A collective system of atoms in a high-quality cavity can be described by a nonlinear interaction which arises due to the Lamb shift of the energy levels due to the cavity vacuum [Agarwal et al., Phys. Rev. A 56, 2249 (1997)]. We show how this collective interaction can be used to perform quantum logic. In particular we produce schemes to realize controlled-NOT gates not only for two-qubit but also for three-qubit systems. We also discuss realizations of Toffoli gates. Our effective Hamiltonian is also realized in other systems such as trapped ions or magnetic molecules.

We provide a systematic analysis of the physical generation of single- and two-qubit quantum operations from Hamiltonians available in various quantum systems for scalable quantum information processing. We show that generation of single-qubit operations can be transformed into a steering problem on the Bloch sphere, which represents all $R_z$-equivalence classes of single-qubit operations, whereas the two-qubit problem can be generally transformed into a steering problem in a tetrahedron representing all the local-equivalence classes of two-qubit operations (the Weyl chamber). We use this approach to investigate several physical examples for the generation of two-qubit operations. The steering approach provides useful guidance for the realization of various quantum computation schemes.

We study fluctuations of the number of Bose condensed atoms in a weakly interacting homogeneous and trapped gases. For a homogeneous system we apply the particle-number-conserving formulation of the Bogoliubov theory and calculate the condensate fluctuations within the canonical and the microcanonical ensembles. We demonstrate that, at least in the low-temperature regime, predictions of the particle-number-conserving and traditional, nonconserving theory are identical, and lead to the anomalous scaling of fluctuations. Furthermore, the microcanonical fluctuations differ from the canonical ones by a quantity which scales normally in the number of particles, thus predictions of both ensembles are equivalent in the thermodynamic limit. We observe a similar behavior for a weakly interacting gas in a harmonic trap. This is in contrast to the trapped, ideal gas, where microcanonical and canonical fluctuations are different in the thermodynamic limit.

Recent developments in the physics of low-density trapped gases make it worthwhile to verify old, well-known results that, while plausible, were based on perturbation theory and assumptions about pseudopotentials. We use and extend recently developed techniques to give a rigorous derivation of the asymptotic formula for the ground-state energy of a dilute gas of $N$ fermions interacting with a short-range, positive potential of scattering length $a$. For spin-$1∕2$ fermions, this is $E\sim E^0+({\hslash }^2∕2m)2\pi N\varrho a$, where $E^0$ is the energy of the noninteracting system and $\varrho$ is the density. A similar formula holds in two dimensions (2D), with $\varrho a$ replaced by $\varrho ∕\mid \ln \left(\varrho a^2\right)\mid$. Obviously this 2D energy is not the expectation value of a density-independent pseudopotential.

We investigate the propagation of density-wave packets in a Bose-Hubbard model using the adaptive time-dependent density-matrix renormalization group method. We discuss the decay of the amplitude with time and the dependence of the velocity on density, interaction strength, and the height of the perturbation in a numerically exact way, covering arbitrary interactions and amplitudes of the perturbation. In addition, we investigate the effect of self-steepening due to the amplitude dependence of the velocity and discuss the possibilities for an experimental detection of the moving wave packet in time-of-flight pictures. By comparing the sound velocity to theoretical predictions, we determine the limits of a Gross-Pitaevskii- or Bogoliubov-type description and the regime where repulsive one-dimensional Bose gases exhibit fermionic behavior.

In this paper we present the results of numerical calculations about the minimal value of detection efficiency for violating the Clauser-Horne inequality for qutrits. Our results show how the use of nonmaximally entangled states greatly improves this limit with respect to maximally entangled ones. A stronger resistance to noise is also found.

High-resolution photoionization spectra following single-photon excitation from the ${}^{1}S_0$ ground state have been recorded for the seven most abundant isotopes of xenon in the range between the first ${}^{2}P_{3∕2}$ and the second ${}^{2}P_{1∕2}$ ionization thresholds. Accurate values for the ionization energies $V_{\text{ion}}\left({}^{2}P_{1∕2}\right)$ and isotope shifts have been derived enabling the determination of the spin-orbit splitting in ${\mathrm{Xe}}^{+}$ with an unprecedented accuracy. The narrow bandwidth of the vuv laser (250 MHz) has enabled the resolution of the hyperfine structure of the autoionizing $n{s}^{\prime }$ series of ${}^{129}\mathrm{Xe}$ and ${}^{131}\mathrm{Xe}$ in the range of principal quantum number $n=30\text{–}150$. Multichannel quantum defect theory (MQDT) has been extended to treat the hyperfine structure of autoionizing Rydberg series and to derive the hyperfine structure of the ${}^{2}P_{1∕2}$ state of the singly charged ion. The MQDT analysis demonstrates the possibility of producing ions in selected hyperfine states by photoionization and enables the characterization of the combined effects of the spin-orbit and hyperfine autoionization.

