A method for calculating ion-atom ionizing collisions is formulated and applied to single ionization of helium induced by energetic proton impact. Within the frozen-core model for the residual helium ion, the four-body problem in the exit channel is recast as an inhomogeneous Schrödinger equation for the Coulomb three-body system $(e^{-},{\text{He}}^{+},p^{+})$. The asymptotic behavior of its solution contains the transition amplitude. We suggest to solve the driven equation in the representation of so-called parabolic convoluted quasi-Sturmian (CQS) basis functions which are constructed using quasi-Sturmians (QSs) for the $(e^{-},{\text{He}}^{+})$ and $(p^{+},{\text{He}}^{+})$ subsystems. By applying the corresponding Coulomb Green's function operators, these QSs are generated from orthogonal complements to square-integrable ($L^2$) Sturmian functions in parabolic coordinates. In the proposed parabolic CQS approach explicit asymptotic expressions for the basis functions provide an expansion of the transition amplitude in terms of “basis amplitudes,” which we express analytically. The proton-electron interaction is treated as a perturbation and is approximated by a truncated Sturmian basis-set expansion. It is found that, at least in the high-energy limit, the ionization amplitude converges pretty fast as the number of terms in the separable expansion for the proton-electron potential is increased. The calculated fully differential cross sections for singly ionizing 1-MeV $p$-He collisions in several kinematical regimes in the scattering plane are found to be in reasonable agreement with experimental data and with the theoretical results obtained using the first Born approximation, the 3C model, and the wave-packet convergent close-coupling method. The theory-experiment discrepancy over the binary peak position observed by other authors remains unexplained.

A study of Cooper minima (CM) arising from the photoionization of $6s$, 5s, and $4s$ subshells of high-$Z$ atoms has been performed using Dirac-Fock (DF), two-channel relativistic-random-phase approximation (RRPA), and fully coupled RRPA. The results show huge splittings between $ns\to \varepsilon p_{3/2}$ and $\mathrm{ns}\to \varepsilon p_{1/2}$ CM which increase with $Z$ owing primarily to the relativistic interactions (spin orbit) that are attractive for the $\varepsilon p_{1/2}$ final state but repulsive for the corresponding $\varepsilon p_{3/2}$. In addition, it was found that correlation in the form of interchannel coupling (essentially configuration interaction in the final continuum states) plays a huge role in determining the location of the CM. For $6s$ photoionization, the $6s\to \varepsilon p_{3/2}$ and $6s\to \varepsilon p_{1/2}$ CM behave completely different as a function of $Z$. It was also found that for $5s$ and $4s$ photoionization, the CM move below the threshold, with increasing $Z$, and, at high enough $Z$, the $5s\to \varepsilon p_{3/2}$ and $4s\to \varepsilon p_{3/2}$ CM re-emerge into the continuum. The calculations have been carried out for the $ns$ subshells of Hg ($Z=80$), Rn ($Z=86$), Ra ($Z=88$), No ($Z=102$), Cn ($Z=112$), and Og ($Z=118$).

Generating a spin vortex in a ${}^{87}\mathrm{Rb}$ dipolar spinor Bose-Einstein condensate in a controllable way is still experimentally challenging. We propose an experimentally easy and tunable way to produce a spin vortex by varying the potential barrier height and the width of an additionally applied optical plug. A topological phase transition occurs from the trivial single-mode approximation phase to the optical-plug-assisted-vortex one, as the barrier height increases and the width lies in an appropriate range. The optical plug causes radial density variation and thus the spin vortex is favored by significantly lowering the intrinsic magnetic dipolar energy. A type of coreless spin vortex, different from the conventional polar core vortex, is predicted by our numerical results. Our proposal removes a major obstacle to investigating the topological phase transition in a ${}^{87}\mathrm{Rb}$ dipolar spinor Bose-Einstein condensate.

We study the existence, stability, and dynamics of vortex dipole and quadrupole configurations in the nonlinear Schrödinger (NLS) equation on the surface of a torus. For this purpose we use, in addition to the full two-dimensional NLS equation on the torus, a recently derived [N.-E. Guenther et al., Phys. Rev. A 101, 053606 (2020)] reduced point-vortex particle model which is shown to be in excellent agreement with the full NLS equation evolution. Horizontal, vertical, and diagonal stationary vortex dipoles are identified and followed, using parameter continuation, along the torus aspect ratio and the chemical potential of the solution. Windows of stability for these solutions are identified. We also investigate stationary vortex quadrupole configurations. After eliminating similar solutions induced by invariances and symmetries, we find a total of 16 distinct configurations ranging from horizontally and vertically aligned quadrupoles to rectangular and rhomboidal quadrupoles to trapezoidal and irregular quadrupoles. The stability for the least unstable and, potentially, stable quadrupole solutions is monitored at both the NLS equation and the reduced model levels. Two quadrupole configurations are found to be stable on small windows of the torus aspect ratio and a handful of quadrupoles are found to be very weakly unstable for relatively large parameter windows. Finally, we briefly study the dark-soliton stripes and their connection, through a series of bifurcation cascades, with steady-state vortex configurations.

