arXiv subjects

Chris H. Greene

Publications and source records attributed to Chris H. Greene.

At least 109 records · Page 6Linked to original sources

arXiv2013

Extension of the correlated Gaussian hyperspherical method to more particles and dimensions

The solution of the hyperangular Schrödinger equation for few-body systems using a basis of explicitly correlated Gaussians remains numerically challenging. This is in part due to the number of basis functions needed as the system size grows, but also due to the fact that the number of numerical integrations increases with the number of hyperangular degrees of freedom. This paper shows that the latter challenge is no more. Using a delta function to fix the hyperradius $R$, all matrix element calculations are reduced to a single numerical integration regardless of system size $n$ or number of dimensions $d$. In the special case of $d$ an even number, the matrix elements of the noninteracting system are fully analytical. We demonstrate the use of the new matrix elements for the 3-, 4-, and 5-body electron-positron systems with zero total angular momentum $L$, positive parity $π$, and varied spins $S_+$ and $S_-$.

physics.atom-ph↗

arXiv2013

Comparison of classical and quantal calculations of helium three-body recombination

A general method to study classical scattering in $n$-dimension is developed. Through classical trajectory calculations, the three-body recombination is computed as a function of the collision energy for helium atoms, as an example. Quantum calculations are also performed for the $J^Π$ = $0^{+}$ symmetry of the three-body recombination rate in order to compare with the classical results, yielding good agreement for $E\gtrsim$ 1 K. The classical threshold law is derived and numerically confirmed for the Newtonian three-body recombination rate. Finally, a relationship is found between the quantum and classical three-body hard hypersphere elastic cross sections which is analogous to the well-known shadow scattering in two-body collisions.

physics.chem-ph↗

arXiv2013

Quasi-1D scattering with general transverse 2D confinement

Confinement induced resonances (CIR) in quasi-1D systems have been theoretically predicted and observed in various ultracold atomic gases. Here a regularized local frame transformation method is developed to treat CIR in a quasi-1D system that has an arbitrary transverse trap shape in general. The method is applied to predict the CIR position in a system whose transverse geometry is a square well.

physics.atom-ph↗

arXiv2013

Resonant Five-body Recombination in an Ultracold Gas of Bosonic Atoms

We combine theory and experiment to investigate five-body recombination in an ultracold gas of atomic cesium at negative scattering length. A refined theoretical model, in combination with extensive laboratory tunability of the interatomic interactions, enables the five-body resonant recombination rate to be calculated and measured. The position of the new observed recombination feature agrees with a recent theoretical prediction and supports the prediction of a family of universal cluster states at negative $a$ that are tied to an Efimov trimer.

cond-mat.quant-gas↗

arXiv2013

Stochastic and equilibrium pictures of the ultracold FFR molecular conversion rate

The ultracold molecular conversion rate occurring in an adiabatic ramp through a Fano-Feshbach resonance is studied and compared in two statistical models. One model, the so-called stochastic phase space sampling (SPSS)[E.Hodby et al., PRL.94 120402(2005)] evaluates the overlap of two atomic distributions in phase space by sampling atomic pairs according to a phase-space criterion. The other model, the chemical equilibrium theory(ChET)[S.Watabe and T.Nikuni, PRA.77 013616(2008)] considers atomic and molecular distributions in the limit of the chemical and thermal equilibrium. The present study applies SPSS and ChET to a prototypical system of K+K K2 in all the symmetry combinations, namely Fermi-Fermi, Bose-Bose, and Bose-Fermi cases. To examine implications of the phase-space criterion for SPSS, the behavior of molecular conversion is analyzed using four distinct geometrical constraints. Our comparison of the results of SPSS with those of ChET shows that while they appear similar in most situations, the two models give rise to rather dissimilar behaviors when the presence of a Bose-Einstein condensate (BEC) strongly affects the molecule formation.

physics.atom-ph↗

arXiv2013

Low-energy Electron collisions with O$_2$: Test of Molecular R-matrix without Diagonalization

Electron collisions with O$_2$ at scattering energies below 1 eV are studied in the fixed-nuclei approximation for a range of internuclear separations using the ab initio molecular R-matrix method. The $^2Π_g$ scattering eigenphases and quantum defects are calculated. The parameters of the resonance and the energy of the bound negative ion are then extracted. Different models of the target that employ molecular orbitals calculated for the neutral target are compared with models based on anionic orbitals. A model using a basis of anionic molecular orbitals yields physically correct results in good agreement with experiment. An alternative method of calculation of the R-matrix is tested, where instead of performing a single complete diagonalization of the Hamiltonian matrix in the inner region, the system of linear equations is solved individually for every scattering energy. This approach is designed to handle problems where diagonalization of an extremely large Hamiltonian is numerically too demanding.

