The fragmentation of the ${\mathrm{H}}_2^{+}$ molecular ion in 25-fs, 800-nm laser pulses in the intensity range 0.05–0.5 P ${\mathrm{W}/\mathrm{c}\mathrm{m}}^2$ is investigated by means of wave-packet propagation calculations. We use a collinear reduced-dimensionality model that represents both the nuclear and electronic motion by one degree of freedom including non-Born-Oppenheimer couplings. In order to reproduce accurately the properties of the “real” three-dimensional molecule, we introduce a modified “soft-core” Coulomb potential with a softening function that depends on the internuclear distance. The analysis of the calculated flux of the outgoing wave packets allows us to obtain fragmentation probabilities and kinetic-energy spectra. Our results show that the relative probabilities for dissociation and Coulomb explosion depend critically on the initial vibrational state of the molecular ion.

Macroscopic quantum coherence of Bose gas in a double-well potential is studied, based on an SU(2) coherent-state path-integral approach. The ground state and fluctuations around it can be obtained by this method. In this picture, one can obtain macroscopic quantum superposition states for attractive Bose gas. The coherent gap of degenerate ground states is obtained with the instanton technique. The phenomenon of macroscopic quantum self-trapping is also discussed.

The explanation presented by Taichenachev et al. [Phys. Rev. A $61,$ 011802 (2000)] according to which the electromagnetically induced absorption (EIA) resonances observed in degenerate two-level systems are due to coherence transfer from the excited to the ground state is experimentally tested in a Hanle-type experiment observing the parametric resonance on the $D1\mathrm{}$ line of ${}^{87}\mathrm{Rb}.$ While EIA occurs in the $F=\overrightarrow{1}{F}^{\prime }=2\mathrm{}$ transition in a cell containing only Rb vapor, collisions with a buffer gas (30 torr of Ne) cause the sign reversal of this resonance as a consequence of collisional decoherence of the excited state. A theoretical model in good qualitative agreement with the experimental results is presented.

The geometrical (total minus dynamical) phase of generally nonadiabatic and noncyclic evolution of initial dressed states, and also arbitrary entangled states, of the two-level system coupled to a quantum oscillator is calculated in closed form. A sudden perturbation of the two-level system leads to a discontinuous phase jump at the instant when the system makes a transition from the initial state. A possible experimental verification in the field of quantum optics is proposed.

Starting from the equations of rotational hydrodynamics we study the macroscopic behavior of a trapped Bose-Einstein condensate containing a large number of vortices. The stationary configurations of the system, the frequencies of the collective excitations, and the expansion of the condensate are investigated as a function of the angular velocity of the vortex lattice. The time evolution of the condensate and of the lattice geometry induced by a sudden deformation of the trap is also discussed and compared with the recent experimental results of P. Engels et al. [Phys. Rev. Lett. 89, 100403 (2002)].

The Heisenberg uncertainty principle states that the product of the noise in a position measurement and the momentum disturbance caused by that measurement should be no less than the limit set by Planck’s constant $ħ/2\mathrm{}$ as demonstrated by Heisenberg’s thought experiment using a γ-ray microscope. Here it is shown that this common assumption is not universally true: a universally valid trade-off relation between the noise and the disturbance has an additional correlation term, which is redundant when the intervention brought by the measurement is independent of the measured object, but which allows the noise-disturbance product much below Planck’s constant when the intervention is dependent. A model of measuring interaction with dependent intervention shows that Heisenberg’s lower bound for the noise-disturbance product is violated even by a nearly nondisturbing precise position measurement. An experimental implementation is also proposed to realize the above model in the context of optical quadrature measurement with currently available linear optical devices.

