The certification of Bell nonlocality or quantum steering implies the use of incompatible measurements. Here we make this connection quantitative. We show how to strengthen robustness-based steering and nonlocality quantifiers in order that they give strong lower bounds to previously proposed incompatibility quantifiers. Our results can be seen from two perspectives. On the one hand, they can be used to estimate how much steering or nonlocality can be demonstrated with a given set of measurements. On the other hand, they give one-sided device-independent and device-independent ways of estimating measurement incompatibility.

The standard closed-orbit theory is extended for the photodetachment of negative ions in a time-dependent electric field. The time-dependent photodetachment rate is specifically studied in the presence of a single-cycle terahertz pulse, based on exact quantum simulations and semiclassical analysis. We find that the photodetachment rate is unaffected by a weak terahertz field, but oscillates complicatedly when the terahertz pulse gets strong enough. Three types of closed classical orbits are identified for the photoelectron motion in a strong single-cycle terahertz pulse, and their connections with the oscillatory photodetachment rate are established quantitatively by generalizing the standard closed-orbit theory to a time-dependent form. By comparing the negative hydrogen and fluorine ions, both the in-phase and antiphase oscillations can be observed, depending on a simple geometry of the contributed closed classical orbits. On account of its generality, the presented theory provides an intuitive understanding from a time-dependent viewpoint for the photodetachment dynamics driven by an external electric field oscillating at low frequency.

We study the photodetachment of an electron from the hydrogen anion due to short, high-frequency laser pulses by numerically solving the time-dependent Schrödinger equation. Simulations are performed to investigate the dependence of the photoelectron spectra on the duration, chirp, and intensity of the pulses. Specifically, we concentrate on the low-energy distributions in the spectra that result from the Raman transitions of the broadband pulses. Contrary to one-photon ionization, the low-energy distribution maintains an almost constant width as the laser bandwidth is expanded by chirping the pulses. In addition, we study the transitions of the ionization dynamics from the perturbative to the strong-field regime. At high intensities, the positions of the net one- and two-photon absorption peaks in the spectrum shift and the peaks split to multiple subpeaks due to multiphoton effects. Moreover, although the one- and two-photon peaks and low-energy distribution exhibit saturation of the ionization yields, the low-energy distribution shows relatively mild saturation.

Motional ground state cooling and internal state preparation are important elements for quantum logic spectroscopy (QLS), a class of quantum information processing. Since QLS does not require the high gate fidelities usually associated with quantum computation and quantum simulation, it is possible to make simplifying choices in ion species and quantum protocols at the expense of some fidelity. Here, we report sideband cooling and motional state detection protocols for ${}^{138}\mathrm{Ba}^{+}$ of sufficient fidelity for QLS without an extremely narrow-band laser or the use of a species with hyperfine structure. We use the two $S_{1/2}$ Zeeman sublevels of ${}^{138}\mathrm{Ba}^{+}$ to Raman sideband cool a single ion to the motional ground state. Because of the small Zeeman splitting, continuous near-resonant Raman sideband cooling of ${}^{138}\mathrm{Ba}^{+}$ requires only the Doppler cooling lasers and two additional acousto-optic modulators. Observing the near-resonant Raman optical pumping fluorescence, we extract relevant experimental parameters and demonstrate a final average motional quantum number $\overline{n}\ll 1$. We additionally employ a second, far-off-resonant laser driving Raman $\pi$ pulses between the two Zeeman sublevels to provide motional state detection for QLS and to confirm the sideband cooling efficiency, measuring a final $\overline{n}=0.15\left(6\right)$.

