In this paper we propose and analyze various operating regimes of a quantum phase gate built on two atoms trapped in two independent dipole traps. The gate operates when the atoms are excited using a two-photon transition from the hyperfine manifold of ground states up to Rydberg states with strong dipole-dipole interaction. Experimental requirements are discussed to reach a fast (microsecond) gate operation.

Various parametrizations for the orbits under local unitary transformations of three-qubit pure states are analyzed. The interconvertibility, symmetry properties, parameter ranges, calculability, and behavior under measurement are looked at. It is shown that the entanglement monotones of any multipartite pure state uniquely determine the orbit of that state under local unitary transformations. It follows that there must be an entanglement monotone for three-qubit pure states which depends on the Kempe invariant defined in Phys. Rev. A 60, 910 (1999). A form for such an entanglement monotone is proposed. A theorem is proved that significantly reduces the number of entanglement monotones that must be looked at to find the maximal probability of transforming one multipartite state to another.

We further verify the impossibility of deleting an arbitrary unknown quantum state, and also show it is impossible to delete two nonorthogonal quantum states as a consequence of unitarity of quantum mechanics. A quantum approximate (deterministic) deleting machine and a probabilistic (exact) deleting machine are constructed. The estimation for the global fidelity characterizing the efficiency of the quantum approximate deleting is given. We then demonstrate that unknown nonorthogonal states chosen from a set with their multiple copies can evolve into a linear superposition of multiple deletions and failure branches by a unitary process if and only if the states are linearly independent. It is notable that the proof for necessity is somewhat different from Pati’s [Phys. Rev. Lett. 83, 2849 (1999)]. Another deleting machine for the input states that are unnecessarily linearly independent is also presented. The bounds on the success probabilities of these deleting machines are derived. So we expound some preliminary analogies between quantum cloning and deleting.

We have developed Bayesian formalism to describe the process of continuous measurement of entangled qubits. We start with the case of two qubits and then generalize it to an arbitrary number of qubits.

On a class of quantum channels which includes the depolarizing channel, the highest fidelity of quantum error-correcting codes of length n and rate R is proven to be lower bounded by $1-\exp \left[-\mathrm{nE}\right(R)+o(n\left)\mathrm{}\right]$ for some function $E\left(R\right).$ The $E\left(R\right)\mathrm{}$ is positive below some threshold $R_0,$ which implies $R_0$ is a lower bound on the quantum capacity.

Spectroscopy has been performed on $\mathrm{the}{}^2{S}_{1/2}(F=0,m_F{=0)-}^2{F}_{7/2}{(F=3,m}_F=0)$ electric octupole transition in ${}^{171}{\mathrm{Yb}}^{+}$ with kilohertz resolution. A quantum jump rate of more than one per second has been achieved, a factor of 100 improvement on previous work. Spectra including the sidebands at the trap secular frequency show the ion to be in the Lambe-Dicke regime and hence the Doppler effect has been eliminated to first order. The dynamic Stark shift is a significant perturbation to the frequency because of the high intensity required to drive the octupole transition. It has been measured as ${42}_{-10}^{+12\mathrm{}}\hspace{0.5em}\mu \mathrm{Hz}{\mathrm{W}}^{-1}{\mathrm{m}}^2$ and with further reduction in the probe laser linewidth, it should be possible to reduce the relative uncertainty in this shift to the parts in ${10}^{18}$ level. The transition is free from the Zeeman effect to first order and has a measured second-order shift of $1.9\left(3\right)\mathrm{}\hspace{0.5em}\mathrm{mHz}(\mu \mathrm{T}{)}^{-2}.$ It should be possible to reduce the relative uncertainty in this shift to below the part in ${10}^{18}$ level. The electric quadrupole shift may be the limiting systematic effect, but cannot yet be observed with the current resolution on the transition.

