The occurrence of exceptional points (EPs) is a fascinating non-Hermitian feature of open systems. A level-repulsion phenomenon between two complex states of an open system can be realized by positioning an EP and its time-reversal ($\mathcal{T}$) conjugate pair in the underlying parameter space. Here, we report interesting nonreciprocal responses of such two conjugate EPs by using a dual-mode planar waveguide system having two $\mathcal{T}$-symmetric active variants concerning the transverse gain-loss profiles. We specifically reveal an all-optical scheme to achieve correlative nonreciprocal light dynamics by using the reverse chirality of two dynamically encircled conjugate EPs in the presence of local nonlinearity. A specific nonreciprocal correlation between two designed $\mathcal{T}$-symmetric waveguide variants is established in terms of their unidirectional transfer of light with a precise selection of modes. Here, the unconventional reverse chiral properties of two conjugate EPs allow the nonreciprocal transmission of two selective modes in the opposite directions of the underlying waveguide variants. An explicit dependence of the nonlinearity level on a significant enhancement of the nonreciprocity in terms of an isolation ratio is explored by investigating the effects of both local Kerr-type and saturable nonlinearities (considered separately). The physical insights and implications of harnessing the features of conjugate EPs in nonlinear optical systems can enable the growth and development of a versatile platform for building nonreciprocal components and devices.

We present a comprehensive theoretical investigation of high-order harmonic generation in ${\mathrm{H}}_2{}^{+}$ molecules within a quantum-optical framework. Our study focuses on characterizing various quantum-optical and quantum-information measures stemming from the correlations established between light and matter. We demonstrate the emergence of entanglement between electron and light states after the laser-matter interaction. We also identify the possibility of obtaining nonclassical states of light in targeted frequency modes by conditioning on specific electronic quantum states, which turn out to be crucial in the generation of highly nonclassical entangled states between distinct sets of harmonic modes. Our findings open up avenues for studying strong-laser-field-driven interactions in molecular systems under a fully quantum-mechanical framework.

Quantum reference frames have attracted renewed interest recently, as their exploration is relevant and instructive in many areas of quantum theory. Among the different types, position and time reference frames have captivated special attention. Here, we introduce and analyze a nonrelativistic framework in which each system contains an internal clock in addition to its external (spatial) degree of freedom and, hence, can be used as a spatiotemporal quantum reference frame. We present expressions for expectation values and variances of relevant observables in different perspectives, as well as relations between these quantities in different perspectives in scenarios with no interactions. In particular, we show that even in these simple scenarios the relative uncertainty between clocks affects the relative spatial spread of the systems.

A major current challenge in solid-state quantum computing is to scale qubit arrays to a larger number of qubits. This is hampered by the complexity of the control wiring for the large number of independently tunable interqubit couplings within these arrays. One approach to simplifying the problem is to use a qubit array with fixed Ising (ZZ) interactions. When simultaneously driving a specific subset of qubits in such a system, the dynamics are confined to a set of commuting $\text{su}\left(2\right)$ subalgebras. Within these $\text{su}\left(2\right)\mathrm{s}$ we describe how to perform X-gates and $\frac{\pi }{2}\text{ZZ}$ rotations robustly against either leakage, which is the main source of error in transmon qubits, or coupling fluctuations, which is the main source of infidelity in flux or semiconductor spin qubits. These gates together with virtual-$z$ gates form a universal set of gates for quantum computing. We construct this set of robust gates for two-edge, three-edge, and four-edge vertices, which compose all existing superconducting qubit and semiconductor spin qubit arrays.

