We reexamine the general solution of a Schrödinger equation in the presence of a time-dependent linear potential in configuration space based on the Lewis-Riesenfeld framework. For comparison, we also solve the problem in momentum space and then Fourier transform the solution to get the general wave function. Appropriately choosing the weight function in the latter method, we can obtain the same wave function as the former method. It is found that a non-Hermitian time-dependent linear invariant can be used to obtain Gaussian-type wave-packet solutions of the time-dependent system. This operator is a specific linear combination of the initial momentum and initial position operators. This fact indicates that the constants of integration such as the initial position and initial momentum that determine the classical motion play important roles in the time-dependent quantum system. The eigenfunction of the linear invariant is interpreted as a wave packet with a “center of mass” moving along the classical trajectory, while the ratio between the coefficients of the initial position and initial momentum determines the width of the wave packet.

Although it is known that the nonlinear Schrödinger equation describes the propagation of light in self-focusing media, the quantization conditions that emerge from its corresponding semiclassical version have not been sufficiently appreciated. For the propagation of an optical pulse in a Kerr-effect microcavity, we find that the transverse energy, intensity, number of particles, and frequency detuning are not arbitrary but are interrelated by quantization conditions. We identify the binding energy of the collective bound state of particles with the energy loss of the pulse and indicate how the energy distribution of photons can be studied from the point of view of a master-equation approach to a heat reservoir interacting with the photons.

We study spectral shifts in intense ultrashort laser pulses propagating in clustered gas jets. Forward- and side-scattered laser pulse spectra were measured as a function of pulse width for chirped pulses, and the forward spectrum and absorption were measured for variably delayed colinear $2\omega$ probe pulses. The observation of redshifts is consistent with our model of rapidly increasing cluster polarizability early in the laser-heated cluster explosion. In addition, there is a blueshift contribution implying the presence of unclustered atoms in the jet. Simulations of intense pulse propagation in cluster jets are in reasonable agreement with the chirped pulse experiment.

Propagators for quantum evolution equation of multipartite systems in the center-of-mass probability representation are introduced. Properties of these propagators and their relation to the Green function of Schrödinger equation and propagator of Moyal evolution equation are studied. Examples of quadratic systems are considered and explicit expressions for the center of mass tomographic propagator are obtained.

We show that quantum information can be encoded into entangled states of multiple indistinguishable particles in such a way that any inertial observer can prepare, manipulate, or measure the encoded state independent of their Lorentz reference frame. Such relativistically invariant quantum information is free of the difficulties associated with encoding into spin or other degrees of freedom in a relativistic context.

We study entanglement swapping through nonmaximally entangled states. The combination of the standard protocol with an optimal scheme for quantum state discrimination leads to a reliable protocol for the conclusive probabilistic generation of maximally entangled states. A possible setup based on cold trapped ions is proposed.

We have experimentally realized the scheme initially proposed as quantum dense coding with continuous variables [Ban, J. Opt. B: Quantum Semiclassical Opt. 1, L9 (1999); Braunstein and Kimble, Phys. Rev. A 61, 042302 (2000)]. In our experiment, a pair of EPR (Einstein-Podolsky-Rosen) beams is generated from two independent squeezed vacua. After adding a two-quadrature signal to one of the EPR beams, two squeezed beams that contain the signal were recovered. Although our squeezing level is not sufficient to demonstrate the channel capacity gain over the Holevo limit of a single-mode channel without entanglement, our channel is superior to conventional channels such as coherent and squeezing channels. In addition, the optical addition and subtraction processes demonstrated are elementary operations of universal quantum information processing on continuous variables.

It is shown that the entanglement-structure of 3- and $4\text{−}\text{qubit}$ states can be characterized by optimized operators of the Mermin-Klyshko type. It is possible to discriminate between pure $2\text{−}\text{qubit}$ entanglements and higher entanglements. A comparison with a global entanglement measure is made.

