Exact Solutions and Quantum Defect Theory for van der Waals Potentials in Ultracold Molecular Systems

• URL: http://arxiv.org/abs/2202.08694v3
• Date: Thu, 22 May 2025 03:39:15 GMT
• Title: Exact Solutions and Quantum Defect Theory for van der Waals Potentials in Ultracold Molecular Systems
• Authors: Jianwen Jie, Shi Chen, Yue Chen, Ran Qi,
• Abstract summary: We provide exact two-body solutions to the 2D and 3D Schr"odinger equations with isotropic van der Waals potentials.<n>We develop an analytical quantum defect theory applicable to both quasi-2D and 3D geometries.
• Score: 17.17437183390107
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we have provided exact two-body solutions to the 2D and 3D Schr\"odinger equations with isotropic van der Waals potentials of the form \(\pm 1/r^6\). Based on these solutions, we developed an analytical quantum defect theory (QDT) applicable to both quasi-2D and 3D geometries, and applied it to study the scattering properties and bound-state spectra of ultracold polar molecules confined in these geometries. Interestingly, we find that in the attractive (repulsive) van der Waals potential case, the short-range interaction can be effectively modeled by an infinite square barrier (finite square well), which leads to narrow and dense (broad and sparse) resonance structures in the quantum defect parameter. In the quasi-2D attractive case, shape resonances can appear in an ordered fashion across different partial waves, characterized by sharp phase jumps as the scattering energy is varied. Furthermore, the low-energy analytical expansions derived from QDT show excellent agreement with the exact numerical results, validating the accuracy and usefulness of our analytical approach in describing two-body physics governed by long-range van der Waals interactions.

