Characterizing Feshbach resonances in ultracold scattering calculations

Frye, Matthew D.; Hutson, Jeremy M.

doi:10.1103/physreva.96.042705

Cited by 24 publications

(41 citation statements)

References 24 publications

(62 reference statements)

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“…molscat can converge on and characterise the zero-energy Feshbach resonances that appear in the scattering length as a function of external fields [10]. It can do this for resonances both in elastic scattering, where the scattering length has a simple pole characterised by its position and width and the background scattering length, and in inelastic scattering, where the resonant behaviour is more complex and requires additional parameters [9].…”

Section: Characterisation Of Zero-energy Feshbach Resonancesmentioning

confidence: 99%

molscat: A program for non-reactive quantum scattering calculations on atomic and molecular collisions

Hutson

Sueur

2019

Computer Physics Communications

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137

115

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Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Abstractmolscat is a general-purpose program for quantum-mechanical calculations on nonreactive atom-atom, atom-molecule and molecule-molecule collisions. It constructs the coupled-channel equations of atomic and molecular scattering theory, and solves them by propagating the wavefunction or log-derivative matrix outwards from short range to the asymptotic region at long range. It then applies scattering boundary conditions to extract the scattering matrix (S matrix). Built-in coupling cases include atom + rigid linear molecule, atom + vibrating diatom, atom + rigid symmetric top, atom + asymmetric or spherical top, rigid diatom + rigid diatom, rigid diatom + asymmetric top, and diffractive scattering of an atom from a crystal surface. Interaction potentials may be specified either in program input (for simple cases) or with usersupplied routines. For the built-in coupling cases, molscat can loop over total angular momentum (partial wave) and total parity to calculate elastic and inelastic integral cross sections and spectroscopic line-shape cross sections. Post-processors are available to calculate differential cross sections, transport, relaxation and Senftleben-Beenakker cross sections, and to fit the parameters of scattering resonances. molscat also provides an interface for plug-in routines to specify coupling cases (Hamiltonians and basis sets) that are not built in; plug-in routines are supplied to handle collisions of a pair of alkali-metal atoms with hyperfine structure in an applied magnetic field. For low-energy scattering, molscat can calculate scattering lengths and effective ranges and can locate and characterise scattering resonances as a function of an external variable such as the magnetic field. Nature of problem:Quantum-mechanical calculations of scattering properties for non-reactive collisions between atoms and molecules. Solution method:The Schrödinger equation is expressed in terms of coupled equations in the interparticle distance, R. Solutions of the coupled-channel equations are propagated outwards from the classically forbidden region at short range to the asymptotic region. The program calculates scattering S matrices and uses them to calculate scattering properties including elastic, inelastic and line-shape cross sections.Unusual features:1. molscat contains numerous features to handle quantities important in low-energy collisions. It can propagate very efficiently to very long range, and it can calculate low-energy properti...

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Section: Characterisation Of Zero-energy Feshbach Resonancesmentioning

confidence: 99%

molscat: A program for non-reactive quantum scattering calculations on atomic and molecular collisions

Hutson

Sueur

2019

Computer Physics Communications

Self Cite

137

115

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“…This is analogous to the "fully complex" procedure of Ref. [9] and allows convergence on E res and Γ as well as S bg,ii and D ii . In multichannel scattering, we have sometimes found that this procedure converges successfully, even for resonances where uncorrected energy dependence in the background prevents convergence based on the eigenphase sum.…”

Section: Partial Widthsmentioning

confidence: 94%

“…One of the outer points is placed about Γt lo from E res (with tolerance ±ξΓt lo ), and the other is about Γt hi from it (with tolerance ±ξΓt hi ). This strategy is similar to that in our procedures for converging on a zero-energy Feshbach resonance as a function of external field [9]. The three points can be regarded as allowing characterization of E res , Γ, and δ bg , respectively.…”

Section: Theorymentioning

confidence: 99%

Characterizing quasibound states and scattering resonances

Frye

Hutson

2020

Phys. Rev. Research

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Characterizing quasibound states from coupled-channel scattering calculations can be a laborious task, involving extensive manual iteration and fitting. We present an automated procedure that reliably converges on a quasibound state (or scattering resonance) from some distance away. It may be used for both single-channel and multichannel scattering. It produces the energy and width of the state and the phase (or S-matrix eigenphase sum) of the background scattering, and hence the lifetime of the state. It also allows extraction of partial widths for decay to individual open channels. We demonstrate the method on a very narrow state in the Van der Waals complex Ar-H2, which decays only by vibrational predissociation, and on near-threshold states of 85 Rb2, whose lifetime varies over 4 orders of magnitude as a function of magnetic field.