When a quantum system is coupled to two thermal baths at different temperatures, the temperature gradient as a thermodynamic force causes stationary heat flow within the system. We present a theoretical model to study how quantum features of squeezed thermal reservoirs affect the classical formulation of entropy production in terms of generalized forces and flows. Applying the quantum phase-space method to calculate Wigner entropy production helps us identify heat and squeezing fluxes and their corresponding generalized forces in terms of input-noise correlations of both reservoirs. Our study highlights the essential role played by the correlation of the input-noise operators of the thermal squeezed bath, which are asymmetric (squeezed and unsqueezed) and far from thermal equilibrium. Using the framework for an optomechanical system, we find the regime in which heat flows from the cold squeezed thermal bath to the hot thermal bath without violating the second law of thermodynamics and the regime in which entropy production is purely a quantum-mechanical effect. The results can be useful for improving the performance of Gaussian heat engines operating with squeezed thermal reservoirs.

Chiral coupling between quantum emitters and evanescent fields allows directional emission into nanophotonic devices and is now considered to be a vital ingredient for the realization of quantum networks. However, such coupling requires a well-defined circular dipole moment for the emitter—something difficult to achieve for solid-state emitters at room temperature due to thermal population of available spin states. Here, we demonstrate that a two-level emitter with a randomly polarized dipole moment can be made to emit directionally into a circulating cavity if a separate emitter is chirally coupled to the same cavity, for the case when both emitter-cavity couplings are strong but in the bad-cavity regime. Our analysis of this system first considers a transient scenario, which highlights the physical mechanism giving rise to the directional emission of the two-level emitter into the cavity. An alternative setup involving a weak laser field continuously driving the system is also considered, where the directionality (our proposed figure of merit for this scheme) is shown to be significantly more robust against noise processes. The results presented here take the form of approximate analytical expressions backed by complete numerical simulations of the system.

We introduce a theory of quantum error correction (QEC) for a subclass of states. In the standard theory of QEC, the set of all encoded states is formed by an arbitrary linear combination of the codewords. However, this can be more general than required for a given quantum protocol which may only traverse a subclass of states within the Hilbert space. Here we propose the concept of nonlinear QEC (NLQEC), where the encoded states are not necessarily a linear combination of codewords. We introduce a sufficiency criterion for NLQEC with respect to the subclass of states. The new criterion gives a more relaxed condition for the formation of a QEC code, such that under the assumption that the states are within the subclass of states, the errors are correctable. This allows us, for instance, to effectively circumvent the no-go theorems regarding optical QEC for Gaussian states and channels, for which we present explicit examples.

We demonstrate the use of matrix product state (MPS) models for discriminating quantum data on quantum computers using holographic algorithms, focusing on the problem of classifying a translationally invariant quantum state based on $L$ qubits of quantum data extracted from it. We detail a process in which data from single-shot experimental measurements are used to optimize an isometric tensor network, the isometric tensors are compiled into unitary quantum operations using greedy compilation heuristics, parameter optimization on the resulting quantum circuit model removes the postselection requirements of the isometric tensor model, and the resulting quantum model is inferenced on either product state (single-shot measurement) or entangled quantum data. We demonstrate our training and inference architecture on a synthetic dataset of six-site single-shot measurements from the bulk of a one-dimensional transverse field Ising model (TFIM) deep in its antiferromagnetic and paramagnetic phases. We find that increasing the bond dimension of the tensor-network model, amounting to adding more ancilla qubits to the circuit representation, improves both the average number of correct classifications across the dataset and the single-shot probability of correct classification. We experimentally evaluate models on Quantinuum's H1-2 trapped ion quantum computer using entangled input data modeled as translationally invariant, bond dimension 4 MPSs across the known quantum phase transition of the TFIM. Using linear regression on the experimental data near the transition point, we find predictions for the critical transverse field of $h=0.962$ and 0.994 for tensor-network discriminators of bond dimension $\chi =2$ and $\chi =4$, respectively. These predictions compare favorably with the known transition location of $h=1$ despite training on data far from the transition point. Our techniques identify families of short-depth variational quantum circuits in a data-driven and hardware-aware fashion and robust classical techniques to precondition the model parameters, and can be adapted beyond machine learning to myriad applications of tensor networks on quantum computers, such as quantum simulation and error correction.