We have used a Pekeris-type wave function, expressed on a Sturmian basis in terms of perimetric coordinates, in conjunction with the complex coordinate rotation method, to obtain well-converged estimates of the positions and widths of various ${}^{1}S^e$ and ${}^{3}S^e$ resonances of Ps. Calculations employing bases with one and two length scales were performed. We compare our results to earlier estimates. We also discuss the minimum positive charge that a particle of arbitrary mass must possess in order to bind two electrons.

We present experimental measurements of the mean energy in the vicinity of the first and second quantum resonances of the atom-optics kicked rotor for a number of different experimental parameters. Our data are rescaled and compared with the one-parameter $\left(ϵ\right)$ classical scaling function developed to describe the quantum resonance peaks. Additionally, experimental data are presented for the “classical” resonance which occurs in the limit as the kicking period goes to zero. This resonance is found to be analogous to the quantum resonances, and a similar one-parameter classical scaling function is derived, and found to match our experimental results. The widths of the quantum and classical resonance peaks are compared, and their sub-Fourier nature examined.

Based on the time-dependent Gross-Pitaevskii equation we study the evolution of a collapsing and exploding Bose-Einstein condensate in different trap symmetries to see the effect of confinement on collapse and subsequent explosion, which can be verified in future experiments. We make a prediction for the evolution of the shape of the condensate and the number of atoms in it for different trap symmetries (cigar to pancake) as well as in the presence of an optical lattice potential. We also make a prediction for the jet formation in different cases when the collapse is suddenly terminated by changing the scattering length to zero via a Feshbach resonance. In addition to the usual global collapse to the center of the condensate, in the presence of an optical-lattice potential one could also have in certain cases independent collapse of parts of the condensate to local centers, which could be verified in experiments.

We analyze the electromagnetically induced transparency (EIT) in $V$-, $\Lambda$-, and cascade-type schemes in a time-dependent way via the Schrödinger-Maxwell formalism. We derive explicitly the analytical expressions of the space-time dependent probe field, the corresponding phase shift, absorption or amplification, group velocity, and group velocity dispersion for all the three schemes. These simple analytical expressions not only demonstrate explicitly the similarities and essential differences of the three schemes but also provide a convenient basis for investigating how the many-body effects in solids modify the magnitude, spectral shape, and space and time dependence of EIT and EIT-related quantum coherence phenomena.

The possibility of realizing an efficient gaseous laser-beam-generating medium that utilizes $\Lambda$-type coherently phased (i.e., “dressed”) atoms for the active laser species, but that does not inherently require the use of external laser beams for pumping, is explored. Specifically, it is investigated if multiphoton stimulated hyper-Raman scattering (SHRS) processes driven by fluorescence radiation generated in a continuous electrical discharge present within the vapor-containing cell could produce continuous-wave (cw) optical gain at the $\Lambda$-atom resonance frequencies ${\omega }_o$ and ${\omega }_o^{\prime }$. It is deduced that such gain could result from $n$-photon $(n⩾4)$ SHRS processes only if absorption of fluorescence pump light occurs in the first three transitions of the $n$-photon sequence representing the process unit step. Estimates of the amount of optical gain that could be produced in such a system indicate that it should be sufficient to allow multiwatt cw laser operation to occur on one set of $\Lambda$ transitions connecting levels in a “double-$\Lambda$” structure, with the pump light being discharge-produced fluorescence centered about the transitions of the other $\Lambda$ pair. However, to initiate operation of such a device would require injection into the laser optical cavity of intense “starter” laser pulses at both lasing frequencies. What should be an optimal experimental configuration for determining feasibility of the proposed laser device is described. In the suggested configuration, Cs-atom $6S_{1∕2}\text{−}6P_{1∕2}$ transitions form the double-$\Lambda$ structure.

Information storage and database search are attractive areas in the field of nuclear magnetic resonance. Among the notable works reported earlier, an implementation of a parallel search algorithm in a dipolar coupled spin cluster has gained considerable attention [A. Khitrin, V. L. Ermakov, and B. M. Fung, Phys. Rev. Lett. 89, 277902 (2002)]. In this paper, we propose and exemplify that spatial encoding can be successfully utilized in realizing such parallel algorithms. We also introduce an improved protocol of the parallel search algorithm, which can be realized using spatial encoding. The methods have been demonstrated to perform a search operation using 215 bits.

