We investigate the spectral properties and dynamical features of a time-periodic $\mathcal{PT}$-symmetric Hamiltonian on a one-dimensional tight-binding lattice. It is shown that a high-frequency modulation can drive the system under a transition between the broken-$\mathcal{PT}$ and the unbroken-$\mathcal{PT}$ phases. The time-periodic modulation in the unbroken-$\mathcal{PT}$ regime results in a significant broadening of the quasienergy spectrum, leading to a hyperballistic transport regime. Also, near the $\mathcal{PT}$-symmetry breaking the dispersion curve of the lattice band becomes linear, with a strong reduction of quantum wave-packet spreading.

We calculate the amount of entanglement of the multiqubit quantum states employed in the Grover algorithm, by following its dynamics at each step of the computation. We show that genuine multipartite entanglement is always present. Remarkably, the dynamics of any type of entanglement as well as of genuine multipartite entanglement is independent of the number $n$ of qubits for large $n$, thus exhibiting a scale invariance property. We compare this result with the entanglement dynamics induced by a fixed-point quantum search algorithm. We also investigate criteria for efficient simulatability in the context of Grover's algorithm.

We investigate the nonadiabatic implementation of an adiabatic quantum teleportation protocol, finding that perfect fidelity can be achieved through resonance. We clarify the physical mechanisms of teleportation, for three qubits, by mapping their dynamics onto two parallel and mutually coherent adiabatic passage channels. By transforming into the adiabatic frame, we explain the resonance by analogy with the magnetic resonance of a spin-1/2 particle. Our results establish a fast and robust method for transferring quantum states and suggest an alternative route toward high-precision quantum gates.

Aiming at the investigation of above-threshold ionization in superstrong laser fields with highly charged ions, we develop a Coulomb-corrected strong-field approximation (SFA). The influence of the Coulomb potential of the atomic core on the ionized electron dynamics in the continuum is taken into account via the eikonal approximation, treating the Coulomb potential perturbatively in the phase of the quasiclassical wave function of the continuum electron. In this paper the formalism of the Coulomb-corrected SFA for the nonrelativistic regime is discussed, employing velocity and length gauge. Direct ionization of a hydrogenlike system in a strong linearly polarized laser field is considered. The relation of the results in the different gauges to the Perelomov-Popov-Terent'ev imaginary-time method is discussed.

We develop a relativistic Coulomb-corrected strong-field approximation (SFA) for the investigation of spin effects at above-threshold ionization in relativistically strong laser fields with highly charged hydrogenlike ions. The Coulomb-corrected SFA is based on the relativistic eikonal-Volkov wave function describing the ionized electron laser-driven continuum dynamics disturbed by the Coulomb field of the ionic core. The SFA in different partitions of the total Hamiltonian is considered. The formalism is applied for direct ionization of a hydrogenlike system in a strong linearly polarized laser field. The differential and total ionization rates are calculated analytically. The relativistic analog of the Perelomov-Popov-Terent'ev ionization rate is retrieved within the SFA technique. The physical relevance of the SFA in different partitions is discussed.

Diffraction of a surface wave on a rectangular wedge with impedance facets is studied using the Sommerfeld-Malyuzhinets technique. An analog of Landau's bypass rule in the theory of plasma waves is introduced for the selection of a correct branch of the Sommerfeld integral, and the exact solution is given in terms of the imaginary error function. The formula derived is valid both in the “near wave” and “far wave” zones (defined here to be located within the wave zone, in the meaning of the theory of radiation). It is shown that a diffracted surface wave is completely scattered into freely propagating electromagnetic waves and neither reflected nor transmitted surface waves are generated in the case of bare metals, which have a positive real part of the surface impedance. The scattered waves propagate predominantly at a grazing angle along the direction of propagation of the incident surface wave and mainly in the upper hemisphere regarding the wedge facet. The profile of radiated intensity is nonmonotonic and does not resemble the surface-wave profile, which exponentially evanesces with the distance from the wedge facet. Comparison with experiments carried out in the terahertz spectral range at the Novosibirsk Free-Electron Laser facility has shown a good agreement of the theory and the experiments.

We characterize the frequency sensitivity of a cavity-stabilized laser to inertial forces and temperature fluctuations, and perform real-time feedforward to correct for these sources of noise. We measure the sensitivity of the cavity to linear accelerations, rotational accelerations, and rotational velocities by rotating it about three axes with accelerometers and gyroscopes positioned around the cavity. The worst-direction linear acceleration sensitivity of the cavity is $2\left(1\right)\times {10}^{-11}$ g${}^{-1}$ measured over 0–50 Hz, which is reduced by a factor of 50 to below ${10}^{-12}$ g${}^{-1}$ for low-frequency accelerations by real-time feedforward corrections of all of the aforementioned inertial forces. A similar idea is demonstrated in which laser frequency drift due to temperature fluctuations is reduced by a factor of 70 via real-time feedforward from a temperature sensor located on the outer wall of the cavity vacuum chamber.