Here we revisit the quantum-phase-estimation (QPE) algorithm and devise an iterative method to improve the precision of QPE with propagators over a variety of time spans. For a given propagator and a certain eigenstate as input, QPE with a propagator is introduced to estimate the phase corresponding to an eigenenergy. Due to the periodicity of the complex exponential, we can pinpoint the eigenenergy in a branch of comblike ranges by applying QPE with propagators over longer time spans. Thus, by picking up appropriate time spans, the iterative QPE with corresponding propagators can enable us to pinpoint the eigenenergy more precisely. Moreover, even if there are only a few qubits as ancilla qubits, high precision is still available by the proposed iterative method. Our work provides a feasible and promising means toward precise estimations of an eigenvalue on noisy intermediate-scale quantum devices.

The generation of entangled states that display negative values of the Wigner function in the quantum phase space is a challenging task, particularly elusive for massive, and possibly macroscopic, systems such as mechanical resonators. In this work, we propose two schemes based on reservoir engineering for generating Wigner-negative entangled states unconditionally. We consider two noninteracting mechanical resonators that are radiation-pressure coupled to either one or two common cavity fields; the optomechanical coupling with the field(s) features both a linear and quadratic part in the mechanical displacement and the cavity is driven at multiple frequencies. We show analytically that both schemes stabilize a Wigner-negative entangled state that combines the entanglement of a two-mode squeezed vacuum with a cubic nonlinearity, which we dub cubic-phase entangled (CPE) state. We then perform extensive numerical simulations to test the robustness of Wigner-negative entanglement attained by approximate CPE states stabilized in the presence of thermal decoherence.

We propose a scheme to simultaneously cool multiple degenerate mechanical modes in optomechanical systems beyond the resolved sideband regime. In general, one of the main obstacles for cooling degenerate mechanical modes is the so-called dark-mode effect. The Duffing nonlinearities (mechanical nonlinearities) can be used to overcome the dark-mode effect of degenerate mechanical modes. A second-order nonlinear medium (optical nonlinearity) is introduced to accomplish the ground-state cooling of degenerate mechanical modes beyond the resolved sideband regime. We find the dark mode of degenerate mechanical modes can be broken when the mechanical nonlinearities of different mechanical modes are not very close. Our scheme paves the way toward the implementation of simultaneous ground-state cooling of degenerate mechanical modes of optomechanical systems beyond the resolved sideband regime in experiments.

Cooling a mechanical mode to its motional ground state opens up avenues for both scientific and technological advancements in the field of quantum metrology and information processing. We propose a multiparameter optimization scheme for ground-state cooling of a mechanical mode using quantum dots. Applying the master-equation approach, we formulate the optimization scheme over a broad range of system parameters including detunings, decay rates, pumping rates, and coupling strengths. We implement the optimization scheme on two major types of semiconductor quantum-dot systems: colloidal and epitaxial quantum dots. These systems span a broad range of mechanical-mode frequencies, coupling rates, and decay rates. Our optimization scheme lowers the steady-state phonon number in all cases by several orders of magnitude and thereby the effective temperature of the mechanical mode by more than an order of magnitude. We also calculate the net cooling rate by estimating the phonon decay rate and show that the optimized system parameters also result in efficient cooling. The proposed optimization scheme can be readily extended to other driven systems coupled to a mechanical mode.

In this study, we explore an approach aimed at enhancing the transmission or reflection coefficients of absorbing materials through the utilization of joint measurements of entangled photon states. On the one hand, through the implementation of photon catalysis in the reflected channel, we can effectively modify the state of the transmission channel, leading to a notable improvement in the transmission ratio. Similarly, this approach holds potential for significantly amplifying the reflection ratio of absorbing materials, which is useful for detecting cooperative targets. On the other hand, employing statistical counting methods based on the technique of heralding on zero photons, we evaluate the influence of our reflection enhancement protocol for detecting noncooperative targets, which is validated through Monte Carlo simulations of a quantum radar setup affected by Gaussian white noise. Our results demonstrate a remarkable enhancement in the signal-to-noise ratio of imaging, albeit with an increase in mean-square error. These findings highlight the potential practical applications of our approach in the implementation of quantum radar.

