The quantum remote sensing (QRS) is a scheme to add security about the measurement results of a qubit-based sensor. A client delegates a measurement task to a remote server that has a quantum sensor, and eavesdropper (Eve) steals every classical information stored in the server side. By using quantum properties, the QRS provides an asymmetricity about the information gain where the client gets more information about the sensing results than Eve. However, quantum states are fragile against decoherence, and so it is not clear whether such a QRS is practically useful under the effect of realistic noise. Here, we investigate the performance of the QRS with dephasing during the interaction with the target fields. In the QRS, the client and server need to share a Bell pair, and an imperfection of the Bell pair leads to a state preparation error in a systematic way on the server side for the sensing. We consider the effect of both dephasing and state preparation error. The uncertainty of the client side decreases with the square root of the repetition number $M$ for small $M$, which is the same scaling as the standard quantum metrology. On the other hand, for large $M$, the state preparation error becomes as relevant as the dephasing, and the uncertainty decreases logarithmically with $M$. We compare the information gain between the client and Eve. This leads us to obtain the conditions for the asymmetric gain to be maintained even under the effect of dephasing. Then, we can quantify how much information the client can gain while preserving the information asymmetricity.

Experimental benchmark intensity ratios for the angle-differential scattering intensities for electron-impact excitation from the xenon ground state $5p^6$ ${}^1{S}_0$ to its lowest five excited states $5p^{5}6s{\left[3/2\right]}_2$, $5p^{5}6s{\left[3/2\right]}_1$, $5p^{5}6s^{\prime }{\left[1/2\right]}_0$, and (combined) $5p^{5}6s^{\prime }{\left[1/2\right]}_1+5p^{5}6p{\left[1/2\right]}_1$ are reported and compared to predictions from a full-relativistic $B$-spline $R$-matrix close-coupling model as well as earlier experimental work. The above ratios, which provide a stringent test of theoretical electron scattering models, are presented for this heavy rare gas with particular emphasis on the role of spin-exchange and direct excitation processes affecting their angular dependence.

We study the Rabi flopping between the $1s{\sigma }_g$ and $2p{\sigma }_u$ states during the dissociation of hydrogen molecular ions in strong laser fields by numerically simulating the time-dependent Schrödinger equation. Starting either from a certain vibrational state or from coherently superimposed vibrational states weighted with Frank-Condon factors, the dissociative nuclear momentum distributions present multiple angular nodes and maxima due to molecular alignment-dependent Rabi flopping. The Rabi frequency and nuclear angular distribution depend on the laser chirp and laser ellipticity. Rabi flopping also determines the population on the $2p{\sigma }_u$ state and thus the dissociation probability. The deep understanding of Rabi flopping in molecular dissociation gives clues to control ultrafast molecular dynamics.

We investigate the benchmark photoionization of hydrogen atoms triggered by the third harmonic at vacuum ultraviolet laser pulses (at 202 nm) and probe the time delay via resonant quantum states with the weak fundamental laser pulses (at 606 nm). As a result, two different sidebands will emerge below the first above threshold ionization peak. We show that these two sidebands can be established through resonance with the $3d$ and $2p$ states of hydrogen atoms at 202 nm, respectively. Using this scheme, we can extract the angularly dependent time delay of electrons liberated from the $3d$ state with respect to those released from the $2p$ state by comparing the phase differences between two sidebands. Using the attosecond beating scheme of asymmetrical photon transition, we obtain the intrinsic time delay between the $3d$ and $2p$ excited electronic states in the few-photon ionization regime of H atoms, which is ∼103 as. This asymmetric attosecond beating metrology provides insight into electron dynamics of the multiphoton resonant ionization via multi-intermediate states.

