We propose a scheme to study the topic of manipulating the Goos-Hänchen (GH) shift of the reflected beam in an optomechanical cavity (OMC). Our system consists of two mirrors where one is fixed and the other is movable and a two-level atom is trapped inside the OMC. The fixed mirror is partially reflecting, whereas the movable mirror is perfectly reflecting. We theoretically investigated the behavior of the GH shift in the reflected beam when a Gaussian beam is an incident on the OMC. We find that GH shifts can be greatly enhanced in positive or negative directions via manipulating the quantum parameters such as optomechanical strength $g_{\text{mc}}$ and atom-cavity strength $g_{\text{ac}}$ under the influence of beam width of a Gaussian beam. Besides, we study the GH shift in the case of the partially coherent light beam as an incident probe field. Giant negative GH shift is achieved for an incident partially coherent beam in the presence of $g_{\text{mc}}, g_{\text{ac}}$, a measure of global coherence and beam width of a partially coherent beam. The proposed model provides feasibility in practical experiments for studying the behavior of the GH shift.

As existing approaches to get around the restriction of the no-go theorem generally exhibit high ancillary qubit overhead costs, we propose a scheme for universal fault-tolerant quantum computation by using the pieceable fault-tolerant protocol and code switching techniques. In additional, by utilizing the construction of the pieceable fault-tolerant circuit, we adopt a decoding strategy based on a deep-neural-network algorithm to improve the error threshold of the non-Clifford logical gate circuit. We describe our universal construction in detail with a two-level nonuniform concatenated 25-qubit code and perform numerical simulations to analyze the depolarizing noise threshold of a given universal gate set with this code. The resources required to implement this universal gate set are also estimated to further demonstrate the efficiency of our scheme. We compare these results with the existing universal concatenation methods and conclude that our method outperforms them in terms of the lower bound of the error threshold and qubit resource overhead.

We report theoretical determination of the dipole polarizability of the neon atom, including its frequency dependence. Corrections for the relativistic, quantum electrodynamics, finite nuclear mass, and finite nuclear size effects are taken into account. We obtain the value ${\alpha }_0=2.66080\left(36\right)$ for the static polarizability, and ${\alpha }_2=2.850\left(7\right)$ and ${\alpha }_4=4.932\left(14\right)$ for the first two polarizability dispersion coefficients (Cauchy moments); all values are in atomic units (a.u.). In the case of static polarizability, our result agrees with the best experimental determination, Gaiser et al. [Phys. Rev. Lett. 120, 123203 (2018)], but our estimated uncertainty is significantly larger. For the dispersion coefficients, the results obtained in this work appear to be the most accurate to date overall compared to published theoretical and experimental data. We also calculated the static magnetic susceptibility of the neon atom, needed to obtain the refractive index of gaseous neon. Our result, ${\chi }_0=-8.484\left(19\right)\times {10}^{-5}$ a.u., is about 9% larger in absolute value than the recommended experimental value, Rumble et al. [CRC Handbook of Chemistry and Physics (CRC Press, Boca Raton, FL, 2019)].

The interplay between quantum-mechanical and classical evolutions in a chirped-driven Rydberg atom is discussed. It is shown that the system allows two continuing resonant excitation mechanisms, i.e., a successive two-level transitions (ladder climbing) and a continuing classicallike nonlinear phase locking (autoresonance). The persistent 1:1 and 2:1 resonances between the driving and the Keplerian frequencies are studied in detail and characterized in terms of two dimensionless parameters $P_{1,2}$ representing the driving strength and the nonlinearity in the problem, respectively. The quantum-mechanical rotating wave and the classical single-resonance approximations are used to describe the regimes of efficient classical or quantum-mechanical excitation in this two-parameter space.

We show that a class of vector vortex beams possesses a topological property that derives both from the spatially varying amplitude of the field and its varying polarization. This property arises as a consequence of the inherent skyrmionic nature of such beams and is quantified by the associated skyrmion number. We illustrate this idea for some of the simplest vector beams and discuss the physical significance of the skyrmion number in this context.

The frequency-resolved correlations of the fluorescence emitted by a four-level system in the $J=1/2$ to $J=1/2$ transition driven by a linearly polarized laser field are theoretically investigated. In the cross two-photon correlation of the $\pi$ and ${\sigma }^{+}$ transitions, we show that VICs can induce the interference of time orderings between the two-photon paths with different dipole moments, which can serve as a good scheme to exhibit the effects of vacuum-induced coherences (VICs). An external magnetic field can cause frequency differences between two-photon paths with different time orderings. When the differences can be distinguished by detectors, the effects of VICs are destroyed and time asymmetry of the two-photon correlations appears due to the reveal of “which path” information. However, the which path information can be erased by tuning the filtering frequencies so the perfect interference effects of time orderings and time symmetry are restored.

