Systems evolving under the influence of competing two- and three-body interactions are of particular interest in exploring the stability of the equilibrium states of a strongly interacting many-body system. We present a solvable model based on qubit networks, which allows us to investigate the intricate influence of these couplings on the possible asymptotic equilibrium states. We study the asymptotic evolution of finite qubit networks under two- and three-qubit interactions. As representatives of three-qubit interactions we choose controlled unitary interactions (cu-interactions) with one and two control qubits. It is shown that networks with purely three-qubit interactions exhibit different asymptotic dynamics depending on whether we deal with interactions controlled by one or two qubits. However, when we allow three-qubit interactions next to two-qubit interactions, the asymptotics is dictated by two-qubit interactions only. Finally, we prove that the simultaneous presence of two types of three-qubit interactions results in the asymptotic dynamics characteristic for two-qubit cu-interactions.Systems evolving under the influence of competing two- and three-body interactions are of particular interest in exploring the stability of the equilibrium states of a strongly interacting many-body system. We present a solvable model based on qubit networks, which allows us to investigate the intricate influence of these couplings on the possible asymptotic equilibrium states. We study the asymptotic evolution of finite qubit networks under two- and three-qubit interactions. As representatives of three-qubit interactions we choose controlled unitary interactions (cu-interactions) with one and two control qubits. It is shown that networks with purely three-qubit interactions exhibit different asymptotic dynamics depending on whether we deal with interactions controlled by one or two qubits. However, when we allow three-qubit interactions next to two-qubit interactions, the asymptotics is dictated by two-qubit interactions only. Finally, we prove that the simultaneous presence of two types of three-qubit interactions results in the asymptotic dynamics characteristic for two-qubit cu-interactions.

arXiv:1504.03456Journal of Physics A Mathematical and TheoreticalMay 6, 20150 citations

Interactions

Adam Smith

Springer thesesJan 1, 20190 citations

Two-dimensional three-body quadrupole–quadrupole interactions

Jianing Han

Abstract The interactions between dipoles are called dipole–dipole interactions. One type of dipole–dipole interaction is van der Waals interaction. Similar to van der Waals interactions, the interactions between quadrupoles are called quadrupole–quadrupole interactions. Atoms can be treated not only as dipoles but also as quadrupoles. In this article, we study the quadrupole interactions between highly excited atoms or Rydberg atoms. In addition, unlike many other calculations, in which the primary focus was on the one-dimensional two-body quadrupole–quadrupole interactions, the primary aim of this article is to study the two-dimensional few-body quadrupole–quadrupole interactions. Specifically, the two-dimensional three-body interactions are investigated. This research has many applications, such as quadrupole-blockade for quantum computing, creating molecules based on quadrupole interactions, or quadrupole–quadrupole molecules.Abstract The interactions between dipoles are called dipole–dipole interactions. One type of dipole–dipole interaction is van der Waals interaction. Similar to van der Waals interactions, the interactions between quadrupoles are called quadrupole–quadrupole interactions. Atoms can be treated not only as dipoles but also as quadrupoles. In this article, we study the quadrupole interactions between highly excited atoms or Rydberg atoms. In addition, unlike many other calculations, in which the primary focus was on the one-dimensional two-body quadrupole–quadrupole interactions, the primary aim of this article is to study the two-dimensional few-body quadrupole–quadrupole interactions. Specifically, the two-dimensional three-body interactions are investigated. This research has many applications, such as quadrupole-blockade for quantum computing, creating molecules based on quadrupole interactions, or quadrupole–quadrupole molecules.

arXiv:2106.01479Journal of Physics B Atomic Molecular and Optical PhysicsJul 14, 20210 citations

The Four Interactions

WORLD SCIENTIFIC eBooksAug 1, 20110 citations

The Four Interactions

WORLD SCIENTIFIC eBooksFeb 10, 20170 citations

Strongly interacting one-dimensional quantum gas mixtures with weak p -wave interactions

Haiping Hu, Lei Pan, Shu Chen

We study one-dimensional strongly interacting quantum gas mixtures, including both the Bose-Fermi and spin- $1/2$ Fermi-Fermi mixtures, with weak $p$ -wave interaction between intracomponent fermions, and demonstrate that the weak $p$ -wave interaction cannot be omitted in the strong interaction region where the strength of $p$ -wave interaction is comparable with the inverse of the strength of strongly repulsive $s$ -wave interaction. While the total density distribution is not sensitive to the weak $p$ -wave interaction, we find that the $p$ -wave interaction plays an important role in determining the species-dependent (or spin-dependent) density distributions and produces significant physical effects on the low-energy spin dynamics. We also derive effective spin-exchange models for strongly interacting quantum gas mixtures with weak $p$ -wave interaction, which indicate that a quantum phase transition from an antiferromagnetic state to a ferromagnetic state can be induced by tuning the relative strengths of intracomponent and intercomponent interactions.We study one-dimensional strongly interacting quantum gas mixtures, including both the Bose-Fermi and spin-$1/2$ Fermi-Fermi mixtures, with weak $p$-wave interaction between intracomponent fermions, and demonstrate that the weak $p$-wave interaction cannot be omitted in the strong interaction region where the strength of $p$-wave interaction is comparable with the inverse of the strength of strongly repulsive $s$-wave interaction. While the total density distribution is not sensitive to the weak $p$-wave interaction, we find that the $p$-wave interaction plays an important role in determining the species-dependent (or spin-dependent) density distributions and produces significant physical effects on the low-energy spin dynamics. We also derive effective spin-exchange models for strongly interacting quantum gas mixtures with weak $p$-wave interaction, which indicate that a quantum phase transition from an antiferromagnetic state to a ferromagnetic state can be induced by tuning the relative strengths of intracomponent and intercomponent interactions.

arXiv:1511.08430Physical Review AMar 21, 201623 citations

We study one-dimensional strongly interacting quantum gas mixtures, including both the Bose-Fermi and spin-

1/2

Fermi-Fermi mixtures, with weak

p

-wave interaction between intracomponent fermions, and demonstrate that the weak

p

-wave interaction cannot be omitted in the strong interaction region where the strength of

p

-wave interaction is comparable with the inverse of the strength of strongly repulsive

s

-wave interaction. While the total density distribution is not sensitive to the weak

p

-wave interaction, we find that the

p

-wave interaction plays an important role in determining the species-dependent (or spin-dependent) density distributions and produces significant physical effects on the low-energy spin dynamics. We also derive effective spin-exchange models for strongly interacting quantum gas mixtures with weak

p

-wave interaction, which indicate that a quantum phase transition from an antiferromagnetic state to a ferromagnetic state can be induced by tuning the relative strengths of intracomponent and intercomponent interactions.