Spatially Resolved Detection of a Spin-Entanglement Wave in a Bose-Hubbard Chain

Canonical Typicality under General Quantum Channels

With the control of increasingly complex quantum systems, the relevant degrees of freedom we are interested in may not be those traditionally addressed by statistical quantum mechanics. Here, we employ quantum channels to define generalized subsystems, capturing the pertinent degrees of freedom, and obtain their associated canonical state. We show that the generalized subsystem description from almost any microscopic pure state of the whole system will behave similarly to its corresponding canonical state. Such canonical typicality behavior depends on the entropy of the channel used to define the generalized subsystem.

Realizing spin squeezing with Rydberg interactions in an optical clock

Neutral-atom arrays trapped in optical potentials are a powerful platform for studying quantum physics, combining precise single-particle control and detection with a range of tunable entangling interactions1-3. For example, these capabilities have been leveraged for state-of-the-art frequency metrology4,5 as well as microscopic studies of entangled many-particle states6-11. Here we combine these applications to realize spin squeezing-a widely studied operation for producing metrologically useful entanglement-in an optical atomic clock based on a programmable array of interacting optical qubits. In this demonstration of Rydberg-mediated squeezing with a neutral-atom optical clock, we generate states that have almost four decibels of metrological gain. In addition, we perform a synchronous frequency comparison between independent squeezed states and observe a fractional-frequency stability of 1.087(1) × 10-15 at one-second averaging time, which is 1.94(1) decibels below the standard quantum limit and reaches a fractional precision at the 10-17 level during a half-hour measurement. We further leverage the programmable control afforded by optical tweezer arrays to apply local phase shifts to explore spin squeezing in measurements that operate beyond the relative coherence time with the optical local oscillator. The realization of this spin-squeezing protocol in a programmable atom-array clock will enable a wide range of quantum-information-inspired techniques for optimal phase estimation and Heisenberg-limited optical atomic clocks12-16.

Anomalous Behavior of Magnetic Susceptibility Obtained by Quench Experiments in Isolated Quantum Systems

We examine how the magnetic susceptibility obtained by the quench experiment on isolated quantum systems is related to the isothermal and adiabatic susceptibilities defined in thermodynamics. Under the conditions similar to the eigenstate thermalization hypothesis, together with some additional natural ones, we prove that for translationally invariant systems the quench susceptibility as a function of wave vector k is discontinuous at k=0. Moreover, its values at k=0 and the k→0 limit coincide with the adiabatic and the isothermal susceptibilities, respectively. We give numerical predictions on how these particular behaviors can be observed in experiments on the XYZ spin chain with tunable parameters, and how they deviate when the conditions are not fully satisfied.

Localization as an Entanglement Phase Transition in Boundary-Driven Anderson Models

The Anderson localization transition is one of the most well studied examples of a zero temperature quantum phase transition. On the other hand, many open questions remain about the phenomenology of disordered systems driven far out of equilibrium. Here we study the localization transition in the prototypical three-dimensional, noninteracting Anderson model when the system is driven at its boundaries to induce a current carrying nonequilibrium steady state. Recently we showed that the diffusive phase of this model exhibits extensive mutual information of its nonequilibrium steady-state density matrix. We show that this extensive scaling persists in the entanglement and at the localization critical point, before crossing over to a short-range (area-law) scaling in the localized phase. We introduce an entanglement witness for fermionic states that we name the mutual coherence, which, for fermionic Gaussian states, is also a lower bound on the mutual information. Through a combination of analytical arguments and numerics, we determine the finite-size scaling of the mutual coherence across the transition. These results further develop the notion of entanglement phase transitions in open systems, with direct implications for driven many-body localized systems, as well as experimental studies of driven-disordered systems.

Measuring the Single-Particle Density Matrix for Fermions and Hard-Core Bosons in an Optical Lattice

Ultracold atoms in optical lattices provide clean, tunable, and well-isolated realizations of paradigmatic quantum lattice models. With the recent advent of quantum-gas microscopes, they now also offer the possibility to measure the occupations of individual lattice sites. What, however, has not yet been achieved is to measure those elements of the single-particle density matrix, which are off- diagonal in the occupation basis. Here, we propose a scheme to access these basic quantities both for fermions as well as hard-core bosons and investigate its accuracy and feasibility. The scheme relies on the engineering of a large effective tunnel coupling between distant lattice sites and a protocol that is based on measuring site occupations after two subsequent quenches.