We propose a method to retrieve the band structure by measuring the caustic points of the harmonic spectrum generated by the interaction between laser and solid. The relation between the energy ${\omega }_c$ of the spectral caustic points and the external fields $F$ encodes the bandgap of the solid. Specifically, for a simple band structure, ${\varepsilon }_g\left(k\right)={\varepsilon }_0+{\varepsilon }_1[1-cos\left(k{a}_0\right)]$, according to the semiclassical theory, we map the crystal momentum $k_c$ to the caustic point energy ${\omega }_c$ by $F$ since $k_c$ is independent of the parameters ${\varepsilon }_0$ and ${\varepsilon }_1$. Furthermore, for the general band structure, because its first-order form is a simple energy band, we can roughly retrieve the first-order form of the energy band and obtain the accurate band structure by iterative calculation. Using this method, we solve the deviation between the retrieved and the target bandgap near the Brillouin zone boundary. Also, we show that this method is suitable for wide-bandgap materials.

Delocalized Bloch electrons in solids are usually regarded as a kind of representative quantum Fermi gas. To unravel the real-space dynamics of Bloch electrons under a tailoring intraband current, we introduced a quasiparticle picture of a wave packet via superposing the multiple Bloch states within a given crystal-momentum region. We find that temporal characteristics and yield modulation in solid-state high-harmonic generation (HHG) depend sensitively on the crystal-momentum region of generating electron-hole pair. Its mechanism could be clarified by the gradual symmetrization of the time-dependent carrier distribution with the growing tunneling-momentum range. Manipulation of tunneling-momentum range is experimentally feasible via photon-carrier doping of appropriate preexcitation pulse. Finally, we elucidate the role of dephasing in the process of HHG. The scheme of customizing intraband current provides an alternative way to regulate the high-harmonic generation of solids.

Achieving strong optical nonlinearity in a low excitation power level is crucial in micro- and nanophotonics, central to many applications. Here, we explore optical linear and nonlinear responses in a single quantum dot (QD) embedded into a single-mode cavity under the effect of an external magnetic field and a continuous-wave laser excitation in the weak-coupling regime. Using experimentally realistic parameters, we find that the magnetic field introduced in such a coupled cavity-QD system can drastically modify the properties of photons and thus can be employed as a flexible control parameter. Especially, the enhanced optical Kerr nonlinearity can be achieved by tuning the applied magnetic field appropriately, which can reach over 11-fold improvement as compared to the case without the magnetic field. Physically, this is the consequence of the magnetic-field-induced resonance shifts and the cavity-field-mediated interferences. As an example of its applications, in the basis of this attainable strong Kerr nonlinearity, we show a feasible way of generating an optical high-order sideband efficiently, with small sideband spacing, as small as a few tens of megahertz, and low input excitation power, as low as a few nanowatts. Moreover, the manipulation of the high-order sideband is also discussed by changing the magnetic field from 0 to 3 T, where the variation of the sideband power is in good agreement with that of the Kerr nonlinearity. Considering realistic experimental conditions we elaborate the possible implementation of our proposal. In addition to being of fundamental interest, the results of our paper hold potential in optical frequency combs, nonlinear optics, and high precision measurement.

In cavity optomechanics, single-photon detection of Raman scattered photons can be a useful tool for observing nonclassical features of both radiation and motion. While this tool has been employed in experiments with pulsed laser driving of a cavity mode, it has not been readily accessible to experiments with continuous and constant laser driving. To address this, we present a study of a standard optomechanical system where the cavity mode is continuously driven at two different frequencies and where sideband photons are detected by single-photon detectors after frequency filtering the output from the cavity mode around its resonance frequency. We first derive the normalized second-order coherence associated with the detected photons and show that it contains signatures of the quantum nature of the mechanical mode which would be absent with only single-tone driving. To identify model-independent nonclassical features, we derive two inequalities for the sideband photon statistics that should be valid in any classical model of the system. We show that these inequalities are violated in the proposed setup. This is provided that the average phonon occupation number of the mechanical mode is sufficiently small, which in principle can be achieved through sideband cooling intrinsic to the setup. Violation of the first inequality means that there is no well-defined probability distribution of the Glauber-Sudarshan type for the cavity mode. In contrast, a violation of the second inequality means that there is no joint probability distribution for the cavity mode at two times separated by a finite interval, which originates from the noncommutativity of the motional quadratures of the mechanical mode. The proposed setup thus employs a mechanical oscillator in order to generate a steady-state source of nonclassical radiation.

