For many years, coherent states have been a useful tool for understanding fundamental questions in quantum mechanics. Recently, there has been work on developing a consistent way of including constraints into the phase space path integral that naturally arises in coherent-state quantization. This approach has many advantages over other approaches, including the lack of any Gribov problems, the independence of gauge fixing, and the ability to handle second-class constraints without any ambiguous determinants. In this paper, I use this approach to study some examples of time-reparametrization invariant systems, which are of special interest in the field of quantum gravity.

We establish the best possible approximation to a perfect quantum cloning machine that produces two clones out of a single input. We analyze both universal and state-dependent cloners. The maximal fidelity of cloning is shown to be 5/6 for universal cloners. It can be achieved either by a special unitary evolution or by a teleportation scheme. We construct the optimal state-dependent cloners operating on any prescribed two nonorthogonal states and discuss their fidelities and the use of auxiliary physical resources in the process of cloning. The optimal universal cloners permit us to derive an upper bound on the quantum capacity of the depolarizing quantum channel.

A working free-space quantum key distribution (QKD) system has been developed and tested over a 205-m indoor optical path at Los Alamos National Laboratory under fluorescent lighting conditions. Results show that free-space QKD can provide a secure real-time key distribution between parties who have a need to communicate secretly.

An attempt to eavesdrop on a quantum cryptographic channel reveals itself through errors it inevitably introduces into the transmission. We investigate the relationship between the induced error rate and the maximum amount of information the eavesdropper can extract, in both the two-state B92 [B92 refers to the work of C. H. Bennett, Phys. Rev. Lett. 68, 3121 (1992)] and the four-state BB84 [BB84 refers to the work of C. H. Bennett and G. Brassard, in Proceedings of the IEEE International Conference on Computers, Systems, and Signal Processing, Bangalore, India (IEEE, New York, 1984), pp. 175–179] quantum cryptographic protocols. In each case, the optimal eavesdropping method that on average yields the most information for a given error rate is explicitly constructed. Analysis is limited to eavesdropping strategies where each bit of the quantum transmission is attacked individually and independently from other bits. Subject to this restriction, however, we believe that all attacks not forbidden by physical laws are covered. Unlike previous work, the eavesdropper’s advantage is measured in terms of Renyi (rather than Shannon) information, and with respect only to bits received error-free by Bob (rather than all bits). This alters both the maximum extractable information and the optimal eavesdropping attack. The result can be used directly at the privacy amplification stage of the protocol to accomplish secure communication over a noisy channel.

An error prevention procedure based on two-particle encoding is proposed for protecting an arbitrary unknown quantum state from dissipation, such as phase damping and amplitude damping. The schemes, which exhibits manifestation of the quantum Zeno effect, is effective whether quantum bits are decohered independently or cooperatively. We derive the working condition of the scheme, and argue that this procedure has feasible practical implementation.

We solve a problem, which while not fitting into the usual paradigm, can be viewed as a quantum computation. Suppose we are given a quantum system with a Hamiltonian of the form $E|w〉〈w|$ where $|w〉$ is an unknown (normalized) state. The problem is to produce $|w〉$ by adding a Hamiltonian (independent of $|w〉)$ and evolving the system. If $|w〉$ is chosen uniformly at random we can (with high probability) produce $|w〉$ in a time proportional to $N^{1/2}/E$. If $|w〉$ is instead chosen from a fixed, known orthonormal basis we can also produce $|w〉$ in a time proportional to $N^{1/2}/E$ and we show that this time is optimally short. This restricted problem is an analog analogue to Grover’s algorithm, a computation on a conventional (!) quantum computer that locates a marked item from an unsorted list of $N$ items in a number of steps proportional to $N^{1/2}$.

