Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes

Proceedings of the National Academy of Sciences (PNAS), a peer reviewed journal of the National Academy of Sciences (NAS) - an authoritative source of high-impact, original research that broadly spans the biological, physical, and social sciences.

The present work presents three second-order perturbative developments from a complete active space (CAS) zero-order wave function, which are strictly additive with respect to molecular dissociation and intruder state free. They differ by the degree of contraction of the outer-space perturbers. Two types of zero-order Hamiltonians are proposed, both are bielectronic, incorporating the interactions between electrons in the active orbitals, therefore introducing a rational balance between the zero-order wave function and the outer-space. The use of Dyall’s Hamiltonian, which puts the active electrons in a fixed core field, and of a partially contracted formalism seems a promising compromise. The formalism is generalizable to multireference spaces which are parts of a CAS. A few test applications of the simplest variant developed in this paper illustrate its potentialities.

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A solution for the time- and age-dependent connectivity distribution of a growing random network is presented. The network is built by adding sites that link to earlier sites with a probability ${A}_{k}$ which depends on the number of preexisting links $k$ to that site. For homogeneous connection kernels, ${A}_{k}\ensuremath{\sim}{k}^{\ensuremath{\gamma}}$, different behaviors arise for $\ensuremath{\gamma}<1$, $\ensuremath{\gamma}>1$, and $\ensuremath{\gamma}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$. For $\ensuremath{\gamma}<1$, the number of sites with $k$ links, ${N}_{k}$, varies as a stretched exponential. For $\ensuremath{\gamma}>1$, a single site connects to nearly all other sites. In the borderline case ${A}_{k}\ensuremath{\sim}k$, the power law ${N}_{k}\ensuremath{\sim}{k}^{\ensuremath{-}\ensuremath{\nu}}$ is found, where the exponent $\ensuremath{\nu}$ can be tuned to any value in the range $2<\ensuremath{\nu}<\ensuremath{\infty}$.

The n-electron valence state perturbation theory is reformulated in a spin-free formalism, concentrating on the “strongly contracted” and “partially contracted” variants. The new formulation is based on the introduction of average values in the unperturbed state of excitation operators which bear resemblance with analogous ones occurring in the extended Koopmans’ theorem and in the equations-of-motion technique. Such auxiliary quantities, which allow the second-order perturbation contribution to the energy to be evaluated very efficiently, can be calculated at the outset provided the unperturbed four-particle spinless density matrix in the active orbital space is available. A noticeable inequality concerning second-order energy contributions of the same type between the strongly and partially contracted versions is proven to hold. An example concerning the successful calculation of the potential energy curve for the Cr2 molecule is discussed.

The authors study the phenomena of many-body localization in a random field Heisenberg chain. In this paper the authors use a shift-inverse exact diagonalization approach that allows them to study the mid-spectrum spectral properties of the model for system sizes of up to N=22. This has allow the authors to identify the many-body localization edge.

Adiabatic evolution along the instantaneous eigenstate of a time-dependent Hamiltonian is used for robust and high fidelity state transfer in atomic and molecular physics. Shortcuts to adiabaticity (STA) are systematic approaches to accomplish the same final state transfer in a faster manner. This article presents an introduction to STA and reviews different theoretical approaches and applications of STA to a range of scientific and engineering tasks in quantum physics and beyond.

A method is proposed to cool down atoms in a harmonic trap without phase-space compression as in a perfectly slow adiabatic expansion, i.e., keeping the same populations of instantaneous levels in the initial and final traps, but in a much shorter time. This may require that the harmonic trap become transiently an expulsive parabolic potential. The cooling times achieved are shorter than those obtained using optimal-control bang-bang methods and real frequencies.

Abstract. This article reviews the recent theoretical and experimental advances in the study of ultracold gases made of bosonic particles interacting via the longrange, anisotropic dipole-dipole interaction, in addition to the short-range and isotropic contact interaction usually at work in ultracold gases. The specific properties emerging from the dipolar interaction are emphasized, from the meanfield regime valid for dilute Bose-Einstein condensates, to the strongly correlated regimes reached for dipolar bosons in optical lattices. CONTENTS 2 Contents 1

We present a powerful method for calculating the thermodynamic properties of infinite-dimensional Hubbard-type models using an exact diagonalization of an Anderson model with a finite number of sites. The resolution obtained for Green's functions is far superior to that of quantum Monte Carlo calculations. We apply the method to the half-filled Hubbard model for a discussion of the metal-insulator transition, and to the two-band Hubbard model where we find direct evidence for the existence of a superconducting instability at low temperatures.

