The dynamics of a single quantum state embedded in one continuum or several (quasi)continua is one of the most studied phenomena in quantum mechanics. In this paper we investigate its discrete analog and consider short- and long-time dynamics based on numerical and analytical solutions of the Schrödinger equation. In addition to derivation of explicit conditions for initial exponential decay, it is shown that a recent model of this class [L. Guo, A. Grimsmo, A. F. Kockum, M. Pletyukhov, and G. Johansson, Phys. Rev. A 95, 053821 (2017)], describing a qubit coupled to a phonon reservoir with energy dependent coupling parameters, is identical to a qubit interacting with a finite number of parallel regularly spaced bands of states via constant couplings. As a consequence, the characteristic near periodic initial-state revivals can be viewed as a transition of probability between different continua via the reviving initial state. Furthermore, polynomial decay of the reviving peaks is present in any system with constant and sufficiently strong coupling.

We develop an intuitive geometric picture of quantum states, define a particular state distance, and derive a quantum speed limit (QSL) for open systems. Our QSL is attainable because any initial state can be driven to a final state by the particular dynamics along the geodesic. We present the general condition for dynamics along the geodesic for our QSL. As evidence, we consider the generalized amplitude damping dynamics and the dephasing dynamics to demonstrate the attainability. In addition, we also compare our QSL with others by strict analytic processes as well as numerical illustrations, and show our QSL is tight in many cases. It indicates that our paper is significant in tightening the bound of evolution time.

The choice of mathematical representation when describing physical systems is of great consequence, and this choice is usually determined by the properties of the problem at hand. Here we examine the little-known wave operator representation of quantum dynamics and explore its connection to standard methods of quantum dynamics, such as the Wigner phase-space function. This method takes as its central object the square root of the density matrix and consequently enjoys several unusual advantages over standard representations. By combining this with purification techniques imported from quantum information, we are able to obtain a number of results. Not only is this formalism able to provide a natural bridge between phase- and Hilbert-space representations of both quantum and classical dynamics, we also find the wave operator representation leads to semiclassical approximations of both real and imaginary time dynamics, as well as a transparent correspondence to the classical limit. It is then demonstrated that there exist a number of scenarios (such as thermalization) in which the wave operator representation possesses an equivalent unitary evolution, which corresponds to nonlinear real-time dynamics for the density matrix. We argue that the wave operator provides a new perspective that links previously unrelated representations and is a natural candidate model for scenarios (such as hybrids) in which positivity cannot be otherwise guaranteed.

We present and discuss a master equation blueprint for a generic class of quantum measurement-feedback-based models of friction. A desired velocity-dependent friction force is realized on average by random repeated applications of unsharp momentum measurements followed by immediate outcome-dependent momentum displacements. The master equations can describe arbitrarily strong measurement-feedback processes as well as the weak continuous limit resembling diffusion master equations of Caldeira-Leggett type. We show that the special case of linear friction can be equivalently represented by an average over random position measurements with squeezing and position displacements as feedback. In fact, the dissipative continuous spontaneous localization model of objective wave-function collapse realizes this representation for a single quantum particle. We reformulate a consistent many-particle generalization of this model and highlight the possibility of feedback-induced correlations between otherwise noninteracting particles.

We develop a general multiple scattering expansion (MSE) for computing Casimir forces between magneto-dielectric bodies and Casimir-Polder forces between polarizable particles and magneto-dielectric bodies. The approach is based on fluctuating electric and magnetic surface currents and charges. The surface integral equations for these surface fields can be formulated in terms of surface scattering operators (SSOs). We show that there exists an entire family of such operators. One particular member of this family is only weakly divergent and allows for a MSE that appears to be convergent for general magneto-dielectric bodies. We prove a number of properties of this operator, and demonstrate explicitly convergence for sufficiently low and high frequencies, and for perfect conductors. General expressions are derived for the Casimir interaction between macroscopic bodies and for the Casimir-Polder interaction between particles and macroscopic bodies in terms of the SSO, both at zero and finite temperatures. An advantage of our approach over previous scattering methods is that it does not require the knowledge of the scattering amplitude ($T$ operator) of the bodies. A number of simple examples are provided to demonstrate the use of the method. Some applications of our approach have appeared previously [T. Emig and G. Bimonte, Phys. Rev. Lett. 130, 200401 (2023)]. Here we provide additional technical aspects and details of our approach.