The spin-rotational-electronic fine structure of molecular Rydberg and continuum states is considered. The frame transformation from the laboratory frame [Hund’s case (e)] to the molecular frame [Hund’s case (a)] is derived. Symmetry requirements are fully incorporated into the transformation, thus facilitating its practical use. Expressions for the dipole transition amplitudes in Hund’s case (a), again fully symmetrized, are given, as well as their transformation to Hund’s case (e) appropriate for excitation to discrete Rydberg states and the ionization continuum. Various examples of the transformation within the framework of collision theory and of multichannel quantum defect theory are described, and it is shown how the general frame transformation reduces to the transformations for molecules without electron spin. The present formulation can also be applied to the photoionization of aligned and oriented molecules, as well as to “complete” experiments.

This work presents a general framework for assessing the quality and robustness of control over quantum dynamics induced by an optical field $\mathcal{E}\mathrm{}\left(t\right).$ The control process is expressed in terms of a cost functional, including the physical objectives, penalties, and constraints. The first variations of such cost functionals have traditionally been utilized to create designs for the controlling electric fields. Here, the second variation of the cost functional is analyzed to explore (i) whether such solutions are locally optimal, and (ii) their degree of robustness. Both issues may be assessed from the eigenvalues of the stability operator S whose kernel $K(t,\tau )$ is related to $\delta \mathcal{E}\mathrm{}\left(t\right)/\delta \mathcal{E}\left(\tau \right){|}_c$ for $0<t,$ $\tau <~T,$ where $T$ is the target control time. Here $c$ denotes the constraint that the field satisfies the optimal control dynamical equations. The eigenvalues σ of S satisfying $\sigma <1\mathrm{}$ assure local optimality of the control solution, with $\sigma =1\mathrm{}$ being the critical value separating optimal solutions from false solutions (i.e., those with negative second variational curvature of the cost functional). In turn, the maximally robust control solutions with the least sensitivity to field errors also correspond to $\sigma =1.\mathrm{}$ Thus, sufficiently high sensitivity of the field at one time $t$ to the field at another time τ (i.e., $\sigma >1\mathrm{}$) will lead to a loss of local optimality. An expression is obtained for a bound on the stability operator, and this result is employed to qualitatively analyze control behavior. From this bound, the inclusion of an auxiliary operator (i.e., other than the target operator) is shown to act as a stabilizer of the control process. It is also shown that robust solutions are expected to exist in both the strong- and weak-field regimes.

We have observed the microwave transitions between the Mg $3snf$ states and the $3nsl$ states of $4<~l<~6$ using selective field ionization. The intervals can be analyzed using a core-polarization model in which the nonadiabatic effects are included with the quadrupole polarizability of the ${\mathrm{Mg}}^{+}$ ion. Using this model we find the ${\mathrm{Mg}}^{+}$ dipole polarizability $a_d{=33.80\mathrm{}}_{-0.30}^{+0.50\mathrm{}}{a}_0^3.$ We also find the nonadiabatic effects to cancel much of the effect of the quadrupole polarizability, a phenomenon also observed in He.

Sulfur $K\beta$ x-ray-emission spectra from carbonyl sulfide have been measured with resonant excitation at the sulfur $K$ absorption threshold and compared with results of self-consistent field and singles-doubles configuration-interaction calculations. For excitation to the strong 4π absorption resonance, a splitting of the main emission peak is interpreted in terms of influence of the 4π electron on the final valence-hole states. The polarization selectivity of the emission spectrometer was used to distinguish emission polarized parallel versus perpendicular with respect to the polarization of the excitation radiation. The observed polarization dependence is consistent with the molecular symmetries of the calculated intermediate and final states.

The problem of high-precision, variational, bound-state calculations in few-body systems is discussed. The simple and very effective variational procedure developed below makes possible numerical, bound-state computations in few-body systems with extremely high accuracy. This procedure is based on the proposed two-stage strategy, which is used to construct the approximate wave function. The highly accurate numerical results, which include both energetical and geometrical properties, for various three-body systems $[{\mathrm{Ps}}^{-}{,}^{\infty }{\mathrm{H}}^{-}{,}^{\infty }\mathrm{He}$, and ${\mathrm{}\left(\mathrm{ppe}\right)\mathrm{}}^{+}$] are presented.