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“…Recently, Fryeet al [72] published a procedure for extracting parameters, namely the positions B res , widths ΔB, and background scattering lengths a bg , of Feshbach resonances that conform to the Breit-Wigner profile,…”

Section: Zero-field Scattering Lengths and Feshbach Spectramentioning

confidence: 99%

Quantum chaos in Feshbach resonances of the ErYb system

2020

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We investigate ultracold magnetic-field-assisted collisions in the so far unexplored ErYb system. The nonsphericity of the Er atom leads to weakly anisotropic interactions that provide the mechanism for Feshbach resonances to emerge. The resonances are moderately sparsely distributed with a density of 0.1-0.3 G −1 and exhibit chaotic statistics characterized by a Brody parameter η≈0.5-0.7. The chaotic behaviour of Feshbach resonances is accompanied by strong mixing of magnetic and rotational quantum numbers in near-threshold bound states. We predict the existence of broad resonances at fields < 300 G that may be useful for the precise control of scattering properties and magnetoassociation of ErYb molecules. The high number of bosonic Er-Yb isotopic combinations gives many opportunities for mass scaling of interactions. Uniquely, two isotopic combinations have nearly identical reduced masses (differing by less than 10 −5 relative) that we expect to have strikingly similar Feshbach resonance spectra, which would make it possible to experimentally measure their sensitivity to hypothetical variations of proton-to-electron mass ratio. behaviour can be analyzed instead (see pioneering work of Porter and coworkers e.g. [24,25]) and the tools for such analysis include the Random Matrix Theory developed by Wigner [26] and Dyson [27]. For ultracold gases the first evidence of chaos in a Feshbach resonance spectrum was reported in Er dimer by Frisch et al [19]. Since then, the chaotic character of bound states and Feshbach resonances in ultracold collisions was also found for several other systems, for example, in mixtures of Yb atoms in 1 S 0 and 3 P 2 states at large magnetic fields [28], and molecular collisions of Li atom with CaH and CaF [29]. On the other hand, the resonance spacings in collisions of Er and Li atoms in a magnetic field [30], and of highly magnetic europium ( 7 S) with alkali metal atoms [31] have both been shown to follow the non-chaotic poissonian distribution.Here we investigate the interactions and Feshbach spectra between weakly anisotropic lanthanides and heavy spin-singlet atoms using ErYb as a prime example. Ytterbium, alongside Sr, is the most widely used spin-singlet atom with applications for optical clocks, quantum gases and quantum simulation [32][33][34][35]. ErYb should also be very attractive due to the fantastic mass-scalability of both Yb [36,37] and Er (as shown here). Three of the bosonic Yb isotopes, 168 Yb [38] and 170 Yb [39] and 174 Yb [40] form stable Bose-Einstein condensates, and several Fermi and Bose-Fermi and Bose-Bose gases [41, 42] have also been demonstrated experimentally. Er and Yb atoms could form many isotopic mixtures, including two fermion-fermion mixtures with nearly equal masses and very close polarizabilities (hence, trapping properties). While an Er-Yb quantum degenerate mixture has not been achieved yet, it is clearly within the reach of present state-of-the-art techniques. Our predictions could be tested by forming a dual Mott insulator of Er and Yb atoms...

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Characterizing Feshbach resonances in ultracold scattering calculations

Cited by 24 publications

References 24 publications

molscat: A program for non-reactive quantum scattering calculations on atomic and molecular collisions

molscat: A program for non-reactive quantum scattering calculations on atomic and molecular collisions

Characterizing quasibound states and scattering resonances

Quantum chaos in Feshbach resonances of the ErYb system

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