We consider a single slight protuberance in a perfectly conducting plane and investigate the van der Waals (vdW) interaction between this surface and a neutral polarizable particle. When the protuberance is sufficiently smooth that the proximity force approximation (PFA) is well applicable, for a fixed distance of the particle from the plane, the lateral vdW force always points to the protuberance. On the other hand, by making calculations valid beyond the PFA, we show that nontrivial geometric effects arise when we consider an anisotropic particle and manipulate the ratio between the characteristic widths of the protuberance and the fixed particle-plane distance. We predict that, as this ratio decreases, a sign inversion in the lateral vdW force can occur in the sense that, instead of pointing to the protuberance, in certain situations the lateral force points in the opposite direction. Moreover, we show that even when such a sign inversion in the lateral vdW force does not occur for a single protuberance, it can arise when two or more protuberances are put together, distinguishing between sign inversions originated by individual or collective effects. In addition, we show that all these effects have their classical counterparts, involving a neutral particle with a permanent electric dipole moment. The prediction of such geometric effects on the lateral vdW force may be relevant for better controlling the interaction between a particle and a corrugated surface in classical and quantum physics.

The experimental generalized oscillator strengths (GOSs) for the valence-shell excitations of heavy water in 6.50–12.17 eV are determined by fast electron scattering with an incident electron energy of 1500 eV and an energy resolution of 80 meV. The experimental data of the $\tilde{A}{}^1{B}_1\leftarrow \tilde{X}{}^1{A}_1$ transition between ${\mathrm{H}}_2\mathrm{O}$ and ${\mathrm{D}}_2\mathrm{O}$ show significant discrepancies around the minimum, and further theoretical calculations with nuclear effects accounted are recommended. The comparisons of the present GOSs of $\tilde{A}{}^1{B}_1\leftarrow \tilde{X}{}^1{A}_1$ and $\tilde{B}{}^1{A}_1\leftarrow \tilde{X}{}^1{A}_1$ transitions in ${\mathrm{D}}_2\mathrm{O}$ with theoretical calculations within the first Born approximation and the second Born approximation indicate that the higher Born terms become prominent at large momentum transfers. In particular, the GOSs of the dipole-forbidden transition ${}^1{A}_2\leftarrow \tilde{X}{}^1{A}_1$ are extracted, benefiting from the present high-energy electron scattering, where most of electronic dipole-forbidden transitions are not involved. By extrapolating the GOSs to the zero momentum transfer, the optical oscillator strengths for the corresponding dipole-allowed transitions are determined, which provide an independent cross-check for previous optical measurements. Moreover, the integral Born cross sections are scaled to an accurate level with the aid of the binding energy–excitation energy–scaling method. The relevant experimental data in this work can supplement the molecular database with electron collision data involving heavy water.

Tunneling ionization of an atom in ultrashort laser pulses is considered. When the driving laser pulse is switched on and off with a steep slope, the photoelectron momentum distribution (PMD) shows an edge effect because of the photoelectron diffraction by the time slit of the pulse. The trivial diffraction pattern of the edge effect consisting of fast oscillations in the PMD disguises in the deep nonadiabatic regime the physically more interesting features in the spectrum, which originate from the photoelectron dynamics. We point out the precise conditions for how to avoid this scenario experimentally, and if unavoidable in theory we put forward an efficient method to remove the edge effect in the PMD. This allows us to highlight the nonadiabatic dynamical features of the PMD, which will be indispensable in additional investigations in complex computationally demanding scenarios. The method is first demonstrated with a one-dimensional problem, and further applied in three dimensions for the attoclock. The method is validated by a comparison of analytical results via the strong-field approximation with numerical solutions of the time-dependent Schrödinger equation.

Since the idea of quantum turbulence was first proposed by Feynman and later realized in experiments of superfluid helium and Bose-Einstein condensates, much emphasis has been put on finding signatures that distinguish quantum turbulence from its classical counterpart. Here we show that quantum turbulence in rotating condensates is fundamentally different from the classical case. While rotating quantum turbulence develops a negative temperature state with self-organization of the kinetic energy in quantized vortices, it also displays an anisotropic dissipation mechanism and a different, non-Kolmogorovian, scaling of the energy at small scales. This scaling is compatible with Vinen turbulence and also has been found in recent simulations of condensates with multicharged vortices. An elementary explanation for the scaling is presented in terms of disorder in the vortices positions.

