When a neutral atom moves in a properly designed laser field, its center-of-mass motion may mimic the dynamics of a charged particle in a magnetic field, with the emergence of a Lorentz-like force. In this Colloquium the physical principles at the basis of this artificial (synthetic) magnetism are presented. The corresponding Aharonov-Bohm phase is related to the Berry's phase that emerges when the atom adiabatically follows one of the dressed states of the atom-laser interaction. Some manifestations of artificial magnetism for a cold quantum gas, in particular, in terms of vortex nucleation are discussed. The analysis is then generalized to the simulation of non-Abelian gauge potentials and some striking consequences are presented, such as the emergence of an effective spin-orbit coupling. Both the cases of bulk gases and discrete systems, where atoms are trapped in an optical lattice, are addressed.

/pdf/colloquium-artificial-gauge-potentials-for-neutral-atoms-1vpmk7ly98.pdf

Colloquium: Artificial gauge potentials for neutral atoms

In this report, we summarize and describe the recent unique updates and additions to the Molcas quantum chemistry program suite as contained in release version 8. These updates include natural and spin orbitals for studies of magnetic properties, local and linear scaling methods for the Douglas-Kroll-Hess transformation, the generalized active space concept in MCSCF methods, a combination of multiconfigurational wave functions with density functional theory in the MC-PDFT method, additional methods for computation of magnetic properties, methods for diabatization, analytical gradients of state average complete active space SCF in association with density fitting, methods for constrained fragment optimization, large-scale parallel multireference configuration interaction including analytic gradients via the interface to the Columbus package, and approximations of the CASPT2 method to be used for computations of large systems. In addition, the report includes the description of a computational machinery for nonlinear optical spectroscopy through an interface to the QM/MM package Cobramm. Further, a module to run molecular dynamics simulations is added, two surface hopping algorithms are included to enable nonadiabatic calculations, and the DQ method for diabatization is added. Finally, we report on the subject of improvements with respects to alternative file options and parallelization.

https://hal-amu.archives-ouvertes.fr/hal-01409053/document

Molcas 8: New capabilities for multiconfigurational quantum chemical calculations across the periodic table.

Gauge fields are central in our modern understanding of physics at all scales. At the highest energy scales known, the microscopic universe is governed by particles interacting with each other through the exchange of gauge bosons. At the largest length scales, our Universe is ruled by gravity, whose gauge structure suggests the existence of a particle—the graviton—that mediates the gravitational force. At the mesoscopic scale, solid-state systems are subjected to gauge fields of different nature: materials can be immersed in external electromagnetic fields, but they can also feature emerging gauge fields in their low-energy description. In this review, we focus on another kind of gauge field: those engineered in systems of ultracold neutral atoms. In these setups, atoms are suitably coupled to laser fields that generate effective gauge potentials in their description. Neutral atoms ‘feeling’ laser-induced gauge potentials can potentially mimic the behavior of an electron gas subjected to a magnetic field, but also, the interaction of elementary particles with non-Abelian gauge fields. Here, we review different realized and proposed techniques for creating gauge potentials—both Abelian and non-Abelian—in atomic systems and discuss their implication in the context of quantum simulation. While most of these setups concern the realization of background and classical gauge potentials, we conclude with more exotic proposals where these synthetic fields might be made dynamical, in view of simulating interacting gauge theories with cold atoms.

https://iopscience.iop.org/article/10.1088/0034-4885/77/12/126401/pdf

Light-induced gauge fields for ultracold atoms

One of the most promising suggested applications of quantum computing is solving classically intractable chemistry problems. This may help to answer unresolved questions about phenomena such as high temperature superconductivity, solid-state physics, transition metal catalysis, and certain biochemical reactions. In turn, this increased understanding may help us to refine, and perhaps even one day design, new compounds of scientific and industrial importance. However, building a sufficiently large quantum computer will be a difficult scientific challenge. As a result, developments that enable these problems to be tackled with fewer quantum resources should be considered important. Driven by this potential utility, quantum computational chemistry is rapidly emerging as an interdisciplinary field requiring knowledge of both quantum computing and computational chemistry. This review provides a comprehensive introduction to both computational chemistry and quantum computing, bridging the current knowledge gap. Major developments in this area are reviewed, with a particular focus on near-term quantum computation. Illustrations of key methods are provided, explicitly demonstrating how to map chemical problems onto a quantum computer, and how to solve them. The review concludes with an outlook on this nascent field.

Quantum computational chemistry

Practical challenges in simulating quantum systems on classical computers have been widely recognized in the quantum physics and quantum chemistry communities over the past century. Although many approximation methods have been introduced, the complexity of quantum mechanics remains hard to appease. The advent of quantum computation brings new pathways to navigate this challenging and complex landscape. By manipulating quantum states of matter and taking advantage of their unique features such as superposition and entanglement, quantum computers promise to efficiently deliver accurate results for many important problems in quantum chemistry, such as the electronic structure of molecules. In the past two decades, significant advances have been made in developing algorithms and physical hardware for quantum computing, heralding a revolution in simulation of quantum systems. This Review provides an overview of the algorithms and results that are relevant for quantum chemistry. The intended audience is both quantum chemists who seek to learn more about quantum computing and quantum computing researchers who would like to explore applications in quantum chemistry.

