We have performed calculations of attosecond laser-atom interactions for laser intensities where interesting two- and three-photon effects become relevant. In particular, we examine the case of “hole burning” in the initial orbital. Hole burning is present when the laser-pulse duration is shorter than the classical radial period because the electron preferentially absorbs the photon near the nucleus. We also examine how the three-photon Raman process can lead to a time delay in the outgoing electron for the energy near one-photon absorption. For excitation out of the hydrogen $2s$ state, an intensity of $2.2\times {10}^{16}$ W/cm${}^2$ leads to a 6-as delay of the outgoing electron. We argue that this delay is due to the hole burning in the initial state.

We present an extension of the time-dependent configuration-interaction singles (TDCIS) method to the computation of the electron kinetic-energy spectrum in photoionization processes. Especially for strong and long ionizing light pulses, the detection of the photoelectron poses a computational challenge because propagating the outgoing photoelectron wave packet requires large grid sizes. Two different methods that allow for the extraction of the asymptotic photoelectron momentum are compared regarding their methodological and computational performance. The first method follows the scheme of Tong et al. [X. M. Tong, K. Hino, and N. Toshima, Phys. Rev. A 74, 031405(R) (2006)], where the photoelectron wave function is absorbed by a real splitting function. The second method following that presented by Tao and Scrinzi [L. Tao and A. Scrinzi, New J. Phys. 14, 013021 (2012)], measures the flux of the electron wave packet through a surface at a fixed radius. With both methods the full angle- and energy-resolved photoelectron spectrum is obtained. Combined with the TDCIS scheme, it is possible to analyze the dynamics of the outgoing electron in a channel-resolved way and, additionally, to study the dynamics of the bound electrons in the parent ion. As an application, one-photon and above-threshold ionization of argon following strong XUV irradiation are studied via energy- and angle-resolved photoelectron spectra.

We explore a single-photon approach to Rydberg state excitation and Rydberg blockade. Using detailed theoretical models, we show the feasibility of direct excitation, predict the effect of background electric fields, and calculate the required interatomic distance to observe Rydberg blockade. We then measure and control the electric field environment to enable coherent control of Rydberg states. With this coherent control, we demonstrate Rydberg blockade of two atoms separated by 6.6(3) $\mu$m. When compared with the more common two-photon excitation method, this single-photon approach is advantageous because it eliminates channels for decoherence through photon scattering and ac Stark shifts from the intermediate state while moderately increasing Doppler sensitivity.

A two-component Bose-Einstein condensate whose dynamics is described by a system of coupled Gross-Pitaevskii equations accommodates waves with different symmetries. A first type of waves corresponds to excitations for which the motion of both components is locally in phase. For the second type of waves, the two components have a counterphase local motion. When the values of the inter- and intracomponent interaction constants are different, the long-wavelength behavior of these two modes corresponds to two types of sound with different velocities. In the limit of weak nonlinearity and small dispersion, the first mode is described by the well-known Korteweg-de Vries equation. In the same limit, we show that the second mode can be described by the Gardner equation if the values of the two intracomponent interaction constants are sufficiently close. This leads to a rich variety of nonlinear excitations (solitons, kinks, algebraic solitons, breathers) which do not exist in the Korteweg-de Vries description.

Consider an impurity particle injected in a degenerate one-dimensional gas of noninteracting fermions (or, equivalently, Tonks-Girardeau bosons) with some initial momentum $p_0$. We examine the infinite-time value of the momentum of the impurity, $p_{\infty }$, as a function of $p_0$. A lower bound on $|p_{\infty }\left(p_0\right)|$ is derived under fairly general conditions. The derivation, based on the existence of the lower edge of the spectrum of the host gas, does not resort to any approximations. The existence of such bound implies the perpetual motion of the impurity in a one-dimensional gas of noninteracting fermions or Tonks-Girardeau bosons at zero temperature. The bound admits an especially simple and useful form when the interaction between the impurity and host particles is everywhere repulsive.

