We study the performance of an adiabatic geometric phase gate with a quantized driving field numerically and develop an analytical approximation that shows how the qubit becomes entangled with the driving field. This results in a scaling of the gate error probability versus the energy in the control field that has the same form as that found for dynamic, nonadiabatic gates, but with a prefactor that would typically be several orders of magnitude larger, because of the adiabaticity constraint. In the approximation we have used, which should be valid for sufficiently large control fields, the main source of decoherence (and hence error) is the “which path” information carried by the photons that would be radiated by the driven qubit.

Numerous physical systems have been proposed for constructing quantum computers, but formidable obstacles stand in the way of making even modest systems with a few hundred quantum bits (qubits). Several approaches utilize the spin of an electron as the qubit. Here it is suggested that the spin of electrons floating on the surface of liquid helium will make excellent qubits. These electrons can be electrostatically held and manipulated much like electrons in semiconductor heterostructures, but being in a vacuum the spins on helium suffer much less decoherence. In particular, the spin-orbit interaction is reduced so that moving the qubits with voltages applied to gates has little effect on their coherence. Remaining sources of decoherence are considered, and it is found that coherence times for electron spins on helium can be expected to exceed $100\mathrm{s}$. It is shown how to obtain a controlled-NOT operation between two qubits using the magnetic dipole-dipole interaction.

We propose schemes for generating multiple-atom entangled states and a multiple-photon Greenberger-Horne-Zeilinger state, respectively, based on the input-output relation of the cavity. The numerical simulations show that produced multiple-particle entangled states have high fidelity even if the atoms are not localized in the Lamb-Dicke regime. Some practical quantum noises, such as atomic spontaneous emission and output coupling inefficiency, only decrease the success probability but exert no influence on the fidelity of prepared multiple-particle entangled states. The successful probabilities of our protocols approach unity in the ideal case. In addition, no need for individually addressing keeps the schemes easy to implement from the experimental point of view.

We study the influence of electron-scattering processes on the angular distributions of point particles moving through a free-electron gas. Previous calculations for slow ions are extended to all (nonrelativistic) velocities. The formulation is based on the extension of the multiple-scattering theory to the case of particles moving through a free-electron gas, using Lindhard’s dielectric function to separately evaluate the contributions of binary (electron-hole) and collective (plasmon) excitations. We find that the angular spread of the beam of particles is dominated by binary collisions. The results for the width of the angular distribution are compared with an integral expression derived by Lindhard.

Cross sections for $\mathrm{He}+{\mathrm{H}}_2$ collisions are reported for rovibrational states near dissociation at translational energies less than $1000{\mathrm{cm}}^{-1}$. In contrast to our previously reported cross sections for lower-lying initial rotational states, the excited rotational states near dissociation give rise to shape resonances for energies between 0.001 and $1{\mathrm{cm}}^{-1}$. The emergence of these resonances with increasing rotational level is opposite to the trend found for $\mathrm{He}+\mathrm{C}\mathrm{O}$ where the shape resonance strength decreases with rotational level for low-lying states. Quasiresonant energy transfer and low energy excitation thresholds are also discussed and it is found that there are 11 rovibrationally excited states that are stable against collision at ultracold temperatures.

An ultrashort strong nonresonant pulse induces transient phenomena in an optically thick medium consisting of an ensemble of nondegenerate two-level atoms (nonadiabatic transitions, transient light-shifts,…). A weak resonant pulse propagates in the system and we study theoretically and numerically the temporal and spectral modifications that are induced. Moreover, we show that the atomic media, modified by a strong pulse can act as a “pulse-shaper” device that can modify, in a controlled way, the shape of the weak pulse. It maps out the transient light shift induced by the strong pulse and reduces efficiently the long time dispersion tail of the weak pulse. We study and discuss the physical phenomena that allow such shaping effects and the necessary conditions to satisfy in order to observe them.

We present a detailed description of small displacement and tilt measurements of a Gaussian beam using split detectors and ${\mathrm{TEM}}_{10}$ homodyne detectors. Theoretical analysis and an experimental demonstration of measurements of these two conjugate variables are given. A comparison between the experimental efficiency of each scheme proves that the standard split detection is only 64% efficient relative to the ${\mathrm{TEM}}_{10}$ homodyne detection, which is optimal for beam displacement and tilt. We also demonstrate experimentally that squeezed light in the appropriate spatial modes allows measurements beyond the quantum noise limit for both types of detectors. Finally, we explain how to choose the detection scheme best adapted to a given application.