Solving Quantum Impurity Problems in and out of Equilibrium with the Variational Approach

A versatile and efficient variational approach is developed to solve in- and out-of-equilibrium problems of generic quantum spin-impurity systems. Employing the discrete symmetry hidden in spin-impurity models, we present a new canonical transformation that completely decouples the impurity and bath degrees of freedom. Combining it with Gaussian states, we present a family of many-body states to efficiently encode nontrivial impurity-bath correlations. We demonstrate its successful application to the anisotropic and two-lead Kondo models by studying their spatiotemporal dynamics and universal behavior in the correlations, relaxation times, and the differential conductance. We compare them to previous analytical and numerical results. In particular, we apply our method to study new types of nonequilibrium phenomena that have not been studied by other methods, such as long-time crossover in the ferromagnetic easy-plane Kondo model. The present approach will be applicable to a variety of unsolved problems in solid-state and ultracold-atomic systems.

Measurement-Based Entanglement of Noninteracting Bosonic Atoms

We demonstrate the ability to extract a spin-entangled state of two neutral atoms via postselection based on a measurement of their spatial configuration. Typically, entangled states of neutral atoms are engineered via atom-atom interactions. In contrast, in our Letter, we use Hong-Ou-Mandel interference to postselect a spin-singlet state after overlapping two atoms in distinct spin states on an effective beam splitter. We verify the presence of entanglement and determine a bound on the postselected fidelity of a spin-singlet state of (0.62±0.03). The experiment has direct analogy to creating polarization entanglement with single photons and hence demonstrates the potential to use protocols developed for photons to create complex quantum states with noninteracting atoms.

Full-Counting Many-Particle Dynamics: Nonlocal and Chiral Propagation of Correlations

The ability to measure single quanta allows the complete characterization of small quantum systems known as full-counting statistics. Quantum gas microscopy enables one to observe many-body systems at the single-atom precision. We extend the idea of full-counting statistics to nonequilibrium open many-particle dynamics and apply it to discuss the quench dynamics. By way of illustration, we consider an exactly solvable model to demonstrate the emergence of unique phenomena such as nonlocal and chiral propagation of correlations, leading to a concomitant oscillatory entanglement growth. We find that correlations can propagate beyond the conventional maximal speed, known as the Lieb-Robinson bound, at the cost of probabilistic nature of quantum measurement. These features become most prominent at the real-to-complex spectrum transition point of an underlying parity-time-symmetric effective non-Hermitian Hamiltonian. A possible experimental situation with quantum gas microscopy is discussed.

Phase diagram and re-entrant fermionic entanglement in a hybrid Ising-Hubbard ladder

The degree of fermionic entanglement is examined in an exactly solvable Ising-Hubbard ladder, which involves interacting electrons on the ladder's rungs described by Hubbard dimers at half-filling on each rung, accounting for intrarung hopping and Coulomb terms. The coupling between neighboring Hubbard dimers is assumed to have an Ising-like nature. The ground-state phase diagram consists of four distinct regions corresponding to the saturated paramagnetic, the classical antiferromagnetic, the quantum antiferromagnetic, and the mixed classical-quantum phase. We have exactly computed the fermionic concurrence, which measures the degree of quantum entanglement between the pair of electrons on the ladder rungs. The effects of the hopping amplitude, the Coulomb term, temperature, and magnetic fields on the fermionic entanglement are explored in detail. It is shown that the fermionic concurrence displays a re-entrant behavior when quantum entanglement is being generated at moderate temperatures above the classical saturated paramagnetic ground state.

Spatial entanglement patterns and Einstein-Podolsky-Rosen steering in Bose-Einstein condensates

Many-particle entanglement is a fundamental concept of quantum physics that still presents conceptual challenges. Although nonclassical states of atomic ensembles were used to enhance measurement precision in quantum metrology, the notion of entanglement in these systems was debated because the correlations among the indistinguishable atoms were witnessed by collective measurements only. Here, we use high-resolution imaging to directly measure the spin correlations between spatially separated parts of a spin-squeezed Bose-Einstein condensate. We observe entanglement that is strong enough for Einstein-Podolsky-Rosen steering: We can predict measurement outcomes for noncommuting observables in one spatial region on the basis of corresponding measurements in another region with an inferred uncertainty product below the Heisenberg uncertainty bound. This method could be exploited for entanglement-enhanced imaging of electromagnetic field distributions and quantum information tasks.