Variational hybrid quantum-classical optimization is one of the most promising avenues to show the advantages of noisy intermediate-scale quantum computers in solving hard problems, such as finding the minimum-energy state of a Hamiltonian or solving some machine-learning tasks. In these devices, noise is unavoidable and impossible to error correct, yet its role in the optimization process is not well understood, especially from the theoretical viewpoint. Here we consider a minimization problem with respect to a variational state, iteratively obtained via a parametric quantum circuit, taking into account both the role of noise and the stochastic nature of quantum measurement outcomes. We show that the accuracy of the result obtained for a fixed number of iterations is bounded by a quantity related to the quantum Fisher information of the variational state. Using this bound, we study the convergence property of the quantum approximate optimization algorithm under realistic noise models, showing the robustness of the algorithm against different noise strengths.

We present momentum-resolved coincidence measurements of strong-field single and double ionization of deuterated water $\left({\mathrm{D}}_2\mathrm{O}\right)$ using intense few-cycle laser pulses. We measure the vector momentum of electrons and ions resulting from the laser-molecule interaction. This enables us to measure the photoelectron spectrum for electrons in coincidence with fragment ions having different momenta, which can be related to different final states of the cation and dication. The photoelectron spectra for different fragment ion momenta show striking differences, which can be interpreted in terms of the removal of electrons from different molecular orbitals, including the highest occupied molecular orbital (HOMO), as well as more deeply bound ones (e.g., HOMO-2). We discuss our measurements in light of calculations which model the strong-field light matter interaction.

In many of the approximate functionals in one-body reduced-density-matrix (1RDM) functional theory, the approximate two-body reduced density matrix (2RDM) in the natural orbital representation only depends on the natural occupation numbers. In Phys. Rev. A 92, 012520 (2015), Wang and Knowles initialized a discussion of to what extent this simplification is valid by introducing two different ${\mathrm{H}}_4$ geometries with identical natural occupation numbers but different 2RDMs. Gritsenko has argued that this feature is due symmetry [Phys. Rev. A 97, 026501 (2018)]. This work aims to contribute to the discussion on the following points: (1) one should rather speak of symmetry-restricted variants of the universal functional than saying that the universal functional is symmetry dependent; (2) the unitary invariance of degenerate NOs can lead to large deviations in the 2RDM elements, especially the phase of the NOs; (3) symmetry-restricted functionals are constructed for the ${\mathrm{H}}_4$ geometries considered by Wang and Knowles, whose structure could serve as guide in the construction of approximate 1RDM functionals.

The Schrödinger equation for the $nP$ $(4\le n\le 10)$ states of lithium is solved using the Rayleigh-Ritz variational method in Hylleraas coordinates, where the asymptotic behavior of the wave function that is specific to a Rydberg state is built in explicitly to improve the accuracy of the solution. The nonrelativistic variational energies of the $nP$ $(4\le n\le 10)$ states reach an accuracy of ${10}^{-13}$ to ${10}^{-14}$. In addition, the fine-structure splittings of these states are also calculated and compared with experimental results.

We have developed a perturbative method to model the resonant ionization of atomic systems in fluctuating laser fields. The perturbative method is based on an expansion in terms of the multitime cumulants, a suitable combination of moments (field's coherence functions), used to represent the field's statistical properties. The second-order truncated expansion is expressed in terms of the radiation's power spectrum and the intensity autocorrelation function. We investigate the range of validity of the model in terms of the field's coherence temporal length and peak intensity and have compared the results with conventional Monte Carlo calculations. We apply the theory in the case of a near-resonant ionization of the helium $2s2p$ autoionizing state with a self-amplified spontaneous emission free-electron laser pulse with square-exponentially dependent first-order coherence function. The ionization lineshape profile acquires a Voight profile; the degree of the Gaussian or Lorentzian character of the lineshape will depend crucially on the field's coherence time.

Flux ladders constitute the minimal setup enabling a systematic understanding of the rich physics of interacting particles subjected simultaneously to strong magnetic fields and a lattice potential. In this paper, the ground-state phase diagram of a flux-ladder model is mapped out using extensive density-matrix renormalization-group simulations. The emphasis is put on parameters which can be experimentally realized exploiting the internal states of potassium atoms as a synthetic dimension. The focus is on accessible observables such as the chiral current and the leg-population imbalance. Considering a particle filling of one boson per rung, we report the existence of a Mott-insulating Meissner phase as well as biased-ladder phases on top of superfluids and Mott insulators. Furthermore, we demonstrate that quantum quenches from suitably chosen initial states can be used to probe the equilibrium properties in the transient dynamics. Concretely, we consider the instantaneous turning on of hopping matrix elements along the rungs or legs in the synthetic flux-ladder model, with different initial particle distributions. We show that clear signatures of the biased-ladder phase can be observed in the transient dynamics. Moreover, the behavior of the chiral current in the transient dynamics is discussed. The results presented in this paper provide guidelines for future implementations of flux ladders in experimental setups exploiting a synthetic dimension.

A scheme for dynamical stabilization of entanglement quantified by the quantum Fisher information is analyzed numerically and analytically for bimodal and spin-1 Bose-Einstein condensates in the context of atomic interferometry. The scheme consists of twisting dynamics followed by a single rotation of a state which limits further evolution around stable center fixed points in the mean-field phase space. The resulting level of entanglement is of the order or larger than at the moment of rotation. It is demonstrated that the readout measurement of parity quantifies the level of entanglement during the entire evolution.

