We report an experimental study of an all-optical three-photon-absorption resonance (known as an “$N$ resonance”) and discuss its potential application as an alternative to atomic clocks based on coherent population trapping. We present measurements of the $N$-resonance contrast, width and light shift for the $D_1$ line of ${}^{87}\mathrm{Rb}$ with varying buffer gases, and find good agreement with an analytical model of this resonance. The results suggest that $N$ resonances are promising for atomic clock applications.

The quantum-shutter approach to tunneling time scales [G. García-Calderón and A. Rubio, Phys. Rev. A 55, 3361 (1997)], which uses a cutoff plane wave as the initial condition, is extended to consider certain type of wave packet initial conditions. An analytical expression for the time-evolved wave function is derived. The time-domain resonance, the peaked structure of the probability density (as the function of time) at the exit of the barrier, originally found with the cutoff plane wave initial condition, is studied with the wave packet initial conditions. It is found that the time-domain resonance is not very sensitive to the width of the packet when the transmission process occurs in the tunneling regime.

We propose a quantum secret sharing protocol between multiparty ($m$ members in group 1) and multiparty ($n$ members in group 2) using a sequence of single photons. These single photons are used directly to encode classical information in a quantum secret sharing process. In this protocol, all members in group 1 directly encode their respective keys on the states of single photons via unitary operations; then, the last one (the $m\mathrm{th}$ member of group 1) sends $1∕n$ of the resulting qubits to each of group 2. Thus the secret message shared by all members of group 1 is shared by all members of group 2 in such a way that no subset of each group is efficient to read the secret message, but the entire set (not only group 1 but also group 2) is. We also show that it is unconditionally secure. This protocol is feasible with present-day techniques.

Two different diagrammatic construction schemes for obtaining the propagator for inelastic electronic scattering are presented. Both are discussed for the three cases that the target molecule of interest is closed-shell itself or has a closed-shell anion or cation. The “direct approach” yields the inelastic propagator directly, but has the drawback that it requires the evaluation of a large number of diagrams already in low orders. The “Dyson approach” uses Dyson-type equations for the inelastic propagator and employs a diagrammatic construction scheme for the generalized one-particle densities only. It therefore requires a considerably lower number of diagrams. Results are given up to first order for both methods and all three cases. Alternative approaches are briefly discussed and compared with our methods.

We study a general teleportation scheme with an arbitrary two-party pure state and derive a tight bound of the teleportation fidelity with a predesigned estimation of the unknown state to be teleported. This bound shows a piecewise balance between information gain and state disturbance. We also explain possible physical significance of the balance.

Recently, cesium atoms in optical lattices subjected to cycles of unequally spaced pulses have been found to show interesting behavior: they represent an experimental demonstration of a Hamiltonian ratchet mechanism, and they show strong variability of the dynamical localization lengths as a function of initial momentum. The behavior differs qualitatively from corresponding atomic systems pulsed with equal periods, which are a textbook implementation of a well-studied quantum chaos paradigm, the quantum $\delta$-kicked rotor ($\delta$-QKR). We investigate here the properties of the corresponding eigenstates (Floquet states) in the parameter regime of the recent experiments and compare them with those of the eigenstates of the $\delta$-QKR at similar kicking strengths. We show that by studying the properties of the Floquet states we can shed light on the form of the observed ratchet current, as well as variations in the dynamical localization length.

We address the challenging proposition of using real experimental parameters in a three-dimensional (3D) numerical simulation of fast rotating Bose-Einstein condensates. We simulate recent experiments [V. Bretin, S. Stock, Y. Seurin, and J. Dalibard, Phys. Rev. Lett. 92, 050403 (2004); S. Stock, V. Bretin, S. Stock, F. Chevy, and J. Dalibard, Europhys. Lett. 65, 594 (2004)] using an anharmonic (quadratic-plus-quartic) confining potential to reach rotation frequencies $\left(\Omega \right)$ above the trap frequency $\left({\omega }_{\perp }\right)$. Our numerical results are obtained by propagating the 3D Gross-Pitaevskii equation in imaginary time. For $\Omega ⩽{\omega }_{\perp }$, we obtain an equilibrium vortex lattice similar (as the size and number of vortices) to experimental observations. For $\Omega >{\omega }_{\perp }$ we observe the evolution of the vortex lattice into an array of vortices with a central hole. Since this evolution was not visible in experiments, we investigate the 3D structure of vortex configurations and 3D effects on vortex contrast. Numerical data are also compared to recent theory [D. E. Sheehy and L. Radzihovsky, Phys. Rev. A 70, 063620 (2004)] describing vortex lattice inhomogeneities and a remarkably good agreement is found.

We present theoretical models of two-dimensional (2D) microcavity lasers. The relation between stationary lasing modes and resonances or metastable states is elucidated for arbitrary shapes of 2D resonant microcavities.

We consider a $\Lambda$-type model of the Bose-Einstein condensate of sodium atoms interacting with the light. Coefficients of the Kerr nonlinearity in the condensate can achieve large and negative values, providing the possibility for effective control of group velocity and dispersion of the probe pulse. We find a regime when the observation of the “slow” and “fast” light propagating without absorption becomes achievable due to the strong nonlinearity. An effective two-level quantum model of the system is derived and studied. Our approach is based on a possibility of establishing a connection of the underlying algebra with the $su\left(2\right)$ algebra within the formalism of the polynomial algebras of excitations (PAE). We propose an efficient way for the generation of sub-Poissonian fields in the Bose-Einstein condensate at time-scales much shorter than the characteristic decay time in the system. We show that the quantum properties of the probe pulse can be controlled in BEC by the classical coupling field.

