Experimental and theoretical studies of one-electron capture in collisions of ${\mathrm{He}}^{2+}$ ions with ${\mathrm{H}}_2\mathrm{O}$ molecules have been carried out in the range $0.025\text{–}12\mathrm{keV}{\mathrm{amu}}^{-1}$ corresponding to typical solar wind velocities of $70\text{–}1523\mathrm{km}{\mathrm{s}}^{-1}$. Translational energy spectroscopy (TES), photon emission spectroscopy (PES), and fragment ion spectroscopy were employed to identify and quantify the collision mechanisms involved. Cross sections for selective single electron capture into $n=1$, 2, and 3 states of the ${\mathrm{He}}^{+}$ ion were obtained using TES while PES provided cross sections for capture into the ${\mathrm{He}}^{+}\left(2p\right)$ and ${\mathrm{He}}^{+}\left(3p\right)$ states. Our model calculations show that ${\mathrm{He}}^{+}(n=2)$ and ${\mathrm{He}}^{+}(n=3)$ formation proceeds via a single-electron process governed by the nucleus-electron interaction. In contrast, the ${\mathrm{He}}^{+}\left(1s\right)$ formation mechanism involves an exothermic two-electron process driven by the electron-electron interaction, where the potential energy released by the electron capture is used to remove a second electron thereby resulting in fragmentation of the ${\mathrm{H}}_2\mathrm{O}$ molecule. This process is found to become increasingly important as the collision energy decreases. The experimental cross sections are found to be in reasonable agreement with cross sections calculated using the Demkov and Landau-Zener models.

The atomic-recoil effect leads to large (25%) asymmetries in a nearly ideal form of saturation spectroscopy based on Ca atoms that have been laser-cooled to . Starting with spectra from the more familiar Doppler-broadened domain, we show how the fundamental asymmetry between absorption and stimulated emission of light manifests itself when shorter spectroscopic pulses lead to the Fourier transform regime. These effects occur on frequency scales much larger than the size of the recoil shift itself, and have not been described before in saturation spectroscopy. These results directly impact precision spectroscopic measurements.

Spin-exchange collisions often play a dominant role in the broadening of Zeeman resonances in an alkali-metal vapor. Contrary to intuitive expectations, at high alkali-metal densities this broadening can be completely eliminated by operating in a low magnetic field, allowing construction of ultrasensitive atomic magnetometers. We describe a detailed study of the Zeeman resonance frequencies and linewidths as a function of the magnetic field, alkali-metal density, and the degree of spin polarization of the atoms. Due to the nonlinear nature of the density matrix equations describing the spin-exchange collisions both the gyromagnetic ratio and the linewidth change as a function of the polarization. The results of experimental measurements are in excellent agreement with analytical and numerical solutions of the density matrix equations.

We study the energies and decay of elementary excitations in weakly interacting Bose-Einstein condensates within a finite-temperature gapless second-order theory. The energy shifts for the high-lying collective modes turn out to be systematically negative compared with the Hartree-Fock-Bogoliubov-Popov approximation and the decay of the low-lying modes is found to exhibit collapse and revival effects. In addition, perturbation theory is used to qualitatively explain the experimentally observed Beliaev decay process of the scissors mode.

We propose a relatively robust scheme to generate maximally entangled states of (i) an atom and a cavity photon, (ii) two atoms in their ground states, and (iii) two photons in two spatially separate high-$Q$ cavities. It is based on the interaction via fractional adiabatic passage of a three-level atom traveling through a cavity mode and a laser beam. The presence of optical phases is emphasized.

We investigate the problem of propagation of three-component resonant light pulses with adiabatically varying amplitudes through a medium consisting of atoms with the tripod level configuration. By means of both analytic and numerical methods we find the two modes of shape-preserving pulse propagation. The pulse propagation velocity of the fast mode is equal to the speed of light in vacuum, whereas the group velocity of the other (slow) mode is significantly slowed down. These two modes represent a general asymptotic solution of the problem of adiabatic pulse propagation, i.e., a pulse of any shape, which is consistent with the adiabaticity conditions, and a finite duration evolves at large propagation distances (and, correspondingly, at large times of interaction with the medium) to a well-separated pair of fast and slow pulses. The experimental requirements for adiabatic pulse propagation in a tripod medium are similar to that needed for observation of slow light propagation in a medium with the $\Lambda$ configuration of levels. However, the tripod scheme offers a different possibility, which is absent in the $\Lambda$-medium case: collisions of fast and slow pulses. It is found numerically that after such a collision the shapes of the pulses change, so these pulses do not match the classical definition of a soliton.