By constructing a quantum filtering system to synthesize the spectral and spatial properties of stimulated radiation, the directionality of spectrally correlated nonclassical properties of resonance fluorescence from a three-body quantum antenna is investigated. The quantum antenna consists of three two-level quantum emitters, two of which are identical and strongly driven by an external laser field to radiate the collective resonance fluorescence with three distinct spectral components. The collective stimulated radiation is shaped by the remaining auxiliary emitter via its spontaneous emission, which is assumed to be resonant with the higher-frequency spectral component of the two identical emitters. Due to the presence of the auxiliary emitter, highly directional nonclassicality of the spectral correlations can be generated, which is the consequence of the internal interference of the source and the spatial interference of the radiation field. The electric dipole-dipole interaction between the undriven emitter and the dressed two-body radiating source plays a crucial role in breaking the rotational symmetry of nonclassical signals, which is embodied by various photon correlation functions with a frequency-resolved version for different spectral combinations. By correlating the two opposite sidebands, the frequency-resolved intensity-intensity correlation functions can signal highly directional nonclassicality, and the frequency-resolved two-mode entanglement along a specific emission direction can be tested by the frequency-resolved anomalous correlation function. While the directional nonclassical correlations between the central-frequency and the three-body collective higher-frequency components can be identified through the frequency-resolved intensity-field correlation function. These various frequency-resolved correlation functions characterize the spatial asymmetry of nonclassical properties of the collective stimulated radiation from different perspectives, including the particle properties and the quantum coherences of the filtered photons. When the three-body collective higher-frequency sidebands are correlated with the central band and the lower-frequency sideband, respectively, the schemes of using the auxiliary undriven emitter to generate optimal nonclassical correlations with well-defined directions are discussed analytically. In addition, the results obtained from the three-body quantum antenna and a dressed two-body quantum antenna are compared.

Dicke superrandiance is a cooperative phenomenon which arises from the collective coupling of an ensemble of atoms to the electromagnetic radiation. Here we discuss the quantifying of quantum coherence for the Dicke model of superradiance in the mean-field approximation. We found the single-atom $l_1$ norm of coherence is given by the square root of the normalized average intensity of radiation emitted by the superradiant system. This validates quantum coherence as a useful figure of merit towards the understanding of superradiance phenomenon in the mean-field approach. In particular, this result suggests probing the single-atom coherence through the radiation intensity in superradiant systems, which might be useful in experimental realizations where is unfeasible to address atoms individually. Furthermore, given the nonlinear unitary dynamics of the time-dependent single-atom state that effectively describes the system of $N$ atoms, we analyze the quantum speed limit time and its interplay with the $l_1$ norm of coherence. We verify the quantum coherence speeds up the evolution of the superradiant system, i.e., the more coherence stored on the single-atom state, the faster the evolution. These findings unveil the role played by quantum coherence in superradiant systems, which in turn could be of interest for communities of both condensed matter physics and quantum optics.

Ultrafast laser excitation can create coherent superpositions of electronic states in molecules and trigger ultrafast flow of electron density on a few femtosecond timescale. While recent attosecond experiments have addressed real-time observation of these primary photochemical processes, the underlying roles of simultaneous nuclear motions and how they modify and disturb the valence electronic motion remain uncertain. Here, we investigate coherent electronic-vibrational dynamics induced among multiple vibronic levels of ionic bromine (${\mathrm{Br}}_2^{+}$), including both spin-orbit ($X^2{\mathrm{\Pi }}_{3/2,g}-X^2{\mathrm{\Pi }}_{1/2,g}$) and valence ($A^2{\mathrm{\Pi }}_{3/2,u}-{}^4{\mathrm{\Sigma }}_{3/2,u}$) electronic superpositions, using attosecond transient absorption spectroscopy. Decay, revival, and apparent frequency shifts of electronic coherences are measured via characteristic quantum beats on the Br-$3d$ core-level absorption signals. Quantum-mechanical simulations attribute the observed electronic decoherence to broadened phase distributions of nuclear wave packets on anharmonic potentials. Molecular vibronic structure is further revealed to be imprinted as discrete progressions in electronic beat frequencies. These results provide a future basis to interpret complex charge-migration dynamics in polyatomic systems.

Universal quantum computation is usually associated with interaction among two-level quantum subsystems, as this interaction is commonly viewed as a necessity to achieve universal quantum computation. In this work we show that, contrary to this intuition, universal quantum computation can be achieved without interaction among initially independent two-level quantum subsystems. We call it counterfactual universal quantum computation. As special cases, we show how to achieve counterfactual communication of quantum states, counterfactual quantum swapping, and counterfactual quantum erasure codes. To ease practical implementation, we analyze counterfactual universal quantum computation with realistic devices, including the effects of finite execution time, photon loss, and atom missing. Besides the theoretical interest of illustrating the mysterious and counterintuitive nature of quantum physics, our work has practical applications to color imaging of ancient arts, upon which light is forbidden to shine.