How to prepare quantum states that follow classical paths

We present an alternative quantization procedure for the one-dimensional non-relativistic quantum mechanics. We show that, for the case of a free particle and a particle in a box, the complete classical and quantum correspondence can be obtained using this formulation. The resulting wave packets do not disperse and strongly peak on the classical paths. Moreover, for the case of the free particle, they satisfy minimum uncertainty relation.Comment: 10 pages, 3 figures, to appear in Europhysics Letter

Correlations in an expanding gas of hard-core bosons

We consider a longitudinal expansion of a one-dimensional gas of hard-core bosons suddenly released from a trap. We show that the broken translational invariance in the initial state of the system is encoded in correlations between the bosonic occupation numbers in the momentum space. The correlations are protected by the integrability and exhibit no relaxation during the expansion

Attractive ultracold bosons in a necklace optical potential

We study the ground state properties of the Bose-Hubbard model with attractive interactions on a M-site one-dimensional periodic -- necklace-like -- lattice, whose experimental realization in terms of ultracold atoms is promised by a recently proposed optical trapping scheme, as well as by the control over the atomic interactions and tunneling amplitudes granted by well-established optical techniques. We compare the properties of the quantum model to a semiclassical picture based on a number-conserving su(M) coherent state, which results into a set of modified discrete nonlinear Schroedinger equations. We show that, owing to the presence of a correction factor ensuing from number conservation, the ground-state solution to these equations provides a remarkably satisfactory description of its quantum counterpart not only -- as expected -- in the weak-interaction, superfluid regime, but even in the deeply quantum regime of large interactions and possibly small populations. In particular, we show that in this regime, the delocalized, Schroedinger-cat-like quantum ground state can be seen as a coherent quantum superposition of the localized, symmetry-breaking ground-state of the variational approach. We also show that, depending on the hopping to interaction ratio, three regimes can be recognized both in the semiclassical and quantum picture of the system.Comment: 11 pages, 7 figures; typos corrected and references added; to appear in Phys. Rev.

Hubbard ring: currents induced by change of magnetic flux

We investigate currents in a quantum ring threaded by a magnetic flux which can be varied in an arbitrary way from an initial value $\phi_i$ at time $t_i$ to a final value $\phi_f$ at time $t_f$. Dynamics of electrons in the ring is described by the Hubbard and the extended Hubbard models. We demonstrate that time dependence of the induced current bears information on electron correlations. In the case of the Hubbard model with infinite on--site repulsion we prove that the current for $t>t_f$ is independent of the flux variation before $t_f$. Additionally, this current is fully determined by a solution of the initial equilibrium problem and the value of $\phi_f$. Apart from mesoscopic rings our results pose important implications for designing of quantum motors built out as the ring--shaped optical lattice

Mesoscopic superposition and sub-Planck-scale structure in molecular wave packets

We demonstrate the possibility of realizing sub-Planck-scale structures in the mesoscopic superposition of molecular wave packets involving vibrational levels. The time evolution of the wave packet, taken here as the SU(2) coherent state of the Morse potential describing hydrogen iodide molecules, produces macroscopicquantum- superposition-like states, responsible for the above phenomenon. We investigate the phase-space dynamics of the coherent state through the Wigner function approach and identify the interference phenomena behind the sub-Planck-scale structures. The optimal parameter ranges are specified for observing these features.Comment: 4 pages, 3 figure

Production of high energy particles in laser and Coulomb fields and e^+e^- antenna

A strong laser field and the Coulomb field of a nucleus can produce e^{+}e^{-} pairs. It is shown for the first time that there is a large probability that electrons and positrons created in this process collide after one or several oscillations of the laser field. These collisions can take place at high energy resulting in several phenomena. The quasielastic collision e^{+}e^{-} -> e^{+}e^{-} allows acceleration of leptons in the laser field to higher energies. The inelastic collisions allow production of high energy photons e^{+}e^{-}-> 2 gamma and muons, e^{+}e^{-} -> mu^{+}mu^{-}. The yield of high-energy photons and muons produced via this mechanism exceeds exponentially their production through conventional direct creation in laser and Coulomb fields. A relation of the phenomena considered with the antenna-mechanism of multiphoton absorption in atoms is discussed.Comment: 4 page

Reformulation of the strong-field approximation for light-matter interactions

We consider the interaction of hydrogen-like atoms with a strong laser field and show that the strong field approximation and all its variants may be grouped into a set of families of approximation schemes. This is done by introducing an ansatz describing the electron wave packet as the sum of the initial state wave function times a phase factor and a function which is the perturbative solution in the Coulomb potential of an inhomogeneous time-dependent Schr\"odinger equation. It is the phase factor that characterizes a given family. In each of these families, the velocity and length gauge version of the approximation scheme lead to the same results at each order in the Coulomb potential. By contrast, irrespective of the gauge, approximation schemes belonging to different families give different results. Furthermore, this new formulation of the strong field approximations allows us to gain deeper insight into the validity of the strong field approximation schemes. In particular, we address two important questions: the role of the Coulomb potential in the output channel and the convergence of the perturbative series in the Coulomb potential. In all the physical situations we consider here, our results are compared to those obtained by solving numerically the time-dependent Schr\"odinger equation.Comment: 19 pages, 9 figures, submitted for publicatio

Joint measurements via quantum cloning

We explore the possibility of achieving optimal joint measurements of noncommuting observables on a single quantum system by performing conventional measurements of commuting self adjoint operators on optimal clones of the original quantum system. We consider the case of both finite dimensional and infinite dimensional Hilbert spaces. In the former we study the joint measurement of three orthogonal components of a spin 1/2, in the latter we consider the case of the joint measurements of any pair of noncommuting quadratures of one mode of the electromagnetic field. We show that universally covariant cloning is not ideal for joint measurements, and a suitable non universally covariant cloning is needed.Comment: 8 page

Momentum Analysis in Strong-field Double Ionization

We provide a basis for the laser intensity dependence of the momentum distributions of electrons and ions arising from strong-field non-sequential double ionization (NSDI) at intensities in the range $I=1-6.5 \times 10^{14} W/cm^2$. To do this we use a completely classical method introduced previously \cite{ho-etal05}. Our calculated results reproduce the features of experimental observations at different laser intensities and depend on just two distinct categories of electon trajectories.Comment: 5 pages, 7 figure

Exact number conserving phase-space dynamics of the M-site Bose-Hubbard model

The dynamics of M-site, N-particle Bose-Hubbard systems is described in quantum phase space constructed in terms of generalized SU(M) coherent states. These states have a special significance for these systems as they describe fully condensed states. Based on the differential algebra developed by Gilmore, we derive an explicit evolution equation for the (generalized) Husimi-(Q)- and Glauber-Sudarshan-(P)-distributions. Most remarkably, these evolution equations turn out to be second order differential equations where the second order terms scale as 1/N with the particle number. For large N the evolution reduces to a (classical) Liouvillian dynamics. The phase space approach thus provides a distinguished instrument to explore the mean-field many-particle crossover. In addition, the thermodynamic Bloch equation is analyzed using similar techniques.Comment: 11 pages, Revtex