A numerical study showing the excitation and control of second-order modulation instability (MI) dynamics in nonlinear optical fibers via two optical seed fields located under the MI gain spectrum is presented. The phase dependence of the two weak input seed fields on the temporal and spectral second-order MI dynamics, i.e., on the frequency generation process, is investigated. The considered approach allows the generation and control of asymmetric MI spectra, modifiable via the phase relation of the initial seed fields with considerably small amplitudes. An optimal frequency relation of the seed fields for the highest possible influence could be identified. Furthermore, the phase-dependent effect of second-order MI is discussed for a pulsed excitation and higher-order perturbative effects, such as higher-order dispersion, Raman scattering, and self-steepening.

In an recent work with the title “Asking Photons Where They Have Been,” Danan et al. experimentally demonstrate an intriguing behavior of photons in an interferometer [Phys. Rev. Lett. 111, 240402 (2013)]. In their words: “The photons tell us that they have been in the parts of the interferometer through which they could not pass.” They interpret the results using the two-state vector formalism of quantum theory and say that, although an explanation of the experimental results in terms of classical electromagnetic waves in the interferometer is possible (and they provide a partial description), it is not so intuitive. Here we present a more detailed classical description of their experimental results, showing that it is actually intuitive. The same description is valid for the quantum wave function of the photons propagating in the interferometer. In particular, we show that it is essential that the wave propagates through all parts of the interferometer to describe the experimental results. We hope that our work helps to give a deeper understanding of these interesting experimental results.

We study an analog of the equations describing transverse electric (TE) and transverse magnetic (TM) modes in a planar waveguide with an arbitrary continuous dependence of the electric permittivity and magnetic permeability on coordinates with the stationary Schrödinger equation. The effective potential energies involved in the Schrödinger equation for TE and TM modes are found. In general, the effective potential energies for TE and TM modes are different but in the limit of a weak dependence of the permittivity and permeability on coordinates they coincide. In the case when the product of a position-dependent permittivity and permeability is constant, it means that the refractive index is constant, and we find that the TE and TM modes are described by the supersymmetric quantum mechanics.

We investigate theoretically quantum effects of a cavity-atom system in which the upper two levels of a cascade-type three-level atom interact with a cavity field mode in the ultrastrong-coupling regime. By exploiting the virtual photons carried by atom-cavity dressed states, we indicate how two external driving fields induce Raman transitions such that a cavity photon pair can be generated with a high probability. We present analytical and numerical solutions of the system and determine the rate of photons transmitted out of the cavity. In addition, we show that the transmitted photons exhibit a bunching behavior in the steady state. Our scheme demonstrates that atom-cavity dressed states in the ultrastrong-coupling regime can serve as intermediate states to invoke nonlinear optical processes.

We provide a general framework for the identification of open quantum systems. By looking at the input-output behavior, we try to identify the system inside a black box in which some Markovian time evolution takes place. Due to the generally irreversible nature of the dynamics, it is difficult to assure full controllability over the system. Still, we show that the system is identifiable up to similarity under a certain rank condition. The framework also covers situations relevant to standard quantum process tomography, where we do not have enough control over the system but have a tomographically complete set of initial states and observables. Remarkably, the similarity cannot in general be reduced to unitarity even for unitary systems, and the spectra of Hamiltonians are not identifiable without additional knowledge.

Polarization-singularity C points, a form of line singularities, are the vectorial counterparts of the optical vortices of spatial modes and fundamental optical features of polarization-spatial modes. Their generation in tailored beams has been limited to so-called “lemon” and “star” C points that contain symmetric dislocations in state-of-polarization patterns. In this Rapid Communication we present the theory and laboratory measurements of two complementary methods to generate isolated asymmetric C points in tailored beams, of which symmetric lemon and star patterns are limiting cases; and we report on the generation of so-called “monstar” patterns, an asymmetric C point with characteristics of both lemons and stars.