There has been much interest recently in the analysis of optomechanical systems incorporating dielectric nano- or microspheres inside a cavity field. We analyze here the situation when one of the mirrors of the cavity itself is also allowed to move. We reveal that the interplay between the two oscillators yields a cross-coupling that results in, e.g., appreciable cooling and squeezing of the motion of the sphere, despite its nominal quadratic coupling. We also discuss a simple modification that would allow this cross-coupling to be removed at will, thereby yielding a purely quadratic coupling for the sphere.

We investigate nonequilibrium phase transitions for driven atomic ensembles interacting with a cavity mode and coupled to a Markovian dissipative bath. In the thermodynamic limit and at low frequencies, we show that the distribution function of the photonic mode is thermal, with an effective temperature set by the atom-photon interaction strength. This behavior characterizes the static and dynamic critical exponents of the associated superradiance transition. Motivated by these considerations, we develop a general Keldysh path-integral approach that allows us to study physically relevant nonlinearities beyond the idealized Dicke model. Using standard diagrammatic techniques, we take into account the leading-order corrections due to the finite number $N$ of atoms. For finite $N$, the photon mode behaves as a damped classical nonlinear oscillator at finite temperature. For the atoms, we propose a Dicke action that can be solved for any $N$ and correctly captures the atoms’ depolarization due to dissipative dephasing.

In this paper an invariant of motion for Hamiltonian systems is introduced: the Casimir companion. For systems with simple dynamical algebras (e.g., coupled spins, harmonic oscillators) our invariant is useful in problems that consider adiabatically varying the parameters in the Hamiltonian. In particular, it has proved useful in optimal control of changes in these parameters. The Casimir companion also allows simple calculation of the entropy of nonequilibrium ensembles.

We consider the decoherence of a quantum system $S$ coupled to a quantum environment $E$. For states chosen uniformly at random from the unit hypersphere in the Hilbert space of the closed system $S+E$ we derive a scaling relationship for the sum of the off-diagonal elements of the reduced density matrix of $S$ as a function of the size $D_E$ of the Hilbert space of $E$. This sum decreases as $1/\sqrt{D_E}$ as long as $D_E\gg 1$. We test this scaling prediction by performing large-scale simulations which solve the time-dependent Schrödinger equation for a ring of spin-$1/2$ particles, four of them belonging to $S$ and the others to $E$, and for this ring with small world bonds added in $E$ and/or between $S$ and $E$. The spin-1/2 particles experience nearest-neighbor interactions that are identical for the interactions within $S$ and random for the interactions within $E$ and between $S$ and $E$, or that are all identical. Provided that the time evolution drives the whole system from the initial state toward a scaling state, a state which has similar properties as states belonging to the class of quantum states for which we derived the scaling relationship, the scaling prediction holds. We examine various interaction parameters and initial states for our model system to find whether or not the time evolution reaches the class of states that have the scaling property. For the homogeneous ring we find that the evolution for select initial states does not reach these scaling states. This conclusion is not modified if we add some homogeneous random connections. For a ring we find that some randomness in the interaction parameters is required so that most initial configurations are driven toward the scaling state. Furthermore, if the amount of randomness is small the time required to reach the scaling states may be very large. For the case of all random interactions in $E$ the ring is driven toward the scaling state. Adding small world bonds between $S$ and $E$ with random interaction strengths may decrease the time required to reach the scaling state or may prevent the scaling state from being reached. For the latter case we show that increasing the complexity of the environment by adding extra connections within the environment suffices to observe the predicted scaling behavior.

In spite of their potential usefulness, the characterizations of Wigner functions for Bose and Fermi statistics given by O’Connell and Wigner himself almost thirty years ago [Phys. Rev. A 30, 2613 (1984)] have drawn little attention. With an eye towards applications in quantum chemistry, we revisit and reformulate them in a more convenient way.

We present two constructions for the Toffoli gate which substantially reduce resource costs in fault-tolerant quantum computing. The first contribution is a Toffoli gate requiring Clifford operations plus only four $T=\exp (i\pi {\sigma }^z/8)$ gates, whereas conventional circuits require seven $T$ gates. An extension of this result is that adding $n$ control inputs to a controlled gate requires $4n$ $T$ gates, whereas the best prior result was $8n$. The second contribution is a quantum circuit for the Toffoli gate which can detect a single ${\sigma }^z$ error occurring with probability $p$ in any one of eight $T$ gates required to produce the Toffoli gate. By postselecting circuits that did not detect an error, the posterior error probability is suppressed to lowest order from $4p$ (or $7p$, without the first contribution) to $28p^2$ for this enhanced construction. In fault-tolerant quantum computing, this construction can reduce the overhead for producing logical Toffoli gates by an order of magnitude.