An electron wave packet tunneling through a barrier has a transmission (or “group delay”) time ${\tau }_g$ that, for a rectangular barrier, is commonly held to become independent of the barrier width $L$ as the width increases (the McColl-Hartman effect). In the present study, it is shown that first, the McColl-Hartman effect for a rectangular barrier is dependent upon $L$ as the Gamow tunneling factor $\theta \left(k\right)$ vanishes, and ${\tau }_g$ is only independent of $L$ when $\theta \left(k\right)$ is large; and second, for a triangular barrier to model field emission, although ${\tau }_g$ can be large for small field, it vanishes when the energy matches the barrier height.

Global control strategies for arrays of qubits are a promising pathway to scalable quantum computing. A continuous-wave global field provides decoupling of the qubits from background noise. However, this approach is limited by variability in the parameters of individual qubits in the array. Here we show that by modulating a global field simultaneously applied to the entire array, we are able to encode qubits that are less sensitive to the statistical scatter in qubit resonance frequency and microwave amplitude fluctuations, which are problems expected in a large-scale system. We name this approach the SMART (sinusoidally modulated, always rotating, and tailored) qubit protocol. We show that there exist optimal modulation conditions for qubits in a global field that robustly provide improved coherence times. We discuss in further detail the example of spins in silicon quantum dots, in which universal one- and two-qubit control is achieved electrically by controlling the spin-orbit coupling of individual qubits and the exchange coupling between spins in neighboring dots. This paper provides a high-fidelity qubit operation scheme in a global field, significantly improving the prospects for scalability of spin-based quantum computer architectures.

The focusing of a propagating untrapped Bose-Einstein condensate is studied theoretically. We use a scaling solution method comprising a time-dependent scaling function to analytically examine the dynamics of a falling Bose-Einstein condensate in different regimes of propagation including the expansion and compression zones. Our model is based on the Gross–Pitaevskii equation which involves the interparticle interactions between atoms and, consequently, their influence on the focused structures. We investigate the focused profile characteristic factors such as the resolution and peak density for various cases of the focusing optical potential parameters as well as the factors associated with the moving cloud. Our results are compared with numerical solutions of the Gross–Pitaevskii equation.

We theoretically investigate supersolidity in three-dimensional dipolar Bose-Einstein condensates. We focus on the role of trap geometry in determining the dimensionality of the resulting droplet arrays, which range from one-dimensional to zigzag, through to two-dimensional supersolids in circular traps. Supersolidity is well established in one-dimensional arrays, and may be just as favorable in two-dimensional arrays provided that one appropriately scales the atom number to the trap volume. We develop a tractable variational model—which we benchmark against full numerical simulations—and use it to study droplet crystals and their excitations. We also outline how exotic ring and stripe states may be created with experimentally feasible parameters. Our work paves the way for future studies of two-dimensional dipolar supersolids in realistic settings.

We study the magneto-optical response of exciton polaritons in $p$-orbital flat bands in a two-dimensional Lieb lattice of semiconductor microcavity pillars. At low excitation density, we detail the influence of an external magnetic field on the exciton component, which enables magnetic tuning of the flat-band states. In the high-density regime, one can induce a spin population imbalance by circularly polarized pumping leading to an effective nonlinear Zeeman splitting. We show how the interplay between the symmetry of the orbital wave function, photonic spin-orbit coupling, and real and effective Zeeman splittings gives rise to real-space flat-band patterns with tilted orbital wave functions in the regime of dynamical polariton condensation. These results demonstrate the ability to optically and magnetically manipulate the spatial, spectral, and polarization properties of polariton condensates in the flat energy bands of a Lieb lattice.