We report an experimental investigation of higher vibrational levels $({\nu }^{\prime }>2)$ of the C $1\overrightarrow{s}{\pi }^{*}$ excitation in CO utilizing resonant Auger electron spectroscopy. These vibrational states are not readily seen in a total yield absorption spectrum, whereas they are shown to be discernable in a partial electron yield spectrum. Furthermore, the nature of the spectator part between $E_{\mathrm{Bin}}=26.5\mathrm{}$ and 30 eV, being subject of an ongoing debate, is discussed on the grounds of the presented experimental data. The experiments indicate that the formally used adiabatic framework for the multitude of close lying ${}^2\Pi$ potential curves is inappropriate, but that a diabatic treatment can be used for the interpretation of the spectra.

The first measurement of highly resolved photoionization cross sections of the ground state of C II was reported recently by Kjeldsen et al. [Astrophys. J. 524, L143 (1999)]. The observed resonance features showed good agreement with the theoretical calculations in the close-coupling approximation [S. Nahar, Astrophys. J. Suppl. Ser. 101, 423 (1995)]. However, there were several observed resonances that were missing in the theoretical predictions. The earlier theoretical calculation was carried out in $\mathrm{LS}$ coupling where the relativistic effects were not included. Present paper reports photoionization cross sections including relativistic effects in the Breit-Pauli R-matrix (BPRM) approximation. The configuration interaction eigenfunction expansion for the core ion C III consists of 20 fine-structure levels dominated by the configurations from ${1s}^2{2s}^2$ to ${1s}^{2}2s3d.$ Detailed features in the calculated cross sections exhibit the missing resonances due to fine structure. The results provide a benchmark for the accuracy of BPRM photoionization cross sections, as needed for the recent and ongoing experiments for high-resolution photoionization cross sections at synchrotron-radiation sources.

The line shapes of peaks in electron spectra due to decay of autoionizing states of Ne, formed in collisions of Ne with Al solid targets, were studied as a function of surface roughness. Strong variations in these line shapes were observed. These were modeled by taking into account the level shifts of the excited and ionic states of the atom in front of the surface and various resonant and Auger capture and loss processes. It is shown that rather complex line shapes may be expected. The electron spectrum generally possesses a peak at energies in the vicinity of that corresponding to autoionization of a free atom, as well as a high-energy tail and a secondary maximum. The intensity of the secondary maximum depends on how close to the surface most excited atoms decay and hence depends on surface flatness.

We analyze the classical phase space of the hydrogen atom in crossed magnetic and circularly polarized microwave fields in the high-frequency regime, using the Chirikov resonance overlap criterion and the renormalization map. These methods are used to compute thresholds to large-scale chaos and to ionization. The effect of the magnetic field is a strong stabilization of a set of invariant tori that bound the trajectories and prevent stochastic ionization. In order to ionize, larger amplitudes of the microwave field are necessary in the presence of a magnetic field.

A method for determination of atomic lifetimes from the value of dispersion coefficient $C_6$ of molecular potentials correlating to two ground-state atoms is proposed. The method is illustrated with atomic Cs using $C_6$ deduced from high-resolution Feshbach spectroscopy. The following lifetimes are determined: ${\tau }_{{6P}_{1/2}}=34.80\mathrm{}\pm 0.07\hspace{0.5em}\mathrm{ns}$ and ${\tau }_{{6P}_{3/2}}=30.39\mathrm{}\pm 0.06\hspace{0.5em}\mathrm{ns}.$ The underlying electric-dipole matrix elements are required for a refined analysis of parity violation in ${}^{133}\mathrm{Cs}.$ We also obtain static polarizability of the Cs ground state, $\alpha \mathrm{}\left(0\right)=400.49\mathrm{}\left(81\right)\mathrm{}$ atomic units. It is demonstrated that the uncertainties may be considerably reduced as the coefficient $C_6$ is constrained further.

We study the time evolution of a two-dimensional multicomponent Bose-Einstein condensate in an external harmonic trap with arbitrary time-dependent frequency. We show analytically that the time evolution of the total mean-square radius of the wave packet is determined in terms of the same solvable equation as in the case of a single-component condensate. The dynamics of the total mean-square radius is also the same for a rotating as well as a nonrotating multicomponent condensate. We determine the criteria for the collapse of the condensate at a finite time. Generalizing our previous work on a single-component condensate, we show explosion-implosion duality in the multicomponent condensate.