We prove that every unitary acting on any multipartite system and having operator Schmidt rank equal to 2 can be diagonalized by local unitaries. This then implies that every such multipartite unitary is locally equivalent to a controlled unitary with every party but one controlling a set of unitaries on the last party. We also prove that any bipartite unitary of Schmidt rank 2 is locally equivalent to a controlled unitary where either party can be chosen as the control, and at least one party can control with two terms, which implies that each such unitary can be implemented using local operations and classical communication (LOCC) and a maximally entangled state on two qubits. These results hold regardless of the dimensions of the systems on which the unitary acts.

We consider the readout process on a probe made of $N$ qubits (two-level systems) in a quantum single-parameter estimation scheme. The parameter-dependent evolution of the probe as well as the measurements that are done for readout are assumed to be fixed. We find the optimal initial states of the probe that will saturate the quantum Cramér-Rao bound under these conditions. The relation between the optimal state of the $N$-qubit probe and that of the one-qubit probe is obtained for both entangling and nonentangling dynamics for the probe qubits. We study the limitations placed on the optimal initial state of the probe and on the achievable measurement uncertainty by the restrictions on the readout procedure.

The complete pattern of Rydberg binding energies of the 18 $n=9$ levels of nickel with $L=6$, 7, and 8 was measured using microwave plus resonant-excitation Stark-ionization spectroscopy. The measured pattern is consistent with the form predicted with the effective potential model, showing significant structure proportional to scalar products of tensor operators of order 0–4. The variation of the structure with $L$ separates the various contributing terms and provides determinations of several properties of the Ni${}^{+}$ core ion. These include the quadrupole moment, $Q$ $=$ −0.469 78(9) a.u., the hexadecapole moment, Π $=$ 0.36(5) a.u., the scalar and tensor dipole polarizabilities, ${\alpha }_{D,0}=$ 7.949(2) a.u., ${\alpha }_{D,2}=0.905$(12) a.u., the scalar quadrupole polarizability, ${\alpha }_{Q,0}=55$(8) a.u., the $g$ value, $g_J=1.257$(14), and the vector hyperpolarizability, ${\beta }_{D,1}=0.454$(24) a.u.

Time-dependent close-coupling (TDCC), $R$-matrix-with-pseudostates (RMPS), and time-independent distorted-wave (TIDW) methods are used to calculate electron-impact ionization cross sections for the carbon atom. The TDCC and RMPS results for the $1s^{2}2s^{2}2p^2$ ground configuration are in reasonable agreement with the available experimental measurements, while the TIDW results are $30\%$ higher. Ionization of the $1s^{2}2s2p^3$ excited configuration is performed using the TDCC, RMPS, and TIDW methods. Ionization of the $1s^{2}2s^{2}2p3l$ ($l=0$–2) excited configurations is performed using the TDCC and TIDW methods. The ionization cross sections for the excited configurations are much larger than for the ground state. For example, the peak cross section for the $1s^{2}2s^{2}2p3p$ excited configuration is an order of magnitude larger than the peak cross section for the $1s^{2}2s^{2}2p^2$ ground configuration. The TDCC results are again found to be substantially lower than the TIDW results. The ionization cross-section results will permit the generation of more accurate, generalized collisional-radiative ionization coefficients needed for modeling moderately dense carbon plasmas.

We observe the population dynamics within a metastable neon magneto-optical trap (MOT) through the measurement of the average squared Clebsch-Gordan coefficient $C^2$ over a range of laser detunings. The magnitude of $C^2$ is dependent on the internal quantum state of an atom interacting with the light field and is found to show a strong dependence on the applied laser detuning. Previously it has been reported [Townsend et al., Phys. Rev. A 52, 1423 (1995)] that trapped atoms in a MOT are pumped towards the states that interact most strongly with the local field and therefore the measured value of $C^2$ is larger than the average over all possible transitions. For the ${}^3{P}_2$-to-${}^3{D}_3$ cooling transition in metastable neon the average $C^2$ value is equal to 0.46; however, we have measured $0.29\pm 0.03<C^2<0.73\pm 0.09$. We explain this range of values for $C^2$ by considering the possible transition rates between the different magnetic sublevels in the system. This result has significant consequences when trap populations are measured via fluorescence in a MOT.