Total angular momentum representation for state-to-state quantum scattering of cold molecules in a magnetic field

Abstract

We show that the integral cross sections for state-to-state quantum scattering of cold molecules in a magnetic field can be efficiently computed using the total angular momentum representation despite the presence of unphysical Zeeman states in the eigenspectrum of the asymptotic Hamiltonian. We demonstrate that the unphysical states arise due to the incompleteness of the space-fixed total angular momentum basis caused by using a fixed cutoff value $J_{\text{max}}$ for the total angular momentum of the collision complex $J$. As a result, certain orbital angular momentum ($l$) basis states lack the full range of $J$ values required by the angular momentum addition rules, resulting in the appearance of unphysical states. We find that by augmenting the basis with a full range of $J$-states for every $l$, it is possible to completely eliminate the unphysical states from quantum scattering calculations on molecular collisions in external fields. To illustrate the procedure, we use the augmented basis sets to calculate the state-to-state cross sections for rotational and spin relaxation in cold collisions of ${}^{40}$CaH$(X^2{\Sigma }^{+},v=0,N=1,M_N=1,M_S=1/2)$ molecules with ${}^4$He atoms in a magnetic field. We find excellent agreement with benchmark calculations, validating our proposed procedure. We find that $N$-conserving spin relaxation to the lowest-energy Zeeman state of the $N=1$ manifold, $|11\frac{1}{2}⟩\to |1-1-\frac{1}{2}⟩$ is nearly completely suppressed due to the lack of spin-rotation coupling between the fully spin-stretched Zeeman states. Our results demonstrate the possibility of rigorous, computationally efficient, and unphysical state-free quantum scattering calculations on cold molecular collisions in an external magnetic field.

References in corpus (13)

• Cold molecules: Progress in Quantum Engineering of Chemistry and Quantum Matter
• Schemes for robust quantum computation with polar molecules
• Controlling electronic spin relaxation of cold molecules with electric fields
• Ultracold Rb-OH collisions and prospects for sympathetic cooling
• Cold N+NH Collisions in a Magnetic Trap
• Mechanism of Collisional Spin Relaxation in Triplet-Sigma Molecules
• Dynamical generation of spin squeezing in ultra-cold dipolar molecules
• Magnetic Feshbach resonances in collisions of ${}^{23}$Na${}^{40}$K with ${}^{40}$K
• Cold collisions of N atoms and NH molecules in magnetic fields
• Complete quantum coherent control of ultracold molecular collisions
• Efficient method for quantum calculations of molecule - molecule scattering properties in a magnetic field
• Quantum spin state selectivity and magnetic tuning of ultracold chemical reactions of triplet alkali-metal dimers with alkali-metal atoms
• Total angular momentum representation for atom-molecule collisions in electric fields

Cited by in corpus (4)

• Spectrum of Feshbach resonances in NaLi $+$ Na collisions
• Nuclear spin relaxation in cold atom-molecule collisions
• Ultracold molecular collisions in magnetic fields: Efficient incorporation of hyperfine structure in the total rotational angular momentum representation
• Hyperfine and Zeeman interactions in ultracold collisions of molecular hydrogen with atomic lithium