As an analogy of best separable approximation (BSA) in the framework of entanglement theory, here we concentrate on the notion of best incoherent approximation, with application to characterizing and quantifying quantum coherence. From both analytical and numerical perspectives, we have demonstrated that the weight-based coherence measure displays some unusual properties, in sharp contrast to other popular coherence quantifiers. First, by deriving a closed formula for single-qubit states, we have shown the exact value of weight-based coherence measure does not depend solely on the off-diagonal element but relies on the geometry of a given qubit state, thus exhibiting a rich structure even in this simplest case. Second, albeit the fact that almost all popular coherence measures only assign a maximal value to pure maximally coherent states, we have demonstrated the existence of mixed maximally coherent states (MMCS) with respect to this coherence measure and discussed the characteristic feature of MMCS in high-dimensional Hilbert spaces. Especially, we present several important families of MMCS by gaining insights from the numerical simulations. Moreover, it is pointed out that some considerations in this work can be generalized to general convex resource theories and a numerical method of improving the computational efficiency for finding the BSA is also discussed.

We present a scheme that allows integration of the Berry curvature and thus determination of the Chern number of a qubit eigenstate manifold. Our proposal continuously couples the qubit with a meter system while it explores a quasiadiabatic path in the manifold. The accumulated change of one of the meter observables then provides an estimate of the Chern number. By varying the initial state of the meter, we explore the delicate interplay between the measurement precision and the disturbance of the qubit. A simple argument yields a correction factor that allows estimation of the Chern number, even when the qubit is significantly disturbed during the probing. The Chern number arises from the geometric phase accumulated during the exploration, while we observe the dynamic phase to produce a broadening of the meter wave function. We show that a protocol, relying on three subsequent explorations, allows cancellation of the dynamic phase while the geometric phase is retained.

Measurement-based quantum computation with continuous variables in an optical setup shows great promise toward implementation of large-scale quantum computation, where the time-domain multiplexing approach enables us to generate the large-scale cluster state used to perform measurement-based quantum computation. To make effective use of the advantage of the time-domain multiplexing approach, in this paper, we propose the method to generate the large-scale three-dimensional cluster state which is a platform for topologically protected measurement-based quantum computation. Our method combines a time-domain multiplexing approach with a divide-and-conquer approach and has two advantages for implementing large-scale quantum computation. First, the squeezing level for verification of the entanglement of the three-dimensional cluster states is experimentally feasible. The second advantage is the robustness against analog errors derived from the finite squeezing of continuous variables during topologically protected measurement-based quantum computation. Therefore, our method is a promising approach to implement large-scale quantum computation with continuous variables.

A detailed theoretical framework for highly excited Rydberg molecules is developed based on the generalized local frame transformation. Our approach avoids the use of pseudopotentials and yields analytical expressions for the body-frame reaction matrix. The latter is used to obtain the molecular potential energy curves, but equally it can be employed for photodissociation, photoionization, and other processes. To illustrate the reliability and accuracy of our treatment we consider the ${\mathrm{Rb}}^{*}$-Rb Rydberg molecule and compare our treatment with state-of-the-art alternative approaches. As a second application, the present formalism is used to reanalyze the vibrational spectra of ${\mathrm{Sr}}^{*}$-Sr molecules, providing additional physical insight into their properties and a comparison of our results with corresponding measurements.

We propose a method for simulating an Unruh-DeWitt detector, coupled to a $1+1$-dimensional massless scalar field, with a suitably engineered ${\chi }^{\left(2\right)}$ nonlinear interaction. In this simulation, the parameter playing the role of the detector acceleration is played by the relative inverse-group-velocity gradient inside the nonlinear material. We identify experimental parameters that tune the detector energy gap, acceleration, and switching function. This system can simulate time-dependent acceleration, time-dependent detector energy gaps, and nonvacuum initial detector-field states. Furthermore, for very short materials, the system can simulate the weak anti-Unruh effect, in which the response of the detector decreases with acceleration.

The generation of electron vortex beams and the conversion of these beams into beams without angular momentum by means of astigmatic optical systems, or vice versa, has been pursued in the optical and the electron microscopy community, but also in the accelerator community in the past decades. Despite different conceptual approaches similar results have been achieved. By adapting the Courant-Snyder theory, which was originally developed for the description of optical properties of accelerators, to the description of laser modes, it is shown that identical mode converters have been developed for charged particle and for light beams, and that the Courant-Snyder phase and the Gouy phase are equivalent.