Following a recent work by Hillery et al. [Phys. Rev. A 68, 032314 (2003)], we introduce a scattering model of a quantum random walk (SQRW) on a hybercube. We show that this type of quantum random walk can be reduced to the quantum random walk on the line and we derive the corresponding hitting amplitudes. We investigate the scattering properties of the hypercube, connected to the semi-infinite tails. We prove that the SQRW is a generalized version of the coined quantum random walk. We show how to implement the SQRW efficiently using a quantum circuit with standard gates. We discuss one possible version of a quantum search algorithm using the SQRW. Finally, we analyze symmetries that underlie the SQRW and may simplify its solution considerably.

A theoretical comparison of the behavior of the antihydrogen $\left(\overline{\mathrm{H}}\right)$ and hydrogen $\left(\mathrm{H}\right)$ atoms in external electric and magnetic fields is made. It is shown that observable differences arise in the spectroscopic properties of $\mathrm{H}$ and $\overline{\mathrm{H}}$ atoms in parallel electric and magnetic fields of the order of 475 V∕cm and 0.12 T, respectively.

Measurements are reported of rate constants for electron attachment to ${\mathrm{C}}_6{\mathrm{F}}_{5}X$ $(X=\mathrm{Cl},\mathrm{Br},\mathrm{I})$ and thermal electron detachment from ${\mathrm{C}}_6{\mathrm{F}}_5{\mathrm{Cl}}^{-}$ over the temperature range $300–550\mathrm{K}$ in $133\mathrm{Pa}$ of He gas in a flowing-afterglow Langmuir-probe apparatus. This is the first case we know of where the parent anion has sufficiently low electron detachment energy that detachment (from ${\mathrm{C}}_6{\mathrm{F}}_5{\mathrm{Cl}}^{-}$ in this case) has been observed in competition with a channel for dissociative electron attachment yielding a thermally stable anion (here, ${\mathrm{Cl}}^{-}$). Because of this competition, it is shown that a simple mass spectrometric determination of the product branching fractions at long times will lead to erroneous results at elevated temperatures. The electron density profiles provide evidence for a new plasma decay process involving the detaching and nondetaching anions trapped in the space charge field of the positive ions. Electron attachment rate constants were found to be $1.0\times {10}^{-7}$, $1.1\times {10}^{-7}$, and $2.0\times {10}^{-7}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$, at $300\mathrm{K}$, for ${\mathrm{C}}_6{\mathrm{F}}_5\mathrm{Cl}$, ${\mathrm{C}}_6{\mathrm{F}}_5\mathrm{Br}$, and ${\mathrm{C}}_6{\mathrm{F}}_5\mathrm{I}$, respectively, estimated accurate to $\pm 25\%$ except for ${\mathrm{C}}_6{\mathrm{F}}_5\mathrm{I}$, where there is $\pm 30\%$ uncertainty. Rate constants for ${\mathrm{C}}_6{\mathrm{F}}_5\mathrm{Cl}$ changed little over our temperature range, while those for ${\mathrm{C}}_6{\mathrm{F}}_5\mathrm{Br}$, and ${\mathrm{C}}_6{\mathrm{F}}_5\mathrm{I}$ increased with temperature. Electron detachment occurred only for ${\mathrm{C}}_6{\mathrm{F}}_5{\mathrm{Cl}}^{-}$ in our temperature range. Detachment rate constants were immeasurable at room temperature but approached $4000{\mathrm{s}}^{-1}$ at $550\mathrm{K}$. From these data the electron affinity (EA) for ${\mathrm{C}}_6{\mathrm{F}}_5\mathrm{Cl}$ was determined, EA $\left({\mathrm{C}}_6{\mathrm{F}}_5\mathrm{Cl}\right)=0.75\pm 0.08\mathrm{eV}$. G3(MP2) calculations (based on Møller-Plesset perturbation theory) were carried out for the neutral and anion and yielded $\mathrm{EA}\left({\mathrm{C}}_6{\mathrm{F}}_5\mathrm{Cl}\right)=0.728\mathrm{eV}$.

We use a Langevin approach to analyze the quantum noise in coherent anti-Stokes Raman spectroscopy in several experimental scenarios: with continuous-wave input fields acting simultaneously and with fast sequential pulsed lasers where one field scatters off the coherence generated by other fields and for interactions within a cavity and in free space. In all cases, the signal and quantum noise due to spontaneous decay and decoherence in the medium are shown to be described by the same general expression. Our theory in particular shows that for short interaction times, the medium noise is not important and the efficiency is limited only by the intrinsic quantum nature of the photon. We obtain fully analytic results without making an adiabatic approximation; the fluctuations of the medium and the fields are solved self-consistently.

