Identifying the real and imaginary parts of wave functions with coordinates and momenta, quantum evolution may be mapped onto a classical Hamiltonian system. In addition to the symplectic form, quantum mechanics also has a positive-definite real inner product that provides a geometrical interpretation of the measurement process. Together they endow the quantum Hilbert space with the structure of a Käller manifold. Quantum control is discussed in this setting. Quantum time evolution corresponds to smooth Hamiltonian dynamics and measurements to jumps in the phase space. This adds additional power to quantum control, nonunitarily controllable systems becoming controllable by “measurement plus evolution.” A picture of quantum evolution as the Hamiltonian dynamics in a classical-like phase space is the appropriate setting to carry over techniques from classical to quantum control. This is illustrated by a discussion on optimal control and sliding mode techniques.

We present the results of a set of quantal and classical calculations designed for simulating the photoelectron spectra observed when atoms are submitted to an intense laser field. We have concentrated the discussion on the range of parameters where conspicuous enhancements are observed in the high-energy part of the above-threshold ionization (ATI) spectra. Our results confirm that these enhancements result from a resonant transfer of population into the Rydberg states. Subsequent multiple returns, with elastic or inelastic recollisions of the electrons with the nucleus, when they are released in the continuum, also play an essential part. Our analysis highlights also the similarities as well as the differences observed in simulations, depending on the choice of the model potential, i.e., if it is either long range (Coulomb-like) or short range (with an exponentially decreasing tail).

We investigate the band structure of a Bose-Einstein condensate in a one-dimensional periodic potential by calculating stationary solutions of the Gross-Pitaevskii equation, which have the form of Bloch waves. We demonstrate that loops (“swallow tails”) in the band structure occur both at the Brillouin zone boundary and at the center of the zone, and they are therefore a generic feature. A physical interpretation of the swallow tails in terms of periodic solitons is given. The linear stability of the solutions is investigated as a function of the strength of the mean-field interaction, the magnitude of the periodic potential, and the wave vector of the condensate. The regions of energetic and dynamical stability are identified by considering the behavior of the Gross-Pitaevskii energy functional for small deviations of the condensate wave function from a stationary state. It is also shown how for long-wavelength disturbances the stability criteria may be obtained within a hydrodynamic approach.

We study the thermalization dynamics of an impurity cloud inside a Bose-Einstein condensate at finite temperature, introducing a suitable Boltzmann equation. Some values of the temperature and of the initial impurity energy are considered. We find that below the Landau critical velocity, the stimulation effects reduce the depletion rate of the macroscopic initial impurity population. For appropriate parameters, the collisions cool the condensate. The maximum cooling per impurity atom is obtained with multiple collisions. A cooling method is outlined.

An algebraic method is introduced for an analytical solution of the eigenvalue problem of the Tavis-Cummings Hamiltonian, based on polynomially deformed su(2), i.e., ${\mathrm{su}}_n\mathrm{}\left(2\right)\mathrm{}$ algebras. In this method the eigenvalue problem is solved in terms of a specific perturbation theory, developed here up to third order. Generalization to the N-atom case of the Rabi frequency and dressed states is also provided. A remarkable enhancement of spontaneous emission of $\mathcal{N}$ atoms in a resonator is found to result from collective effects.

We present an experimental study of a vertical-cavity surface-emitting laser with polarized optical feedback. The system displays single-mode low-frequency fluctuations for a large interval of pump current. The dynamics is determined by phenomena extending on a wide range of time scales. In particular, we show, besides rare power drops (events), a periodic structure within the single event, a slow temporal drift in this pattern, and a coherence extending over several events.

Motivated by the results of Macchiavello and Palma on entanglement-enhanced information transmission over a quantum channel with correlated noise, we demonstrate how the entanglement teleportation scheme of Lee and Kim gives rise to two uncorrelated generalized depolarizing channels. In an attempt to find a teleportation scheme that yields two correlated generalized depolarizing channels, we discover a teleportation scheme that allows one to learn about the entanglement in an entangled pure input state, without decreasing the amount of entanglement associated with it.

Three-body nonadditive forces in systems of three spin-polarized alkali-metal atoms (Li, Na, K, Rb, and Cs) are investigated using high-level ab initio calculations. The nonadditive forces are found to be large, especially near the equilateral equilibrium geometries. For Li, they increase the three-atom potential well depth by a factor of 4 and reduce the equilibrium interatomic distance by $1.07\mathrm{\AA }.$ The nonadditive forces originate principally from chemical bonding arising from $\mathrm{sp}$ mixing effects.

We investigate the particle-number fluctuations due to the collective excitations created in a two-dimensional (2D) and a quasi-2D Bose-Einstein condensates (BECs) at low temperature. We find that the fluctuations display an anomalous behavior, i.e., for the 2D BEC they are proportional to $N^2,$ where N is the total number of particles. For the quasi-2D BEC, the particle-number fluctuations are proportional not only to $N^2$ but also to the square root of the trapping frequency in the strongly confined direction.

A behavior of a two-qubit system coupled by the electric capacitance has been studied quantum mechanically. We found that the interaction is essentially the same as the one for the dipole-dipole interaction; i.e., qubit-qubit coupling of the NMR quantum gate. Therefore, a quantum gate could be constructed by the same operation sequence for the NMR device if the coupling is small enough. The result gives an information to the effort of development of the devices assuming capacitive coupling between qubits.