Small-area bistable lasing spots (about $10\mu \mathrm{m}$ full width at half maximum) can be created at different positions within the aperture of a broad-area vertical-cavity surface-emitting laser (aperture diameter $80\mu \mathrm{m}$) with frequency-selective feedback from a grating in Littrow configuration, and an additional pinhole localizing feedback to a part of the laser. Their characteristics are analyzed depending on the grating tuning, injection current, and feedback strength. These spots are considered to be good candidates for self-localized cavity solitons, if the perturbation by boundaries can be reduced using devices with larger diameter.

A relation between entanglement and criticality of spin chains is established. The entanglement we exploit is shared between auxiliary particles, which are isolated from each other, but are coupled to the same critical spin-$1∕2$ chain. We analytically evaluate the reduced density matrix, and numerically show the entanglement of the auxiliary particles in the proximity of the critical points of the spin chain. We find that the entanglement induced by the spin chain may reach 1, and it can signal very well the critical points of the chain. A physical understanding and experimental realization with trapped ions are presented.

The interaction of relativistically strong tailored laser pulses with an atomic system is considered. Due to special tailoring of the laser pulse, the suppression of the relativistic drift of the ionized electron and a dramatic enhancement of the rescattering probability is shown to be achievable. The high harmonic generation rate in the relativistic regime is calculated and shown to be increased by several orders of magnitude compared to the case of conventional laser pulses. The energies of the revisiting electron at the atomic core can approach the MeV domain, thus rendering hard x-ray harmonics and nuclear reactions with single atoms feasible.

We demonstrate that it is possible, in principle, to perform a Ramsey-type interference experiment to exhibit a coherent superposition of a single atom and a diatomic molecule. This gedanken experiment, based on the techniques of Aharonov and Susskind [Phys. Rev. 155, 1428 (1967)], explicitly violates the commonly accepted superselection rule that forbids coherent superpositions of eigenstates of differing atom number. A Bose-Einstein condensate plays the role of a reference frame that allows for coherent operations analogous to Ramsey pulses. We also investigate an analogous gedanken experiment to exhibit a coherent superposition of a single boson and a fermion, violating the commonly accepted superselection rule forbidding coherent superpositions of states of differing particle statistics. In this case, the reference frame is realized by a multimode state of many fermions. This latter case reproduces all of the relevant features of Ramsey interferometry, including Ramsey fringes over many repetitions of the experiment. However, the apparent inability of this proposed experiment to produce well-defined relative phases between two distinct systems each described by a coherent superposition of a boson and a fermion demonstrates that there are additional, outstanding requirements to fully “lift" the univalence superselection rule.

Time-domain balanced homodyne detection is performed on two well-separated temporal modes sharing a single photon. The reconstructed density matrix of the two-mode system is used to prove and quantify its entangled nature, while the Wigner function is employed for an innovative tomographic test of Bell’s inequality based on the theoretical proposal by Banaszek and Wodkiewicz [Phys. Rev. Lett. 82, 2009 (1999)]. Provided some auxiliary assumptions are made, a clear violation of the Banaszek-Bell inequality is found.

In this work, a theoretical study on electron-$\mathrm{C}{\mathrm{F}}_2$ collisions in the low and intermediate energy range is reported. More specifically, calculated elastic differential, integral and momentum transfer cross sections, as well as total absorption cross sections are presented in the $(1–500)\mathrm{eV}$ energy range. A complex optical potential is used to represent the electron-molecule interaction dynamics, whereas the iterative Schwinger variational method combined with the distorted-wave approximation is used to solve the scattering equations. A comparison of the present results is made with the available theoretical and experimental results for electron collisions with $\mathrm{C}{\mathrm{F}}_2$ as well as with ${\mathrm{O}}_3$ (an isoelectronic molecule of $\mathrm{C}{\mathrm{F}}_2$).