physics.chem-ph↗

arXiv2013

Quantum Defect Theory for High Partial Wave Cold Collisions

We extend Multichannel Quantum Defect Theory (MQDT) to ultracold collisions involving high partial wave quantum numbers $L$. This requires a careful standardization of the MQDT reference wave functions at long range to ensure their linear independence. To illustrate the simplicity and accuracy of the resulting theory, we perform a comprehensive calculation of $L\le 2$ Fano-Feshbach resonances in the range 0-1000 G for the scattering of $^{40}$K + $^{87}$Rb in their lowest hyperfine states.

physics.atom-ph↗

arXiv2013

Lorentz meets Fano spectral line shapes: A universal phase and its laser control

Symmetric Lorentzian and asymmetric Fano line shapes are fundamental spectroscopic signatures that quantify the structural and dynamical properties of nuclei, atoms, molecules, and solids. This study introduces a universal temporal-phase formalism, mapping the Fano asymmetry parameter q to a phase ϕ of the time-dependent dipole-response function. The formalism is confirmed experimentally by laser-transforming Fano absorption lines of autoionizing helium into Lorentzian lines after attosecond-pulsed excitation. We also prove the inverse, the transformation of a naturally Lorentzian line into a Fano profile. A further application of this formalism amplifies resonantly interacting extreme-ultraviolet light by quantum-phase control. The quantum phase of excited states and its response to interactions can thus be extracted from line-shape analysis, with scientific applications in many branches of spectroscopy.

physics.atom-ph↗

arXiv2012

Rydberg states of triatomic hydrogen and deuterium

The triatomic hydrogen ion (H$_3^+$) has spurred tremendous interest in astrophysics in recent decades, and Rydberg states of H$_3$ have also maintained an important role for understanding H$_3^+$ experiments. In a previous study [J. Chem. Phys. \textbf{133}, 234302 (2010)], radiative transitions between neutral H$_3$ Rydberg states were calculated at wavelengths near 7 microns, and could be compared with mid-infrared laser lines observed in hydrogen/rare gas discharges. The present study extends the investigation to wavelengths near 10 -- 13 microns. Rydberg states of D$_3$ are also treated.

physics.atom-ph↗

arXiv2012

Universal three-body recombination via resonant d-wave interactions

For a system of three identical bosons interacting via short-range forces, when two of the atoms are about to form a two-body s-wave dimer, there exists an infinite number of three-body bound states. This effect is the well-known Efimov effect. These three-body states (Efimov states) are found to be universal for ultracold atomic gases and the lowest Efimov state crosses the three-body break-up threshold when the s-wave two-body scattering length is $a \approx -9.73 r_{\rm vdW}$, $r_{\rm vdW}$ being the van der Waals length. This article focuses on a generalized version of this Efimov scenario, where two of the atoms are about to form a two-body d-wave dimer, which leads to strong d-wave interactions. In a recent paper [B. Gao, Phys. Rev. A. {\bf 62}, 050702(R) (2000)], Bo Gao has predicted that for broad resonances the d-wave dimer is always formed near $a \approx 0.956 r_{\rm vdW}$. Here we find that a single universal three-body state associated with the d-wave dimer is also formed near the three-body break-up threshold at $a \approx 1.09 r_{\rm vdW}$ and its signature can be found through enhancement of the three-body recombination. The three-body effective potential curves that are crucial for understanding the recombination dynamics are also calculated and analyzed. An improved method to calculate the couplings, effective potential curves, and recombination rate coefficients is presented.

physics.atom-ph↗

arXiv2012

Universal three-body parameter in heteronuclear atomic systems

In Efimov physics, a three-body parameter (3BP), previously regarded as nonuniversal, uniquely defines bound and scattering properties of three particles. A universal 3BP, however, have been recently shown in experiments and theory in ultracold homonuclear gases. Our present study further predicts a universal 3BP for heteronuclear atomic systems near broad Feshbach resonances, and provides physical interpretations for its origin. We show that for a system composed of two light and one heavy atoms, the physical origin of the universal 3BP is similar to the homonuclear case while for systems composed by one light and two heavy atoms the universality of the 3BP is now mostly controlled by the heavy-heavy interatomic properties. This new universality is explained by the universal properties of the van der Waals interactions in a simple Born-Oppenheimer (BO) picture. Finally, we show the numerically determined 3BPs for some combinations of alkali atoms used in ultracold experiments.