Several authors have described the basic requirements essential to build a scalable quantum computer. Because many physical implementation schemes for quantum computing rely on nearest-neighbor interactions, there is a hidden quantum communication overhead to connect distant nodes of the computer. In this paper, we propose a physical solution to this problem, which, together with the key building blocks, provides a pathway to a scalable quantum architecture using nonlocal interactions. Our solution involves the concept of a quantum bus that acts as a refreshable entanglement resource to connect distant memory nodes, providing an architectural concept for quantum computers analogous to the von Neumann architecture for classical computers.

We report experimental and theoretical electron spectra within the very low-electron-energy range below 30 eV. Doubly differential cross sections for ionization of different noble gases (He, Ne, Ar, Kr, Xe) by impact of 100-keV and 225-keV protons are reported. A pronounced structure in the low-energy region of emitted-electron spectra is observed with different intensities for the different targets. We compare our experimental findings with two theoretical models: the first-order Born approximation and the “continuum-distorted-wave–eikonal-initial-state” model using different optimized central potentials to calculate the bound and continuum states of the target. We attribute our experimental observation to a signature of the predicted low-energy binary peak.

We point out a connection between anomalous transport in an optical lattice and Tsallis’ generalized statistics. Specifically, we show that the momentum equation for the semiclassical Wigner function which describes atomic motion in the optical potential, belongs to a class of transport equations recently studied by Borland [Phys. Lett. A 245, 67 (1998)]. The important property of these ordinary linear Fokker-Planck equations is that their stationary solutions are exactly given by Tsallis distributions. An analytical expression of the Tsallis index q in terms of the microscopic parameters of the quantum-optical problem is given and the spatial coherence of the atomic wave packets is discussed.

We calculate the spatial correlation function and momentum distribution of a phase-fluctuating, elongated three-dimensional condensate in a trap and in free expansion. We take the inhomogeneous density profile into account via a local-density approximation. We find an almost Lorentzian momentum distribution, in stark contrast with a Heisenberg-limited Thomas-Fermi condensate.

We report the confinement of large clouds of ultracold ${}^{85}\mathrm{Rb}$ atoms in a standing-wave dipole trap formed by the two counterpropagating modes of a high-$Q$ ring cavity. Studying the properties of this trap, we demonstrate loading of higher-order transverse cavity modes and excite recoil-induced resonances.

Entanglement, or quantum inseparability, is a crucial resource in quantum information applications, and therefore the experimental generation of separated yet entangled systems is of paramount importance. Experimental demonstrations of inseparability with light are not uncommon, but such demonstrations in physically well-separated massive systems, such as distinct gases of atoms, are new and present significant challenges and opportunities. Rigorous theoretical criteria are needed for demonstrating that given data are sufficient to confirm entanglement. Such criteria for experimental data have been derived for the case of continuous-variable systems obeying the Heisenberg-Weyl (position-momentum) commutator. To address the question of experimental verification more generally, we develop a sufficiency criterion for arbitrary states of two arbitrary systems. When applied to the recent study by Julsgaard, Kozhekin, and Polzik [Nature 413, 400 (2001)] of spin-state entanglement of two separate, macroscopic samples of atoms, our criterion confirms the presence of spin entanglement.

We calculate a tunneling time distribution by means of Nelson’s quantum mechanics and investigate its statistical properties. The relationship between the average and deviation of tunneling time suggests the existence of “wave-particle duality” in the tunneling phenomena.

We show the equivalence of the functions $G_{\mathrm{p}}\mathrm{}\left(t\right)\mathrm{}$ and $|\Psi \mathrm{}(d,t)\mathrm{}{|}^2$ for the “passage time” in tunneling. The former, obtained within the framework of the real-time Feynman histories approach to the tunneling time problem, uses the Gell-Mann and Hartle’s decoherence functional, and the latter involves an exact analytical solution to the time-dependent Schrödinger equation for cutoff initial waves.

We investigate multipartite entanglement in relation to the process of quantum state exchange. In particular, we consider such entanglement for a certain pure state involving two groups of N trapped atoms. The state, which can be produced via quantum state exchange, is analogous to the steady-state intracavity state of the subthreshold optical nondegenerate parametric amplifier. We show that, first, it possesses some $2N$-way entanglement. Second, we place a lower bound on the amount of such entanglement in the state using a measure called the entanglement of minimum bipartite entropy.

We show that quantum feedback control can be used as a quantum-error-correction process for errors induced by a weak continuous measurement. In particular, when the error model is restricted to one, perfectly measured, error channel per physical qubit, quantum feedback can act to perfectly protect a stabilizer codespace. Using the stabilizer formalism we derive an explicit scheme, involving feedback and an additional constant Hamiltonian, to protect an $\left(n-1\right)$-qubit logical state encoded in n physical qubits. This works for both Poisson (jump) and white-noise (diffusion) measurement processes. Universal quantum computation is also possible in this scheme. As an example, we show that detected-spontaneous emission error correction with a driving Hamiltonian can greatly reduce the amount of redundancy required to protect a state from that which has been previously postulated [e.g., Alber et al., Phys. Rev. Lett. 86, 4402 (2001)].