We present results of relativistic calculations of even-order harmonic generation from various atomic targets. The even-order harmonics appear due to the relativistic nondipole effects. We take these relativistic effects into account by using an approach based on the solution of the time-dependent Dirac equation. The spectra of the nondipole even harmonics look qualitatively similar to the spectra of the dipole harmonics obeying the same classical cutoff rule. The temporal dynamics of the formation of the nondipole harmonics is, however, distinctly different from the process of dipole harmonics formation. Even-order harmonics emission is strongly suppressed at the beginning of the laser pulse, and the emission times of the nondipole harmonics are shifted with respect to the bursts of the dipole emission. These features are partly explained by a simple modification of the classical three-step model which takes into account selection rules governing the emission of harmonic photons.

We present an experimental realization of dynamic self-trapping and nonexponential tunneling in a multistate system consisting of ultracold sodium spinor gases confined in moving optical lattices. Taking advantage of the fact that the tunneling process between different momentum states in the sodium spinor system is resolvable over a broader dynamic energy scale than previously observed in rubidium scalar gases, we demonstrate that the tunneling dynamics in the multistate system strongly depends on an interaction induced nonlinearity and is influenced by the spin degree of freedom under certain conditions. We develop a rigorous multistate tunneling model to describe the observed dynamics. Combined with our recent observation of spatially manipulated spin dynamics, these results open up prospects for alternative multistate ramps and state transfer protocols.

In a recent paper, Griffiths [Phys. Rev. A 107, 062219 (2023)] analyzed a protocol for transmission of information between two parties introduced by Salih et al. [Phys. Rev. Lett. 110, 170502 (2013)]. There is a considerable controversy about the counterfactuality of this protocol, and Griffiths suggested to resolve it by introducing a new measure of channel usage, which he called “Cost.” I argue that this measure is not appropriate because the original interaction-free measurement protocol which triggered the definition of the concept of counterfactuality is not counterfactual according to this measure.

This is a response to comments and criticisms found in the preceding Comment [Phys. Rev. A 108, 056201 (2023)] by Vaidman on the paper in Phys. Rev. A 107, 062219 (2023).

Spin dynamics in the constant homogeneous magnetic field is studied analytically and numerically in the regime when the radiative losses are strong. Analytically we treat photon emission as a continuous process, which allows us to describe system dynamics with a set of differential equations for both energy and spin of the electrons. The developed model predicts that the radiative losses significantly damps polarization buildup in the classical regime, i.e., when Lorentz invariant quantum parameter $\chi \ll 1$. The spin-resolved Monte Carlo-based algorithm for simulating spin dynamics is developed and verified. As expected, for the classical regime, the theoretical solution is in very good agreement with numerical simulations. In the strong-field QED regime $\chi >1$ the model predictions and the numerical results coincide to each other only in order of magnitude.

Quantum coherence is one of the characteristic features of quantum mechanics and underpins many quantum mysteries. To eliminate the influence of the reference basis on the coherence of a quantum state and uncover its intrinsic properties, it is common to study coherence by averaging over different reference bases. Using the metric-adjusted skew information, we explore three natural approaches to average coherence of a state: average over all orthonormal bases, average over all elements of an operator orthonormal base, and average over a complete family of mutually unbiased bases. We establish the equivalence among these three types of average coherence and interpret the unified average coherence as the coherence of a quantum state relative to a depolarizing channel. Additionally, we employ the unified average coherence to introduce a notion of quantum $f$ entropy (where $f$ is an operator monotone function associated with the metric-adjusted skew information) and demonstrate that quantum $f$ entropy possesses properties analogous to the ubiquitous von Neumann entropy. Furthermore, we illuminate some connections between quantum $f$ entropy and quasientropy, and compare $f$ entropy with von Neumann entropy, Rényi entropy, and Tsallis entropy for some typical states.

Near-term quantum devices generally suffer from shallow circuit depth and hence limited expressivity due to noise and decoherence. To address this, we propose tensor-network-assisted parametrized quantum circuits, which concatenate a classical tensor-network operator with a quantum circuit to effectively increase the circuit's expressivity without requiring a physically deeper circuit. We present a framework for tensor-network-assisted variational quantum algorithms that can solve quantum many-body problems using shallower quantum circuits. We demonstrate the efficiency of this approach by considering two examples of unitary matrix-product operators and unitary tree tensor networks, showing that they can both be implemented efficiently. Through numerical simulations, we show that the expressivity of these circuits is greatly enhanced with the assistance of tensor networks. We apply our method to two-dimensional Ising models and one-dimensional time-crystal Hamiltonian models with up to 16 qubits and demonstrate that our approach consistently outperforms conventional methods using shallow quantum circuits.