Quantum simulations with ultracold atoms in optical lattices

Quantum simulation, a subdiscipline of quantum computation, can provide valuable insight into difficult quantum problems in physics or chemistry. Ultracold atoms in optical lattices represent an ideal platform for simulations of quantum many-body problems. Within this setting, quantum gas microscopes enable single atom observation and manipulation in large samples. Ultracold atom-based quantum simulators have already been used to probe quantum magnetism, to realize and detect topological quantum matter, and to study quantum systems with controlled long-range interactions. Experiments on many-body systems out of equilibrium have also provided results in regimes unavailable to the most advanced supercomputers. We review recent experimental progress in this field and comment on future directions.

Photonic simulation of entanglement growth and engineering after a spin chain quench

The time evolution of quantum many-body systems is one of the most important processes for benchmarking quantum simulators. The most curious feature of such dynamics is the growth of quantum entanglement to an amount proportional to the system size (volume law) even when interactions are local. This phenomenon has great ramifications for fundamental aspects, while its optimisation clearly has an impact on technology (e.g., for on-chip quantum networking). Here we use an integrated photonic chip with a circuit-based approach to simulate the dynamics of a spin chain and maximise the entanglement generation. The resulting entanglement is certified by constructing a second chip, which measures the entanglement between multiple distant pairs of simulated spins, as well as the block entanglement entropy. This is the first photonic simulation and optimisation of the extensive growth of entanglement in a spin chain, and opens up the use of photonic circuits for optimising quantum devices.

The complete maximisation of the entanglement between two complementary blocks of spins due to the dynamics of spin chains remains to be observed. Here, Pitsios et al. simulate such dynamics by propagating single photons in an integrated photonic circuit.

Epidemic Dynamics in Open Quantum Spin Systems

We explore the nonequilibrium evolution and stationary states of an open many-body system that displays epidemic spreading dynamics in a classical and a quantum regime. Our study is motivated by recent experiments conducted in strongly interacting gases of highly excited Rydberg atoms where the facilitated excitation of Rydberg states competes with radiative decay. These systems approximately implement open quantum versions of models for population dynamics or disease spreading where species can be in a healthy, infected or immune state. We show that in a two-dimensional lattice, depending on the dominance of either classical or quantum effects, the system may display a different kind of nonequilibrium phase transition. We moreover discuss the observability of our findings in laser driven Rydberg gases with particular focus on the role of long-range interactions.

Parity-time-symmetric quantum critical phenomena

Synthetic non-conservative systems with parity-time (PT) symmetric gain–loss structures can exhibit unusual spontaneous symmetry breaking that accompanies spectral singularity. Recent studies on PT symmetry in optics and weakly interacting open quantum systems have revealed intriguing physical properties, yet many-body correlations still play no role. Here by extending the idea of PT symmetry to strongly correlated many-body systems, we report that a combination of spectral singularity and quantum criticality yields an exotic universality class which has no counterpart in known critical phenomena. Moreover, we find unconventional low-dimensional quantum criticality, where superfluid correlation is anomalously enhanced owing to non-monotonic renormalization group flows in a PT-symmetry-broken quantum critical phase, in stark contrast to the Berezinskii–Kosterlitz–Thouless paradigm. Our findings can be experimentally tested in ultracold atoms and predict critical phenomena beyond the Hermitian paradigm of quantum many-body physics.

Parity-time (PT) symmetry has been mainly studied in optical and weakly interacting open quantum systems without many-body correlations. Here the authors show that in a strongly correlated many-body system the interplay between correlations and PT symmetry leads to the emergence of new critical phenomena.

Quantum Mutual Information as a Probe for Many-Body Localization

We demonstrate that the quantum mutual information (QMI) is a useful probe to study many-body localization (MBL). First, we focus on the detection of a metal-insulator transition for two different models, the noninteracting Aubry-André-Harper model and the spinless fermionic disordered Hubbard chain. We find that the QMI in the localized phase decays exponentially with the distance between the regions traced out, allowing us to define a correlation length, which converges to the localization length in the case of one particle. Second, we show how the QMI can be used as a dynamical indicator to distinguish an Anderson insulator phase from a MBL phase. By studying the spread of the QMI after a global quench from a random product state, we show that the QMI does not spread in the Anderson insulator phase but grows logarithmically in time in the MBL phase.

Floquet Realization and Signatures of One-Dimensional Anyons in an Optical Lattice

We propose a simple scheme for mimicking the physics of one-dimensional anyons in an optical-lattice experiment. It relies on a bosonic representation of the anyonic Hubbard model to be realized via lattice-shaking-induced resonant tunneling against potential offsets, which are created by a combination of a lattice tilt and strong on-site interactions. No lasers additional to those used for the creation of the optical lattice are required. We also discuss experimental signatures of the continuous interpolation between bosons and fermions when the statistical angle θ is varied from 0 to π. Whereas the real-space density of the bosonic atoms corresponds directly to that of the simulated anyonic model, this is not the case for the momentum distribution. Therefore, we propose to use Friedel oscillations in the density as a probe for continuous fermionization of the bosonic atoms.

