The coherent states for the quantum mechanics on a torus and their basic properties are discussed.

We present a robust construction of a set of logic gates operating on a system of qubits encoded in the rovibrational eigenstates of an ${\mathrm{Na}}_2$ molecule using the optical adiabatic population transfer (APT) phenomenon. We demonstrate the operation of a complete universal gate set for quantum computation on a two-qubit system with gate fidelities approaching 99.99%. Like other APT-based processes, the method is robust against substantial fluctuations in the intensity of the laser pulse. Our construction is easily scalable to deal with a larger number of qubits. With the aid of the set of gates thus shown we may construct pulse sequences for a wide class of quantum logic operations. We also show how to produce a representation of Bell states from a representation of product states with essentially perfect fidelity. Our scheme can be realized in all diatomic and polyatomic molecules that possess easily accessible and well characterized excited electronic states.

We study the measurement for the unambiguous discrimination of two mixed quantum states that are described by density operators ${\rho }_1$ and ${\rho }_2$ of rank $d$, the supports of which jointly span a $2d$-dimensional Hilbert space. Based on two conditions for the optimum measurement operators and on a canonical representation for the density operators of the states, two equations are derived that allow the explicit construction of the optimum measurement, provided that the expression for the fidelity of the states has a specific simple form. For this case, the problem is mathematically equivalent to distinguishing pairs of pure states, even when the density operators are not diagonal in the canonical representation. The equations are applied to the optimum unambiguous discrimination of two mixed states that are similar states, given by ${\rho }_2=U{\rho }_1{U}^{†}$, and that belong to the class where the unitary operator $U$ can be decomposed into multiple rotations in the $d$ mutually orthogonal two-dimensional subspaces determined by the canonical representation.

A reexamination of the photoassociation spectrum of the external well of the $0_g^{-}$ potential of ${\mathrm{Cs}}_2$ converging to the $(6s_{1∕2}+6p_{3∕2})$ limit is performed, in order to resolve inconsistencies arising from a previously published paper [Phys. Rev. Lett. 85, 1408 (2000)]. We use the same analytical description of the potential as in an other previous analysis [Phys. Rev. A 66, 052506 (2002)], but we make a shift of 2 in the assignment of the observed vibrational lines. The agreement between experimental and calculated energy positions is improved and the intensities calculated using the new potential account well for all available data. The fitting procedure reveals a strong interdependence of the parameters of the model, which limits the accuracy of the determination of the radiative lifetimes of the $6p^2{P}_{1∕2}$ and $6p^2{P}_{3∕2}$ atomic levels. Only a more precise experimental study could allow one to improve the determination of these lifetime values.

Partially correlated ground-state electron densities for some spherical light atoms are calculated, into which nonrelativistic ionization potentials represent essential input data. The nuclear cusp condition of Kato is satisfied precisely. The basic theoretical starting point, however, is Hartree-Fock (HF) theory for the $N$ electrons under consideration but with nonintegral nuclear charge $Z^{\prime }$ slightly different from the atomic number $Z$ $(=N)$. This HF density is scaled with a parameter $\lambda$, near to unity, to preserve normalization. Finally, some tests are performed on the densities for the atoms Ne and Ar, as well as for Be and Mg.

The presence of loss limits the precision of an approach to phase measurement using maximally entangled states, also referred to as NOON states. A calculation using a simple beam-splitter model of loss shows that, for all nonzero values $L$ of the loss, phase measurement precision degrades with increasing number $N$ of entangled photons for $N$ sufficiently large. For $L$ above a critical value of approximately 0.785, phase measurement precision degrades with increasing $N$ for all values of $N$. For $L$ near zero, phase measurement precision improves with increasing $N$ down to a limiting precision of approximately $1.018L\text{radians}$, attained at $N$ approximately equal to $2.218∕L$, and degrades as $N$ increases beyond this value. Phase measurement precision with multiple measurements and a fixed total number of photons $N_T$ is also examined. For $L$ above a critical value of approximately 0.586, the ratio of phase measurement precision attainable with NOON states to that attainable by conventional methods using unentangled coherent states degrades with increasing $N$, the number of entangled photons employed in a single measurement, for all values of $N$. For $L$ near zero this ratio is optimized by using approximately $N=1.279∕L$ entangled photons in each measurement, yielding a precision of approximately $1.340\sqrt{L∕N_T}\text{radians}$.

We address a quantitative determination of the degree of polarization of type-II unpolarized light via the computation of the distance between the polarization distribution and the uniform distribution associated with fully unpolarized light (i.e., type-I unpolarized light or natural light). We determine the maximum degree of polarization for type-II unpolarized light and the states reaching it. We show that the degree of polarization can be arbitrarily large, approaching complete polarization for increasing mean photon numbers.

The magnetic moment ($g$ factor) of the negative muon bound in the $1s$ state of Zn, Ge, Cd, and Pb atoms was measured. A considerable difference between the present experimental results and that of theoretical calculations and results from earlier measurements is observed.

The dynamics of a dark soliton in an elongated Bose-Einstein condensate is studied at finite temperatures. In addition to accurately reproducing all stages of the decay of the soliton observed in the experiment of Burger et al. [Phys. Rev. Lett. 83, 5198 (1999)], our numerical simulations reveal the existence of an experimentally accessible parameter regime for which phase-imprinted dark solitons can execute at least one full axial oscillation prior to their decay. The dependence of the decay time scale on temperature and initial soliton depth is analyzed and the role of interatomic collisions quantified.