The criteria for validity of adiabaticity for nonlinear wave equations are considered within the context of atomic matter waves tunneling from macroscopically populated optical standing-wave traps loaded from a Bose-Einstein condensate. We show that, even when the optical standing wave is slowly turned on and the condensate behaves adiabatically during this turn-on, once the tunneling time between wells in the optical lattice becomes longer than the nonlinear time scale, adiabaticity breaks down and a significant spatially varying phase develops across the condensate wave function from well to well. This phase drastically affects the contrast of the fringe pattern in Josephson-effect interference experiments, and the condensate coherence properties in general.

We show that there exists bistability in coherent photoassociation of a Bose-Einstein condensate and investigate the corresponding quantum fluctuations. The simple analytical expressions obtained demonstrate clearly how to sweep adiabatically the frequency of the driving laser to convert a condensate of atoms into a condensate of molecules in an optimum and deterministic way.

A recent work [H. H. Arnaut and G. A. Barbosa, Phys. Rev. Lett. 85, 286 (2000)] has shown eigenstates describing pairs of photons from spontaneous parametric down-conversion, which are eigenstates of orbital, intrinsic, and total momentum. Experimental demonstration of transfer of angular momentum to parametric down-converted photons has also been achieved [A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001)]. This work shows conditions for phase matching and examples are given for a Laguerre-mode pump beam. Polar and azimuthal angles are connected by phase matching giving a peculiar divergence pattern for the down-converted light. Full entanglement of polarization and angular-momentum states of photons is discussed.

This paper presents a wide-ranging theoretical and experimental study of nonadiabatic transient phenomena in a $\Lambda$ electromagnetically induced transparency system when a strong coupling field is rapidly switched on or off. The theoretical treatment uses a Laplace transform approach to solve the time-dependent density matrix equation. The experiments are carried out in a ${}^{87}\mathrm{Rb}$ magneto-optical trap. The results show transient probe gain in parameter regions not previously studied, and provide insight into the transition dynamics between bare and dressed states.

A mechanism for operation bistability of passive mode-locked lasers is discovered. It explains why self-starting requires a critical minimum strength of seed fluctuations. There are two contributing factors: (a) a small-scale structure of the spectral loss curve due to a parasitic frequency-dependent loss, (b) phase modulation of the resulting pulses due to nonlinearity and frequency dispersion of the refractive index of intracavity elements. We discuss applications to actual experimental systems.

A triple basis set in Hylleraas coordinates is used to obtain improved variational bounds for the nonrelativistic energy and other properties of He, ${\mathrm{H}}^{-},$ and ${\mathrm{Ps}}^{-}.$ The accuracy, numerical stability, and computational efficiency are compared with recent work based on quasirandom basis sets. The Kato cusp conditions are used to assess the accuracy of the wave functions at short distances.

We study cooling of the collective vibrational motion of two ${}^{138}{\mathrm{Ba}}^{+}$ ions confined in an electrodynamic trap and irradiated by laser light close to the resonances $S_{1/2}-P_{1/2}$ (493 nm) and $P_{1/2}-D_{3/2}$ (650 nm). The motional state of the ions is monitored by a spatially resolving photomultiplier. Depending on detuning and intensity of the cooling lasers, macroscopically different motional states corresponding to different ion temperatures are observed. We also derive the ions’ temperature from detailed analytical calculations of laser cooling taking into account the Zeeman structure of the energy levels involved. The observed motional states perfectly match the calculated temperatures. Significant heating is observed in the vicinity of the dark resonances of the Zeeman-split $S_{1/2}-D_{3/2}$ Raman transitions. Here two-photon processes dominate the interaction between lasers and ions. Parameter regimes of laser light are identified that imply most efficient laser cooling.

We show that the unitary evolution of a harmonic oscillator coupled to a two-level system can be undone by a suitable manipulation of the two-level system—more specifically, by a quasi-instantaneous phase change. This enables us to isolate the dissipative evolution to which the oscillator may be exposed in addition. With this method we study the decoherence time of a photon mode in cavity QED, and that of the quantized harmonic motion of trapped ions. We comment on the relation to spin echoes and multipath interferometry.