We show that $2n$ random classical bits are both necessary and sufficient for encrypting any unknown state of n quantum bits in an informationally secure manner. We also characterize the complete set of optimal protocols in terms of a set of unitary operations that comprise an orthonormal basis in a canonical inner product space. Moreover, a connection is made between quantum encryption and quantum teleportation that allows for a different proof of optimality of teleportation.

In this paper, we propose a scheme for teleportating a superposition of atomic center-of-mass momentum states to a superposition of the cavity field using quantum controlled-NOT gate via atomic scattering in the Bragg regime and cavity quantum electrodynamics.

In this paper, we present cross sections for elastic scattering of low-energy electrons by $X{\mathrm{H}}_{3}Y{\mathrm{H}}_3$ $(X,$ $Y=\mathrm{C},$ Si, Ge, and Sn) molecules. To compute the cross sections we used the Schwinger multichannel method with pseudopotentials at the fixed-nuclei static-exchange approximation. In order to make a comparative study of the scattering cross sections of the $X{\mathrm{H}}_{3}Y{\mathrm{H}}_3$ molecules, which have the same number of valence electrons, we also present the results of previous calculations for ${\mathrm{C}}_2{\mathrm{H}}_6,$ ${\mathrm{Si}}_2{\mathrm{H}}_6,$ and ${\mathrm{Ge}}_2{\mathrm{H}}_6.$

We present results of calculations of the angular distributions of K-shell photoelectrons from fixed-in-space CO and ${\mathrm{N}}_2$ molecules emitted by circularly polarized light. These calculated distributions account well for the strong circular dichroism recently reported in measurements of photoelectron distributions in these two systems. The calculations also serve to identify regions of photoelectron energy where pronounced circular dichroism can be expected in these spectra.

We present a theoretical study of the angular distribution of emitted electrons of a sodium cluster, irradiated by short and intense laser pulses. While the polarization of the excitation field tends to focus a directional emission, the dynamical correlations tend to thermalize the electrons, giving rise to a more isotropic ionization. The competition between these processes is investigated using a semiclassical model Vlasov-Ühling-Uhlenbeck, where the dynamical correlations are taken in account by the electron-electron correlations in the Markovian approximation, the widely known Ühling-Uhlenbeck collision term. The results are compared to a semiclassical pure mean-field propagation (Vlasov equation) to work out the influence of dynamical correlations on the angular distribution of the electron emission. The trends with laser intensity and frequency are explored. The time evolution of the angular distributions shows that direct emission processes are stronger in the early phase of the processs, while isotropic thermal emission dominates later.

We have performed classical molecular-dynamics simulations of the fragmentation collisions of neutral fullerenes $({\mathrm{C}}_{24},$ ${\mathrm{C}}_{60},$ ${\mathrm{C}}_{100},$ and ${\mathrm{C}}_{240})$ with a hard wall. The interactions between the carbon atoms are modeled by a Tersoff potential and the position of each carbon atom at each time step is calculated using a sixth-order predictor-corrector method. The statistical distribution of the fragments depends on impact energy. At low energies, the fragment distribution appears symmetric, with both the large and small fragment distributions well fitted by an exponential function of the same exponent, the value of which decreases with impact energy. At intermediate energies, the distribution of the smallest fragments can be fitted equally well by a power law or an exponential function. At high impact energies, the entire fragmentation pattern is well described by a single exponential function, the exponent increasing with energy. The observed tendencies in fragment distributions as well as the obtained exponents are in agreement with experimental observations. The fragmentation behavior of the four investigated fullerenes is very similar, and it is noted that ${\mathrm{C}}_{60}$ appears to be the most stable.

The possibility of laser cooling of alkaline-earth-metal atoms and ytterbium atoms using a two-photon transition is analyzed. We consider a ${}^1{S}_0{-}^1{S}_0$ transition with excitation in near resonance with the ${}^1{P}_1$ level. This greatly increases the two-photon transition rate, allowing an effective transfer of momentum. The experimental implementation of this technique is discussed and we show that for calcium, for example, two-photon cooling can be used to achieve a Doppler limit of $123\mu \mathrm{K}.$ The efficiency of this cooling scheme and the main loss mechanisms are analyzed.

Photoassociation spectroscopy experiments on ${}^{40}\mathrm{Ca}$ atoms close to the dissociation limit ${4s4s}^1{S}_0-{4s4p}^1{P}_1$ are presented. The vibronic spectrum was measured for detunings of the photoassociation laser ranging from 0.6 to 68 GHz with respect to the atomic resonance. In contrast to previous measurements, the rotational splitting of the vibrational lines was fully resolved. Full quantum-mechanical numerical simulations of the photoassociation spectrum were performed which allowed us to put constraints on the possible range of the calcium scattering length between ${50a}_0$ and ${300a}_0.$

We propose and analyze a series of nondestructive dynamic detectors for Bose-Einstein condensates based on photodetectors operating at the shot-noise limit. These detectors are compatible with real-time feedback to the condensate. The signal-to-noise ratio of different detection schemes are compared subject to the constraint of minimal heating due to photon absorption and spontaneous emission. This constraint leads to different optimal operating points for interference-based schemes. We find the somewhat counterintuitive result that without the presence of a cavity, interferometry causes as much destruction as absorption for optically thin clouds. For optically thick clouds, cavity-free interferometry is superior to absorption, but it still cannot be made arbitrarily nondestructive. We propose a cavity-based measurement of atomic density which can in principle be made arbitrarily nondestructive for a given signal-to-noise ratio.

A development of the theory of multilayer systems is presented. It shows precisely how to calculate thicknesses and number of layers to get reflectivity close to unity for a given arbitrary critical angle. Application of the proposed approach to real systems is demonstrated.