Manipulation of cold atoms by lasers has so far been studied solely within the framework of the conventional dipole approximation, and the atom-light interaction has been treated using low order perturbation theory. Laser control of atomic motions has been ascribed exclusively to the corresponding light-induced dipole forces. In this work, we present a general theory to derive the potential experienced by an atom in a monochromatic laser field in a context analogous to the Born-Oppenheimer approximation for molecules in the field-free case. The formulation goes beyond the dipole approximation and gives rise to the field-atom coupling potential terms which so far have not been taken into consideration in theoretical or experimental studies. Contrary to conventional approaches, our method is based upon the many electron Floquet theory and remains valid also for high intensity laser fields (i.e., for a strongly nonperturbative atom-light interaction). As an illustration of the developed theory, we investigate the trapping of cold atoms in optical lattices. We find that for some atoms for specific laser parameters, despite the absence of the dipole force, the laser trapping is still possible due to the electric quadrupole forces. Namely, we show that by using realistic laser parameters one can form a quadrupole optical lattice which is sufficiently strong to trap Ca and Na atoms.

We theoretically investigate the physics of interacting Bose-Einstein condensates at equilibrium in a weak (possibly random) potential. We develop a perturbation approach to derive the condensate wave function for an amplitude of the potential smaller than the chemical potential of the condensate and for an arbitrary spatial variation scale of the potential. Applying this theory to disordered potentials, we find in particular that, if the healing length is smaller than the correlation length of the disorder, the condensate assumes a delocalized Thomas-Fermi profile. In the opposite situation where the correlation length is smaller than the healing length, we show that the random potential can be significantly smoothed and, in the mean-field regime, the condensate wave function can remain delocalized, even for very small correlation lengths of the disorder.

We consider spin-polarized mixtures of cold fermionic atoms on the BEC side of the Feshbach resonance. We demonstrate that a strongly anisotropic confining potential can give rise to a double-peak structure in the axial distribution of the density difference and a polarization-dependent aspect ratio of the minority species. Both phenomena appear as a result of the breakdown of the local density approximation for the phase-separated regime. We speculate on the implications of our findings for the unitary regime.

We propose an inductive procedure to classify $N$-partite entanglement under stochastic local operations and classical communication provided such a classification is known for $N-1$ qubits. The method is based upon the analysis of the coefficient matrix of the state in an arbitrary product basis. We illustrate this approach in detail with the well-known bipartite and tripartite systems, obtaining as a by-product a systematic criterion to establish the entanglement class of a given pure state without resourcing to any entanglement measure. The general case is proved by induction, allowing us to find an upper bound for the number of $N$-partite entanglement classes in terms of the number of entanglement classes for $N-1$ qubits.

High-precision variational calculations for the rovibrational states in the range of the total orbital momentum $L=0–4$ and vibrational quantum number $v=0–4$ for the $\mathrm{H}_2{}^{+}$ and $\mathrm{H}{\mathrm{D}}^{+}$ molecular ions are presented. Relativistic and radiative corrections of orders $R_{\infty }{\alpha }^2$, $R_{\infty }{\alpha }^2(m∕M)$, $R_{\infty }{\alpha }^3$, $R_{\infty }{\alpha }^3(m∕M)$, and, partially, $R_{\infty }{\alpha }^4$ are taken into consideration as well as the finite size structure of proton and deuteron. It is found that the relative theoretical uncertainty due to uncalculated contributions of orders $R_{\infty }{\alpha }^4$ and higher to the reference transition frequency interval $(L=0,v=0)\to (0,1)$ is about $1\mathrm{ppb}$.

The low-energy behavior of the partial-wave Jost function for scattering by a long-range $1∕r^s$ $(s>2)$ central potential is investigated analytically using the linear variant of the variable-phase equation. An exact expansion of the Jost function in powers of the wave number $k$ is derived iteratively and shown to be simpler compared to the modified effective-range expansion of the phase shift. Improved expansions are determined explicitly for $s=3$ and $s=4$. It is suggested that the Jost function offers a practical alternative for interpolating low-energy cross sections and extracting scattering lengths; this is illustrated by fitting the Jost function, up to a normalizing constant, to the integral cross section for elastic collisions of slow electrons with ${\mathrm{N}}_2$ molecules.