Optimal control of complex atomic quantum systems

Quantum technologies will ultimately require manipulating many-body quantum systems with high precision. Cold atom experiments represent a stepping stone in that direction: a high degree of control has been achieved on systems of increasing complexity. However, this control is still sub-optimal. In many scenarios, achieving a fast transformation is crucial to fight against decoherence and imperfection effects. Optimal control theory is believed to be the ideal candidate to bridge the gap between early stage proof-of-principle demonstrations and experimental protocols suitable for practical applications. Indeed, it can engineer protocols at the quantum speed limit – the fastest achievable timescale of the transformation. Here, we demonstrate such potential by computing theoretically and verifying experimentally the optimal transformations in two very different interacting systems: the coherent manipulation of motional states of an atomic Bose-Einstein condensate and the crossing of a quantum phase transition in small systems of cold atoms in optical lattices. We also show that such processes are robust with respect to perturbations, including temperature and atom number fluctuations.

Quantum Correlations, Separability, and Quantum Coherence Length in Equilibrium Many-Body Systems

Nonlocality is a fundamental trait of quantum many-body systems, both at the level of pure states, as well as at the level of mixed states. Because of nonlocality, mixed states of any two subsystems are correlated in a stronger way than what can be accounted for by considering the correlated probabilities of occupying some microstates. In the case of equilibrium mixed states, we explicitly build two-point quantum correlation functions, which capture the specific, superior correlations of quantum systems at finite temperature, and which are directly accessible to experiments when correlating measurable properties. When nonvanishing, these correlation functions rule out a precise form of separability of the equilibrium state. In particular, we show numerically that quantum correlation functions generically exhibit a finite quantum coherence length, dictating the characteristic distance over which degrees of freedom cannot be considered as separable. This coherence length is completely disconnected from the correlation length of the system-as it remains finite even when the correlation length of the system diverges at finite temperature-and it unveils the unique spatial structure of quantum correlations.

Quantum spin dynamics and entanglement generation with hundreds of trapped ions

Quantum simulation of spin models can provide insight into problems that are difficult or impossible to study with classical computers. Trapped ions are an established platform for quantum simulation, but only systems with fewer than 20 ions have demonstrated quantum correlations. We studied quantum spin dynamics arising from an engineered, homogeneous Ising interaction in a two-dimensional array of (9)Be(+) ions in a Penning trap. We verified entanglement in spin-squeezed states of up to 219 ions, directly observing 4.0 ± 0.9 decibels of spectroscopic enhancement, and observed states with non-Gaussian statistics consistent with oversqueezed states. The good agreement with ab initio theory that includes interactions and decoherence lays the groundwork for simulations of the transverse-field Ising model with variable-range interactions, which are generally intractable with classical methods.

Ultra-precise holographic beam shaping for microscopic quantum control

High-resolution addressing of individual ultracold atoms, trapped ions or solid state emitters allows for exquisite control in quantum optics experiments. This becomes possible through large aperture magnifying optics that project microscopic light patterns with diffraction limited performance. We use programmable amplitude holograms generated on a digital micromirror device to create arbitrary microscopic beam shapes with full phase and amplitude control. The system self-corrects for aberrations of up to several λ and reduces them to λ/50, leading to light patterns with a precision on the 10^-4 level. We demonstrate aberration-compensated beam shaping in an optical lattice experiment and perform single-site addressing in a quantum gas microscope for ⁸⁷Rb.

Single atom detection in ultracold quantum gases: a review of current progress

The recent advances in single atom detection and manipulation in experiments with ultracold quantum gases are reviewed. The discussion starts with the basic principles of trapping, cooling and detecting single ions and atoms. The realization of single atom detection in ultracold quantum gases is presented in detail and the employed methods, which are based on light scattering, electron scattering, field ionization and direct neutral particle detection are discussed. The microscopic coherent manipulation of single atoms in a quantum gas is also covered. Various examples are given in order to highlight the power of these approaches to study many-body quantum systems.