A single-loop scenario is proposed to realize nonadiabatic geometric quantum computation. Conventionally, a so-called multiloop approach is used to remove the dynamical phase accumulated in the operation process for geometric quantum gates. More intriguingly, we here illustrate in detail how to use a special single-loop method to remove the dynamical phase and thus to construct a set of universal quantum gates based on the nonadiabatic geometric phase shift. The present scheme is applicable to NMR systems and may be feasible in other physical systems.

We report discrepancies between the results presented in Fig. 1 of a recent paper of Yasuike and Someda [Phys. Rev. A66, 053410 (2002)] and our independent calculation. At the frequency $\omega =0.55\mathrm{a.u.}$, we find that the state of the one-dimensional modified Pöschl-Teller potential, described by the authors as light induced and originating from a shadow of the field-free ground state, is in fact physical for ${\alpha }_0<10\mathrm{a.u.}$ and its origin is the zero-energy antibound state of the bare potential. For $\omega =0.45\mathrm{a.u.}$, we also find differences in one of the presented quasienergy trajectories in the low ${\alpha }_0$ region $({\alpha }_0<0.4\mathrm{a.u.})$, but we confirm the starting point at $E=-0.5\mathrm{a.u.}$ for both quasienergies, as found by Yasuike and Someda.

The preceding Comment has clarified a conjecture made in our paper. In this Reply, we add further insight to the results presented in the Comment concerning the behaviors of pole trajectories outside the resonance sectors.

Excitation of the autoionizing states of helium by electron impact is shown in calculations in the $S$-wave limit to leave a clear signature in the singly differential cross section for the $(e,2e)$ process. It is suggested that such behavior should be seen generally in $(e,2e)$ experiments on atoms that measure the single differential cross section.

Recent studies have shown that logarithmic divergence of entanglement entropy as a function of the size of a subsystem is a signature of criticality in quantum models. We demonstrate that the ground-state entanglement entropy of $n$ sites for the ferromagnetic Heisenberg spin-$\frac{1}{2}$ chain of the length $L$ in a sector with fixed magnetization $y$ per site grows as $\frac{1}{2}{\log }_2[n(L-n)∕L]C\left(y\right)$, where $C\left(y\right)=2\mathrm{\pi }e(\frac{1}{4}-y^2)$.

Electron-impact excitation and ionization of helium is studied in the $S$-wave model. The problem is treated in full dimensionality using a time-dependent formulation of the exterior complex scaling method that does not involve the solution of large linear systems of equations. We discuss the steps that must be taken to compute stable ionization amplitudes. We present total excitation, total ionization, and single differential cross sections from the ground and $n=2$ excited states and compare our results with those obtained by others using a frozen-core model.

We report on cw measurements of probe beam absorption and four-wave-mixing spectra in a ${}^{85}\mathrm{Rb}$ magneto-optical trap taken while the trap is in operation. The trapping beams are used as pump light. We concentrate on the central feature of the spectra at small pump-probe detuning and attribute its narrow resonant structures to the superposition of Raman transitions between light-shifted sublevels of the ground atomic state and to atomic recoil processes. These two contributions have different dependencies on trap parameters and we show that the former is inhomogeneously broadened. The strong dependence of the spectra on the probe-beam polarization indicates the existence of large optical anisotropy of the cold-atom sample, which is attributed to the recoil effects. We point out that the recoil-induced resonances can be isolated from other contributions, making pump-probe spectroscopy a highly sensitive diagnostic tool for atoms in a working magneto-optical trap.

We show that rovibrational state selectivity can be achieved by chirped adiabatic passage of molecules that are adiabatically aligned by a nonresonant laser field. We develop the tools to design the appropriate frequency and amplitude modulations that allow us to select a given route in the Hilbert space that leads to a final complete excitation of the chosen state, by infrared or by Raman processes. This method allows us to select a given vibrational state in a well-defined rotational $J$ state.