Obtaining effective spontaneous radiative transition channels is a fundamental topic in the preparation of ultracold rovibrational ground states of molecules. Herein, the ranges of prospective transition channels in the NaCs dimer are predicted via exploring the complex energy level structure and transition properties. The potential energy curves of Λ-$S$ states and Ω states, spectroscopy constants, absolute energies of bound states, and transition information (Frank-Condon factors, lifetimes, transition dipole moments) have been researched. With this purpose, the results of our experiment on binding energies of the $b^3{\mathrm{\Pi }}_0{}^{+}$ rovibrational states are analyzed; the transition from the higher (photoassociated) ${}^1\mathrm{\Pi }$ state to the ground $X^1{\mathrm{\Sigma }}^{+}$ state is discussed. The wavelengths of the two lasers are predicted as 622.8-656.7 nm and 896.3-969.8 nm with the $B^1{\mathrm{\Pi }}_1$ and $c^3{\mathrm{\Sigma }}_1^{+}$ states, respectively, for the stimulated raman adiabatic passage method.

We consider a particle governed by a one-dimensional Hamiltonian in which artificial periodic spin-orbit coupling and the Zeeman lattice have incommensurate periods. Using the best rational approximations to such a quasiperiodic Hamiltonian, the problem is reduced to a description of spinor states in a superlattice. In the absence of constant Zeeman splitting, the system acquires an additional symmetry, which hinders the localization. However, if the lattices are deep enough, then localized states can appear even for Zeeman field with a zero or small mean value. Spatial distribution of localized modes is nearly uniform and is directly related to the topological properties of the effective superlattice: center-of-mass coordinates of modes are determined by Zak phases computed from the superlattice band structure. The best rational approximations feature the “memory” effect: Each rational approximation holds the information about the energies and spatial distribution of the modes obtained under preceding, less accurate approximations. Dispersion of low-energy initial wave packets is characterized by the law $\propto t^{\beta }$, with $\beta$ varying between $1/2$ at the initial stage and 1 at longer, but still finite-time, evolution. The dynamics of initial wave packets, exciting mainly localized modes, manifests quantum revivals.

We investigate theoretically macroscopic quantum coherence and tripartite entanglement in a three-mode magnomechanical system with a yttrium iron garnet sphere, which is simultaneously driven by a magnetic pump and a microwave field pump to establish an effective magnomechanical coupling. We discuss mainly the dependence of quantum properties on the driving power, the cavity field detuning and decay, the magnomechanical coupling strength, the bias magnetic field, and the temperature of an environment. It is found that the quantum coherence of the system can be attained easily in a large range of parameters. In contrast, tripartite photon-magnon-phonon entanglement can only be realized in a relatively small range of optical and magnetic parameters. In particular, the quantum coherence of the mechanical mode can be larger than that of the photon and magnon modes, which means that the environmental incoherence of the mechanical mode in the cavity magnomechanical system can be suppressed significantly. These results may help manipulate simultaneously the macroscopic quantum coherence and the tripartite entanglement of massive objects in coupled magnomechanical system, which may have potential applications for realizing highly tunable information processing through the flexible control of quantum properties.

Zitterbewegung of massless particles with an arbitrary spin is analyzed in various representations. Dynamics of the group velocity of a massless particle as a whole and of the corresponding radius vector is determined. This radius vector defines any fixed point of the envelope of the moving wave packet characterizing the particle and its group velocity differs from the group velocities of any points of the wavefront. We consider free massless scalar and Dirac particles, the photon, and massive and massless particles with an arbitrary spin and describe them in different representations. For particles with an arbitrary spin, the generalized Feshbach-Villars representation and the Foldy-Wouthuysen one are used. Zitterbewegung takes place in any representation except for the Foldy-Wouthuysen one. Formulas describing the motion of a “trembling” free particle are the same in any representation. In the Foldy-Wouthuysen representation, the operators of the velocity and momentum of a free particle are proportional and Zitterbewegung does not take place. Since the radius vector (position) and velocity operators are the quantum-mechanical counterparts of the classical position and velocity just in the Foldy-Wouthuysen representation, Zitterbewegung is not observable. The same conclusion has been previously made for free massive particles. For relativistic massive particles with spins 0, 1/2, 1 and massless particles with spins 0, 1/2 in arbitrarily strong electromagnetic fields, independent of the external fields Zitterbewegung does not appear in the Foldy-Wouthuysen representation either. This conclusion is made for leading terms in the Hamiltonian proportional to the zero and first powers of the Planck constant and for such terms proportional to ${\hslash }^2$ which describe contact interactions.

