We derive the elastic collision rate for a harmonically trapped Fermi gas in the extreme unitarity limit where the s-wave scattering cross section is $\sigma \mathrm{}\left(k\right)=4\mathrm{}\pi {/k}^2,$ with $ħk$ the relative momentum. The collision rate is given in the form $\Gamma =\gamma {I(T/T}_F)$—the product of a universal collision rate $\gamma {=k}_B{T}_F/\left(6\mathrm{}\pi ħ\right)$ and a dimensionless function of the ratio of the temperature T to the Fermi temperature $T_F.$ We find that I has a peak value of $\simeq 4.6$ at ${T/T}_F\simeq 0.4,$ $I\simeq 82{(T/T}_F{)}^2$ for ${T/T}_F<~0.15,$ and $I\simeq {2(T}_F{/T)}^2$ for ${T/T}_F>\mathrm{1.5.}\mathrm{}$ We estimate the collision rate for recent experiments on a strongly-interacting degenerate Fermi gas of atoms.

We theoretically study a pulsed stimulated two-photon Raman outcoupler for an atom laser using a full three-dimensional description. A finite-temperature trapped Bose-condensed atomic gas is treated self-consistently by the Hartree-Fock-Bogoliubov equations. The model is closely related to a recent experiment on optical outcoupling [E. W. Hagley et al., Science 283, 1706 (1999)]. We analyze the momentum distribution of the output atoms and show how the output beam may be used as a probe of the quantum state for the trapped atomic gas and how it could be engineered and controlled in a nonlinear way.

We develop a distillation protocol for multilevel qubits (qudits) using generalized beam splitters like in the proposal of Pan et al. for ordinary qubits. We find an acceleration with respect to the scheme of Bennet et al. when extended to qudits. It is also possible to distill entangled pairs of photons carrying orbital angular momenta states that conserve the total angular momenta as those produced in recent experiments.

We have theoretically and experimentally studied how a Mach-Zehnder interferometer with an additional mirror transforms a light beam composed of the second lowest transverse modes, ${\mathrm{HG}}_{10},$ ${\mathrm{HG}}_{01},$ ${\mathrm{LG}}_{01},$ and ${\mathrm{LG}}_{0-1}$ (HG denotes Hermite-Gaussian mode; LG denotes Laguerre-Gaussian mode). In certain conditions, the interferometer divides the incident beam into the ${\mathrm{HG}}_{10}$ and ${\mathrm{HG}}_{01}$ components as a transverse-mode beam splitter. We propose a practical device involving the two interferometers for quantum cryptography, in which a photon carries two bits corresponding to the polarization and the transverse mode.

A quantum cryptography scheme based on entanglement between a single-particle state and a vacuum state is proposed. The scheme utilizes linear optics devices to detect the superposition of the vacuum and single-particle states. Existence of an eavesdropper can be detected by using a variant of Bell’s inequality.

We present a calculation of the static and dynamic dipole polarizability of the helium atom using a variationally stable treatment that incorporates the coupled-channel hyperspherical representation of the wave functions. Inclusion of logarithmic terms in intermediate functions as well as the effect of an optimization procedure for the variational parameter are analyzed. When available, our coupled-channel results are compared with other values in the literature.

We demonstrate, both experimentally and theoretically, clear manifestation of the second Born effects in the angular distributions of two ejected electrons produced by a 500 eV electron impact on the He atom in the so-called $\mathrm{}(e,3e)\mathrm{}$ reaction. The second Born contribution, due to subsequent interaction of the projectile with the target, is most prominent for glancing collisions with small momentum transfer. However, these effects are absent for hard knock-out collisions with large momentum transfer.