An observation on a pathological behavior of an exact density functional derived from either relativistic (Dirac) or nonrelativistic (Lévy-Leblond) quantum-mechanical equation is reported. As expected, in the case of a one-electron atom the variational minimum of this functional is equal to the exact ground-state energy. However, apart from the correct density, this minimum is reached also by an infinite set of densities which do not correspond to the exact wave function. This paradoxical property of the functional is related to the multicomponent structure of both Dirac and Lévy-Leblond wave functions. In particular, imposing the correct boundary conditions upon the trial densities removes only a part of the fake solutions. The results of this study demonstrate that in density-functional theories derived from models based on multicomponent wave functions, one should not expect any simple relation between the accuracy of the energy and the correctness of the corresponding density.

With the growing efforts in isolating solid-state qubits from external decoherence sources, the origins of noise inherent to the material start to play a relevant role. One representative example is charged impurities in the device material or substrate, which typically produce telegraph noise and can hence be modeled as bistable fluctuators. In order to demonstrate the possibility of the active suppression of the disturbance from a single fluctuator, we theoretically implement an elementary bang-bang control protocol, a protocol based on sudden pulses. We numerically simulate the random walk of the qubit state on the Bloch sphere with and without bang-bang compensation by means of a stochastic Schrödinger equation and compare it with an analytical saddle-point solution of the corresponding Langevin equation in the long-time limit. We find that the deviation with respect to the noiseless case is significantly reduced when bang-bang pulses are applied, being scaled down approximately by the ratio of the bang-bang period to the typical flipping time of the bistable fluctuation. Our analysis gives not only the effect of bang-bang control on the variance of these deviations, but also their entire distribution. As a result, we expect that bang-bang control works as a high-pass filter on the spectrum of noise sources. This indicates how the influence of $1∕f$ noise ubiquitous to the solid-state world can be reduced.

Spin-resolved measurements of the ${\mathrm{Ar}}^{*}{\left(2p_{1∕2,3∕2}^{-1}4s_{1∕2}\right)}_{J=1}$ resonantly excited $L_{2,3}{M}_{2,3}{M}_{2,3}$ Auger decay have been performed. The low resolution Auger spectrum, which due to cancellation between different multiplet components should exhibit virtually zero dynamic spin polarization, reveals an unexpected nonvanishing polarization effect. Calculations within a relativistic distorted wave approximation explain this effect as configuration-interaction (CI) induced. The CI generates experimentally unresolved fine structure components with low and high total angular momentum, giving rise to asymmetric cases where the high $J$ part of certain multiplets is suppressed by internal selection rules for diagram lines. In this case, only the low $J$ components survive with no partner for spin-polarization cancellation.

We demonstrate the production of micron-sized high-density atom clouds of interest for mesoscopic quantum information processing. We evaporate atoms from $60\mu \mathrm{K}$, $3\times {10}^{14}\mathrm{atoms}∕{\mathrm{cm}}^3$ samples contained in a highly anisotropic optical lattice formed by interfering diffracted beams from a holographic phase plate. After evaporating to $1\mu \mathrm{K}$ by lowering the confining potential, in less than a second the atom density reduces to $8\times {10}^{13}{\mathrm{cm}}^{-3}$ at a phase space density approaching unity. Adiabatic recompression of the atoms then increases the density to levels in excess of $1\times {10}^{15}{\mathrm{cm}}^{-3}$. The resulting clouds are typically $8\mu \mathrm{m}$ in the longest dimension. Such samples are small enough to enable mesoscopic quantum manipulation using the Rydberg blockade and have the high densities required to investigate collision phenomena.

Using a recent reformulation of Floquet theory [S. Guérin and H. R. Jauslin, Adv. Chem. Phys. 125, 1 (2003)], we discuss the dynamical role of the absolute phase in the photofragmentation of molecules subjected to laser pulses. We show how the dependence of Floquet states on an absolute phase is related to the complexity of the dressed molecular scheme and to the multiphoton character of the molecular dynamics. The general theory is applied to the study of the photodissociation of $\mathrm{H}_2{}^{+}$ in a $400\text{‐}\mathrm{nm}$ periodic laser pulse, repeated with a frequency lying in the IR. The dependence of the dynamics on the phase of the pulse envelope is highlighted through an effect previously called dynamical dissociation quenching (DDQ) [F. Châteauneuf et al., J. Chem. Phys. 108, 3974 (1998)] and through photofragment kinetic energy spectra. These spectra allow us to map out the Floquet content of the dynamics—i.e., its multiphoton character both with respect to the carrier-wave frequency, which gives rise to the usual bond-softening mechanism, and with respect to the pulse modulation frequency in the IR. The synchronization of this pulse modulation with the wave packet motion governs the DDQ effect in this uv-visible pulsed excitation case.