Microwave-optical interactions and hybrid entangled states are crucial for building hybrid quantum networks. In this work, we propose an approach for realizing a cross-Kerr nonlinear interaction between microwave and optical cavities using an ensemble of nitrogen-vacancy centers (NV ensemble). This cross-Kerr interaction is achieved by an NV ensemble dispersively coupled to a microwave cavity and an optical cavity. As an application, we show that the cross-Kerr interaction can be used to create a hybrid entangled state of a discrete-variable (DV) optical qubit and a continuous-variable (CV) optical qubit. The DV optical qubit here refers to a qubit, with two logic states encoded via the vacuum and single-photon states of the optical cavity. The CV optical qubit means a qubit, whose two logic states are encoded through two quasi-orthogonal coherent states or cat states of the microwave cavity. Our method is quite simple because it only requires a single-step operation. Numerical simulations demonstrate that high-fidelity generation of the proposed hybrid state is feasible within current experimental technology. This proposal is universal and the NV ensemble can be replaced by other quantum transducers, such as magnons, rare-earth-doped crystals, and silicon-vacancy centers.

In this article we present a benchmark for resource characterization in the process of controlled quantum state reconstruction and secret sharing for general three-qubit states. This is achieved by providing a closed expression for the reconstruction fidelity, which relies on the genuine tripartite correlation and the bipartite channel between the dealer and the reconstructor characterized by the respective correlation parameters. We formulate the idea of quantum advantage in approximate state reconstruction as surpassing the classical limit set at $\frac{2}{3}$. This article introduces new interoperability between teleportation and state reconstruction. This is detailed through a case-by-case analysis of relevant correlation matrices. We reformulate the idea of quantum secret sharing by setting up additional constraints on the teleportation capacity of the bipartite channels between dealer and shareholders by ensuring that, individually, the shareholders cannot reconstruct the secret. We believe that this will give us an ideal picture of how quantum secret sharing should be.

A numerical method is proposed for simulation of composite open quantum systems. It is based on Lindblad master equations and adiabatic elimination. Each subsystem is assumed to converge exponentially towards a stationary subspace, slightly impacted by some decoherence channels and weakly coupled to the other subsystems. This numerical method is based on a perturbation analysis with an asymptotic expansion. It exploits the formulation of the slow dynamics with reduced dimension. It relies on the invariant operators of the local and nominal dissipative dynamics attached to each subsystem. Second-order expansion can be computed only with local numerical calculations. It avoids computations on the tensor-product Hilbert space attached to the full system. This numerical method is particularly well suited for autonomous quantum error correction schemes. Simulations of such reduced models agree with complete full model simulations for typical gates acting on one and two cat qubits (z, zz, and cnot) when the mean photon number of each cat qubit is less than eight. For larger mean photon numbers and gates with three cat qubits (zzz and ccnot), full model simulations are almost impossible whereas reduced model simulations remain accessible. In particular, one observes numerically the simultaneous capture of the dominant phase-flip error rate and of the very small bit-flip error rate with its exponential suppression versus the mean photon number.

In 2020 and 2021, the author introduced quantum algorithms for solving the Navier-Stokes equations and systems of nonlinear partial differential equations (PDEs), respectively. These algorithms make use of three quantum oracles. In this paper, we show how all three oracles can be implemented as quantum circuits. We cost the circuit implementations, determining their depth, width, and number of non-Clifford gates used as a function of user-specified (i) error tolerances, and (ii) algorithm success probability. With these quantum oracle circuits in hand, the quantum Navier-Stokes and PDE algorithms are now completely specified as quantum circuits.

We present measurements of the total projectile-electron-loss cross sections in ${\mathrm{O}}^{-} + {\mathrm{N}}_2$ collisions in the energy range from 2.5 to 8.5 keV. Two different techniques, beam attenuation and the growth rate, are employed. The cross sections measured using the growth-rate method show a threshold behavior. We analyze the cross-section velocity dependence in the framework of a collision between a quasifree electron, loosely bound to the projectile, and the molecular target. Within the free-collision model, we deduce and test a simple analytical expression for the expected velocity threshold taking into account the angular distribution of electron velocities within the anion.