We show that it is possible to define a Lorentz-covariant reduced spin density matrix for massive particles. Such a matrix allows one to calculate the mean values of observables connected with spin measurements (average polarizations). Moreover, it contains not only information about polarization of the particle but also information about its average kinematical state. We also use our formalism to calculate the correlation function in the Einstein-Podolsky-Rosen–Bohm type experiment with massive relativistic particles.

The energy spectrum of the Coulomb potential with minimal length commutation relations $[X_i,P_j]=i\hslash \{{\delta }_{ij}(1+\beta P^2)+{\beta }^{\prime }{P}_i{P}_j\}$ is determined both numerically and perturbatively for arbitrary values of ${\beta }^{\prime }∕\beta$ and angular momenta $\ell$. The constraint on the minimal length scale from precision hydrogen spectroscopy data is of the order of a few ${\mathrm{GeV}}^{-1}$, weaker than previously claimed.

We study the Casimir energy of a massless scalar field that obeys Dirichlet boundary conditions on a hyperboloid facing a plate. We use the optical approximation including the first six reflections and compare the results with the predictions of the proximity force approximation and the semiclassical method. We also consider finite size effects by contrasting the infinite with a finite plate. We find sizable and qualitative differences between the optical method and the more traditional approaches.

Quantum-state filtering is a variant of the unambiguous state discrimination problem: the states are grouped in sets and we want to determine to which particular set a given input state belongs. The simplest case, when the $N$ given states are divided into two subsets and the first set consists of one state only while the second consists of all of the remaining states, is termed quantum-state filtering. We derived previously the optimal strategy for the case of $N$ nonorthogonal states, $\{\mid {\psi }_1⟩,\dots ,\mid {\psi }_N⟩\}$, for distinguishing $\mid {\psi }_1⟩$ from the set $\{\mid {\psi }_2⟩,\dots ,\mid {\psi }_N⟩\}$ and the corresponding optimal success and failure probabilities. In a previous paper [Phys. Rev. Lett. 90, 257901 (2003)], we sketched an appplication of the results to probabilistic quantum algorithms. Here we fill the gaps and give the complete derivation of the probabilstic quantum algorithm that can optimally distinguish between two classes of Boolean functions, that of the balanced functions and that of the biased functions. The algorithm is probabilistic, it fails sometimes but when it does it lets us know that it did. Our approach can be considered as a generalization of the Deutsch-Jozsa algorithm that was developed for the discrimination of balanced and constant Boolean functions.

We consider the possibilities offered by Gaussian states and operations for two honest parties, Alice and Bob, to obtain privacy against a third eavesdropping party, Eve. We first extend the security analysis of the protocol proposed in [Navascués et al. Phys. Rev. Lett. 94, 010502 (2005)]. Then, we prove that a generalized version of this protocol does not allow one to distill a secret key out of bound entangled Gaussian states.

The radiative electron capture into high-$Z$, few-electron ions is studies in the framework of the density matrix, based on Dirac’s equation. In this formalism, all the properties of the photons and the (remaining) ions can be described, independent from their initial shell structure or polarization. Detailed computations have first been carried out for the total and angle-differential cross sections, following the capture of an electron into hydrogen-${\mathrm{U}}^{91+}$ and lithiumlike ${\mathrm{U}}^{89+}$ ions. From these calculations, which were performed in two different approximations, it is shown that many-electron interactions affect the angular distribution at low projectile energies by about 5%. Apart from describing the (angular-dependent) capture cross sections, our formalism is also appropriate to explore the subsequent $K\alpha ,\beta$ photon emission, if the electron is captured into an excited state of the ion, the polarization of the photons and ions as well as the interplay of the radiative with other, nonradiative capture processes in the future.

The exact dynamics of the rotational degrees of freedom of diatomic molecules, in the presence of sequentially applied radiation pulses, is studied. The radiation pulses induce chaos in the rotational phase space. In the adiabatic limit, this induced chaos is found to cause a transition to high angular momentum states due to chaos induced avoided crossings among Floquet states. The effect of finite temperature on the distribution of transitions is also discussed.

We study the coherent off-equilibrium spin mixing inside an atomic condensate. Using mean-field theory and adopting the single-spatial-mode approximation, the condensate spin dynamics is found to be well described by that of a nonrigid pendulum and displays a variety of periodic oscillations in an external magnetic field. Our results illuminate several recent experimental observations and provide critical insights into the observation of coherent interaction-driven oscillations in a spin-1 condensate.

We report on the experimental characterization of energetic and dynamical instability, two mechanisms responsible for the breakdown of Bloch waves in a Bose-Einstein condensate interacting with a one-dimensional (1D) optical lattice. A clear separation of these two regimes is obtained by performing measurements at different temperatures of the atomic sample. The time scales of the two processes have been determined by measuring the losses induced in the condensate. A simple phenomenological model is introduced for energetic instability while a full comparison is made between the experiment and the 3D Gross-Pitaevskii theory that accounts for dynamical instability.

We study the ground-state properties of hard-core bosons trapped by arbitrary confining potentials on one-dimensional optical lattices. A recently developed exact approach based on the Jordan-Wigner transformation is used. We analyze the large distance behavior of the one-particle density matrix, the momentum distribution function, and the lowest natural orbitals. In addition, the low-density limit in the lattice is studied systematically, and the results obtained compared with the ones known for the hard-core boson gas without the lattice.

A light beam is said to be position squeezed if its position can be determined to an accuracy beyond the standard quantum limit. We identify the position and momentum observables for bright optical beams and show that position and momentum entanglement can be generated by interfering two position, or momentum, squeezed beams on a beam splitter. The position and momentum measurements of these beams can be performed using a homodyne detector with local oscillator of an appropriate transverse beam profile. We compare this form of spatial entanglement with split detection-based spatial entanglement.