Through numerical simulations, statistical and dynamical properties of extreme events in a broad-area semiconductor laser with intracavity saturable absorber are investigated. By inclusion of a diffusion coefficient for the field, formation of rogue waves in a state of extended turbulence is studied and shown to be affected by harmonic perturbations. In particular, we propose a control technique based on periodic modulation of the pump parameter which can either drive the state of the system closer to or away from the chaotic attractors respectively enhancing or suppressing the generation of rogue waves. By statistical and dynamical analysis of the events in terms of intensity and optical gain, we show that when the system is under resonant modulation with frequency close to that of the dominant oscillations in the turbulent state (which is equal to the relaxation oscillation frequency typical of semiconductor lasers), more rogue waves are triggered with larger intensities and shorter lifetimes. On the other hand, off-resonant modulations restrain the formation of rogue waves where they appear in lower intensities and longer lifetimes. An example of special cases where the proposed scheme can completely forbid or allow the emission of rogue waves is also presented.

High-fidelity Bragg pulses are an indispensable tool for state-of-the-art atom interferometry experiments. In this paper, we introduce an analytic theory for such pulses. Our theory is based on the pivotal insight that the physics of Bragg pulses can be accurately described by the adiabatic theorem. We show that efficient Bragg diffraction is possible with any smooth and adiabatic pulse shape and that high-fidelity Gaussian pulses are exclusively adiabatic. Our results give strong evidence that adiabaticity according to the adiabatic theorem is a necessary requirement for high-performance Bragg pulses. Our model provides an intuitive understanding of the Bragg condition, also referred to as the condition on the “pulse area.” It includes corrections to the adiabatic evolution due to Landau-Zener processes as well as the effects of a finite atomic velocity distribution. We verify our model by comparing it to an exact numerical integration of the Schrödinger equation for Gaussian pulses diffracting four, six, eight, and ten photon recoils. Our formalism provides an analytic framework to study systematic effects as well as limitations to the accuracy of atom interferometers employing Bragg optics that arise due to the diffraction process.

The resonant interaction between x-ray photons and nuclei is one of the most exciting subjects in the burgeoning field of x-ray quantum optics. A resourceful platform used to date is thin-film x-ray cavities with embedded layers or Mössbauer nuclei such as ${}^{57}\mathrm{Fe}$. A quantum optical model based on the classical electromagnetic Green's function is developed to investigate theoretically the nuclear response inside the x-ray cavity. The model is versatile and provides an intuitive picture about the influence of the cavity structure on the resulting spectra. We test its predictive powers with the help of the semiclassical coherent scattering formalism simulations and discuss our results on increasing complexity of layer structures.

The conventional photon blockade is studied in a three-wave-mixing system. The analytic conditions for realizing the photon blockade are obtained by analyzing the eigenvalues of the system Hamiltonian, which is expanded by an effective single excited space for the high-frequency mode. The numerical results are calculated by solving the master equation in a truncated Fock space, which agrees well with the analytic conditions. Different from the other schemes of the conventional photon blockade, photon antibunching can be realized in the three modes of the three-wave-mixing system simultaneously due to the nature of the system.

The Hong-Ou-Mandel effect provides a mechanism to determine the distinguishability of a photon pair by measuring the bunching rates of two photons interfering at a beam splitter. Of particular interest is the distinguishability in time, which can be used to probe a time delay. Photon detectors themselves give some timing information, however, while that resolution may dwarf that of an interferometric technique, typical analyses reduce the interference to a binary event, neglecting temporal information in the detector. By modeling detectors with number and temporal resolution we demonstrate a greater precision than coincidence rates or temporal data alone afford. Moreover, the additional information can allow simultaneous estimation of a time delay alongside calibration parameters, opening up the possibility of calibration-free protocols and approaching the precision of the quantum Cramér-Rao bound.

We propose an adaptive quantum state estimation method for nonstationary quantum states and verify the method by numerical simulations and experimental investigations. Adaptive quantum state estimation provides an asymptotically optimal scheme for estimating an unknown input quantum state by updating the measurement configuration upon the detection of each quantum. However, previous methods are only valid for quanta with the same quantum state (a stationary state). By adopting the likelihood function for a fixed number of recent detection results, our sequential adaptive quantum state estimation allows quantum states changing in time to be estimated. The numerical simulation results and experimental demonstration using photons agree well with the theoretical predictions. This method will find applications in various fields where dynamically changing quantum states need to be estimated.

