Carbon $1s$ photoelectron spectra of CO molecules in gas phase were recorded in the tender x-ray energy range, from 2.3 to 6.9 keV. The intensity ratios of individual peaks from $\nu =0$ to 3 within the vibrational progression of the C $1s$ photoelectron spectrum were determined at the various photon energies and are shown to be strongly affected by the photoelectron recoil effect. The experimental vibrational intensity ratios are compared with theoretical predictions at different levels of accuracy. Developments of the recoil model, using generalized Franck-Condon factors, rovibrational coupling, Morse potential energy curves, and accurate angular averaging are presented and applied to the analysis of the experimental results.

Experiments involving ultracold molecules require sufficiently long lifetimes, which can be very short for excited rovibrational states in the molecular potentials. For alkali-metal atoms such as rubidium, a lowest rovibrational molecular state can both be found in the electronic singlet and triplet configurations. The molecular singlet ground state is absolutely stable. However, the lowest triplet state can decay to a deeper bound singlet molecule due to a radiative decay mechanism that involves the interatomic spin-orbit interaction. We investigate this mechanism, and find the lifetime of rubidium molecules in the lowest triplet rovibrational state to be about 20 min.

In this paper, we theoretically study x-ray multiphoton ionization dynamics of heavy atoms taking into account relativistic and resonance effects. When an atom is exposed to an intense x-ray pulse generated by an x-ray free-electron laser (XFEL), it is ionized to a highly charged ion via a sequence of single-photon ionization and accompanying relaxation processes, and its final charge state is limited by the last ionic state that can be ionized by a single-photon ionization. If x-ray multiphoton ionization involves deep inner-shell electrons in heavy atoms, energy shifts by relativistic effects play an important role in ionization dynamics, as pointed out in Phys. Rev. Lett. 110, 173005 (2013). On the other hand, if the x-ray beam has a broad energy bandwidth, the high-intensity x-ray pulse can drive resonant photoexcitations for a broad range of ionic states and ionize even beyond the direct one-photon ionization limit, as first proposed in Nat. Photon. 6, 858 (2012). To investigate both relativistic and resonance effects, we extend the xatom toolkit to incorporate relativistic energy corrections and resonant excitations in x-ray multiphoton ionization dynamics calculations. Charge-state distributions are calculated for Xe atoms interacting with intense XFEL pulses at a photon energy of 1.5 keV and 5.5 keV, respectively. For both photon energies, we demonstrate that the role of resonant excitations in ionization dynamics is altered due to significant shifts of orbital energy levels by relativistic effects. Therefore, it is necessary to take into account both effects to accurately simulate multiphoton multiple ionization dynamics at high x-ray intensity.

We examine the possibility of traveling-wave solutions within the nonlinear Euler-Heisenberg electrodynamics. Since this theory resembles in its form the electrodynamics in matter, it is a priori not clear if there exist traveling-wave solutions with a new dispersion relation for $\omega \left(k\right)$ or if the Euler-Heisenberg theory stringently imposes $\omega =k$ for any arbitrary ansatz $\mathbf{E}\left(\xi \right)$ and $\mathbf{B}\left(\xi \right)$ with $\xi \equiv \mathbf{k}·\mathbf{r}-\omega t$. We show that the latter scheme applies for the Euler-Heisenberg theory, but point out the possibility of new solutions with $\omega \ne k$ if we go beyond the Euler-Heisenberg theory, allowing strong fields. In case of the Euler-Heisenberg theory the quantum-mechanical effect of the traveling-wave solutions remains in $\hslash$ corrections to the energy density and the Poynting vector.

Through the study of the power spectra of a monochromatic light beam reflected by metallic mirrors, fluctuations in their reflectance are observed. The power spectra were obtained down to a factor ${10}^{-6}$ below the standard quantum limit, with a dynamic range of ${10}^5$ in frequency and power, using methods we developed. The properties of the spectra are investigated, and their dependence on the material is analyzed. The physics underlying the phenomenon is also discussed. These fluctuations provide a window into the degrees of freedom responsible for the reflection process in metals.

We study ultrastrong-coupling quantum-phase-transition phenomena in a few-qubit system. In the one-qubit case, three second-order transitions occur and the Goldstone mode emerges under the condition of ultrastrong-coupling strength. Moreover, a first-order phase transition occurs between two different superradiant phases. In the two-qubit case, a two-qubit Hamiltonian with qubit-qubit interactions is analyzed fully quantum mechanically. We show that the quantum phase transition is inhibited even in the ultrastrong-coupling regime in this model. In addition, in the three-qubit model, the superradiant quantum phase transition is retrieved in the ultrastrong-coupling regime. Furthermore, the $N$-qubit model with $U\left(1\right)$ symmetry is studied and we find that the superradiant phase transition is inhibited or restored with the qubit-number parity.