We discuss the frequency and visibility of atom-molecule Ramsey fringes observed in recent experiments by Claussen et al. [Phys. Rev. A 67, 060701 (2003)]. In these experiments a ${}^{85}\mathrm{Rb}$ Bose-Einstein condensate was exposed to a sequence of magnetic field pulses on the high-field side of the $155\mathrm{G}$ Feshbach resonance. The observed oscillation frequencies largely agree with the theoretically predicted magnetic field dependence of the binding energy of the highest excited diatomic vibrational state, except for a small region very close to the singularity of the scattering length. Our analytic treatment of the experiment, as well as our dynamical simulations, follow the magnitude of the measured oscillation frequencies as well as the visibilities of the Ramsey fringes. We show that significant deviations from a purely binary dynamics, with an associated binding frequency, occur when the spatial extent of the molecular wave function becomes comparable with the mean distance between the atoms in the dilute gas. The experiments thus clearly identify the conditions under which diatomic molecules may be identified as a separate entity of the gas or, conversely, when the concept of binary physics in a many-body environment is bound to break down.

We analyze and compare three different strategies, all aimed at controlling and eventually halting decoherence. The first strategy hinges upon the quantum Zeno effect, the second makes use of frequent unitary interruptions (“bang-bang” pulses and their generalization, quantum dynamical decoupling), and the third uses a strong, continuous coupling. Decoherence is shown to be suppressed only if the frequency $N$ of the measurements or pulses is large enough or if the coupling $K$ is sufficiently strong. Otherwise, if $N$ or $K$ is large, but not extremely large, all these control procedures accelerate decoherence. We investigate the problem in a general setting and then consider some practical examples, relevant for quantum computation.

Among initialization schemes for ensemble quantum computation beginning at thermal equilibrium, the scheme proposed by Schulman and Vazirani [in Proceedings of the 31st ACM Symposium on Theory of Computing (STOC’99) (ACM Press, New York, 1999), pp. 322–329] is known for the simple quantum circuit to redistribute the biases (polarizations) of qubits and small time complexity. However, our numerical simulation shows that the number of qubits initialized by the scheme is rather smaller than expected from the von Neumann entropy because of an increase in the sum of the binary entropies of individual qubits, which indicates a growth in the total classical correlation. This result—namely, that there is such a significant growth in the total binary entropy—disagrees with that of their analysis.

We study macroscopic observables defined as the total value of a physical quantity over a collection of quantum systems. We show that previous results obtained for an infinite ensemble of identically prepared systems lead to incorrect conclusions for finite ensembles. In particular, exact measurement of a macroscopic observable significantly disturbs the state of any finite ensemble. However, we show how this disturbance can be made arbitrarily small when the measurements are of finite accuracy. We demonstrate a general trade-off between state disturbance and measurement coarseness as a function of the size of the ensemble. Using this trade-off, we show that the histories generated by any sequence of finite accuracy macroscopic measurements always generate a consistent family in the absence of large-scale entanglement for sufficiently large ensembles. Hence, macroscopic observables behave “classically” provided that their accuracy is coarser than the quantum correlation length scale of the system. The role of these observable is also discussed in the context of NMR quantum information processing and bulk ensemble quantum state tomography.

