }$ (Hg1201). We have measured the Hall ($R_H$), Seebeck ($S$), and Nernst ($\nu$) coefficients of underdoped Hg1201 in magnetic fields large enough to suppress superconductivity. The high-field $R_H(T)$ and $S(T)$ are found to drop with decreasing temperature and become negative, as also observed in YBCO at comparable doping. In YBCO, the negative $R_H$ and $S$ are signatures of a small electron pocket caused by Fermi-surface reconstruction, attributed to charge-density-wave modulations observed in the same range of doping and temperature. We deduce that a similar Fermi-surface reconstruction takes place in Hg1201, evidence that density-wave order exists in this material. A striking similarity is also found in the normal-state Nernst coefficient $\nu (T)$, further supporting this interpretation. Given the model nature of Hg1201, Fermi-surface reconstruction appears to be common to all hole-doped cuprates, suggesting that density-wave order is a fundamental property of these materials.

Despite much interest in engineering new topological surface (edge) states using structural defects, such topological surface states have not been observed yet. We show that recently imaged tilt boundaries in gated multilayer graphene should support topologically protected gapless edge states. We approach the problem from two perspectives: the microscopic perspective of a tight-binding model and an ab initio calculation on a bilayer, and the symmetry-protected topological (SPT) state perspective for a general multilayer. Hence, we establish the tilt-boundary edge states as the first concrete example of the edge states of symmetry-protected $\mathbb{Z}$-type SPT, protected by no-valley mixing, electron-number conservation, and time-reversal $T$ symmetries. Further, we discuss possible phase transitions between distinct SPTs upon symmetry changes. Combined with a recently imaged tilt-boundary network, our findings may explain the long-standing puzzle of subgap conductance in gated bilayer graphene. This proposal can be tested through future transport experiments on tilt boundaries. In particular, the tilt boundaries offer an opportunity for the in situ imaging of topological edge transport.

We study, theoretically and numerically, a minimal model for phonons in a disordered system. For sufficient disorder, the vibrational modes of this classical system can become Anderson localized, yet this problem has received significantly less attention than its electronic counterpart. We find rich behavior in the localization properties of the phonons as a function of the density, frequency, and spatial dimension. We use a percolation analysis to argue for a Debye spectrum at low frequencies for dimensions higher than one, and for a localization-delocalization transition (at a critical frequency) above two dimensions. We show that in contrast to the behavior in electronic systems, the transition exists for arbitrarily large disorder, albeit with an exponentially small critical frequency. The structure of the modes reflects a divergent percolation length that arises from the disorder in the springs without being explicitly present in the definition of our model. Within the percolation approach, we calculate the speed of sound of the delocalized modes (phonons), which we corroborate with numerics. We find the critical frequency of the localization transition at a given density and find good agreement of these predictions with numerical results using a recursive Green-function method that was adapted for this problem. The connection of our results to recent experiments on amorphous solids is discussed.