We propose a scheme of generating and verifying mesoscopic-level entanglement between two atomic ensembles using nonresonant stimulated Raman scattering. Entanglement can be generated by direct detection or balanced homodyne detection of the Stokes fields from the two cells after they interfere on a beam splitter. The entanglement of the collective atomic fields can be transferred to the anti-Stokes fields in a readout process. By measuring the operator moments of the anti-Stokes fields, we can verify the presence of entanglement. We model the effects of practical factors such as Stokes-field detector quantum efficiency and additive thermal noise in the entanglement generating process, and anti-Stokes-field losses in the entanglement verification process, and find achievable regimes in which entanglement can be verified at the levels of tens to hundreds of atomic excitations in the ensembles.

We construct a genuine $(2N+1)$-qubit entangled state to perform controlled teleportation of an arbitrary $N$-qubit state. The constructed state is a complementarity to the genuine $2N$-qubit entangled state constructed by Yeo and Chua for $N=2$ [Phys. Rev. Lett. 96, 060502 (2006)] and by Chen, Zhu, and Guo for any $N$ [Phys. Rev. A 74, 032324 (2006)]. We also quantify the entanglement of the state and classify it with the well-known $GHZ$ and $W$ states by means of the recently proposed generalized global entanglement and the associated auxiliary measures [Phys. Rev. A 74, 022314 (2006)]. Our study is of general importance with respect to exploring and exploiting the genuine multiqubit entanglement.

Recently, there have been a number of works investigating the entanglement properties of distinct noncomplementary parts of discrete and continuous bosonic systems in ground and thermal states. The relativistic fermionic case, however, has yet to be expressly addressed. In this paper we investigate the entanglement between a pair of far-apart regions of the $(3+1)$-dimensional massless Dirac vacuum via a previously introduced distillation protocol [Reznik et al., Phys. Rev. A 71, 042104 (2005)]. We show that entanglement persists over arbitrary distances, and that as a function of $L∕R$, where $L$ is the distance between the regions and $R$ is their typical scale, it decays no faster than $\sim \exp [-(L∕R{)}^2]$. We discuss the similarities with and differences from analogous results obtained for the massless Klein-Gordon vacuum.

We investigate the spatial structure and temporal dynamics created in a Bose-Einstein condensate by radio-frequency atom laser-output couplers using a one-dimensional mean-field model. We compare the behavior of a “pure” two-state atom laser to the multilevel systems demonstrated in laboratories. In particular, we investigate the peak homogeneous output flux, classical fluctuations in the beam, and the onset of a bound state which shuts down the atom laser output.

We present a one-step scheme for direct implementation of an $N$-qubit controlled-phase gate with atoms trapped in a high-$Q$ optical cavity without resorting to a sequence of single- and two-qubit gates. The interaction time that is required to implement the scheme does not rise with increasing number of qubits. This might lead to more efficient construction of quantum circuits and quantum algorithms.

We present calculations for a coherent population transfer [stimulated Raman adiabatic passage (STIRAP)] between the two lowest electronic ground states of the KRb molecule. In contrast to previous work on STIRAP in molecular systems, position dependent transition dipole moments are included in the calculation to take the mixed singlet-triplet nature of the intermediate state into account. Additionally, we incorporate the kinetic energy term and position dependent electronic states of the molecule. Transfer efficiencies of up to 58% can be achieved for moderate laser pulses in the picosecond range. Calculations with constant transition dipole moments show a much higher transfer of 94% and thus overestimate the efficiency significantly.

Cluster states, a special type of highly entangled states, are a universal resource for measurement-based quantum computation. Here, we propose an efficient one-step generation scheme for cluster states in semiconductor quantum dot molecules, where qubits are encoded on singlet and triplet states of two coupled quantum dots. By applying a collective electrical field or simultaneously adjusting interdot bias voltages of all double-dot molecules, we get a switchable Ising-like interaction between any two adjacent quantum molecule qubits. The initialization, the single-qubit measurement, and the experimental parameters are discussed. It is shown that preparation of large cluster states and one-way quantum computation are implementable in semiconductor quantum dots with the present techniques.

We demonstrate the ability to coherently control ultracold atomic Rb collisions using frequency-chirped light on the nanosecond time scale. For certain center frequencies of the chirp, the rate of inelastic trap-loss collisions induced by negatively chirped light is dramatically suppressed compared to the case of a positive chirp. We attribute this to a fundamental asymmetry in the system: an excited wave packet moves inward on the attractive molecular potential. For a positive chirp, the resonance condition moves outward in time, while for a negative chirp, it moves inward, in the same direction as the excited wave packet; this allows multiple interactions between the wave packet and the light, enabling the wave packet to be returned coherently to the ground state. Classical and quantum calculations support this interpretation.

At the soft-x-ray free-electron laser FLASH in Hamburg, we have studied multiphoton ionization on neon and helium by ion mass-to-charge spectroscopy. The experiments were performed in a focused beam at 42.8 and $38.4\mathrm{eV}$ photon energy and irradiance levels up to ${10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$. Direct, sequential, and resonant two-, three-, and four-photon excitations were investigated by quantitative measurements as a function of the absolute photon intensity. The atomic and ionic photoionization cross sections derived indicate a clear dominance of sequential compared to direct multiphoton processes.

We investigate the dynamics of nonclassical correlations between two particles in a harmonic trap which interact in a pointlike manner. Via a quantum-jump approach we add a specific damping model. The correlations between the particles are quantified using a Bell-type correlation function, adapted for the continuous-variable case. They clearly exceed the classical border and show collapses and revivals. Their destruction due to decoherence strongly depends on the initial separation of the particles and on the damping constant.