We report an alternate type of nonlinear waveguides, photorefractive surface nonlinearly chirped waveguide arrays, which can be directly induced by photorefractive surface waves in virtue of diffusion and drift nonlinearities. The amplitude of such nonlinearly chirped waveguide arrays has an apodized envelope owing to the diffusion nonlinearity. The refractive-index change of the apodized tails converges to a nonzero value which can be handily adjusted by an external electric field. Moreover, the chirp parameters such as amplitude, sign (positive or negative), and initial position can be conveniently adjusted by an external electric field, background illumination, incident beam, etc. Then the guided-wave properties of this type of waveguide arrays are analyzed by using the transfer matrix method. Owing to the flexible tail and the nonlinear chirp, the dispersion curves of the index-guided modes can be tailored by an external electric field and the dispersion curves of ordinary and extraordinary Bragg guided modes couple, intertwine, and anticross with each other. Meanwhile, there is a clear “competition” in the coupling hybrid mode near anticrossing.

Quantum transition probabilities and quantum entanglement for two-qubit states of a four-level trapped ion quantum system are computed for time-evolving ionic states driven by Jaynes-Cummings Hamiltonians with interactions mapped onto a $\text{SU}\left(2\right)\otimes \text{SU}\left(2\right)$ group structure. Using the correspondence of the method of simulating a $3+1$ dimensional Dirac-like Hamiltonian for bispinor particles into a single trapped ion, one preliminarily obtains the analytical tools for describing ionic state transition probabilities as a typical quantum oscillation feature. For Dirac-like structures driven by generalized Poincaré classes of coupling potentials, one also identifies the $\text{SU}\left(2\right)\otimes \text{SU}\left(2\right)$ internal degrees of freedom corresponding to intrinsic parity and spin polarization as an adaptive platform for computing the quantum entanglement between the internal quantum subsystems which define two-qubit ionic states. The obtained quantum correlational content is then translated into the quantum entanglement of two-qubit ionic states with quantum numbers related to the total angular momentum and to its projection onto the direction of the trapping magnetic field. Experimentally, the controllable parameters simulated by ion traps can be mapped into a Dirac-like system in the presence of an electrostatic field which, in this case, is associated to ionic carrier interactions. Besides exhibiting a complete analytical profile for ionic quantum transitions and quantum entanglement, our results indicate that carrier interactions actively drive an overall suppression of the quantum entanglement.

We experimentally investigate a scheme for studying lattice transport phenomena, based on the controlled momentum-space dynamics of ultracold atomic matter waves. In the effective tight-binding models that can be simulated, we demonstrate that this technique allows for a local and time-dependent control over all system parameters, and additionally allows for single-site resolved detection of atomic populations. We demonstrate full control over site-to-site off-diagonal tunneling elements (amplitude and phase) and diagonal site energies, through the observation of continuous-time quantum walks, Bloch oscillations, and negative tunneling. These capabilities open up new prospects in the experimental study of disordered and topological systems.

A well-known situation in which a non-Markovian dynamics of an open quantum system $S$ arises is when this is coherently coupled to an auxiliary system $M$ in contact with a Markovian bath. In such cases, while the joint dynamics of $S\text{−}M$ is Markovian and obeys a standard (bipartite) Lindblad-type master equation (ME), this is in general not true for the reduced dynamics of $S$. Furthermore, there are several instances (e.g., the dissipative Jaynes-Cummings model) in which a closed ME for the $S$'s state cannot even be worked out. Here, we find a class of bipartite Lindblad-type MEs such that the reduced ME of $S$ can be derived exactly and in a closed form for any initial product state of $S\text{−}M$. We provide a detailed microscopic derivation of our result in terms of a mapping between two collision models.

The predictive information required for proper trajectory sampling of a stochastic process can be more efficiently transmitted via a quantum channel than a classical one. This recent discovery allows quantum information processing to drastically reduce the memory necessary to simulate complex classical stochastic processes. It also points to a new perspective on the intrinsic complexity that nature must employ in generating the processes we observe. The quantum advantage increases with codeword length: the length of process sequences used in constructing the quantum communication scheme. In analogy with the classical complexity measure, statistical complexity, we use this reduced communication cost as an entropic measure of state complexity in the quantum representation. Previously difficult to compute, the quantum advantage is expressed here in closed form using spectral decomposition. This allows for efficient numerical computation of the quantum-reduced state complexity at all encoding lengths, including infinite. Additionally, it makes clear how finite-codeword reduction in state complexity is controlled by the classical process's cryptic order, and it allows asymptotic analysis of infinite-cryptic-order processes.

