The differential cross section of double bremsstrahlung (emission of two photons) from high-energy electron in the electric field of heavy atoms is derived. The results are obtained with the exact account of the atomic field by means of the quasiclassical approximation to the wave functions and the Green's function in the external field. It is shown that the Coulomb corrections to the differential cross section (the difference between the exact result and the result obtained in the leading Born approximation) correspond to small momentum transfers. The Coulomb corrections to the differential cross section of double bremsstrahlung are accumulated in the factor, which coincides with the corresponding factor in the differential cross section of single bremsstrahlung. At small momentum transfer, the Coulomb corrections to the differential cross section are very sensitive to the parameters of screening while the Coulomb corrections to the cross section integrated over the momentum transfer have the universal form.

We present a quantum password checking protocol where secrecy is protected by the laws of quantum mechanics. The passwords are encoded in quantum systems that can be compared but have a dimension too small to allow reading the encoded bits. We study the protocol under different replay attacks and show it is robust even for poorly chosen passwords. We also describe a possible implementation with conventional optical elements.

We quantify the amount of correlation generated between two different output modes in imperfect cloning and deletion processes. We use three different measures of quantum correlations and investigate their role in determining the fidelity of cloning and deletion. We obtain a bound on the total correlation generated in the successive processes of cloning and deleting operations. This bound displays a different kind of complementary relationship between the quantum correlations required in generating a copy of a quantum state and the amount of correlation required to bring it back to the original state by deleting and vice versa. Our result shows that the better we clone (delete) a state, the more difficult it will be to bring the state back to its original form by the process of deleting (cloning).

We consider unambiguous discrimination of three pure quantum states. Necessary and sufficient conditions to decide which states should be detected for optimal measurement of unambiguous discrimination are provided in terms of inner products and the geometric phase $\mathrm{\Phi }$. We get the optimal measurement and the optimal failure probability when the optimal unambiguous discrimination does not require the detection of every given quantum state. When at least two quantum states are orthogonal to each other, we supply the optimal measurement and optimal failure probability in analytic form. When all three quantum states are not orthogonal to each other and $\mathrm{\Phi }\ne 0$, we find an analytic condition to determine the zero and nonzero elements for an optimal positive operator valued measure. We explain how to determine the solution in a geometric manner. Using the known solution of a case where the mutual inner products are real, we check the necessary and sufficient conditions when $\mathrm{\Phi }=\pi$ and analyze the property of the singular point when $\mathrm{\Phi }=0$ and the relation between the optimal points.

A formulation of a multiconfiguration time-dependent Hartree-Fock (MCTDHF) method with nuclear motion is tested by application to a three-body breakup problem, the dissociative photoionization cross section of the ${\mathrm{H}}_2^{+}$ ion. The representation of the wave function in terms of a set of Slater determinants used for all nuclear geometries, with a prescribed parametric dependence upon the nuclear geometry such that the cusps follow the nuclei, times a complete basis expansion in the nuclear degrees of freedom shows promise as a method for treating nonadiabatic electronic and nuclear motion in molecules. However, the method used here for diatomics, in which the parametric dependence is prescribed through the choice of prolate spheroidal coordinates, produces qualitatively incorrect steplike behavior in the calculated cross section near onset. Modifications to the prolate spheroidal coordinate system that would improve this nonadiabatic diatomic MCTDHF representation are proposed.

We develop the complex-scaled multiconfigurational spin-tensor electron propagator (CMCSTEP) technique for the theoretical determination of resonance parameters with electron-atom–molecule systems including open-shell and highly correlated (nondynamical correlation) atoms and molecules. The multiconfigurational spin-tensor electron propagator method developed and implemented by Yeager and his coworkers in real space gives very accurate and reliable ionization potentials and electron affinities. The CMCSTEP method uses a complex-scaled multiconfigurational self-consistent field state as an initial state along with a dilated Hamiltonian where all of the electronic coordinates are scaled by a complex factor. We apply the CMCSTEP and the related ${\text{M}}_1$ methods to get the ${\text{B}}^{-}$ shape resonance parameters using $14s11p$ and $14s11p5d$ basis sets with $1s2s2p3s$, $1s2s2p3s3p$, $1s2s2p3d$, $2s2p3s3p$, $2s2p3d$, and $2s2p3s3p3d$ complete active spaces. The CMCSTEP and ${\text{M}}_1$ resonance positions and widths are obtained for the $1s^{2}2s^{2}2p^2{}^{1}D$, $1s^{2}2s2p^3{}^{3}D$, and $1s2s^{2}2p^3{}^{3}D$, ${}^{3}S$, and ${}^{3}P$ shape resonances.