Related papers

• Three-dimensional quantum anomalous Hall effect in Weyl semimetals [24.511994395713693]
  The quantum anomalous Hall effect (QAHE) is a quantum phenomenon in which a two-dimensional system exhibits a quantized Hall resistance $h/e2$ in the absence of magnetic field. In this work, we extend this novel phase to three dimensions and thus propose a three-dimensional QAHE exhibiting richer and more versatile transport behaviors. This three-dimensional QAHE not only fill the gap in the Hall effect family but also holds significant potentials in device applications such as in-memory computing.
  arXiv  Detail & Related papers  (2025-01-02T18:23:37Z)
• Bound polariton states in the Dicke-Ising model [41.94295877935867]
  We present a study of hybrid light-matter excitations in cavity QED materials.<n>We derive the exact excitations of the system in the thermodynamic limit.
  arXiv  Detail & Related papers  (2024-06-17T18:00:01Z)
• Aharonov-Bohm Scattering From Knots [0.0]
  The Aharonov-Bohm effect is perhaps the first example in which the the interplay between classical topology and quantum theory was explored. Several attempts were made to generalize the Aharonov-Bohm effect by modifying the simple solenoidal current distribution.
  arXiv  Detail & Related papers  (2024-05-29T10:13:53Z)
• Analytical solutions of the Schr\"{o}dinger equation for two confined atoms with van der Waals interaction [0.0]
  We derive solutions of the Schr"odinger equation for the isotropic van der Waals interaction in a symmetric harmonic trap. We deduce the energy spectrum of the two-body relative motion and relate the spectrum to scattering lengths for $s$ wave and $p$ wave.
  arXiv  Detail & Related papers  (2024-02-02T13:42:39Z)
• Unveiling the Quantum Toroidal Dipole in Nanosystems: Quantization, Interaction Energy, and Measurement [44.99833362998488]
  We investigate a quantum particle confined to a toroidal surface in the presence of a filiform current along the system's rotational axis. Our analysis reveals that the interaction between the particle and the current induces a non-zero toroidal dipole in the particle's stationary states.
  arXiv  Detail & Related papers  (2024-01-26T13:31:32Z)
• Quench dynamics in higher-dimensional Holstein models: Insights from Truncated Wigner Approaches [41.94295877935867]
  We study the melting of charge-density waves in a Holstein model after a sudden switch-on of the electronic hopping. A comparison with exact data obtained for a Holstein chain shows that a semiclassical treatment of both the electrons and phonons is required in order to correctly describe the phononic dynamics.
  arXiv  Detail & Related papers  (2023-12-19T16:14:01Z)
• Variational manifolds for ground states and scarred dynamics of blockade-constrained spin models on two and three dimensional lattices [0.0]
  We introduce a variational manifold of simple tensor network states for the study of a family of constrained models that describe spin-1/2 systems. Our method can be interpreted as a generalization of mean-field theory to constrained spin models.
  arXiv  Detail & Related papers  (2023-11-15T13:52:21Z)
• Energetics of the dissipative quantum oscillator [22.76327908349951]
  We discuss some aspects of the energetics of a quantum Brownian particle placed in a harmonic trap. Based on the fluctuation-dissipation theorem, we analyze two distinct notions of thermally-averaged energy. We generalize our analysis to the case of the three-dimensional dissipative magneto-oscillator.
  arXiv  Detail & Related papers  (2023-10-05T15:18:56Z)
• Effective quantum electrodynamics: One-dimensional model of the relativistic hydrogen-like atom [0.0]
  We consider a one-dimensional effective quantum electrodynamics model of the relativistic hydrogen-like atom. The present work may be considered as a step toward the development of a quantum-chemistry effective QED theory of atoms and molecules.
  arXiv  Detail & Related papers  (2023-05-23T07:55:01Z)
• Slow semiclassical dynamics of a two-dimensional Hubbard model in disorder-free potentials [77.34726150561087]
  We show that introduction of harmonic and spin-dependent linear potentials sufficiently validates fTWA for longer times. In particular, we focus on a finite two-dimensional system and show that at intermediate linear potential strength, the addition of a harmonic potential and spin dependence of the tilt, results in subdiffusive dynamics.
  arXiv  Detail & Related papers  (2022-10-03T16:51:25Z)
• Photon generation and entanglement in a double superconducting cavity [105.54048699217668]
  We study the dynamical Casimir effect in a double superconducting cavity in a quantum electrodynamics architecture. We study the creation of photons when the walls oscillate harmonically with a small amplitude.
  arXiv  Detail & Related papers  (2022-07-18T16:43:47Z)
• Localization and melting of interfaces in the two-dimensional quantum Ising model [0.0]
  We study the non-equilibrium evolution of coexisting ferromagnetic domains in the two-dimensional quantum Ising model. We demonstrate that the quantum-fluctuating interface delimiting a large bubble can be studied as an effective one-dimensional system.
  arXiv  Detail & Related papers  (2022-03-17T17:48:51Z)
• New Class of Landau Levels and Hall Phases in a 2D Electron Gas Subject to an Inhomogeneous Magnetic Field: An Analytic Solution [0.0]
  Solution provides access to many properties of a two-dimensional, non-interacting, electron gas in the thermodynamic limit. Radially distorted Landau levels can be identified as well as magnetic field induced density and current oscillations close to the magnetic impurity.
  arXiv  Detail & Related papers  (2022-01-13T16:52:02Z)
• Quantum correlations, entanglement spectrum and coherence of two-particle reduced density matrix in the Extended Hubbard Model [62.997667081978825]
  We study the ground state properties of the one-dimensional extended Hubbard model at half-filling. In particular, in the superconducting region, we obtain that the entanglement spectrum signals a transition between a dominant singlet (SS) to triplet (TS) pairing ordering in the system.
  arXiv  Detail & Related papers  (2021-10-29T21:02:24Z)
• Stochastic Variational Approach to Small Atoms and Molecules Coupled to Quantum Field Modes [55.41644538483948]
  We present a variational calculation (SVM) of energies and wave functions of few particle systems coupled to quantum fields in cavity QED. Examples for a two-dimensional trion and confined electrons as well as for the He atom and the Hydrogen molecule are presented.
  arXiv  Detail & Related papers  (2021-08-25T13:40:42Z)
• Relativistic aspects of orbital and magnetic anisotropies in the chemical bonding and structure of lanthanide molecules [60.17174832243075]
  We study the electronic and ro-vibrational states of heavy homonuclear lanthanide Er2 and Tm2 molecules by applying state-of-the-art relativistic methods. We were able to obtain reliable spin-orbit and correlation-induced splittings between the 91 Er2 and 36 Tm2 electronic potentials dissociating to two ground-state atoms.
  arXiv  Detail & Related papers  (2021-07-06T15:34:00Z)
• Light-matter interactions near photonic Weyl points [68.8204255655161]
  Weyl photons appear when two three-dimensional photonic bands with linear dispersion are degenerated at a single momentum point, labeled as Weyl point. We analyze the dynamics of a single quantum emitter coupled to a Weyl photonic bath as a function of its detuning with respect to the Weyl point.
  arXiv  Detail & Related papers  (2020-12-23T18:51:13Z)
• $\mathcal{P}$,$\mathcal{T}$-odd effects for RaOH molecule in the excited vibrational state [77.34726150561087]
  Triatomic molecule RaOH combines the advantages of laser-coolability and the spectrum with close opposite-parity doublets. We obtain the rovibrational wave functions of RaOH in the ground electronic state and excited vibrational state using the close-coupled equations derived from the adiabatic Hamiltonian.
  arXiv  Detail & Related papers  (2020-12-15T17:08:33Z)
• Resonant enhancement of three-body loss between strongly interacting photons [47.30557822621873]
  Rydberg polaritons provide an example of a rare type of system where three-body interactions can be as strong or even stronger than two-body interactions. We show how the shape and strength of dissipative three-body forces can be universally enhanced for Rydberg polaritons.
  arXiv  Detail & Related papers  (2020-10-19T18:21:49Z)
• Geometric Quantum Information Structure in Quantum Fields and their Lattice Simulation [0.0]
  An upper limit to distillable entanglement has an exponential decay defined by a geometric decay constant. When regulated at short distances with a spatial lattice, this entanglement abruptly vanishes beyond a dimensionless separation. We highlight potential impacts of the distillable entanglement structure on effective field theories, lattice QCD calculations and future quantum simulations.
  arXiv  Detail & Related papers  (2020-08-09T04:26:49Z)
• Fractional quantum Hall physics and higher-order momentum correlations in a few spinful fermionic contact-interacting ultracold atoms in rotating traps [0.0]
  This paper provides benchmark results for $N$-body spin-unresolved, as well as spin-resolved, momentum correlations measurable in time-of-flight experiments with individual particle detection. The application of a small perturbing stirring potential induces, at the ensuing avoided crossings, formation of symmetry broken states exhibiting ordered polygonal-ring structures. Analysis of the calculated LLL wavefunction enables a two-dimensional generalization of the Girardeau one-dimensional 'fermionization' scheme, originally invoked for mapping of bosonic-type wave functions to those of spinless fermions.
  arXiv  Detail & Related papers  (2020-06-17T02:08:13Z)
• Analytical solution for the spectrum of two ultracold atoms in a completely anisotropic confinement [12.864072516318716]
  We study the system of two ultracold atoms in a three-dimensional (3D) or two-dimensional (2D) completely anisotropic harmonic trap. We derive the equation J_3D(E) = 1/a_3D (J_2D(E) = ln a_2D) for the eigen-energy E of this system in the 3D (2D) case, with a_3D and a_2D being the corresponding s-wave scattering lengths.
  arXiv  Detail & Related papers  (2020-02-06T09:28:55Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.