We consider the task of performing quantum state tomography on a $d$-level spin qudit, using only measurements of spin projection onto different quantization axes. After introducing a basis of operators closely related to the spherical harmonics, which obey the rotational symmetries of spin qudits, we map our quantum tomography task onto the classical problem of signal recovery on the sphere. We then provide algorithms with $O\left(r{d}^3\right)$ serial runtime, parallelizable down to $O\left(r{d}^2\right)$ for: (i) computing a priori upper bounds on the expected error with which spin projection measurements along $r$ given axes can reconstruct an unknown qudit state, and (ii) estimating a posteriori the statistical error in a reconstructed state. Our algorithms motivate a simple randomized tomography protocol for which we find that using more measurement axes can yield substantial benefits that plateau after $r\approx 3d$.

Matrices with the displacement structures of circulant, Toeplitz, and Hankel types as well as matrices with structures generalizing these types are omnipresent in computations of sciences and engineering. In this paper we present efficient and memory-reduced quantum algorithms for solving linear systems with such structures by devising an approach to implement the block-encodings of these structured matrices. More specifically, by decomposing $n\times n$ dense matrices into linear combinations of displacement matrices, we first deduce the parametrized representations of the matrices with displacement structures so that they can be treated similarly. With such representations, we then construct $\epsilon$-approximate block-encodings of these structured matrices in two different data access models, i.e., the black-box model and the quantum random access memory (QRAM) data structure model. It is shown the quantum linear system solvers based on the proposed block-encodings provide a quadratic speedup with respect to the dimension over classical algorithms in the black-box model and an exponential speedup in the QRAM data structure model. In particular, these linear system solvers subsume known results with significant improvements and also can motivate new instances where there was no specialized quantum algorithm before. As an application, one of the quantum linear system solvers is applied to the linear prediction of time series, which justifies the claimed quantum speedup is achievable for problems of practical interest.

Quantum metrology is superior to classical metrology in parameter estimation. This is because quantum states have coherence that, however, does not exist in classical states. Previous works were limited to the study of the relationship between quantum Fisher information (QFI) and coherence of the initial probe state only for a specific single-qubit parameter estimation process (e.g., a process described by a single-qubit spin angular momentum operator $J_z$). Here, we consider a more general case and study the relationship between QFI and coherence of the initial probe state for a single-qubit general parameter estimation process, which is described by a single-qubit spin angular momentum operator $J_{\vec{n}}$ with a general unit vector $\vec{n}$. We find that the QFI is proportional to the square of coherence of the initial probe state, when the single-qubit bases are eigenstates of the spin angular momentum operator $J_{\vec{n}}$ describing the parametrization process. We also design and conduct a linear optical experiment to support our theory. The experimental results are in good agreement with the theoretical ones. This work provides an important guideline for enhancing the precision of parameter estimation.

The fine-structure splitting $1s^{2}2s^{2}2p {}^2{P}_{1/2}{\text{−}}^2{P}_{3/2}$ transitions in boronlike ${\mathrm{S}}^{11+}$ and ${\mathrm{Cl}}^{12+}$ were experimentally measured with a high precision spectrometer at the Shanghai high-temperature superconducting electron beam ion trap. The $M1$ transition wavelengths for ${\mathrm{S}}^{11+}$ and ${\mathrm{Cl}}^{12+}$ were determined to be 760.9635(29) and 574.1539(26) nm (in air), respectively. Compared to the previously observed results, the accuracies of current experimental results are improved by more than ten times and 200 times for ${\mathrm{S}}^{11+}$ and ${\mathrm{Cl}}^{12+}$, respectively. Additionally, the $M1$ transition energies in ${\mathrm{S}}^{11+}$ and ${\mathrm{Cl}}^{12+}$ were evaluated within the ab initio QED framework to compare with the experimental data. The present experimental results agree with the theoretical calculations and provide a possibility to test QED effects and correlation effects with high accuracy in few-electron highly charged ions.