For the Casimir piston filled with an inhomogeneous medium, we regularized and expressed the Casimir energy with cylinder kernel coefficients by using the first-order perturbation theory. When the refractive index of the medium is smoothly inhomogeneous (i.e., derivatives of all orders exist), a logarithmically cutoff-dependent term and a quadratically cutoff-dependent term in the Casimir energy are found. We show that in the piston model these terms vanish in the force and thus the Casimir force is always cutoff independent, but these terms will remain in the force in the half-space model and must be removed by additional regularizations. We give explicit benchmark solutions to the first-order corrections of both Casimir energy and Casimir force for an exponentially decaying profile. The present method can be extended to other inhomogeneous profiles. Our results should be useful for future relevant calculations and experimental studies.

The generalized Klein-Nishina formula for Compton scattering of charged particles by a finite train of pulses is derived in the framework of quantum electrodynamics. The formula also applies to classical Thomson scattering provided that frequencies of generated radiation are smaller that the cutoff frequency. The validity of the formula for incident pulses of different durations is illustrated by numerical examples. The positions of the well-resolved Compton peaks, with the clear labeling by integer orders, opens up the possibility of the precise diagnostics of properties of relativistically intense, short laser pulses. This includes their peak intensity, the carrier-envelope phase, and their polarization properties.

The implementation of weak-value amplification requires the pre- and postselection of states of a quantum system, followed by the observation of the response of the meter, which interacts weakly with the system. Data acquisition from the meter is conditioned to successful postselection events. Here we derive an optimal postselection procedure for estimating the coupling constant between system and meter and show that it leads both to weak-value amplification and to the saturation of the quantum Fisher information, under conditions fulfilled by all previously reported experiments on the amplification of weak signals. For most of the preselected states, full information on the coupling constant can be extracted from the meter data set alone, while for a small fraction of the space of preselected states, it must be obtained from the postselection statistics.

Optimal control theory is a powerful tool for improving figures of merit in quantum information tasks. Finding the solution to any optimal control problem via numerical optimization depends crucially on the choice of the optimization functional. Here, we derive a functional that targets the full set of two-qubit perfect entanglers, gates capable of creating a maximally entangled state out of some initial product state. The functional depends on easily computable local invariants and unequivocally determines whether a gate is a perfect entangler. Optimization with our functional is most useful if the two-qubit dynamics allows for the implementation of more than one perfect entangler. We discuss the reachable set of perfect entanglers for a generic Hamiltonian that corresponds to several quantum information platforms of current interest.

The difficulty of an optimization task in quantum information science depends on the proper mathematical expression of the physical target. Here we demonstrate the power of optimization functionals targeting an arbitrary perfect two-qubit entangler, which allow generation of a maximally entangled state from some initial product state. We show for two quantum information platforms of current interest, i.e., nitrogen vacancy centers in diamond and superconducting Josephson junctions, that an arbitrary perfect entangler can be reached faster and with higher fidelity than both specific two-qubit gates and local equivalence classes of two-qubit gates. Our results are obtained using two independent optimization approaches, underscoring the critical role of the optimization target.

We consider the problem of constructing a “universal set” of Markovian processes, such that any Markovian open quantum system, described by a one-parameter semigroup of quantum channels, can be simulated through sequential simulations of processes from the universal set. In particular, for quantum systems of dimension $d$, we explicitly construct a universal set of semigroup generators, parametrized by $d^2-3$ continuous parameters, and prove that a necessary and sufficient condition for the dynamical simulation of a $d$-dimensional Markovian quantum system is the ability to implement (a) quantum channels from the semigroups generated by elements of the universal set of generators, and (b) unitary operations on the system. Furthermore, we provide an explicit algorithm for simulating the dynamics of a Markovian open quantum system using this universal set of generators, and show that it is efficient, with respect to this universal set, when the number of distinct Lindblad operators (representing physical dissipation processes) scales polynomially with respect to the number of subsystems.

Current quantum computing architectures lack the size and fidelity required for universal fault-tolerant operation, limiting the practical implementation of key quantum algorithms to all but the smallest problem sizes. In this work we propose an alternative method for general-purpose quantum computation that is ideally suited for such “prethreshold” superconducting hardware. Computations are performed in the $n$-dimensional single-excitation subspace (SES) of a system of $n$ tunably coupled superconducting qubits. The approach is not scalable, but allows many operations in the unitary group SU($n$) to be implemented by a single application of the Hamiltonian, bypassing the need to decompose a desired unitary into elementary gates. This feature makes large, nontrivial quantum computations possible within the available coherence time. We show how to use a programmable SES chip to perform fast amplitude amplification and phase estimation, two versatile quantum subalgorithms. We also show that an SES processor is well suited for Hamiltonian simulation, specifically simulation of the Schrödinger equation with a real but otherwise arbitrary $n\times n$ Hamiltonian matrix. We discuss the utility and practicality of such a universal quantum simulator, and propose its application to the study of realistic atomic and molecular collisions.