So far much theoretical consideration of experiments on the Bose-Einstein condensation (BEC) of alkali-metal atoms in harmonic traps is based on the Gross-Pitaevskii (GP) equation. In this paper, we attempt to formulate the BEC in the language of quantum field theory and to estimate the quantum and thermal fluctuation effects, which are neglected in the approximation using the GP equation. First, the formulation at zero temperature is developed, and then it is extended to the finite-temperature case by means of thermofield dynamics. We treat the zero-energy mode with care, so that the canonical commutation relations hold. As a result, an infrared divergence appears, but it can be renormalized into the observed condensate number. Numerical calculations are performed. For illustration, the corrections at one-loop level to the original GP equation are given. We also calculate numerically the effects of quantum and thermal fluctuations on the distribution of condensed atoms.

The spherical wave functions of the charge-dyon bound system in a rectangular spherical quantum dot of infinite and finite height are calculated. The transcendental equations, defining the energy spectra of the systems, are obtained. The dependence of the energy levels on the wall sizes is found.

Ionization and/or fragmentation of large organic molecules in strong laser fields can be quantitatively understood as a transition from adiabatic to nonadiabatic dynamics of the electronic degrees of freedom. Measurements of fragmentation patterns demonstrate regular trends as a function of the size and electronic structure of a molecule. A theoretical model is presented that agrees quantitatively with the measurements for a series of polycyclic aromatic molecules.

We investigate vortex-antivortex pair creation in a supersonically expanding and contracting quasi-two-dimensional Bose-Einstein condensate at zero temperature. For sufficiently large-amplitude condensate oscillations, pair production provides the leading dissipation mechanism. The condensate oscillations decay in a nonexponential manner, and the dissipation rate depends strongly on the oscillation amplitude. These features allow one to distinguish the decay due to pair creation from other possible damping mechanisms. An experimental observation of the predicted oscillation behavior of the superfluid gas provides a direct confirmation of the hydrodynamical analogy of quantum electrodynamics and quantum vortex dynamics in two spatial dimensions.

We propose a model describing the interaction of an electron confined in a spherical box with a polar molecule in the center of the box, including an inner repulsive potential. As a preparation to its investigation, we calculate the average radius of a dipole-bound nonconfined electron, for which a closed form expression is found. The angular dependence of the wave function is also discussed, with implications for the choice of basis functions for ab initio calculations. The Schrödinger equation in the spherical box is then solved. The negative energy eigenstates of the system and the dependence of the ground-state energy on the radius of the confining sphere are obtained. Interestingly, a very simple expression is found for the total number of negative energy levels for a given dipole strength and confining sphere radius.

A neutron-spin experimental test of the quantum Zeno effect (QZE) is discussed from a practical point of view, where the nonideal efficiency of the magnetic mirrors, used for filtering the spin state, is taken into account. In the idealized case, the number N of (ideal) mirrors can be indefinitely increased, yielding an increasingly better QZE. In contrast, in a practical situation with imperfect mirrors, there is an optimal number of mirrors, $N_{\mathrm{opt}},$ at which the QZE becomes maximum: more frequent measurements would deteriorate the performance. However, a quantitative analysis shows that a good experimental test of the QZE is still feasible. These conclusions are of general validity: in a realistic experiment, the presence of losses and imperfections leads to an optimal frequency $N_{\mathrm{opt}},$ which is in general finite. One should not increase N beyond $N_{\mathrm{opt}}.$ A convenient formula for $N_{\mathrm{opt}},$ valid in a broad framework, is derived as a function of the parameters characterizing the experimental setup.

The effect of noise on quantum teleportation of a spin-$\frac{1}{2}$ state using an entangled pair is studied. We calculate the time evolution of the density matrix of the three involved particles due to their coupling with the environmental degrees of freedom. We evaluate the fidelity of transmission as a function of time under a variety of conditions and compare the fidelities obtained for different entangled states. We find that for a generic coupling to environment, use of the singlet state for the entangled pair yields the highest fidelity in noisy conditions.

