Using a ${}^{21}\mathrm{Ne}{-}^3\mathrm{He}$ Zeeman maser, we compared the frequency shift of the ${}^{21}\mathrm{Ne}$ nuclear Zeeman resonance induced by polarized Rb vapor to the shift induced in the ${}^3\mathrm{He}$ nuclear Zeeman resonance. The ${}^3\mathrm{He}-\mathrm{Rb}$ shift has recently been measured with high precision [M.V. Romalis and G.D. Cates, Phys. Rev. A 58, 3004 (1998)], permitting the conversion of our differential measurement to an absolute value for the ${}^{21}\mathrm{Ne}-\mathrm{Rb}$ shift. We report a value of ${\kappa }_{21}=32.0\mathrm{}\pm 2.9$ for the $\mathrm{Rb}{-}^{21}\mathrm{Ne}$ contact shift enhancement factor at a temperature of approximately $128°\mathrm{C}.$ We also propose high-precision differential contact shift measurements, the absolute accuracy of which could be limited by the error in the ${}^3\mathrm{He}$ contact shift.

Highly excited Rydberg states of H-like or He-like silicon are formed when ${\mathrm{Si}}^{14+}$ or ${\mathrm{Si}}^{13+}$ ions capture a single electron from an $n=10\mathrm{}$ Rydberg target. Previous studies of the capture process indicate that a few $n$’s near $n=76\mathrm{}$ or $n=72,$ respectively, are formed in the two cases. When these products are subjected to a weak external electric field $(E\approx 20\mathrm{V}/\mathrm{c}\mathrm{m}),$ an enhanced rate of decay directly to the $1S$ ground state results as long-lived high-$L$ states are mixed with the rapidly decaying P states. The yield of these $\mathrm{nP}-1S$ x rays approaches a limit when the external field is sufficient to fully Stark mix the Rydberg manifold and this limiting yield can be used to deduce the fraction of Rydberg ions which are formed in states of low m $(m=-1,0,1).$ Measured values of this yield indicate a low-$m$ fraction of about $40\%.$

We examine the time-dependent quantum depletion of a trapped Bose-Einstein condensate arising from a rapid increase of the scattering length. Our solution indicates that a significant buildup of incoherent atoms can occur within a characteristic time that is short compared with the harmonic trap period. We discuss how the depletion density and the characteristic time depend on the physical parameters of the condensate.

Three-wave interactions occurring in conditions of type I phase matching in a uniaxial crystal are considered in the general case of noncollinear wave propagation. It is demonstrated that, if one among the interacting fields at ${\omega }_i\mathrm{}(i=1,2,3\mathrm{})\mathrm{}$ is virtually unaffected in amplitude by the interaction, the remaining two fields at ${\omega }_j\left(j\ne i\right)$ are holographic replicas of each other, the constant field acting as the reference field in holography. Experiments are presented in which a holographic image of an object consisting in a pointlike light source is obtained by either up- or down-conversion for any choice of the object- and reference-field frequencies among ${\omega }_1,$ ${\omega }_2,$ and ${\omega }_3.$

Experimental study of the soliton dynamics of a passively mode-locked fiber ring laser revealed a state of bound-soliton operation in the laser, where two solitons bind together tightly with fixed pulse separation. We further report on the properties of the bound-soliton emission of the laser. In particular, we demonstrate both experimentally and numerically that, like the single-pulse soliton operation of the laser, the bound soliton emission is another intrinsic feature of the laser.

We report studies of a third-order correlation function that records the conditional time evolution of the field of a fraction of a photon. We present results in the strong-coupling regime of cavity QED, where the detection of a photon from the cavity prepares a state with a well-defined phase that evolves back to equilibrium via a damped vacuum Rabi oscillation. We perform a homodyne measurement conditioned on the photon detection to observe the regression of the field amplitude. The measured field-photon correlation is nonclassical and can be used to determine the spectrum of squeezing in an efficiency independent way.