We propose a method to speed up adiabatic passage techniques in two-level and three-level atoms extending to the short-time domain their robustness with respect to parameter variations. It supplements or substitutes the standard laser beam setups with auxiliary pulses that steer the system along the adiabatic path. Compared to other strategies, such as composite pulses or the original adiabatic techniques, it provides a fast and robust approach to population control.

Ionization is the dominant response of atoms and molecules to intense laser fields and is at the basis of several important techniques, such as the generation of attosecond pulses that allow the measurement of electron motion in real time. We present experiments in which metastable xenon atoms were ionized with intense 7-micrometer laser pulses from a free-electron laser. Holographic structures were observed that record underlying electron dynamics on a sublaser-cycle time scale, enabling photoelectron spectroscopy with a time resolution of almost two orders of magnitude higher than the duration of the ionizing pulse.

We provide a new quantum algorithm that efficiently determines the quality of a least-squares fit over an exponentially large data set by building upon an algorithm for solving systems of linear equations efficiently [Harrow et al., Phys. Rev. Lett. 103, 150502 (2009)]. In many cases, our algorithm can also efficiently find a concise function that approximates the data to be fitted and bound the approximation error. In cases where the input data are pure quantum states, the algorithm can be used to provide an efficient parametric estimation of the quantum state and therefore can be applied as an alternative to full quantum-state tomography given a fault tolerant quantum computer.

We provide an approximate analytical expression of the mass-radius relation of a Newtonian self-gravitating Bose-Einstein condensate (BEC) with short-range interactions described by the Gross-Pitaevskii-Poisson system. These equations model astrophysical objects such as boson stars and, presumably, dark matter galactic halos. Our study connects the noninteracting case studied by Ruffini and Bonazzola (1969) to the Thomas-Fermi limit studied by B\"ohmer and Harko (2007). For repulsive short-range interactions (positive scattering lengths), there exists configurations of arbitrary mass but their radius is always larger than a minimum value. For attractive short-range interactions (negative scattering lengths), equilibrium configurations only exist below a maximum mass. Above that mass, the system is expected to collapse and form a black hole. We also study the radius versus scattering length relation for a given mass. We find that equilibrium configurations only exist above a (negative) minimum scattering length. Our approximate analytical solution, based on a Gaussian ansatz, provides a very good agreement with the exact solution obtained by numerically solving a nonlinear differential equation representing hydrostatic equilibrium. Our analytical treatment is, however, easier to handle and permits one to study the stability problem, and derive an expression of the pulsation period, by developing an analogy with a simple mechanical problem.

Normal mode analysis of proteins of various sizes, ranging from 46 (crambin) up to 858 residues (dimeric citrate synthase) were performed, by using standard approaches, as well as a recently proposed method that rests on the hypothesis that low-frequency normal modes of proteins can be described as pure rigid-body motions of blocks of consecutive amino-acid residues. Such a hypothesis is strongly supported by our results, because we show that the latter method, named RTB, yields very accurate approximations for the low-frequency normal modes of all proteins considered. Moreover, the quality of the normal modes thus obtained depends very little on the way the polypeptidic chain is split into blocks. Noteworthy, with six amino-acids per block, the normal modes are almost as accurate as with a single amino-acid per block. In this case, for a protein of n residues and N atoms, the RTB method requires the diagonalization of an n x n matrix, whereas standard procedures require the diagonalization of a 3N x 3N matrix. Being a fast method, our approach can be useful for normal mode analyses of large systems, paving the way for further developments and applications in contexts for which the normal modes are needed frequently, as for example during molecular dynamics calculations.

The effect of nonorthogonality in the broken symmetry approach to magnetic coupling has been explicitly considered for the first time in Hartree−Fock and a variety of DFT methods. On the basis of the results for three different systems, representative of a variety of physical situations it is shown that the most often quoted trend concerning the much larger degree of delocalization of magnetic orbitals obtained from DFT, as opposed to Hartree−Fock, is not fully justified. A new and simple way to relate the overlap integral entering into the calculation and the spin density is proposed and tested in a variety of model systems.

