We investigate the role of the permutationally invariant part of the density matrix (PIDM) in capturing the properties of the ground state of the system during a quantum phase transition. In the context of quantum state tomography, PIDM is known to be obtainable with only a low number of measurement settings, namely $O\left(L^2\right)$, where $L$ is the system size. Considering the transverse-field Ising chain and the $XXZ$ chain as examples, we compute the second-order Rényi entropy of PIDM for the ground state by using the density-matrix renormalization-group algorithm. In the transverse-field Ising chain with ferromagnetic interaction, the ground state is permutationally invariant both in the limits of zero and infinite field, leading to a vanishing Rényi entropy of PIDM. The latter exhibits a broad peak as a function of the transverse field around the quantum critical point, which gets more pronounced for larger system size. In the antiferromagnetic case, the peak structure disappears and the Rényi entropy diverges like $O\left(L\right)$ in the whole field range of the ordered phase. In the $XXZ$ model with ferromagnetic interaction, the ground state is permutationally invariant in the full parameter regime of easy-axis anisotropy, causing the Rényi entropy of PIDM to vanish. In the easy-plane region, the Rényi entropy of PIDM grows almost linearly as a function of the system size. In the antiferromagnetic case, the Rényi entropy of PIDM takes finite values at any point in parameter space; importantly, its minimum appears at the phase-transition point. We discuss the cause of these behaviors of the Rényi entropy of PIDM, examining the possible application of this experimentally tractable quantity to the analysis of phase-transition phenomena.

In this paper we explore how quantum scientific machine learning can be used to tackle the challenge of weather modeling. Using parametrized quantum circuits as machine learning models, we consider two paradigms: supervised learning from weather data and physics-informed solving of the underlying equations of atmospheric dynamics. In the first case, we demonstrate how a quantum model can be trained to accurately reproduce real-world global stream function dynamics at a resolution of $4^{\circ }$. We detail a number of problem-specific classical and quantum architecture choices used to achieve this result. Subsequently, we introduce the barotropic vorticity equation (BVE) as our model of the atmosphere, which is a third-order partial differential equation (PDE) in its stream function formulation. Using the differentiable quantum circuits algorithm, we successfully solve the BVE under appropriate boundary conditions and use the trained model to predict unseen future dynamics to high accuracy given an artificial initial weather state. While challenges remain, our results mark an advancement in terms of the complexity of PDEs solved with quantum scientific machine learning.

Quantum energy teleportation (QET) is an energy extraction protocol via local operation and classical communication (LOCC). In this paper, we analyze QET with the correlation matrix and find the essence of QET is a quantum steering process. We propose an extended QET called strong QET protocol and define the QET passive state, which shows that quantum correlation is not a sufficient condition for QET. We also compare QET in noisy channels with direct energy extraction schemes, which indicates the advantage of our method in dealing with quantum operations. Furthermore, we extend the method to the $N$-qubit QET and give numerical examples.

Generating high-fidelity spin-spin entanglement is an essential task of quantum repeater networks for the distribution of quantum information across long distances. Solid-state-based spin-photon interfaces are promising candidates to realize nodes of a quantum network, but are often limited by spectral diffusion of the optical transition, which results in phase errors on the entangled states. Here, we introduce a method to correct phase errors from quasi-static frequency fluctuations after the entangled state is generated, by shelving the emitters in the excited state to refocus the unknown phase. For quasi-static frequency fluctuations, the fidelity is determined only by the lifetime of the excited state used for shelving, making it particularly suitable for systems with a long-lived shelving state with correlated spectral diffusion. Such a shelving state may be found in Kramers doublet systems such as rare-earth emitters and color centers in Si or SiC interfaced with nanophotonic cavities with a strongly frequency-dependent Purcell enhancement. The protocol can be used to generate high-fidelity entangled spin pairs without reducing the rate of entanglement generation.

Hybridizing different degrees of freedom or physical platforms potentially offers various advantages in building scalable quantum architectures. We study the hybrid quantum system of a single electron trapped on a solid neon surface, where the motional states of an electron interact with microwave photons in an on-chip superconducting cavity. By applying a nonuniform magnetic field with a gradient along the vibrational axis, the spin-orbit coupling of the electron's spin degree of freedom and its lateral motion can be engineered. We show that the electron's spin states with ultralong coherence time as a quantum memory can be explored to store the quantum information of a superconducting qubit. As an extension, we also propose to implement high-quality quantum state transfer between the spin states of two electrons trapped in spatially separated superconducting cavities. The present work may have practical applications for realizing floating-electron-based hybrid quantum computation.

We perform a numerical and analytical investigation of microwave-to-optical conversion based on four-wave mixing in Rydberg atoms. Our work demonstrates that both all-resonant and off-resonant frequency-mixing configurations achieve near-unit photon conversion efficiencies. We review the conditions that can lead to the presence of two possible dark states. We find that for both configurations, one of the dark states can be detrimental at high microwave powers, and show that an additional limitation to all-resonant frequency mixing is microwave-induced fluorescence. Finally, we confirm that the off-resonant configuration is more appropriate as it allows for efficient photon conversion on a wider range of input microwave intensities with reduced total power of the auxiliary fields.