The multiple-plateau structure is a characteristic of high-order harmonic spectra in solids, resulting from strong interband couplings involving three or more bands. Here we show that high-order harmonic generation (HHG) in a two-band Su-Schrieffer-Heeger (SSH) system also exhibits a multiple-plateau structure under disorder effect. For weak external driving fields, the harmonic spectrum of disordered SSH chains exhibits an additional plateau and has a higher cutoff frequency compared with that of ordered SSH chains. The phase analysis of the harmonic spectra from various disordered SSH chains reveals that the second HHG plateau emerges from the interference between different regions. Through time-frequency analysis, we show that the harmonic phase corresponding to the caustic point is more localized than its neighboring orders.

We propose an experimental approach for determining thermodynamic properties of ultracold atomic gases with short-range interactions. As a test case, we focus on the one-dimensional (1D) Bose gas described by the integrable Lieb-Liniger model. The proposed approach relies on deducing the Helmholtz or Landau free energy directly from measurements of local atom-atom correlations by utilizing the inversion of a finite-temperature version of the Hellmann-Feynman theorem. We demonstrate this approach theoretically by deriving approximate analytic expressions for the free energies in specific asymptotic regimes of the 1D Bose gas and find excellent agreement with the exact results based on the thermodynamic Bethe ansatz available for this integrable model.

Directional near-field coupling can enable many applications, such as directional routing, on-chip information processing, and chiral quantum optics. This directional near-field coupling is generally face dependent, since the induced near-field radiation pattern is dependent on which face (e.g., the upper or lower face) of the dipolar source is facing toward the outcoupler. In other words, the dipolar sources in the directional near-field coupling intrinsically have two faces (e.g., Janus faces), whose corresponding near-field coupling strength and coupling directionality might be distinct. Here, we outline a general physical framework to control these Janus faces in the directional near-field coupling and find that they can have the feature of an oriented misalignment. To be specific, the upper and lower radiation patterns of excited surface waves can have the same shape but are misaligned with a twist angle. For example, the twist angle can be any acute angle if the source is composed of a Huygens dipole and an electric dipole, and it can be any obtuse angle if the source is constructed by a circular electric dipole and a magnetic dipole.

The emission linewidth in active medium emerges due to homogeneous and inhomogeneous broadening. We demonstrate that in lasers with inhomogeneous broadening there is a critical pump rate, above which the special mode forms. This mode consists of locked-in oscillations of cavity mode and of the active atoms with different transition frequencies. Below the critical value of the pump rate, the radiation spectrum of the laser has a Gaussian profile, provided that inhomogeneous broadening is dominant. Above the critical value of pump rate, the special mode mostly determines the laser radiation spectrum. As a result, the spectrum attains Lorentz shape characteristic for homogeneous broadening. The formation of the special mode precedes lasing and that the critical pump rate plays the role of lasing prethreshold. We suggest a system where such a transition could be experimentally observed separately from lasing. We obtain expressions for the threshold and generation frequency of a single-mode laser where both homogeneous and inhomogeneous broadening are present.

Self-$Q$-switching facilitates the generation of pulsed lasers without resorting to conventional $Q$-switched techniques, while there has been limited research and theoretical development in this area. In this paper, we introduce an interference-based self-$Q$-switching phenomenon and conduct a comprehensive numerical analysis. Our findings reveal distinct properties when compared to traditional $Q$-switching, underscoring the role of interferometers. Through a combination of experimental measurements and waveguide simulations, we propose a self-$Q$-switching mechanism based on jitter-induced filtering. This mechanism aligns well with our experimental observations and provides an explanation from the perspective of the frequency domain. This research contributes to the understanding of self-$Q$-switching theory and its excitation.