Quantum Chemistry in the Age of Quantum Computing.

A new potential energy surface for ozone is developed. It is based on high level ab initio data and includes an accurate description of the barrier region. Full quantum reactive scattering calculations using a coupled channel approach and hyperspherical coordinates are performed on this surface for various isotopic compositions of ozone. Collision lifetimes are obtained over a wide energy range, which gives the spectrum of rovibrational metastable states (scattering resonances). This spectrum is discovered to be very nonstatistical. The spectrum of resonances is dense below the isotopic zero-point-energy threshold and sparse above it. This feature is explained by the opening of additional dissociation channels at higher energies. This behavior is a general quantum mechanical effect that should occur in other triatomic molecules.

Metastable states of ozone calculated on an accurate potential energy surface

The theoretical methodology for including the effects of the geometric phase in quantum reactive scattering and bound-state calculations is reviewed. Two approaches are discussed:  one approach is based on solving the standard Born−Oppenheimer equation but with double-valued boundary conditions, and the second approach is based on solving a generalized Born−Oppenheimer equation with single-valued boundary conditions. The generalized Born−Oppenheimer equation contains a vector potential which is mathematically equivalent to that of a magnetic solenoid. The recently developed numerical methodology for solving the generalized Born−Oppenheimer equation is reviewed, and several applications of this methodology in chemical reaction dynamics and molecular spectra are discussed. New results from accurate six dimensional quantum reactive scattering calculations for the D + H2(v, j) → HD(v‘, j‘) + H and H + H2(v, j) → H2(v‘, j‘) + H reactions are presented. These calculations are performed both with and without the...

Geometric phase effects in chemical reaction dynamics and molecular spectra

A clear explanation for an anomalous isotope effect in ozone formation is given in terms of the energy transfer mechanism, where the metastable states of ozone are formed first, and then stabilized by collisions with other atoms. Unusual nonstatistical properties of metastable states spectra discovered earlier [J. Chem. Phys. 118, 6298 (2003)] are incorporated into the kinetics model, where different metastable states are treated as different species, and the stabilization step is treated approximately. The population of the ozone metastable states builds up and decays through three possible O2+O channels. When different isotopes of oxygen are involved the three channels become open at different energies because of the differences in the quantum zero-point-energies (ΔZPE) of the different O2 molecules. The spectrum of metastable states is anomalously dense below the ΔZPE threshold and these states are accessible only from the lower entrance channel. Also, these low-lying metastable states are stabilized v...

Formation of ozone: Metastable states and anomalous isotope effect

The general vector potential (gauge theory) approach for including geometric phase effects in accurate 3D quantum scattering calculations in hyperspherical coordinates is presented. A hybrid numerical technique utilizing both the DVR (discrete variable representation) and the FBR (finite basis representation) is developed. This method overcomes the singular behavior of the vector potential terms giving accurate surface function solutions to the complex Hermitian nuclear Schrodinger equation. The hybrid DVR/FBR technique is applied explicitly to HO2 for zero total angular momentum. The resulting complex surface functions include the geometric phase effects due to the C2v conical intersection. The O2 permutation symmetry is implemented to give real double‐valued surface functions which exhibit both even and odd symmetry. The surface function eigenvalues are compared to calculations without the geometric phase. The results indicate that geometric phase effects should be significant for H+O2 scattering even a...

Geometric phase effects in H+O2 scattering. I. Surface function solutions in the presence of a conical intersection

A DIM (diatomics in molecules) model utilizing a large basis set (34 2A‘ and 32 2A’ states) was used to obtain the potential energy surfaces relevant to the chemical reaction H+O2→OH+O. The ground state, 12A‘, surface was fitted to 910 accurate ab initio points of Walch et al. [J. Chem. Phys. 94, 7068 (1991)]. The resulting fit accurately describes the C2v conical intersection in the regions for which ab initio data are available, and the linear conical intersection is accurately described in the H+O2 region. It is also an accurate global fit with an rms deviation of 0.096 eV (2.22 kcal/mol). The behavior of the low‐lying excited states, 12A’, 22A‘, and 22A’, appears to be qualitatively correct everywhere and quantitative near the low‐lying conical intersections. The DIM formulation allows the computation of the gauge potential relevant for the description of the geometric phase and non‐adiabatic effects in multi‐surface reactive scattering calculations.

Brian K. Kendrick

Papers

Metastable states of ozone calculated on an accurate potential energy surface

Geometric phase effects in chemical reaction dynamics and molecular spectra

Formation of ozone: Metastable states and anomalous isotope effect

Geometric phase effects in H+O2 scattering. I. Surface function solutions in the presence of a conical intersection

Potential energy surfaces for the low‐lying 2A‘ and 2A’ States of HO2: Use of the diatomics in molecules model to fit ab initio data