In the Einstein–Podolsky–Rosen experiment, when Alice makes a measurement on her part of a bipartite system, Bob's part is collapsed to, or steered to, a specific ensemble. Moreover, by reading her measurement outcome, Alice can specify which state in the ensemble Bob's system is steered to and with which probability. The possible states that Alice can steer Bob's system to are called steered states. In this work, we study the subset of steered states which are pure after normalization. We illustrate that these pure steered states, if they exist, often carry interesting information about the shared bipartite state. This information content becomes particularly clear when we study the purification of the shared state. Some applications are discussed. These include a generalization of the fundamental lemma in the so-called “all-versus-nothing proof of steerability” for systems of arbitrary dimension.

Quantum illumination is one of the most basic ways to realize the quantum radar for detection of low-reflectivity targets embedded in a thermal-noise bath. It preserves a strong advantage over the classical counterparts even though its fragile quantum entanglement is completely destroyed by a large amount of noise and losses. In this paper, we describe and analyze a discrete-variable quantum illumination system with ancillary degrees of freedom of entangled photon pairs. Comparing the error probability bound, i.e., the quantum Chernoff bound, we identify that this system indeed offers higher accuracy than the single-photon illumination and quantum illumination with single degree of freedom of entangled photon pairs. Furthermore, the utilization of ancillary degrees of freedom exponentially enhances signal-to-noise ratio over quantum illumination without ancillary degrees of freedom. It means that this system reduces the necessary amount of signal photons to accurately determine whether the object is present or absent in the target region, which is absolutely crucial to the stealthiness of the radar system.

We implement a quantum optimal control algorithm based on automatic differentiation and harness the acceleration afforded by graphics processing units (GPUs). Automatic differentiation allows us to specify advanced optimization criteria and incorporate them in the optimization process with ease. We show that the use of GPUs can speedup calculations by more than an order of magnitude. Our strategy facilitates efficient numerical simulations on affordable desktop computers and exploration of a host of optimization constraints and system parameters relevant to real-life experiments. We demonstrate optimization of quantum evolution based on fine-grained evaluation of performance at each intermediate time step, thus enabling more intricate control on the evolution path, suppression of departures from the truncated model subspace, as well as minimization of the physical time needed to perform high-fidelity state preparation and unitary gates.

We carried out a systematic high-precision relativistic study of the forbidden magnetic dipole and electric quadrupole transitions in ${\mathrm{Ca}}^{+}$, Rb, ${\mathrm{Sr}}^{+}$, Cs, ${\mathrm{Ba}}^{+}$, Fr, ${\mathrm{Ra}}^{+}, {\mathrm{Ac}}^{2+}$, and ${\mathrm{Th}}^{3+}$. This work is motivated by the importance of these transitions for tests of fundamental physics and precision measurements. The relative importance of the relativistic, correlation, and Breit correction contributions and contributions of negative-energy states is investigated. Recommended values of reduced matrix elements are presented together with their uncertainties. The matrix elements and resulting lifetimes are compared with other theoretical values and with experiment where available.

The scattering matrices of $e+{\mathrm{O}}^{+}\left(2p^3{}^{4}S_{3/2},{}^{2}D_{3/2,5/2}\right)$ with $J^{\pi }=3^{-}$ in various energy regions including discrete and adjacent continuum are calculated using our modified eigenchannel $R$-matrix method. The analytical properties of the scattering matrices for this multichannel scattering process with strong interchannel interactions are unveiled by our method. Based on the scattering matrices, all energy levels (including an infinite number of Rydberg states and autoionization resonance states without missing any one) can be calculated accurately in the framework of multichannel quantum defect theory (MQDT). The MQDT parameters (i.e., scattering matrices) can be checked and/or calibrated with available precise spectroscopy data. In the present work, the calculation precision of the scattering matrices of $J^{\pi }=3^{-}$ is determined to be about 2%, which should meet the needs of future calculations for the important $e+{\mathrm{O}}^{+}$ collision process in astrophysics research.

