We present exact solutions of a two-body problem for spin- $1/2$ fermions with isotropic spin-orbit (SO) coupling and interacting with an arbitrary short-range potential. We find that in each partial-wave scattering channel, the parametrization of a two-body wave function at short interparticle distance depends on the scattering amplitudes of all channels. This reveals the mixed-partial-wave scattering induced by SO couplings. By comparing with results from a square-well potential, we investigate the validity of original pseudopotential models in the presence of SO coupling. We find the $s$ -wave pseudopotential provides a good approximation for low-energy solutions near $s$ -wave resonances, given the length scale of SO coupling much longer than the potential range. However, near $p$ -wave resonance the $p$ -wave pseudopotential gives low-energy solutions that are qualitatively different from exact ones, based on which we conclude that the $p$ -wave model can not be applied to the fermion system if the SO coupling strength is larger or comparable to the Fermi momentum.We present exact solutions of a two-body problem for spin-$1/2$ fermions with isotropic spin-orbit (SO) coupling and interacting with an arbitrary short-range potential. We find that in each partial-wave scattering channel, the parametrization of a two-body wave function at short interparticle distance depends on the scattering amplitudes of all channels. This reveals the mixed-partial-wave scattering induced by SO couplings. By comparing with results from a square-well potential, we investigate the validity of original pseudopotential models in the presence of SO coupling. We find the $s$-wave pseudopotential provides a good approximation for low-energy solutions near $s$-wave resonances, given the length scale of SO coupling much longer than the potential range. However, near $p$-wave resonance the $p$-wave pseudopotential gives low-energy solutions that are qualitatively different from exact ones, based on which we conclude that the $p$-wave model can not be applied to the fermion system if the SO coupling strength is larger or comparable to the Fermi momentum.

arXiv:1112.1122Physical Review AFeb 14, 201258 citations

Spin-waves in the paramagnetic phase

J L Beeby, J. Hubbard

Physics Letters AMar 1, 196818 citations

Quantum Scattering

Edward B. Manoukian

Springer eBooksJan 16, 20070 citations

Calculation of spin-polarized muonium-muonium and spin-polarized hydrogen-hydrogen scattering

M.-S. Wu, Y. Zhang, Jun-Yi Zhang +2 more

In this paper, we investigate spin-polarized muonium-muonium and spin-polarized hydrogen-hydrogen scattering for total orbital angular momentum $L=0$ using the non-Born-Oppenheimer confined variational method combined with explicitly correlated Gaussian basis functions. Our approach yielded accurate $S$ -wave phase shifts and elastic cross sections at scattering momenta below $0.6{a}_{0}^{\ensuremath{-}1}$, where ${a}_{0}$ is the Bohr radius. By utilizing the effective range formula, we determined the $S$ -wave scattering lengths to be $3.70{a}_{0}$ and $1.35{a}_{0}$ for spin-polarized muonium-muonium and spin-polarized hydrogen-hydrogen scattering, respectively.In this paper, we investigate spin-polarized muonium-muonium and spin-polarized hydrogen-hydrogen scattering for total orbital angular momentum $L=0$ using the non-Born-Oppenheimer confined variational method combined with explicitly correlated Gaussian basis functions. Our approach yielded accurate $S$-wave phase shifts and elastic cross sections at scattering momenta below $0.6{a}_{0}^{\ensuremath{-}1}$, where ${a}_{0}$ is the Bohr radius. By utilizing the effective range formula, we determined the $S$-wave scattering lengths to be $3.70{a}_{0}$ and $1.35{a}_{0}$ for spin-polarized muonium-muonium and spin-polarized hydrogen-hydrogen scattering, respectively.