Compared with entanglement with multiple types of noise, entanglement including only one type of error is a favorable fundamental resource not only for quantum communication but also for distributed quantum computation. We consider protocols that present single-error-type entanglement for distant qubits via coherent-state transmission over a lossy channel. Such a protocol is regarded as a subroutine to serve entanglement for larger protocol to yield a final output, such as ebits or pbits. In this paper, we provide a subroutine protocol which achieves the global optimal for typical jointly convex yield functions monotonically nondecreasing with respect to the singlet fraction, such as an arbitrary convex function of a singlet fraction, two-way distillable entanglement, and two-way distillable key. Entanglement generation based on remote nondestructive parity measurement protocol [K. Azuma et al., Phys. Rev. A 85, 062309 (2012)] is identified as such an optimal subroutine.

Constructing optimal thermodynamic processes in quantum systems relies on managing the balance between the average excess work and its stochastic fluctuations. Recently it has been shown that two different quantum generalizations of thermodynamic length can be utilized to determine protocols with either minimal excess work or minimal work variance. These lengths measure the distance between points on a manifold of control parameters, and optimal protocols are achieved by following the relevant geodesic paths given some fixed boundary conditions. Here we explore this problem in the context of Gaussian quantum states that are weakly coupled to an environment and derive general expressions for these two forms of thermodynamic length. We then use this to compute optimal thermodynamic protocols for various examples of externally driven Gaussian systems with multiple control parameters.

The protocol of quantum annealing is applied to an optimization problem with a one-dimensional continuous degree of freedom, a variant of the problem proposed by Shinomoto and Kabashima. The energy landscape has a number of local minima, and the classical approach of simulated annealing is predicted to have a logarithmically slow convergence to the global minimum. We show by extensive numerical analyses that quantum annealing yields a power-law convergence, thus an exponential improvement over simulated annealing. The power is larger, and thus the convergence is faster, than a prediction by an existing phenomenological theory for this problem. Performance of simulated annealing is shown to be enhanced by introducing quasiglobal searches across energy barriers, leading to a power-law convergence but with a smaller power than in the quantum case and thus a slower convergence classically even with quasiglobal search processes. We also reveal how diabatic quantum dynamics, quantum tunneling in particular, steers the systems toward the global minimum by a meticulous choice of annealing schedule. This latter result explicitly contrasts the role of tunneling in quantum annealing against the classical counterpart of stochastic optimization by simulated annealing.

Hybrid quantum gates have recently drawn considerable attention. They play significant roles in connecting quantum information processors with qubits of different encoding and have important applications in the transmission of quantum states between a quantum processor and a quantum memory. In this work, we propose a single-step implementation of a multitarget-qubit controlled-not gate with one superconducting (SC) qubit simultaneously controlling $n$ target cat-state qubits. In this proposal, the gate is implemented with $n$ microwave cavities coupled to a three-level SC qutrit. The two logic states of the control SC qubit are represented by the two lowest levels of the qutrit, while the two logic states of each target cat-state qubit are represented by two quasi-orthogonal cat states of a microwave cavity. This proposal operates essentially through the dispersive coupling of each cavity with the qutrit. The gate realization is quite simple because it requires only a single-step operation. There is no need of applying a classical pulse or performing a measurement. The gate operation time is independent of the number of target qubits, thus it does not increase as the number of target qubits increases. Moreover, because the third higher energy level of the qutrit is not occupied during the gate operation, decoherence from the qutrit is greatly suppressed. As an application of this hybrid multitarget-qubit gate, we further discuss the generation of a hybrid Greenberger-Horne-Zeilinger (GHZ) entangled state of SC qubits and cat-state qubits. As an example, we numerically analyze the experimental feasibility of generating a hybrid GHZ state of one SC qubit and three cat-state qubits within present circuit QED technology. This proposal is quite general and can be extended to implement a hybrid controlled-not gate with one matter qubit (of different type) simultaneously controlling multiple target cat-state qubits in a wide range of physical systems, such as multiple microwave or optical cavities coupled to a three-level natural or artificial atom.