Accurate linear and nonlinear polarizabilities were obtained from finite-field self-consistent field, fourth-order many-body perturbation theory and coupled-cluster calculations for the triply bonded linear molecules $\mathrm{H}\mathrm{—}\mathrm{C}\mathrm{\equiv }\mathrm{N}$ and $\mathrm{H}\mathrm{—}\mathrm{C}\mathrm{\equiv }\mathrm{P}.$ The mean dipole polarizability and the anisotropy of HCN at the CCSD(T) level of theory is $\overline{\alpha }=16.74\mathrm{}$ and $\Delta \alpha {=8.38e}^2{a}_0^2{E}_H^{-1}.$ For HCP the respective values are 35.47 and 16.24 $e^2{a}_0^2{E}_H^{-1}.$ Electron correlation reduces significantly the magnitude of the first dipole hyperpolarizability $\left({\beta }_{\alpha \beta \gamma }\right)$ of both molecules. The CCSD(T) values of the mean $\overline{\beta }$ are [self-consistent-field (SCF) values in parentheses] $-2.8$ $(-7.6)$ for HCN and 28.5 (36.7) $e^3{a}_0^3{E}_H^{-2}$ for HCP. Electron correlation modifies mainly the longitudinal component of the second hyperpolarizability tensor ${\gamma }_{\alpha \beta \gamma \delta }$ for both HCN and HCP. The CCSD(T) mean value for HCN is $\overline{\gamma }=22.0\mathrm{}\times {10}^2,$ 17.4% higher than the SCF value of $18.8\times {10}^2{e}^4{a}_0^4{E}_H^{-3}.$ For HCP $\overline{\gamma }=10.2\mathrm{}\times {10}^3$ at the CCSD(T) level, only 2.2% above the SCF result of $99.8\times {10}^2{e}^4{a}_0^4{E}_H^{-3}.$ For the quadrupole polarizability, fourth-order many-body perturbation theory yields $C_{zz,zz}=68.58,$ $C_{xz,xz}=40.51,$ $C_{xx,xx}=34.98\mathrm{}$ $e^2{a}_0^4{E}_H^{-1}$ for HCN, and $C_{zz,zz}=202.28,$ $C_{xz,xz}=114.44,$ $C_{xx,xx}=106.38\mathrm{}$ $e^2{a}_0^4{E}_H^{-1}$ for HCP, with $z$ as the molecular axis.

We present lifetime measurements of the ${7p}^2{P}_{3/2}$ and ${7p}^2{P}_{1/2}$ levels of Fr. We use a time-correlated single-photon counting technique on a cold sample of ${}^{210}\mathrm{Fr}$ atoms in a magneto-optic trap. We excite the atoms with the trapping and repumping beams of the magneto-optic trap and detect the decay of the atomic fluorescence. The results are a precision experimental test of the atomic many-body perturbation theory applied to the heaviest alkali metal. The lifetime results are 21.02(11) ns and 29.45(11) ns for the ${7p}^2{P}_{3/2}$ and ${7p}^2{P}_{1/2}$ levels, respectively. This gives a line strength ratio ${\mathcal{S}}_{1/2}$/${\mathcal{S}}_{3/2}$ of 0.526(3) for these levels in Fr. To study sources of systematic errors we measure the lifetimes of ${5p}^2{P}_{3/2}$ and ${5p}^2{P}_{1/2}$ in stable ${}^{87}\mathrm{Rb}$ and obtain 26.20(9) ns and 27.64(4) ns, respectively.

A recently developed method of precise atomic calculations [Phys. Rev. A 54, 3948 (1996)] which combines many-body perturbation theory with the configuration-interaction method is used to calculate the 24 lowest energy levels of Ba. $B$-spline functions in a cavity of a finite radius are used as a unified many-purpose basis set. The calculation reproduces the experimental removal energies for Ba within a fraction of a per cent. Advantages of the new method and $B$ splines are discussed.