A strongly driven cavity containing a single resonant strongly coupled atom exhibits a phase bistability. The phase of the field is strongly correlated with the phase of the atomic dipole. It has been shown previously that phase-sensitive monitoring of the field emitted by the cavity would induce conditional quantum jumps between orthogonal atomic dipole states (“dressed” states). Here we show that such monitoring can be used to fix the atom into a single dressed state. As soon as a state-changing quantum jump is inferred from the measurement of the field, the atomic state is flipped using a $\pi$ pulse. We study this feedback scheme analytically and numerically. We show that the occupation probability of the desired fixed state can be as high as $1-1/8\eta C_1,$ where $C_1\gg 1$ is the single-atom cooperativity and $\eta$ the detection efficiency (which does not have to be close to unity). The control of the atomic dynamics is manifest in the fluorescence spectrum. The widths of all three peaks are modified from the usual Mollow spectrum, and almost all of the area under one of the sidebands is transferred to the other sideband. This is as expected, as one of the dressed states is essentially unoccupied, and transitions out of it do not occur. In addition, the width of the central peak goes to zero. This indicates coherent scattering due to the nonzero mean atomic dipole created by the feedback.

We consider cloning transformations of equatorial qubits $|{\psi }_{\phi }〉=1/\sqrt{2}\left(|0〉{+e}^{i\phi }|1〉\right)$ and qutrits $|{\psi }_{\phi ,\theta }〉=1/\sqrt{3}\left(|0〉{+e}^{i\phi }|1〉{+e}^{i\theta }|2〉\right),$ with the transformation covariant for rotation of the phases $\phi$ and $\theta .$ The optimal cloning maps are derived without simplifying assumptions from first principles, for any number of input and output qubits, and for a single-input qutrit and any number of output qutrits. We also compare the cloning maps for global and single-particle fidelities, and we show that the two criteria lead to different optimal maps.

New experiments were proposed recently to investigate the regime of cold atomic and molecular ion-atom collision processes in a special hybrid neutral-atom–ion trap under high-vacuum conditions. We study the collisional cooling of laser precooled ${\mathrm{Ca}}^{+}$ ions by ultracold Na atoms. Modeling this process requires knowledge of the radiative lifetime of the excited singlet $A{}^1{\Sigma }^{+}$ state of the $(\mathrm{NaCa}{)}^{+}$ molecular system. We calculate the rate coefficient for radiative charge transfer using a semiclassical approach. The dipole radial matrix elements between the ground and the excited states, and the potential curves were calculated using complete active space self-consistent field and Möller-Plesset second-order perturbation theory with an extended Gaussian basis, 6-311+G $\mathrm{}\left(3df\right).$ The semiclassical charge-transfer rate coefficient was averaged over a thermal Maxwellian distribution. In addition, we also present elastic collision cross sections and the spin-exchange cross section. The rate coefficient for charge transfer was found to be $2.3\times {10}^{-16}{\mathrm{cm}}^3/\sec ,$ while those for the elastic and spin-exchange cross sections were found to be several orders of magnitude higher $(1.1\mathrm{}\times {10}^{-8}{\mathrm{cm}}^3/\sec$ and $2.3\times {10}^{-9}{\mathrm{cm}}^3/\sec ,$ respectively). This confirms our assumption that the milli-Kelvin regime of collisional cooling of calcium ions by sodium atoms is favorable with the respect to low loss of calcium ions due to the charge transfer.

The two-body scattering length a for ${}^4\mathrm{He}$ atoms is much larger than their effective range $r_s.$ As a consequence, low-energy few-body observables have universal characteristics that are independent of the interaction potential. Universality implies that, up to corrections suppressed by $r_s/a,$ all low-energy three-body observables are determined by a and a three-body parameter ${\Lambda }_{*}.$ We give simple expressions in terms of a and ${\Lambda }_{*}$ for the trimer binding-energy equation, the atom-dimer scattering phase shifts, and the rate for three-body recombination at threshold. We determine ${\Lambda }_{*}$ for several ${}^4\mathrm{He}$ potentials from the calculated binding energy of the excited state of the trimer and use it to obtain the universality predictions for the other low-energy observables. We also use the calculated values for one potential to estimate the effective range corrections for the other potentials.

We investigate the time evolution of a Bose-Einstein condensate in a periodic optical potential. Using an effective mass formalism, we study the equation of motion for the envelope function modulating the Bloch states of the lattice potential. In particular, we show how the negative effective-mass affects the dynamics of the condensate.