We examine the instantaneous ionization amplitudes and instantaneous ionization rates for the process of tunneling ionization. We show that the endpoint contribution usually neglected in the asymptotic evaluation of the amplitudes, may be significant. For weak fields the instantaneous ionization rate is largely defined by this contribution. For higher field strengths of the order of 0.1 a.u., the account of this contribution allows one to reproduce numerically computed instantaneous ionization rates with higher accuracy.

We use Floquet theory to study the maximum value of the stroboscopic group velocity in a one-dimensional tight-binding model subjected to an on-site staggered potential varying sinusoidally in time. The results obtained by numerically diagonalizing the Floquet operator are analyzed using a variety of analytical schemes. In the low-frequency limit we use adiabatic theory, while in the high-frequency limit the Magnus expansion of the Floquet Hamiltonian turns out to be appropriate. When the magnitude of the staggered potential is much greater or much less than the hopping, we use degenerate Floquet perturbation theory; we find that dynamical localization occurs in the former case when the maximum group velocity vanishes. Finally, starting from an “engineered” initial state where the particles (taken to be hard-core bosons) are localized in one part of the chain, we demonstrate that the existence of a maximum stroboscopic group velocity manifests in a light-cone-like spreading of the particles in real space.

The Riemann hypothesis, which states that the nontrivial zeros of the Riemann zeta function all lie on a certain line in the complex plane, is one of the most important unresolved problems in mathematics. We propose here an approach to finding a physical system to study the Riemann zeros, which is based on applying a time-periodic driving field. This driving allows us to tune the quasienergies of the system (the analog of the eigenenergies for static systems), so that they are directly governed by the zeta function. We further show by numerical simulations that this allows the Riemann zeros to be measured in currently accessible cold-atom experiments.

We obtain the band structure of a particle moving in a magnetic spin texture, classified by its chirality and structure factor, in the presence of spin-orbit coupling. This rich interplay leads to a variety of novel topological phases characterized by the Berry curvature and their associated Chern numbers. We suggest methods of experimentally exploring these topological phases by Hall drift measurements of the Chern number and Berry phase interferometry to map the Berry curvature.

We describe the enhanced magnetic transition temperatures $T_c$ of two-component fermions in three-dimensional layered Lieb lattices, which are created in cold-atom experiments. We determine the phase diagram at half filling using the dynamical mean-field theory. The dominant mechanism of enhanced $T_c$ gradually changes from the ($\delta$-functional) flat-band to the (logarithmic) Van Hove singularity as the interlayer hopping increases. We elucidate that the interaction induces an effective flat-band singularity from a dispersive flat (or narrow) band. We offer a general analytical framework for investigating the singularity effects, where a singularity is treated as one parameter in the density of states. This framework provides a unified description of the singularity-induced phase transitions, such as magnetism and superconductivity, where the weight of the singularity characterizes physical quantities. This treatment of the flat-band provides the transition temperature and magnetization as a universal form (i.e., including the Lambert function). We also elucidate a specific feature of the magnetic crossover in magnetization at finite temperatures.

We report experimental bifurcation diagrams of a semiconductor laser, biased well above threshold, subjected to external optical feedback. As feedback is increased, we see a quasiperiodic route to chaos interrupted by several windows of periodicity corresponding to limit cycles, differing in frequency by multiples of the external-cavity free-spectral range that have developed around external-cavity modes (ECMs) whose frequency is slightly larger than that of the solitary laser. Successive windows correspond to the transition between two limit cycles either on the same or neighboring ECMs. For larger feedback, the laser operates in a chaotic regime around numerous negatively shifted external-cavity modes. These experimental observations detail the bifurcations leading to fully developed chaos in this system, and further provide detailed insight on the standard theoretical framework applied to these lasers.

We study quantum phase transitions in non-Hermitian XY and transverse-field Ising spin chains, in which the non-Hermiticity arises from the imaginary magnetic field. Analytical and numerical results show that at exceptional points, coalescing eigenstates in these models are close to W, distant Bell, and GHZ states, which can be steady states in the dynamical preparation scheme proposed by Lee et al. [T. E. Lee et al., Phys. Rev. Lett. 113, 250401 (2014)]. By selecting proper initial states, numerical simulations demonstrate the time evolution process to the target states with high fidelity.