Structured light, as a general term for arbitrary states of amplitude, phase, and polarization in optical fields, is highly topical because of a myriad of applications it has fostered. A geometric description to graphically group classes of structured light has obvious benefits, with some notable advances in analogous Poincaré sphere (PS) mapping for both spin and orbital angular momentum (OAM), as well as ray-optical PS approaches for propagation-invariant fields, but all limited in dimensionality they can describe. Here we propose a generalized SU(2) PS for arbitrary dimensional structured light. The states on it represent extended families of beams with multidimensional ray-wave structures, accurately described by SU(2) symmetry groups. We outline how to construct this mapping theoretically, revealing insights into mode transformations involving OAM and geometric phase, and fully verify its efficacy experimentally. The generality of our approach is evident by the reduction to prior PS representations as special cases. We also demonstrate an extension of our approach to explain a more general high-dimensional vector beam. This construction naturally accounts for the salient topology of the classical PSs while bringing to more new degrees of freedom and dimensions for tailoring a larger variety of quantum-to-classical structured beams for a variety of applications.

We propose to implement a solid-state rotation sensor by employing a many-body quantum spin system which takes the advantages of the easy controllability of the electron spin and the robustness provided by the collective nuclear spin state. The sensor consists of a central electron spin coupled to many surrounding nuclear spins. Previously, this central spin system has been suggested to realize a quantum memory. Here, we further utilize the collective nuclear spins, which store a certain quantum state, to detect the macroscopic rotation. Different from other nuclear spin-based gyroscopes, our proposal does not directly manipulate nuclear spins via nuclear magnetic resonance technique. We analytically and numerically investigate the effects of partial nuclear polarization and decoherence on the sensitivity. We also briefly introduce the procedure to generate entanglement between nuclear spins through the quantum memory technique and to utilize this entanglement to enhance the sensing performance. Our proposal paves the way to the experimental realization of a compact solid-state, full-electrical, and spin-based gyroscope.

We study the level structures of palladium-like ${\mathrm{I}}^{7+}$ $(Z=53)$ and ${\mathrm{Ba}}^{10+}$ $(Z=56)$ and the behavior of their metastable states with an electron beam ion trap. The difference in the level structures between ${\mathrm{I}}^{7+}$ and ${\mathrm{Ba}}^{10+}$ arising from the configuration crossing between $4d^{-1}5p$ and $4d^{-1}4f$ around the atomic number $Z$ = 56 causes significant differences in the lifetimes of the metastable states. ${\mathrm{Ba}}^{10+}$ has several long-lived levels $(>{10}^{-3} \mathrm{s})$ in the electron configurations $4d^{-1}5s$ and $4d^{-1}4f$, whereas the lifetime of the same $4d^{-1}4f$ levels in ${\mathrm{I}}^{7+}$ is much shorter due to the appearance of deexcitation channels to a lower energy level in $4d^{-1}5p$. The extreme ultraviolet spectra identified through comparison with theoretical simulations based on a collisional-radiative model evince the level crossing between the $4d^{-1}5p$ and $4d^{-1}4f$ configurations in ${\mathrm{Ba}}^{10+}$. Additionally, we investigate the ionization processes from the metastable states in palladium-like ions by observing the electron energy dependence of the prominent visible line $(4d^{-1}:{{}^2\mathrm{D}}_{5/2}\text{−}{{}^2\mathrm{D}}_{3/2})$ of rhodium-like ${\mathrm{I}}^{8+}$ and ${\mathrm{Ba}}^{11+}$. The electron energy dependencies reflecting the properties of the metastable states show a difference between iodine and barium, which can be explained by the populations of the metastable states calculated with theoretical simulations.

We present the possibility of spin-dependent Kapitza-Dirac scattering based on a two-photon interaction only. The interaction scheme is inspired from a Compton scattering process, for which we explicitly show the mathematical correspondence to the spin dynamics of an electron diffraction process in a standing light wave. The spin effect has the advantage that it already appears in a Bragg scattering setup with arbitrary low field amplitudes, for which we have estimated the diffraction count rate in a realistic experimental setup at available x-ray free-electron laser facilities.

Ultracold collisions of LiO molecules in the ${}^2{\mathrm{\Pi }}_{3/2}$ ground state are considered, under the influence of either an external magnetic or electric field. Inelastic collisions are shown to be suppressed in the presence of modest laboratory-strength magnetic and electric fields. The rate of elastic collisions that rethermalize the thermal distribution and the corresponding low rate of heating state-changing collisions suggest that quantum degeneracy or even molecular Bose-Einstein condensation of LiO gas may be attainable, provided that the initial temperatures in the millikelvin range are achievable.

We construct a class of Hamiltonians that describe the photodetection process from beginning to end. Our Hamiltonians describe the creation of a photon, how the photon travels to an absorber (such as a molecule), how the molecule absorbs the photon, and how the molecule after irreversibly changing its configuration triggers an amplification process—at a wavelength that may be very different from the photon's wavelength—thus producing a macroscopic signal. We use a simple prototype Hamiltonian to describe the single-photon detection process analytically in the Heisenberg picture, which neatly separates desirable from undesirable effects. Extensions to more complicated Hamiltonians are pointed out.