We address the problem of constructing quantum circuits to implement an arbitrary two-qubit quantum computation. We pursue circuits without ancilla qubits and as small a number of elementary quantum gates as possible. Our lower bound for worst-case optimal two-qubit circuits calls for at least $17$ gates: $15$ one-qubit rotations and $2$ controlled-NOT (CNOT) gates. We also constructively prove a worst-case upper bound of $23$ elementary gates, of which at most four (CNOT gates) entail multiqubit interactions. Our analysis shows that synthesis algorithms suggested in previous work, although more general, entail larger quantum circuits than ours in the special case of two qubits. One such algorithm has a worst case of $61$ gates, of which $18$ may be CNOT gates.

We present a protocol for performing entanglement swapping with intense pulsed beams. In a first step, the generation of amplitude correlations between two systems that have never interacted directly is demonstrated. This is verified in direct detection with electronic modulation of the detected photocurrents. The measured correlations are better than expected from a classical reconstruction scheme. In an entanglement swapping process, a four-partite entangled state is generated. We prove experimentally that the amplitudes of the four optical modes are quantum correlated 3 dB below shot noise, which is consistent with the presence of genuine four-party entanglement.

We present a composite pulse controlled phase gate which, together with a bus architecture, improves the feasibility of a recent quantum computing proposal based on rare-earth-ion-doped crystals. The proposed gate operation is tolerant to variations between ions of coupling strengths, pulse lengths, and frequency shifts. In the absence of decoherence effects, it achieves worst case fidelities above $0.999$ with relative variations in coupling strength as high as $10\%$ and frequency shifts up to several percent of the resonant Rabi frequency of the laser used to implement the gate. We outline an experiment to demonstrate the creation and detection of maximally entangled states in the system.

In this paper, we apply the canonical decomposition of two-qubit unitaries to find pulse schemes to control the proposed Kane quantum computer. We explicitly find pulse sequences for the controlled-NOT, swap, square root of swap, and controlled Z rotations. We analyze the speed and fidelity of these gates, both of which compare favorably to existing schemes. The pulse sequences presented in this paper are theoretically faster, with higher fidelity, and simpler. Any two-qubit gate may be easily found and implemented using similar pulse sequences. Numerical simulation is used to verify the accuracy of each pulse scheme.

Energy levels, transition probabilities, and lifetimes have been determined for all levels of the Ca I spectrum up to $3d4p{}^1{F}_3^o$ using the multiconfiguration Hartree-Fock method with lowest-order relativistic effects included through the Breit-Pauli Hamiltonian. The mixing of singlet and triplet configuration states was found to be considerably stronger in $4s5p{}^{1,3}{P}_1^o$ levels than in $4s4p{}^{1,3}{P}_1^o$ levels. The near degeneracy of the nonrelativistic $3d4p{}^3{F}^o$ and ${}^1{D}^o$ term energies, differing by only $39.59{\mathrm{cm}}^{-1}$ resulted in highly mixed Breit-Pauli levels for $3d4p{}^3{F}_2^o$ and ${}^1{D}_2^o.$ Some intercombination transitions from these levels have transition probabilities of magnitude similar to weaker spin-allowed transitions. The “fine-tuned” transition probability for the $4s4p{}^3{P}_1^o-4s4d{}^1{D}_2$ transition was found to be $1.53\times {10}^3{\mathrm{s}}^{-1},$ in agreement with a quenching rate observed in a doppler cooling experiment [Binnewies et al., Phys. Rev. Lett. 87, 123002 (2001)].

We have measured the forward-backward asymmetry of photoelectron angular distributions produced in the vacuum ultraviolet photoionization of helium. This asymmetry, a consequence of the breakdown of the dipole approximation, measures the real part of the ratio of the quadrupole and dipole matrix elements. In the autoionization region, the strong energy dependence of the asymmetry permits an experimental separation of the ratio of those magnitudes from their phase difference. We experimentally determined the Fano parameters of the ${2p}^2{}^1{D}_2$ quadrupole resonance, and report improved values of the width $\Gamma$ and line profile parameter q from those previously available from electron scattering. Off resonance, the smooth energy dependence of the asymmetry is found to agree well with the theoretical treatment presented here which incorporates higher-multipole effects.