We analyzea direct parity measurement of the state of three superconducting qubits in circuit quantum electrodynamics. The parity is inferred from a homodyne measurement of the reflected and transmitted microwave radiation, and the measurement is direct in the sense that the parity is measured without the need for any quantum circuit operations or for ancilla qubits. Qubits are coupled to two resonant-cavity modes, allowing the steady state of the emitted radiation to satisfy the necessary conditions to act as a pointer state for the parity. However, the transient dynamics violates these conditions, and we analyze this detrimental effect and show that it can be overcome in the limit of a weak measurement signal. Our analysis shows that, with a moderate degree of postselection, it is possible to achieve postmeasurement states with fidelity of order 95%. We believe that this type of measurement could serve as a benchmark for future error correction protocols in a scalable architecture.

Topological quantum error correction codes are known to be able to tolerate arbitrary local errors given sufficient qubits. This includes correlated errors involving many local qubits. In this work, we quantify this level of tolerance, numerically studying the effects of many-qubit errors on the performance of the surface code. We find that if increasingly large-area errors are at least moderately exponentially suppressed, arbitrarily reliable quantum computation can still be achieved with practical overhead. We furthermore quantify the effect of nonlocal two-qubit correlated errors, which would be expected in arrays of qubits coupled by a polynomially decaying interaction, and when using many-qubit coupling devices. We surprisingly find that the surface code is very robust to this class of errors, despite a provable lack of a threshold error rate when such errors are present.

We show an equivalence relation between fault-tolerant circuits for a stabilizer code and fault-tolerant adiabatic processes for holonomic quantum computation (HQC), in the case where quantum information is encoded in the degenerate ground space of the system Hamiltonian. By this equivalence, we can systematically construct a fault-tolerant HQC scheme, which can geometrically implement a universal set of encoded quantum gates by adiabatically deforming the system Hamiltonian. During this process, quantum information is protected from low-weight thermal excitations by an energy gap that does not change with the problem size.

We derive the quantum limit on the error probability exponent for discriminating any $M$ multimode coherent states of light and show that it is four times that of an ideal heterodyne receiver for the same signal set. We then propose a receiver that achieves the quantum limit using auxiliary coherent-state fields, beam splitters, and single-photon detectors. The performance of the receiver is compared to standard measurements for various imaging and communication tasks. A related receiver for discriminating arbitrary multicopy pure quantum states is shown to achieve the $M$-ary quantum Chernoff exponent and does so using only local operations and classical communication.

We study two operational schemes for a coherent Ising machine based on an injection-locked laser network. These schemes gradually increase the pumping rate or the mutual coupling among the slave lasers. We numerically simulate the two schemes against a data search problem implemented with the Ising model in cubic graphs without frustration. We show that the machine can achieve a better success probability and effective computational time to find a target ground state with these gradual schemes than those with the abrupt introduction of the mutual injection which has been studied previously. The computational time simulated with typical parameters is almost constant up to the problem size $M=200$ and turns into a nearly linear scale holding up to $M=1000$.

It is well known that quantum states that can be transformed into each other by local unitary transformations are equal from the information theoretic point of view. This defines equivalence classes of states and allows one to write any state with the minimal number of parameters called the canonical form of the state. We define the equivalence classes of local measurements such that local operations which transform states from one equivalence class into another with the same probability are equivalent. This equivalence relation allows one to write the operators with the minimal number of parameters, which we call canonical operators, and hence the use of the canonical operators simplifies the optimal manipulation of quantum states. We use the canonical local operators for the concentration of three-qubit Greenberger-Horne-Zeilinger states and obtain the optimal concentration protocols in terms of the unitary invariants of quantum states, namely, the bipartite concurrences and the three-tangle.

Theoretical cross sections for single-electron capture in collision of Al${}^{3+}$ ions with helium, neon, and argon targets have been calculated in the 10${}^{-2}$–2 a.u. velocity range ($E_{\mathrm{lab}}$: 0.06 keV through 2.7 MeV). Calculations have been carried out by means of semiclassical collision methods based on multireference configuration interaction potential-energy curves and nonadiabatic couplings. Partial and total cross sections are given and the obtained results agree well with the available experimental data for He and Ar targets while those for neon are considered as prediction.