In this study, we investigate the dynamics of a qubit driven by a pulsed field of finite duration, focusing on smooth pulse shapes that start and end linearly in time. All of these pulse shapes, such as a sine function sampled between two adjacent nodes, provide smooth alternatives to the commonly used rectangular pulse. Owing to its continuity, the sine pulse exhibits weaker power broadening and leads to the rapid vanishing of the wings in the excitation line profile, significantly reducing the sidebands. Additionally, these pulse shapes avert the spurious truncation effects that arise with infinite-duration shapes, such as the Gaussian, where truncation is inevitable. We derive two approximate analytic solutions which describe the ensuing quantum dynamics. Both approximations assume that the field changes linearly at the beginning and end of the driving pulse, and adiabatically in between. The first approximation matches the linear and adiabatic parts at an appropriate instant of time and is expressed in terms of Weber's parabolic cylinder functions. The second, much simpler, approximation uses asymptotics of the Weber function to replace it with simpler functions, along with additional transformations. Both approximations were shown to be highly accurate, with near-complete agreement between theory and observations on two IBM Quantum processors, further validated by measurements of the predicted weaker power broadening and highly suppressed sidebands.

A charged particle moving through a plasma suffers the effects of collisions with the plasma particles; this affects the angular distribution by a process known as multiple scattering. Here we perform a very complete study of the multiple scattering of charged particles in different types of plasmas. First, we reformulate the theory of multiple scattering for plasma media including the statistical effects of thermal equilibrium. To obtain a comprehensive extension of previous works we apply a quantum approach to describe the interaction of charged particles with plasmas, based on the quantum-dielectric-plasma model (QDPM), which includes a full description of the statistical effects on energy exchange processes together with a quantum treatment of electron excitations. We analyze the role of statistical fluctuations produced by the temperature and the recoil effects in the multiple scattering for different particles and plasma conditions. Finally, we incorporate the dominant effect of scattering by the plasma ions through a semiclassical dielectric function that combines a quantum description of plasma electrons with a classical dielectric model for plasma ions. We analyze the partial contributions and total results on the multiple scattering angle for protons, muons, and positrons in various plasma media, including heated solids; the stellar type of plasmas; and the cases protons, deuterons, and tritium ions in Tokamak plasmas.

We present the recovery of six $2S_{1/2}\text{−}n{S}_{1/2}$ two-photon resonances in atomic hydrogen with $8\le n\le 16$. For each transition, we obtain quality factors $\ge 4\times {10}^9$, which we believe are the highest obtained in hydrogen laser spectroscopy excepting the singular $1S_{1/2}\text{−}2S_{1/2}$ two-photon transition. To the best of our knowledge, the transitions with $n\ge 13$ have not been previously observed. These results are enabled by a tightly constrained atomic beam geometry, and by mitigation of the light shift caused by the spectroscopy laser field.

We present a high-precision solution of the Dirac equation by numerically solving the minmax two-center Dirac equation with the finite-element method (FEM). The minmax FEM provide a highly accurate benchmark result for systems with light or heavy atomic nuclear charge $Z$. A result is shown for the molecular ion ${\mathrm{H}}_2{}^{+}$ and the heavy quasimolecular ion ${\mathrm{Th}}_2{}^{179+}$, with estimated fractional uncertainties of approximately ${10}^{-23}$ and approximately ${10}^{-21}$, respectively. The result of the minmax FEM's high precision of the solution of the two-center Dirac equation allows solid control over the required accuracy level and is promising for the application and extension of our method.

Field-inhomogeneity-induced relaxation of atomic spins confined in vapor cells with depolarizing walls is studied. In contrast to nuclear spins, such as noble-gas spins, which experience minimal polarization loss at cell walls, atomic spins in uncoated cells undergo randomization at the boundaries. This distinct boundary condition results in a varied dependence of the relaxation rate on the field gradient. By solving the Bloch-Torrey equation under fully depolarizing boundary conditions, we illustrate that the relaxation rate induced by field inhomogeneity is more pronounced for spins with a smaller original relaxation rate (in the absence of the inhomogeneous field). We establish an upper limit for the relaxation rate through calculations in the perturbation regime. Moreover, we connect it to the spin-exchange-relaxation-free magnetometers, demonstrating that its linewidth is most sensitive to inhomogeneous fields along the magnetometer's sensitive axis. Our theoretical result agrees with the experimental data for cells subjected to small pump power. A deviation in high input-power scenarios arises from pump field attenuation, resulting in a nonuniformly distributed light shift that behaves like an inhomogeneous magnetic field.