Laser excitation of nanometer-sized atomic and molecular clusters offers various opportunities to explore and control ultrafast many-particle dynamics. Whereas weak laser fields allow the analysis of photoionization, excited-state relaxation, and structural modifications on these finite quantum systems, large-amplitude collective electron motion and Coulomb explosion can be induced with intense laser pulses. This review provides an overview of key phenomena arising from laser-cluster interactions with focus on nonlinear optical excitations and discusses the underlying processes according to the current understanding. A general survey covers basic cluster properties and excitation mechanisms relevant for laser-driven cluster dynamics. Then, after an excursion in theoretical and experimental methods, results for single-photon and multiphoton excitations are reviewed with emphasis on signatures from time- and angular-resolved photoemission. A key issue of this review is the broad spectrum of phenomena arising from clusters exposed to strong fields, where the interaction with the laser pulse creates short-lived and dense nanoplasmas. The implications for technical developments such as the controlled generation of ion, electron, and radiation pulses will be addressed along with corresponding examples. Finally, future prospects of laser-cluster research as well as experimental and theoretical challenges are discussed.

Quantum adiabatic processes—that keep constant the populations in the instantaneous eigenbasis of a time-dependent Hamiltonian—are very useful to prepare and manipulate states, but take typically a long time. This is often problematic because decoherence and noise may spoil the desired final state, or because some applications require many repetitions. "Shortcuts to adiabaticity" are alternative fast processes which reproduce the same final populations, or even the same final state, as the adiabatic process in a finite, shorter time. Since adiabatic processes are ubiquitous, the shortcuts span a broad range of applications in atomic, molecular, and optical physics, such as fast transport of ions or neutral atoms, internal population control, and state preparation (for nuclear magnetic resonance or quantum information), cold atom expansions and other manipulations, cooling cycles, wavepacket splitting, and many-body state engineering or correlations microscopy. Shortcuts are also relevant to clarify fundamental questions such as a precise quantification of the third principle of thermodynamics and quantum speed limits. We review different theoretical techniques proposed to engineer the shortcuts, the experimental results, and the prospects.

We study the energy and the static spin structure factor of the ground state of the spin-$1/2$ quantum Heisenberg antiferromagnetic model on the kagome lattice. By the iterative application of a few Lanczos steps on accurate projected fermionic wave functions and the Green's function Monte Carlo technique, we find that a gapless (algebraic) $U(1)$ Dirac spin liquid is competitive with previously proposed gapped (topological) ${\mathbb{Z}}_{2}$ spin liquids. By performing a finite-size extrapolation of the ground-state energy, we obtain an energy per site $E/J=\ensuremath{-}0.4365(2)$, which is equal, within three error bars, to the estimates given by the density-matrix renormalization group (DMRG). Our estimate is obtained for a translationally invariant system, and, therefore, does not suffer from boundary effects, like in DMRG. Moreover, on finite toric clusters at the pure variational level, our energies are lower compared to those from DMRG calculations.

Many-body localization is characterized by a slow logarithmic growth of the entanglement entropy after a global quantum quench while the local memory of an initial density imbalance remains at infinite time. We investigate how much the proximity of a many-body localized phase can influence the dynamics in the delocalized ergodic regime where thermalization is expected. Using an exact Krylov space technique, the out-of-equilibrium dynamics of the random-field Heisenberg chain is studied up to $L=28$ sites, starting from an initially unentangled high-energy product state. Within most of the delocalized phase, we find a sub-ballistic entanglement growth $S(t)\ensuremath{\propto}{t}^{1/z}$ with a disorder-dependent exponent $z\ensuremath{\ge}1$, in contrast with the pure ballistic growth $z=1$ of clean systems. At the same time, anomalous relaxation is also observed for the spin imbalance $\mathcal{I}(t)\ensuremath{\propto}{t}^{\ensuremath{-}\ensuremath{\zeta}}$ with a continuously varying disorder-dependent exponent $\ensuremath{\zeta}$, vanishing at the transition. This provides a clear experimental signature for detecting this nonconventional regime.