Physical Review ANov 13, 20250 citations

Quantum-Mechanical Scattering

Jens Boos

Springer thesesJan 1, 20210 citations

Simulating Meson Scattering on Spin Quantum Simulators

Elizabeth R. Bennewitz, Brayden Ware, Alexander Schuckert +11 more

Studying high-energy collisions of composite particles, such as hadrons and nuclei, is an outstanding goal for quantum simulators. However, preparation of hadronic wave packets has posed a significant challenge, due to the complexity of hadrons and the precise structure of wave packets. This has limited demonstrations of hadron scattering on quantum simulators to date. Observations of confinement and composite excitations in quantum spin systems have opened up the possibility to explore scattering dynamics in spin models. In this article, we develop two methods to create entangled spin states corresponding to wave packets of composite particles in analog quantum simulators of Ising spin Hamiltonians. One wave-packet preparation method uses the blockade effect enabled by beyond-nearest-neighbor Ising spin interactions. The other method utilizes a quantum-bus-mediated exchange, such as the native spin-phonon coupling in trapped-ion arrays. With a focus on trapped-ion simulators, we numerically benchmark both methods and show that high-fidelity wave packets can be achieved in near-term experiments. We numerically study scattering of wave packets for experimentally realizable parameters in the Ising model and find inelastic-scattering regimes, corresponding to particle production in the scattering event, with prominent and distinct experimental signals. Our proposal, therefore, demonstrates the potential of observing inelastic scattering in near-term quantum simulators.Studying high-energy collisions of composite particles, such as hadrons and nuclei, is an outstanding goal for quantum simulators. However, preparation of hadronic wave packets has posed a significant challenge, due to the complexity of hadrons and the precise structure of wave packets. This has limited demonstrations of hadron scattering on quantum simulators to date. Observations of confinement and composite excitations in quantum spin systems have opened up the possibility to explore scattering dynamics in spin models. In this article, we develop two methods to create entangled spin states corresponding to wave packets of composite particles in analog quantum simulators of Ising spin Hamiltonians. One wave-packet preparation method uses the blockade effect enabled by beyond-nearest-neighbor Ising spin interactions. The other method utilizes a quantum-bus-mediated exchange, such as the native spin-phonon coupling in trapped-ion arrays. With a focus on trapped-ion simulators, we numerically benchmark both methods and show that high-fidelity wave packets can be achieved in near-term experiments. We numerically study scattering of wave packets for experimentally realizable parameters in the Ising model and find inelastic-scattering regimes, corresponding to particle production in the scattering event, with prominent and distinct experimental signals. Our proposal, therefore, demonstrates the potential of observing inelastic scattering in near-term quantum simulators.

arXiv:2403.07061Mar 11, 20240 citations

We present exact solutions of a two-body problem for spin-

1/2

fermions with isotropic spin-orbit (SO) coupling and interacting with an arbitrary short-range potential. We find that in each partial-wave scattering channel, the parametrization of a two-body wave function at short interparticle distance depends on the scattering amplitudes of all channels. This reveals the mixed-partial-wave scattering induced by SO couplings. By comparing with results from a square-well potential, we investigate the validity of original pseudopotential models in the presence of SO coupling. We find the

s

-wave pseudopotential provides a good approximation for low-energy solutions near

s

-wave resonances, given the length scale of SO coupling much longer than the potential range. However, near

p

-wave resonance the

p

-wave pseudopotential gives low-energy solutions that are qualitatively different from exact ones, based on which we conclude that the

p

-wave model can not be applied to the fermion system if the SO coupling strength is larger or comparable to the Fermi momentum.

In this paper, we investigate spin-polarized muonium-muonium and spin-polarized hydrogen-hydrogen scattering for total orbital angular momentum

L=0

using the non-Born-Oppenheimer confined variational method combined with explicitly correlated Gaussian basis functions. Our approach yielded accurate

S

-wave phase shifts and elastic cross sections at scattering momenta below $0.6{a}_{0}^{\ensuremath{-}1}$, where

{a}_{0}

is the Bohr radius. By utilizing the effective range formula, we determined the

S

-wave scattering lengths to be

3.70{a}_{0}

and

1.35{a}_{0}

for spin-polarized muonium-muonium and spin-polarized hydrogen-hydrogen scattering, respectively.