Fine structure of the entanglement entropy in the O(2) model

We compare two calculations of the particle density in the superfluid phase of the O(2) model with a chemical potential μ in 1+1 dimensions. The first relies on exact blocking formulas from the Tensor Renormalization Group (TRG) formulation of the transfer matrix. The second is a worm algorithm. We show that the particle number distributions obtained with the two methods agree well. We use the TRG method to calculate the thermal entropy and the entanglement entropy. We describe the particle density, the two entropies and the topology of the world lines as we increase μ to go across the superfluid phase between the first two Mott insulating phases. For a sufficiently large temporal size, this process reveals an interesting fine structure: the average particle number and the winding number of most of the world lines in the Euclidean time direction increase by one unit at a time. At each step, the thermal entropy develops a peak and the entanglement entropy increases until we reach half-filling and then decreases in a way that approximately mirrors the ascent. This suggests an approximate fermionic picture.

Measuring entanglement entropy in a quantum many-body system

Entanglement is one of the most intriguing features of quantum mechanics. It describes non-local correlations between quantum objects, and is at the heart of quantum information sciences. Entanglement is now being studied in diverse fields ranging from condensed matter to quantum gravity. However, measuring entanglement remains a challenge. This is especially so in systems of interacting delocalized particles, for which a direct experimental measurement of spatial entanglement has been elusive. Here, we measure entanglement in such a system of itinerant particles using quantum interference of many-body twins. Making use of our single-site-resolved control of ultracold bosonic atoms in optical lattices, we prepare two identical copies of a many-body state and interfere them. This enables us to directly measure quantum purity, Rényi entanglement entropy, and mutual information. These experiments pave the way for using entanglement to characterize quantum phases and dynamics of strongly correlated many-body systems.

Microscopic Observation of Pauli Blocking in Degenerate Fermionic Lattice Gases

The Pauli exclusion principle is one of the most fundamental manifestations of quantum statistics. Here, we report on its local observation in a spin-polarized degenerate gas of fermions in an optical lattice. We probe the gas with single-site resolution using a new generation quantum gas microscope avoiding the common problem of light induced losses. In the band insulating regime, we measure a strong local suppression of particle number fluctuations and a low local entropy per atom. Our work opens a new avenue for studying quantum correlations in fermionic quantum matter both in and out of equilibrium.

Self-Assembled Wigner Crystals as Mediators of Spin Currents and Quantum Information

Technological applications of many-body structures that emerge in gated devices under minimal control are largely unexplored. Here we show how emergent Wigner crystals in a semiconductor quantum wire can facilitate a pivotal requirement for a scalable quantum computer, namely, transmitting quantum information encoded in spins faithfully over a distance of micrometers. The fidelity of the transmission is remarkably high, faster than the relevant decohering effects, independent of the details of the spatial charge configuration in the wire, and realizable in dilution refrigerator temperatures. The transfer can evidence near unitary many-body nonequilibrium dynamics hitherto unseen in a solid-state device. It could also be useful in spintronics as a method for pure spin current over a distance without charge movement.

Entangling two transportable neutral atoms via local spin exchange

To advance quantum information science, physical systems are sought that meet the stringent requirements for creating and preserving quantum entanglement. In atomic physics, robust two-qubit entanglement is typically achieved by strong, long-range interactions in the form of either Coulomb interactions between ions or dipolar interactions between Rydberg atoms. Although such interactions allow fast quantum gates, the interacting atoms must overcome the associated coupling to the environment and cross-talk among qubits. Local interactions, such as those requiring substantial wavefunction overlap, can alleviate these detrimental effects; however, such interactions present a new challenge: to distribute entanglement, qubits must be transported, merged for interaction, and then isolated for storage and subsequent operations. Here we show how, using a mobile optical tweezer, it is possible to prepare and locally entangle two ultracold neutral atoms, and then separate them while preserving their entanglement. Ground-state neutral atom experiments have measured dynamics consistent with spin entanglement, and have detected entanglement with macroscopic observables; we are now able to demonstrate position-resolved two-particle coherence via application of a local gradient and parity measurements. This new entanglement-verification protocol could be applied to arbitrary spin-entangled states of spatially separated atoms. The local entangling operation is achieved via spin-exchange interactions, and quantum tunnelling is used to combine and separate atoms. These techniques provide a framework for dynamically entangling remote qubits via local operations within a large-scale quantum register.

Diffraction-Unlimited Position Measurement of Ultracold Atoms in an Optical Lattice

We consider a method of high-fidelity, spatially resolved position measurement of ultracold atoms in an optical lattice. We show that the atom-number distribution can be nondestructively determined at a spatial resolution beyond the diffraction limit by tracking the progressive evolution of the many-body wave function collapse into a Fock state. We predict that the Pauli exclusion principle accelerates the rate of wave function collapse of fermions in comparison with bosons. A possible application of our principle of surpassing the diffraction limit to other imaging systems is discussed.