We experimentally demonstrate the underlying physical mechanism of the recently proposed protocol for superreplication of quantum phase gates [W. Dür, P. Sekatski, and M. Skotiniotis, Phys. Rev. Lett. 114, 120503 (2015)], which allows producing up to $N^2$ high-fidelity replicas from $N$ input copies in the limit of large $N$. Our implementation of $1\to 2$ replication of the single-qubit phase gates is based on linear optics and qubits encoded into states of single photons. We employ the quantum Toffoli gate to imprint information about the structure of an input two-qubit state onto an auxiliary qubit, apply the replicated operation to the auxiliary qubit, and then disentangle the auxiliary qubit from the other qubits by a suitable quantum measurement. We characterize the replication protocol by full quantum process tomography and observe good agreement of the experimental results with theory.

The topological phases in a one-dimensional quantum walk can be classified by the coin parameters. By solving for the general exact solutions of bound states in a one-dimensional quantum walk with boundaries specified by different coin parameters, we show that these bound states are Majorana modes with quasienergy $E=0,\pi$. These modes are qualitatively different for different boundary conditions used. For systems with two boundaries, such as finite wires, we find the same exact solution as the single boundary system if the boundary condition is antisymmetric. For a two-boundary system with symmetric boundary conditions in a finite wire, the interaction energy between two Majorana bound states can be computed as a function of the length of the wire and the coin parameter in the wire. Suggestions of observing these modes are provided.

I revisit the problem of the interaction between two dissimilar atoms with one atom in an excited state, recently addressed by Berman [Phys. Rev. A 91, 042127 (2015)], Donaire et al. [Phys. Rev. Lett. 115, 033201 (2015)], and Milonni and Rafsanjani [Phys. Rev. A 92, 062711 (2015)], for which precedent approaches have given conflicting results. In the first place, I discuss to what extent these works provide equivalent results. I show that the phase-shift rate of the two-atom wave function computed by Berman, the van der Waals potential of the excited atom by Donaire et al., and the level shift of the excited atom by Milonni and Rafsanjani possess equivalent expressions in the quasistationary approximation. In addition, I show that the level shift of the ground-state atom computed by Milonni and Rafsanjani is equivalent to its van der Waals potential. A diagrammatic representation of all those quantities is provided. The equivalences among them are, however, not generic. In particular, it is found that for the case of the interaction between two identical atoms excited, the phase-shift rate and the van der Waals potentials differ. Concerning the conflicting results of previous approaches in regards to the spatial oscillation of the interactions, I conclude, in agreement with Berman and with Milonni and Rafsanjani, that they refer to different physical quantities. The impacts of free-space dissipation and finite excitation rates on the dynamics of the potentials are analyzed. In contrast with Milonni and Rafsanjani, the oscillatory versus monotonic spatial forms of the potentials of each atom are found not to be related to the reversible versus irreversible nature of the excitation transfer involved.

The method of complex scaling is used to calculate $S$- and $P$-wave resonance energies and widths below the $\mathrm{Li}(3s,3p,4s,4p)$ excitation thresholds and positronium $n=2$ formation threshold in the positron-lithium system. We use two different types of model potentials to determine the interaction between the core and the valence electron. Explicitly correlated Gaussian basis functions are used to represent the correlation effects between the valence electron, the positron, and the ${\mathrm{Li}}^{+}$ core. A dipole series of resonances are found under the positronium $n=2$ threshold. Furthermore, these resonances are found to agree well with an analytically derived scaling law. The present results are compared with those in the literature.