We present a derivation of the Casimir force between two parallel plane mirrors at zero temperature. The two mirrors and the cavity they enclose are treated as quantum optical networks. They are, in general, lossy and characterized by frequency-dependent reflection amplitudes. The additional fluctuations accompanying losses are deduced from expressions of the optical theorem. A general proof is given for the theorem relating the spectral density inside the cavity to the reflection amplitudes seen by the inner fields. This density determines the vacuum radiation pressure and, therefore, the Casimir force. The force is obtained as an integral over the real frequencies, including the contribution of evanescent waves besides that of ordinary waves, and then as an integral over imaginary frequencies. The demonstration relies only on general properties obeyed by real mirrors which also enforce general constraints for the variation of the Casimir force.

Transverse effects in the laser dynamics due to near dipole-dipole interactions are studied considering the presence of permanent electric dipole moments. The semiclassical two-level Maxwell-Bloch equations are used and a single longitudinal mode is assumed. A traveling wave is selected at threshold when the sum of the cavity detuning and the near dipole-dipole parameter is larger than zero. As a consequence of this, transverse pattern can occur even when the laser frequency is larger than the frequency of the atomic transition. Also, a cutoff in the laser field spectrum arises. We found that the near dipole-dipole interactions significantly modify the stability picture of the traveling waves. Numerical simulations have been carried out and the effect of the near dipole-dipole on the pattern formation is addressed.

The aim of this work is to find ways to trap an atom in a cavity. In contrast to other approaches, we propose a method where the cavity is basically in the vacuum state and the atom is in the ground state. The idea is to induce a spatial dependent ac-Stark shift by irradiating the atom with a weak laser field, so that the atom experiences a trapping force. The main feature of our setup is that dissipation can be strongly suppressed. We estimate the lifetime of the atom as well as the trapping potential parameters, and compare our estimations with numerical simulations.

An isotropic microchip laser is used to study the characteristics of high-order wave functions in a two-dimensional (2D) quantum harmonic oscillator based on the identical functional forms. With a doughnut pump profile, the spontaneous transverse modes are found to, generally, be elliptic and hyperbolic transverse modes. Theoretical analyses reveal that the elliptic transverse modes are analogous to the coherent states of a 2D harmonic oscillator; the formation of hyperbolic transverse modes is a spontaneous mode locking between two identical Hermite-Gaussian modes.

We present a scheme to generate a maximally entangled state of two three-level atoms with a nonresonant cavity by cavity-assisted collisions. Since the cavity field is only virtually excited, no quantum information will be transferred from the atoms to the cavity.

The triple-differential cross section for ionization of a heavy atom is shown to depend on the spin of the incident electron even if this is polarized entirely parallel or antiparallel to its direction of propagation, the atom is unpolarized, and the spins of the ejected electrons are not resolved. Quantitative predictions for the spin asymmetry are presented in a relativistic distorted-wave Born approximation. Simple physical models are introduced to understand both these results and further symmetry properties involving the reversal of a spatial momentum component also.

We consider the effects of the trap environment on atomic and optical quantum statistical properties and on atom-photon correlations in the collective atomic-recoil laser. Atomic and optical statistical properties, as well as atom-photon correlations are dependent on the optical-field intensity and phase. In particular, depending on the values of the optical-field intensity and phase, the field statistics vary from coherent to superchaotic.

Using a quantum theory for an ensemble of three-level atoms $\left(\Lambda \right)$ placed in an optical cavity and driven by electromagnetic fields, we show that the long-lived spin associated with the ground-state sublevels can be squeezed. Two kinds of squeezing are obtained: self-spin squeezing, when the input fields are coherent states and the atomic ensemble exhibits a large nonlinearity; squeezing transfer approaching 100%, when one of the incoming fields is squeezed.

We study nonlocal two-qubit operations from a geometric perspective. By applying a Cartan decomposition to su(4), we find that the geometric structure of nonlocal gates is a 3-torus. We derive the invariants for local transformations, and connect these local invariants to the coordinates of the 3-torus. Since different points on the 3-torus may correspond to the same local equivalence class, we use the Weyl group theory to reduce the symmetry. We show that the local equivalence classes of two-qubit gates are in one-to-one correspondence with the points in a tetrahedron except on the base. We then study the properties of perfect entanglers, that is, the two-qubit operations that can generate maximally entangled states from some initially separable states. We provide criteria to determine whether a given two-qubit gate is a perfect entangler and establish a geometric description of perfect entanglers by making use of the tetrahedral representation of nonlocal gates. We find that exactly half the nonlocal gates are perfect entanglers. We also investigate the nonlocal operations generated by a given Hamiltonian. We first study the gates that can be directly generated by a Hamiltonian. Then we explicitly construct a quantum circuit that contains at most three nonlocal gates generated by a two-body interaction Hamiltonian, together with at most four local gates generated by single-qubit terms. We prove that such a quantum circuit can simulate any arbitrary two-qubit gate exactly, and hence it provides an efficient implementation of universal quantum computation and simulation.

The fast phase gate scheme, in which the qubits are atoms confined in sites of an optical lattice, and gate operations are mediated by excitation of Rydberg states, was proposed by Jaksch et al. [Phys. Rev. Lett. $85,$ 2208 (2000)]. A potential source of decoherence in this system derives from motional heating, which occurs if the ground and Rydberg states of the atom move in different optical lattice potentials. We propose to minimize this effect by choosing the lattice photon frequency $\omega ,$ so that the ground and Rydberg states have the same frequency-dependent polarizability $\alpha \left(\omega \right).\mathrm{}$ The results are presented for the case of Rb.