physics.atom-ph↗

arXiv2012

Laser-assisted electron-argon scattering at small angles

Electron-argon scattering in the presence of a linearly polarized, low frequency laser field is studied theoretically. The scattering geometries of interest are small angles where momentum transfer is nearly perpendicular to the field, which is where the Kroll-Watson approximation has the potential to break down. The Floquet R matrix method solves the velocity gauge Schrödinger equation, using a larger reaction volume than previous treatments in order to carefully assess the importance of the long range polarization potential to the cross section. A comparison of the cross sections calculated with the target potential fully included inside 20 and 100 a.u. shows no appreciable differences, which demonstrates that the long range interaction can not account for the high cross sections measured in experiments.

physics.atom-ph↗

arXiv2012

Estimates of rates for dissociative recombination of NO$_2^+$ + e$^-$ via various mechanisms

We estimate rates for the dissociative recombination (DR) of NO$_2^+$ + e$^-$. Although accurate excited state potential energy curves for the excited states of the neutral are not available, we estimate that the 1 $^2$Φ$_g$ and the 1 $^2$Π$_g$ states of the neutral may intersect the ground state cation potential energy surface near its equilibrium geometry. Using fixed nuclei scattering calculations we estimate the rate for direct DR via these states and find it to be significant. We also perform approximate calculations of DR triggered by the indirect mechanism, which suggest that the indirect DR rate for NO$_2^+$ is insignificant compared to the direct rate.

physics.chem-ph↗

arXiv2012

Origin of the Three-body Parameter Universality in Efimov Physics

In recent years extensive theoretical and experimental studies of universal few-body physics have led to advances in our understanding of universal Efimov physics [1]. The Efimov effect, once considered a mysterious and esoteric effect, is today a reality that many experiments in ultracold quantum gases have successfully observed and continued to explore [2-14]. Whereas theory was the driving force behind our understanding of Efimov physics for decades, recent experiments have contributed an unexpected discovery. Specifically, measurements have found that the so-called three-body parameter determining several properties of the system is universal, even though fundamental assumptions in the theory of the Efimov effect suggest that it should be a variable property that depends on the precise details of the short-range two- and three-body interactions. The present Letter resolves this apparent contradiction by elucidating unanticipated implications of the two-body interactions. Our study shows that the three-body parameter universality emerges because a universal effective barrier in the three-body potentials prevents the three particles from simultaneously getting close to each other. Our results also show limitations on this universality, as it is more likely to occur for neutral atoms and less likely to extend to light nuclei.

cond-mat.quant-gas↗

arXiv2012

Few-body ultracold reactions in a Bose-Fermi mixture

The spectrum of two bosons and two fermions in a trap is calculated using a correlated-Gaussian basis throughout the range of a broad Fano-Feshbach resonance. The calculations provide a few-body solution to the magneto-association of fermionic Feshbach molecules. This solution is used to study the time evolution of the system as the scattering length changes, mimicking experiments with Bose-Fermi mixtures near Fano-Feshbach resonances. The structure of avoided crossings in the few-body spectrum enables an interpretation of the dynamics of the system as a sequence of Landau-Zener transitions. The calculated molecule formation rate is compared with experimental observations.

physics.atom-ph↗

arXiv2011

Universal bound and scattering properties for two dipoles

The bound state and low-energy scattering properties of two oriented dipoles are investigated for both bosonic and fermionic symmetries. Interestingly, a universal scaling emerges for the expectation value of the angular momentum for deeply-bound two-dipole states. This scaling traces to the pendulum motion of two dipoles in strong dipole regime. The low-energy scattering phase shifts of two dipoles also show universal behavior. These universal observations make connections to the scaling laws reported in Refs. [1, 2] for three dipoles. Atomic units are used throughout this work.

physics.atom-ph↗

arXiv2011

Theory of dissociative recombination of highly-symmetric polyatomic ions

A general first-principles theory of dissociative recombination is developed for highly-symmetric molecular ions and applied to H$_3$O$^{+}$ and CH$_3^+$, which play an important role in astrophysical, combustion, and laboratory plasma environments. The theoretical cross-sections obtained for the dissociative recombination of the two ions are in good agreement with existing experimental data from storage ring experiments.

physics.atom-ph↗

arXiv2011

Femtosecond transparency in the extreme ultraviolet

Electromagnetically induced transparency-like behavior in the extreme ultraviolet (XUV) is studied theoretically, including the effect of intense 800 nm laser dressing of He 2s2p (1Po) and 2p^2 (1Se) autoionizing states. We present an ab initio solution of the time-dependent Schrodinger equation (TDSE) in an LS-coupling configuration interaction basis set. The method enables a rigorous treatment of optical field ionization of these coupled autoionizing states into the N = 2 continuum in addition to N = 1. Our calculated transient absorption spectra show encouraging agreement with experiment.

physics.atom-ph↗