Quantum optimal control, a powerful toolbox for engineering an optimal control field modulation that most precisely implements a desired quantum operation in the best way possible, has evolved into one of the cornerstones for enabling quantum technologies. The gradient ascent pulse engineering (GRAPE) algorithm is a widely used method in quantum optimal control, which has achieved great success in different physical platforms. However, its computational complexity increases exponentially with the number of qubits, making it challenging to be implemented for large-scale quantum systems. To mitigate this issue, we present the iterative GRAPE algorithm (iGRAPE), which reduces the optimization problem into a series of lower-dimensional subproblems by incorporating disentanglement operations. Our numerical simulations on physical platforms such as nuclear magnetic resonance and superconducting quantum systems demonstrate that iGRAPE significantly enhances state preparation speed. Specifically, compared to GRAPE, iGRAPE achieves up to a five-fold acceleration in preparing Greenberger–Horne–Zeilinger states using a 12-qubit implementation, and up to a 13-fold acceleration for arbitrary state preparation with eight qubits. To further validate our findings, we conduct experimental validation of iGRAPE on a four-qubit nuclear magnetic resonance system. Overall, iGRAPE offers an efficient solution for implementing optimal control in large-scale quantum systems, holding great potential for advancing quantum technologies during the noisy intermediate-scale quantum era.

We study the electron capture-induced fragmentation of ${\mathrm{N}}_2$ molecules upon impact with ${\mathrm{Ar}}^{8+}$ projectiles at collision velocities 0.4 and 1.0 a.u. The recoil ions and the charge-changing projectiles are recorded in coincidence by combining a cold target recoil ion momentum spectrometer with a projectile final charge state analyzer. The relative contributions between projectile autoionizations and radiative decays are measured for the individual dissociation pairs. The reaction windows and corresponding final projectile states for multiple-electron capture processes are estimated using the extended classical over-the-barrier model. The various dissociation pairs' kinetic energy release (KER) is measured for the associated capture processes. For the dissociating ${\mathrm{N}}_2^{m+}(2\le m\le 6)$ molecular ions, the mean KER values shifted to higher values as capture stabilization increased. The populations of the higher KER regions are explained by the recapture of the loosely bound electrons into the target highly excited states. A simple classical capture model is employed to understand the role of the different projectile states on the KER distributions (KERDs). Our findings thus demonstrate the collision velocity dependence of the projectile's final state populations and its impact on the KERDs in the highly perturbative regime.

The dynamics of dissociative electron attachment to ethanol is experimentally investigated at the Feshbach resonance formed with incident electron energies near 9.5 eV. Highly differential laboratory-frame momentum distributions of ${\mathrm{OH}}^{-}$ fragments are measured for a series of energies spanning the resonance width, using the velocity-map-imaging technique. The ${\mathrm{OH}}^{-}$ kinetic-energy distribution indicates that the C-O breaking dissociation process could either be a three-body dissociation or a two-body dissociation with significant rovibrational excited fragments. The small, but significant, anisotropy in the ${\mathrm{OH}}^{-}$ angular distribution provides signatures of the molecular symmetry of the associated resonant state under the axial recoil approximation, which assumes the dissociation is much faster than any rotation of the dissociation axis. Within these assumptions, the 9.5-eV Feshbach resonance can be assigned to the electronic transition from the ($10a{}^{\prime }$) orbital with its ground-state $C_s$ symmetry to the empty ($4a{}^{″}$) level, involving the simultaneous electron attachment. This dynamics could be a model for C-O dissociation in larger alcohols and ethers.

Recently, the spin polarization of electrons induced by magnetic dipole radiation in a circularly polarized magnetic field was investigated [O. V. Kibis, Phys. Rev. A 105, 043106 (2022)] based on the Weisskopf-Wigner approximation. We reconsider the same subject with a more reasonable treatment of the initial magnetic field. It is found that if the electron is initially in a spin-unpolarized state, its polarization vector $\langle \mathit{\sigma }\rangle$ precesses around the $z$ axis and eventually reaches a radiation equilibrium. The corresponding stable precession frequency is the same as the external magnetic field frequency ${\omega }_0$. In particular, when ${\omega }_0$ is much larger than the magnetic field intensity $B_0, \langle {\sigma }_z\rangle$ will be close to a fixed value of about $2/3$ with time. In addition, we also analyze the influence of the parameters ${\omega }_0$ and $B_0$ on the final polarizability. The results show that there exists a parametric region where electrons can be almost fully polarized and the required time can be reduced to the order of seconds.

Approximate solitonlike out-of-phase spatiotemporal solutions for the wave field envelope in multicore fibers with weakly coupled cores in configurations of a one-dimensional $1\times N$ lattice and a square $N\times N$ lattice are found. The stability of these distributions for pulse durations greater than the critical duration is shown analytically and numerically. Numerical simulation of initially shorter pulses shows that the emission of linear dispersive waves rather quickly transforms them to the found solution with a duration about the critical one.