The effects of coupling of bound states to continuum target states have been investigated for electron-impact excitation of atomic oxygen by using the R matrix with pseudostates approach. The 22 spectroscopic bound and autoionizing states together with the 19 pseudostates are included in the close-coupling expansion. The pseudostates are chosen to simulate the continuum target states. The contribution of the ionization continuum to the cross section varies from 5% to 15% for the excitation of the ${}^{3}P–3s{}^3{S}^o$ (130.4 nm) transition and from 5% to 27% for the ${}^{3}P–3d{}^3{D}^o$ (102.7 nm) transition. Our results are in good agreement with experiments for the ${}^{3}P–3s{}^3{S}^o$ transition, but discrepancies in shape and magnitude of cross sections exist with the recent experiment for the ${}^{3}P–3d{}^3{D}^o$ transition. Further experimental work is essential to resolve the discrepancies.

When a logical qubit is protected using a quantum error-correcting code, the net effect of coding, decoherence (a physical channel acting on qubits in the codeword) and recovery can be represented exactly by an effective channel acting directly on the logical qubit. In this paper we describe a procedure for deriving the map between physical and effective channels that results from a given coding and recovery procedure. We show that the map for a concatenation of codes is given by the composition of the maps for the constituent codes. This perspective leads us to an efficient means for calculating the exact performance of quantum codes with arbitrary levels of concatenation. We present explicit results for single-bit Pauli channels. For certain codes under the symmetric depolarizing channel, we use the coding maps to compute exact threshold error probabilities for achievability of perfect fidelity in the infinite concatenation limit.

Spin-exchange rate coefficients for Rb-${}^3\mathrm{He}$ are measured using three different methods. Two methods, using Rb repolarization and rate balance, require no assumption about the nature of the ${}^3\mathrm{He}$ wall relaxation and agree well; we find spin-exchange rate coefficients of $6.7\times {10}^{-20}{\mathrm{cm}}^3/\mathrm{s}$ and $6.8\times {10}^{-20}{\mathrm{cm}}^3/\mathrm{s}.$ These results agree with a recent repolarization measurement of Baranga and co-workers [Phys. Rev. Lett. 80, 2801 (1998)]. The third method uses the temperature dependence of the ${}^3\mathrm{He}$ relaxation and is 30% larger than the other two, implying a temperature-dependent wall or an unreasonably large value of the anisotropic spin-exchange interaction for $\mathrm{Rb}{-}^3\mathrm{He}.$ In the course of these measurements we developed and tested a new method for Rb density measurements under high power pumping conditions, and a new variant of Rb EPR polarimetry, both of which are described here.

We present numerical data showing that three-qutrit correlations for a pure state, which is not maximally entangled, violate local realism more strongly than three-qubit correlations. The strength of violation is measured by the minimal amount of noise that must be admixed to the system so that the noisy correlations have a local and realistic model.

We study the entanglement of thermal and ground states in the Heisenberg $\mathrm{XX}$ qubit rings with a magnetic field. A general result is found that for even-number rings, pairwise entanglement between nearest-neighbor qubits is independent of both the sign of exchange interaction constants and the sign of magnetic fields. As an example we study the entanglement in the four-qubit model and find that the ground state of this model without magnetic fields is shown to be a four-body maximally entangled state measured by the square N-bit concurrence.

We report on experimental investigation of optical-pulse group-velocity reduction and probe-pulse “regeneration” using a Raman scheme. This scheme, which does not rely on the commonly used on-one-photon-resonance electromagnetically induced transparency (EIT) process, has many advantages over the conventional method that critically relies on the transparency window created by an EIT process. We demonstrate significant reduction of the group velocity, less probe-field loss, reduced probe-pulse distortion, and high probe-pulse regeneration efficiency.

Structural and electronic properties of ${\mathrm{Al}}_k{\mathrm{Ti}}_l{\mathrm{Ni}}_m\mathrm{}(k+l+m=2,3\mathrm{})\mathrm{}$ microclusters have been investigated by performing density-functional-theory calculations within the effective core potential level. Dimers and trimers of the elements aluminum, titanium, and nickel, and their binary and ternary combinations have been studied in their ground states. The optimum geometries, possible dissociation channels, vibrational properties, and electronic structure of the clusters under study are obtained.