The attractive Hubbard model has become a model readily realizable with ultracold atoms on optical lattices. However, the superconducting (superfluid) critical temperatures $T_c$'s are still somewhat smaller than the lowest temperatures achieved in experiments. Here, we consider two possible routes, generically called layering, to increase $T_c$: a bilayer and a simple cubic lattice, both with tunable hopping $t_z$ between attractive Hubbard planes. We have performed minus-sign–free determinant quantum Monte Carlo simulations to calculate response functions such as pairing correlation functions, uniform spin susceptibility, and double occupancy, through which we map out some physical properties. We have found that by a judicious choice of fillings and intensity of on-site attraction, a bilayer can exhibit $T_c$'s between 1.5 and 1.7 times those of the single layer; for the simple-cubic lattice the enhancement can be 30% larger than the maximum for the single layer. We also check the accuracy of both a BCS-like estimate for $T_c$ in the attractive Hubbard model as well as of an upper bound for $T_c$ based on the superfluid density.

The beyond mean-field physics due to quantum fluctuations is often described with the Lee-Huang-Yang correction, which can be approximately written as a simple analytical expression in terms of the mean-field wave function employing local density approximation. This model has proven to be very successful in predicting the dynamics in dipolar Bose-Einstein condensates both qualitatively and quantitatively. Yet a small deviation between experimental results and the theoretical prediction has been observed when comparing experiment and theory of the phase boundary of a free-space quantum droplet. For this reason we revisit the theoretical description of quantum fluctuations in dipolar quantum gases. We study alternative cutoffs, compare them to experimental results, and discuss limitations.

We study a three-dimensional Gross-Pitaevskii equation that describes a static impurity in a dipolar Bose-Einstein condensate. Our focus is on the interplay between the shape of the impurity and the anisotropy of the medium manifested in the energy and the density of the system. Without external confinement, properties of the system are derived with basic analytical approaches. For a system in a harmonic trap, the model is investigated numerically, using the split-step Crank-Nicolson method. Our results demonstrate that the impurity self-energy is minimized when its shape more closely aligns with the anisotropic character of the bath; in particular a prolate deformed impurity aligned with the direction of the dipoles has the smallest self-energy for a repulsive impurity. Our work complements studies of impurities in Bose gases with zero-range interactions and paves the way for studies of dipolar polarons with a Gross-Pitaevskii equation.

Atomic superfluids formed using Bose-Einstein condensates (BECs) in a ring trap are currently investigated in the context of superfluid hydrodynamics, quantum sensing, and matter-wave interferometry. The characterization of the rotational properties of such superfluids is important, but can presently only be performed by using optical absorption imaging, which completely destroys the condensate. Recent studies have proposed coupling the ring BEC to optical cavity modes carrying orbital angular momentum to make minimally destructive measurements of the condensate rotation. The sensitivity of these proposals, however, is bounded below by the standard quantum limit set by the combination of laser shot noise and radiation pressure noise. In this work we provide a theoretical framework that exploits the fact that the interaction between the scattered modes of the condensate and the light reduces to effective optomechanical equations of motion. We present a detailed theoretical analysis to demonstrate that the use of squeezed light and backaction evasion techniques allows the angular momentum of the condensate to be sensed with noise well below the standard quantum limit. Our proposal is relevant to atomtronics, quantum sensing, and quantum information.

The physics of waves in time-varying media provides numerous opportunities for wave control that are unattainable with static media. In particular, Floquet systems with a periodic time modulation are currently of considerable interest. Here we demonstrate how the scattering properties of a finite Floquet medium can be correctly described by a static Floquet scattering matrix, which satisfies a pseudounitary relation. This algebraic property is a consequence of the conservation of wave action for which we formulate here a continuity equation. Using this Floquet scattering matrix, we further demonstrate how it can be used to transfer concepts for wave-front-shaping based on the Wigner-Smith operator from static to Floquet systems. The eigenstates of the corresponding Floquet Wigner-Smith matrix are shown to be light pulses that are optimally shaped in both their spatial and temporal degrees of freedom for the optical micromanipulation of time-varying media.

We thoroughly investigate the Faraday magneto-optical effects in a helically wound nonlinear optical fiber. We find the emergence of an additional rotation angle proportional to the optical intensity, arisen from the nonlinear corrections to both the Verdet constant and the fiber torsion. By analyzing an oscillator model describing the electron motions in the fiber medium, we can obtain the third-order susceptibility in the presence of the magnetic field. According to the Maxwell's equations and the minimal coupling principle in the metric expression of the curved space, we derive the propagation equations of light in a helically wound optical fiber. Finally, we have obtained the analytic expressions of Faraday rotation angle for both linearly and elliptically polarized lights, which explicitly indicates an important nonlinear correction on the Faraday rotation angles. Possible experimental observations and some implications of our theoretical findings are discussed.

We derive a general method for determining the necessary and sufficient conditions for exact factorization $|\mathrm{\Psi }\rangle ={\otimes }_p|{\psi }_p\rangle$ of an eigenstate of a many-body Hamiltonian $H$, based on the quantum covariance matrix of the relevant local operators building the Hamiltonian. The “site” $p$ can be either a single component or a group of subsystems. The formalism is then used to derive exact dimerization and clusterization conditions in spin systems, covering from spin-$s$ singlets and clusters coupled to 0 total spin, to general nonmaximally entangled spin-$s$ dimers (generalized singlets). New results for field-induced dimerization in anisotropic $XYZ$ arrays under a magnetic field are obtained.