Precision vibrational spectroscopy of the molecular hydrogen ions is of significant interest for determining fundamental constants, for searching for new forces, and for testing quantum electrodynamics calculations. Future experiments can profit from the ability of preparing molecular hydrogen ions at ultralow kinetic energy and in preselected internal states, with respect to vibration, rotation, and spin degrees of freedom. For the homonuclear ions (${\mathrm{H}}_2{}^{+}, {\mathrm{D}}_2{}^{+}$), direct laser cooling of the rotational degree of freedom is not feasible. We show by quantum calculations that rotational cooling by cold He buffer gas is an effective approach. For this purpose we have computed the energy-dependent cross sections for rotationally elastic and inelastic collisions, ${\mathrm{h}}_2{}^{+}(v=0,N)+\mathrm{He}\to {\mathrm{h}}_2{}^{+}(v=0,N^{\prime })+\mathrm{He}$ (where $\mathrm{h}=\mathrm{H},\mathrm{D})$, using ab initio coupled-channel calculations. We find that rotational cooling to the lowest rotational state is possible within tens of seconds under experimentally realistic conditions. We furthermore describe possible protocols for the preparation of a single quantum state, where also the spin state is well defined.

It was shown [New J. Phys. 17, 103037 (2015)] that large and robust entanglement between two different mechanical resonators could be achieved, either dynamically or in the steady state, in an optomechanical system in which the two mechanical resonators are coupled to a single cavity mode driven by a suitably chosen two-tone field. An important limitation of the scheme is that the cavity decay rate must be much smaller than the two mechanical frequencies and their difference. Here we show that the entanglement can be remarkably enhanced, and the validity of the scheme can be largely extended, by adding a coherent feedback loop that effectively reduces the cavity decay rate.

In this paper we use numerical simulations to study a two-dimensional (2D) quantum dot (cavity) with two leads for passing currents (electrons, photons, etc.) through the system. By introducing an imaginary potential in each lead the system is made symmetric under parity-time inversion ($\mathcal{PT}$ symmetric). This system is experimentally realizable in the form of, e.g., quantum dots in low-dimensional semiconductors, optical and electromagnetic cavities, and other classical wave analogs. The computational model introduced here for studying spectra, exceptional points (EPs), wave-function symmetries and morphology, and current flow includes thousands of interacting states. This supplements previous analytic studies of few interacting states by providing more detail and higher resolution. The Hamiltonian describing the system is non-Hermitian; thus, the eigenvalues are, in general, complex. The structure of the wave functions and probability current densities are studied in detail at and in between EPs. The statistics for EPs is evaluated, and reasons for a gradual dynamical crossover are identified.

The interaction of qubits with quantized modes of electromagnetic fields has been largely addressed in the quantum optics literature under the rotating wave approximation (RWA), where rapid oscillating terms in the qubit-mode interaction picture Hamiltonian can be neglected. At the same time, it is generally accepted that, provided the interaction is sufficiently strong or for long times, the RWA tends to describe physical phenomena incorrectly. In this work, we extend the investigation of the validity of the RWA to a more involved setup where two qubit-mode subsystems are brought to interaction through their harmonic coordinates. Our treatment is all analytic thanks to a sequence of carefully chosen unitary transformations, which allows us to diagonalize the Hamiltonian within and without the RWA. By also considering qubit dephasing, we find that the purity of the two-qubit state presents non-Markovian features which become more pronounced as the coupling between the modes gets stronger and the RWA loses its validity. In the same regime, there occurs fast generation of entanglement between the qubits, which is also not correctly described under the RWA. The setup and results presented here clearly show the limitations of the RWA in a scenario amenable to exact description and free from numerical uncertainties. Consequently, it may be of interest for the community working with cavity or circuit quantum electrodynamic systems in the strong coupling regime.

We derive algebraic bounds on achievable rates for quantum state transfer and entanglement generation in general quantum systems. We apply these bounds to graph-based models of local quantum spin systems to obtain speed limits on these tasks. A comparison to numerical optimal control results for spin chains suggests that unexplored regions of the dynamical landscape may support enhanced performance of key quantum-information-processing tasks.

We introduce measures of multipartite quantum correlations based on classical correlations in mutually unbiased bases. These classical correlations are measured in terms of the classical mutual information, which has a clear operational meaning. We present sufficient conditions under which these measures are maximized. States that have previously been shown to be particularly important in the context of local operations and classical communication fulfill these conditions and therefore maximize the correlation measures. In addition, we show how the introduced measures can be used to detect high-dimensional tripartite entanglement by using only a few local measurements.