An independent-pair ansatz is developed for the many-body wave function of dilute Bose systems. The pair correlation is optimized by minimizing the expectation value of the full Hamiltonian (rather than the truncated Bogoliubov one) providing a rigorous energy upper bound. In contrast with the Jastrow model, hypernetted chain theory provides closed-form exactly solvable equations for the optimized pair correlation. The model involves both condensate and coherent pairing with number conservation and kinetic-energy sum rules satisfied exactly and the compressibility sum rule obeyed at low density. We compute, for bulk boson matter at a given density and zero temperature, (i) the two-body distribution function, (ii) the energy per particle, (iii) the sound velocity, (iv) the chemical potential, (v) the momentum distribution and its condensate fraction, and (vi) the pairing function, which quantifies the off-diagonal long-range order resulting from the structural properties of the two-particle density matrix. The connections with the low-density expansion and Bogoliubov theory are analyzed at different density values, including the density and scattering length regime of interest of trapped-atom Bose-Einstein condensates. Comparison with the available diffusion Monte Carlo results is also made.

The dispersive properties of nondegenerate optical parametric amplification in quasi-phase-matched (QPM) nonlinear quadratic crystals with an arbitrary grating profile are theoretically investigated in the no-pump-depletion limit. The spectral group delay curve of the amplifier is shown to be univocally determined by its spectral power gain curve through a Hilbert transform. Such a constraint has important implications for the propagation of spectrally narrow optical pulses through the amplifier. In particular, it is shown that anomalous transit times, corresponding to superluminal or even negative group velocities, are possible near local minima of the spectral gain curve. A possible experimental observation of such effects using a QPM lithium niobate crystal is suggested.

We consider the action of a beam splitter with identical degenerate parametric down converters in each of the outputs and show that with single photons injected into each of the input ports, under certain conditions, a superposition of two- and four-photon maximally entangled states may be produced. Also we describe techniques for verifying the generation of the four-photon component of the state. We then discuss the application of such states to quantum photolithography assuming the existence of substrates capable of absorbing four photons. The two-photon component makes no contribution to the background.

We consider a reformulation of QED in which covariant Green functions are used to solve for the electromagnetic field in terms of the fermion fields. It is shown that exact few-fermion eigenstates of the resulting Hamiltonian can be obtained in the canonical equal-time formalism for the case where there are no free photons. These eigenstates lead to two- and three-body Dirac-like equations with electromagnetic interactions. Perturbative and some numerical solutions of the two-body equations are presented for positronium- and muonium-like systems, for various strengths of the coupling.

Following a review of the probe optimization of Slutsky, Rao, Sun, and Fainman [Phys. Rev. A 57, 2383 (1998)] for the standard four-state protocol of quantum key distribution, I generalize the optimization to a variable angle between the signal bases. I calculate the corresponding maximum Renyi information gain by the probe, and determine the optimum probe parameters. A larger set of optimum probe parameters is found for the standard protocol than was known previously.

We report the observation of nonclassical quantum correlations of continuous light variables from an altogether different type of source. It is a frequency nondegenerate optical parametric oscillator below threshold, where signal and idler fields are separated by 740 MHz corresponding to two free spectrum ranges of the parametric oscillator cavity. The degree of entanglement observed, $-3.8\mathrm{dB},$ is the highest to date for a narrow-band tunable source suitable for atomic quantum memory and other applications in atomic physics. Finally we use the latter to visualize the Einstein-Podolsky-Rosen paradox.

It is shown that a nonequilibrium environment can be instrumental in suppressing decoherence between distinct decoherence-free subspaces in quantum registers. The effect is found in the framework of exact coherent-product solutions for model registers decohering in a bath of degenerate harmonic modes, through couplings linear in bath coordinates. These solutions represent a natural nonequilibrium extension of the standard solution for a decoupled initial register state and a thermal environment. Under appropriate conditions, the corresponding reduced register distribution can propagate in an unperturbed manner, even in the presence of entanglement between states belonging to distinct decoherence-free subspaces, and despite persistent bath entanglement. As a byproduct, we also obtain a refined picture of coherence dynamics under bang-bang decoherence control. In particular, it is shown that each radio-frequency pulse in a typical bang-bang cycle induces a revival of coherence, and that these revivals are exploited in a natural way by the time-symmetrized version of the bang-bang protocol.