There is no simple and rigorous relationship between the Kohn-Sham (KS) potential and the genuine excited states of a system. Here we analyze the spectrum of a very accurate KS potential for atomic Ne, and we show, through a quantum-defect analysis, that its highest Rydberg states are in surprisingly good agreement with the corresponding atomic excitations. This indicates that the KS potential is a very accurate approximation of the effective optical potential “felt” by an electron which orbits semiclassically far away in the field of the daughter cation.

Static and dynamic dipole $\alpha \left(\omega \right)$ and quadrupole ${\alpha }_2\left(\omega \right)$ polarizabilities for the $2{}^{1}S$ ground state, and the low-lying $S$ states: $3{}^{1}S$ and $3{}^{3}S$ of Be are calculated using our time-dependent gauge invariant method. The results obtained for the dipole polarizability are compared with previous accurate theoretical data. The quadrupole dynamic polarizabilities proposed here are new, to our knowledge. In all cases dynamic components are calculated for dipole and quadrupole polarizability up to the first two resonances.

Recordings of boron spectra with high-dispersion grating spectroscopy and Fourier transform spectroscopy have provided high-precision wavelengths and transition isotope shifts for all $\mathrm{LS}$-allowed transitions involving the ${2s}^2$, $2s2p$, and ${2p}^2$ configurations in the spectrum of singly ionized boron B II. Large-scale calculations of the same quantities have been performed with the multiconfiguration Hartree-Fock method. There is agreement between the measurements and the calculations within the narrow error limits for all the lines. The calculations also yielded oscillator strengths and hyperfine-structure constants for the same transitions.

In parallel with standard density-functional theory, we study the energy of the ground state of a finite many-body system as a functional of the one-particle density matrix. We show that the formulation of a variational principle that is valid beyond the Hartree-Fock limit requires that two-body correlations be included not only in the ground-state energy but also in the constraints. As an illustration, we apply a linear-response argument to derive formulas for first-order corrections to the Hartree-Fock density matrix. Further analysis suggests an approach in terms of the density matrix of an independent-particle system, which can be introduced by the application of an alternative variational principle. This approach is reminiscent of Kohn-Sham theory, but the effective external potential is not required to be local. This variational method can be implemented in a systematic fashion by means of the linked-cluster expansion. In an appendix we study a variant of the Hohenberg-Kohn theorem for nonlocal potentials.

The transfer reaction of negative muons from $(\mu {p)}_{1s}$ atoms to ${}^3$He and ${}^4$He was studied at 30 K, and the transfer rate to ${}^3$He was determined. Germanium detectors were employed to measure the time distribution of muonic neon x rays in triple-gas mixtures H${}_2$+${}^{3,4}$He+Ne. The rates for the two helium isotopes, normalized to the atomic density of liquid hydrogen, are determined as ${\lambda }_{p^3\mathrm{He}}=(0.29\mathrm{}\pm 0.12)\times {10}^8$ s${}^{-1}$ and ${\lambda }_{p^4\mathrm{He}}$=(0.55$\pm$0.07)$\times$10${}^8$ s${}^{-1}$. The transfer rate to neon was obtained from binary H${}_2$+Ne gas mixtures, measured at the same experimental conditions as for the triple-gas mixtures, with the result ${\lambda }_{p\mathrm{Ne}}$=(0.0677$\pm$0.0032)$\times$10${}^{11}$ s${}^{-1}$.

Energies have been obtained in $\mathrm{LS}$ coupling for low-lying states in ${\mathrm{Sr}}^{\mathrm{-}}$ using a model potential approach including core polarization. An indication has been obtained for the existence of a new quasibound state in ${\mathrm{Sr}}^{\mathrm{-}},$ $5s4d5p{}^4{F}^o,$ bound by 30.0 meV with respect to the $5s5p{}^3{P}^o$ state. Core polarization is essential for obtaining binding for this state. The quasibound ${5s5p}^2{}^4{P}^e$ state is estimated to lie 548.4 meV below the $5s5p{}^3{P}^o$ state of Sr in good agreement with experiment.