The Hamiltonian $H$ for an $n$-electron system in a finite one-electron basis of dimension $m$ is characterized by $d=O\left(m^4\right)$ matrix elements. The eigenstates of this Hamiltonian—i.e., the full-CI states $\Psi$—depend, however, on the usually much larger set of $N=O\left(m^n\right)$ parameters. One can, nevertheless, write a full-CI state as $\Psi =e^S\Phi$ with $\Phi$ a reference function and $S$ an operator familiar from traditional coupled cluster (TCC) theory. The “exact” operator $S$ can be expressed (though in an implicit and rather complicated way) in terms of $d$ parameters. An alternative ansatz $\Psi =e^T\Phi$ with $T$ depending in a very simple way on $d$ parameters only (namely, with $T$ having the same structure in Fock space as $H$) has been studied by Nooijen and by Nakatsuji and been called coupled-cluster with generalized single and double excitations (CCGSD). Nooijen has conjectured that the full-CI equations can be fulfilled with this ansatz. This paper is devoted to a comprehensive analysis of the Nooijen conjecture (NC). Several features make this analysis difficult and even intriguing. (a) One deals with coupled nonlinear systems of equations, for which theorems concerning the existence of their solution are hardly available. (b) There are different possible interpretations of the NC, especially as far as the choice of the reference function $\Phi$ is concerned. (c) There are solutions of the CCGSD equations, for which some elements of $T$ becomes negative infinite, and $e^T$ becomes a projection operator. Such solutions are undesired but difficult to eliminate. We show by direct comparison of the exact wave operator with that of CCGSD theory, for a closed-shell state with $\Phi$ a single Slater determinant, using a perturbation expansion, that CCGSD cannot be exact. This required a reformulation of the CCGSD operator $e^T$ to an equivalent exponential form $e^R$, with $R$ similar to the $S$ of TCC theory, but with constraints on the cluster amplitudes, such that these depend on $d$ parameters only. The CCGSD ansatz simulates three-particle and higher excitations, in a perturbation expansion even with diagrams of the correct topology, but with incorrect energy denominators. Differences to the exact formulation arise to second order in perturbation theory for the wave function and to fourth order in the energy, but even the contributions which are not exact, are often acceptable approximations. Essential for the proof that the CCGSD ansatz is not potentially exact is that the set of one- and two-particle basis operators, into which $H$ can be expanded, does not span a Lie algebra. What matters is actually that the variations of the wave function describable within a CCGSD ansatz are different from those required to satisfy the two-particle contracted Schrödinger equations. The first attempt, due to Nakatsuji, to prove in this philosophy that the CCGSD ansatz is not potentially exact, was essentially correct, but some subtle yet important aspects were not sufficiently stressed. A refinement was given by Mazziotti. Papers by Ronen and Davidson addressed a somewhat academic problem—namely, the possible validity of the CCGSD ansatz for a completely arbitrary reference function—using mainly dimensionality arguments.

We present a single-center model of double photoionization (DPI) of the ${\mathrm{H}}_2$ molecule which combines a multiconfiguration expansion of the molecular ground state with the convergent close-coupling description of the two-electron continuum. Because the single-center final-state wave function is only correct in the asymptotic region of large distances, the model cannot predict the magnitude of the DPI cross sections. However, we expect the model to account for the angular correlation in the two-electron continuum and to reproduce correctly the shape of the fully differential DPI cross sections. We test this assumption in kinematics of recent DPI experiments on the randomly oriented and fixed in space hydrogen molecule in the isotopic form of ${\mathrm{D}}_2$.

Adding a gauge symmetry breaking field $-\nu \sqrt{V}(a_0+a_0^{*})$ to the Hamiltonian of some simplified models of an interacting Bose gas we compute the condensate density and the symmetry breaking order parameter in the limit of infinite volume and prove Bogoliubov’s asymptotic hypothesis ${\lim }_{V\to \infty }⟨a_0⟩∕\sqrt{V}=\mathrm{sgn}\nu {\lim }_{V\to \infty }\sqrt{⟨a_0^{*}{a}_0⟩∕V}$ where the averages are taken in the ground state or in thermal equilibrium states. Letting $\nu$ tend to zero in this equation we obtain that Bose-Einstein condensation occurs if and only if the gauge symmetry is spontaneously broken. The simplification consists in dropping the off-diagonal terms in the momentum representation of the pair interaction. The models include the mean field and the imperfect (Huang-Yang-Luttinger) Bose gas. An implication of the result is that the compressibility sum rule cannot hold true in the ground state of the one-dimensional mean-field Bose gas. Our method is based on a resolution of the Hamiltonian into a family of single-mode $(\mathbf{k}=0)$ Hamiltonians and on the analysis of the associated microcanonical ensembles.

We consider the gravity field of a Bose-Einstein condensate in a quantum superposition. The gravity field then is also in a quantum superposition, which is in principle observable. Hence we have “quantum gravity” far away from the so-called Planck scale.

An experimental realization of the entanglement-assisted “Guess My Number” protocol for the reduction of communication complexity, introduced by Steane and van Dam, would require producing and detecting three-qubit GHZ states with an efficiency $\eta >0.70$, which would require single photon detectors of efficiency $\sigma >0.89$. We propose a modification of the protocol which can be translated into a real experiment using present-day technology. In the proposed experiment, the quantum reduction of the multiparty communication complexity would require an efficiency $\eta >0.05$, achievable with detectors of $\sigma >0.47$, for four parties, and $\eta >0.17$ $(\sigma >0.55)$ for three parties.