We have made an investigation on the resonances for positronium negative ion ${\mathrm{Ps}}^{-}$ in various model plasma environments. The $2s^2{}^{1}S^e$ autoionization resonance state in ${\mathrm{Ps}}^{-}$ ion is determined by calculating the density of resonance states using the stabilization method. We have also performed accurate variational calculations to obtain ground-state energy eigenvalues of ${\mathrm{Ps}}^{-}$ for various Debye lengths. A screened Coulomb potential obtained from the Debye model is used to represent the interaction between the charged particles. A correlated wave function has been used to represent the correlation effect between the three charge particles. The calculated resonance energies and widths for various Debye parameters ranging from infinity to a small value along with the ground-state energies are reported.

A cold beam of ${\mathrm{He}}^{*}\left(2{}^{3}S_1\right)$ atoms is used at grazing incidence to study the quantum reflection on a flat polished silicon surface. We measure the reflectivity as a function of the normal incident velocity component between 3 and $30\mathrm{cm}∕\mathrm{s}$. Our result is in reasonable agreement with a calculation of the attractive van der Waals surface potential using the dielectric function of Si and the dipole polarizability of ${\mathrm{He}}^{*}$. We discuss the influence of the conductivity and of a thin oxide layer on the potential. By comparing our data to those previously measured with ${\mathrm{Ne}}^{*}$ atoms, we are also able to confirm the scaling of the reflectivity with atomic mass.

We investigate the entanglement properties of an ensemble of atoms interacting with a single bosonic field mode via the Dicke (superradiance) Hamiltonian. The model exhibits a quantum phase transition and a well-understood thermodynamic limit, allowing the identification of both quantum and semiclassical many-body features in the behavior of the entanglement. We consider the entanglement between the atoms and the field, an investigation initiated in Lambert et al. [Phys. Rev. Lett. 92, 073602 (2004)]. In the thermodynamic limit, we give exact results for all entanglement partitions and observe a logarithmic divergence of the atom-field entanglement, and discontinuities in the average linear entropy.

A fully quantum mechanical model of two-component Manakov solitons is developed in both the Heisenberg and Schrödinger representations, followed by an analytical, linearized quantum theory of Manakov solitons in the Heisenberg picture. This theory is used to analyze the vacuum-induced fluctuations of Manakov soliton propagation and collision. The vacuum fluctuations induce phase diffusion and dispersion in Manakov soliton propagation. Calculations of the position, polarization angle, and polarization state fluctuations show an increase in collision-induced noise with a decrease in the relative velocity between the two solitons, as expected because of an increase in the interaction length. Fluctuations in both the polarization angle and state are shown to be independent of propagation distance, opening up possibilities for communications, switching, and logic, exploiting these properties of Manakov solitons. Calculations of the phase noise reveal, surprisingly, that the collision-induced fluctuations can be reduced slightly below the level of fluctuations in the absence of collision, due to cross-correlation effects between the collision-induced phase and amplitude fluctuations of the soliton. The squeezing effect of Manakov solitons is also studied and proven, unexpectedly, to have the same theoretical optimum as scalar solitons.

In a previous Letter by Oliveira et al. [Phys. Rev. Lett. 90, 143002 (2003)], the time evolution of the $34S_{1∕2}$ population, resulting from energy-transfer collisions between $33P_{3∕2}+33P_{3∕2}$ Rb atoms in a magneto-optical trap, was explained based on an ultralong-range potential. However, some experimental oscillations observed in the signal could not be reproduced by that model. In this work we reanalyze such a experimental results considering an internuclear separation-dependent colliding atomic pair distribution. This analysis suggests that such a distribution in the ultralong-range Rydberg molecular potential is responsible for the observed oscillations.

We experimentally demonstrate that helical Laguerre-Gaussian light, which carries orbital angular momentum, is not specific in its interaction with chiral matter. Only circular polarization, associated with spin angular momentum, can engage with materials chirality.

Information-theoretic entropy measures are useful tools for quantifying the spreading of quantum states in phase space. In the present paper, we compare the time evolution of the joint entropy for three simple quantum systems: (i) a free Gaussian wave packet, (ii) a wave packet in a monochromatic electromagnetic field, and (iii) a wave packet tunneling through a $\delta$ barrier. As initial condition maximal classical states are used, which minimize the Heisenberg uncertainty and the entropy. It is found that, in all three cases, the joint entropy increases in time.