We predict theoretically and demonstrate experimentally an ellipticity-dependent nonlinear magneto-optic rotation of elliptically polarized light propagating in a medium with atomic coherence. We show that this effect results from hexadecapole and higher-order moments of the atomic coherence, and is associated with an enhancement of Kerr and higher-order nonlinearities accompanied by suppression of the other linear and nonlinear susceptibility terms of the medium. These nonlinearities might be useful for quantum signal processing. In particular, we report an observation of enhancement of the polarization rotation of elliptically polarized light resonant with the ${5S}_{1/2}F=\overrightarrow{2}{5P}_{1/2}F=1\mathrm{}$ transition of ${}^{87}\mathrm{Rb}.$

We investigate the optical detection of single atoms held in a microscopic atom trap close to a surface. Laser light is guided by optical fibers or optical microstructures via the atom to a photodetector. Our results suggest that with present-day technology microcavities can be built around the atom with sufficiently high finesse to permit unambiguous detection of a single atom in the trap with $10\mu \mathrm{s}$ of integration. We compare resonant and nonresonant detection schemes and discuss the requirements for detecting an atom without causing it to undergo spontaneous emission.

Implications of field quantization on Ramsey interferometry are discussed and general conditions for the occurrence of interference are obtained. Interferences do not occur if the fields in two Ramsey zones have a precise number of photons. However, in this case we show how an analog of Hanbury-Brown Twiss photon-photon correlation interferometry can be used to discern a variety of interference effects as the two independent Ramsey zones get entangled by the passage of the first atom. Interferences are restored by working with fields at a single-photon level. Generation of entangled states including states such as $|2,0〉{+e}^{i\theta }|0,2〉$ is discussed.

The interaction of a two-level system with a strong standing wave is examined by the probe field resonant to the adjacent transition in the $\Lambda$ configuration of Ar II. The known peak of electromagnetically induced transparency is observed in the absorption spectrum at the detuning of the probe field proportional to the detuning of the strong field. Along with it, the different structure has been found at the line center, independently of the strong-field frequency. The calculations clarify that the central structure is induced by the higher-order spatial harmonics of the atomic coherence induced at the probe transition. The effect results in steep frequency dependence of the refractive index at the line center.

We propose a method for generating photon pairs from coherent light, using polarization-dependent two-photon absorption. We study the photon statistics of two orthogonally polarized modes by solving a master equation, and show that when we prepare a coherent state in one polarization mode, photon pairs are created in the other mode. The photon pairs have the same frequency as that of the incident light.

Cross sections and rate coefficients for collisions of two spin-polarized metastable hydrogen atoms are calculated at low energies and temperatures using complex scaling and Feshbach projection methods for the determination of the molecular potential-energy curves. The inclusion of the Lamb shift and fine-structure splitting of the excited $n=2\mathrm{}$ atoms leads to an attractive van der Waals potential for two ${2s}_{1/2}$ atoms with an exceptionally large coefficient. The quenching of the metastable atoms is dominated at temperatures below 20 mK by ionization. The calculated values for the total loss rate coefficient at 87 μK and 230 μK are within a factor of 2 or 3 of the error bars of recent measurements of metastable loss rate coefficients.

The one-particle density matrices for hard-core bosons in a one-dimensional harmonic trap are computed numerically for systems with up to 160 bosons. Diagonalization of the density matrix shows that the many-body ground state is not Bose-Einstein condensed. The ground-state occupation, the amplitude of the lowest natural orbital, and the zero momentum peak height scale as powers of the particle number, and the corresponding exponents are related to each other. Close to its diagonal, the density matrix for hard-core bosons is similar to that of noninteracting fermions.

We suggest a general scheme for continuous variable quantum-state engineering based on conditional measurements carried out on entangled twin beam of radiation. Realistic detection schemes such as on/off photodetection, homodyne detection, and joint measurement of two-mode quadratures are analyzed in detail. Imperfections of the apparatuses, such as nonunit quantum efficiency and finite resolution, are taken into account. We show that conditional on/off photodetection provides a reliable scheme to verify nonclassicality, whereas conditional homodyning represents a tunable and robust source of squeezed light. We also describe optical continuous variable teleportation as a conditional measurement, and evaluate the degrading effects of finite amount of entanglement, decoherence due to losses, and nonunit quantum efficiency.