We report on energy loss measurements of slow $\left(v\ll v_0\right)$, highly charged $\left(Q>10\right)$ ions upon transmission through a 1-nm-thick carbon nanomembrane. We emphasize here the scaling of the energy loss with the velocity and charge exchange or loss. We show that a weak linear velocity dependence exists, whereas charge exchange dominates the kinetic energy loss, especially in the case of a large charge capture. A universal scaling of the energy loss with the charge exchange and velocity is found and discussed in this paper. A model for charge-state-dependent energy loss for slow ions is presented in paper II in this series [R. A. Wilhelm and W. Möller, Phys. Rev. A 93, 052709 (2016)].

A model for charge-dependent energy loss of slow ions is developed based on the Thomas-Fermi statistical model of atoms. Using a modified electrostatic potential which takes the ionic charge into account, nuclear and electronic energy transfers are calculated, the latter by an extension of the Firsov model. To evaluate the importance of multiple collisions even in nanometer-thick target materials we use the charge-state-dependent potentials in a Monte Carlo simulation in the binary collision approximation and compare the results to experiment. The Monte Carlo results reproduce the incident charge-state dependence of measured data well [see R. A. Wilhelm et al., Phys. Rev. A 93, 052708 (2016)], even though the experimentally observed charge exchange dependence is not included in the model.

When atoms and molecules are ionized by laser pulses of finite duration and increasingly high intensities, the validity of the much-used dipole approximation, in which the spatial dependence and magnetic component of the external field are neglected, eventually breaks down. We report that, when going beyond the dipole approximation for the description of atoms exposed to ultraviolet light, the spatial dependence of the pulse shape, the envelope, provides the dominant correction, while the spatial dependence of the carrier is negligible. We present a first-order beyond-dipole correction to the Hamiltonian which accounts exclusively for nondipole effects stemming from the carrier envelope of the pulse. We demonstrate by ab initio calculations for hydrogen that this approximation, which we refer to as the envelope approximation, reproduces the full interaction beyond the dipole approximation for absolute and differential observables and proves to be valid for a broad range of high-frequency fields. This is done both for the Schrödinger and the Dirac equation. Moreover, it is demonstrated that the envelope approximation provides an interaction-term which gives rise to faster numerical convergence in terms of partial waves compared to its exact counterpart.

A photoelectron streaking experiment which was conceived as a means to extract the electron wave packet of single-photon ionization has also been employed to retrieve time delays in the fundamental photoemission processes. The discrepancies between the time delays thus measured and those from many sophisticated theoretical calculations have generated a great deal of controversy in recent years. Here we present a careful examination of the methods that were used to retrieve the time delays and demonstrate the difficulty of achieving an accuracy of the retrieved time delays of a few to tens of attoseconds in typical streaking measurements. The difficulty owes more to the lower sensitivity of the streaking spectra to the phase of the photoionization transition dipole than to the spectral phase of the attosecond light pulse in the experiment. The retrieved time delay contains extra errors when the attochirp of the attosecond pulse is large so that the dipole phase becomes negligible compared to it.

Hawking radiation has been regarded as a more general phenomenon than in gravitational physics, in particular in laboratory analogs of the event horizon. Here we consider the fiber-optical analog of the event horizon, where intense light pulses in fibers establish horizons for probe light. Then, we calculate the Hawking spectrum in an experimentally realizable system. We found that the Hawking radiation is peaked around group-velocity horizons in which the speed of the pulse matches the group velocity of the probe light. The radiation nearly vanishes at the phase horizon where the speed of the pulse matches the phase velocity of light.

We demonstrate coupling of light resonant to transition between two excited states of rubidium and long-lived ground-state atomic coherence. In our proof-of-principle experiment a nonlinear process of four-wave mixing is used to achieve light emission proportional to independently prepared ground-state atomic coherence. Strong correlations between stimulated Raman-scattering light heralding the generation of ground-state coherence and the four-wave mixing signal are measured and shown to survive the storage period, which is promising in terms of quantum memory applications. The process is characterized as a function of laser detunings.