Analytical solution for the spectrum of two ultracold atoms in a completely anisotropic confinement
arXiv:2002.02168 · doi:10.1103/PhysRevA.101.053624
Abstract
We study the system of two ultracold atoms in a three-dimensional (3D) or two-dimensional (2D) completely anisotropic harmonic trap. We derive the algebraic 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, and provide the analytical expressions of the functions J_{3D}(E) and J_{2D}(E). In previous researches this type of equation was obtained for spherically or axially symmetric harmonic traps (T. Busch, et. al., Found. Phys. 28, 549 (1998); Z. Idziaszek and T. Calarco, Phys. Rev. A 74, 022712 (2006)). However, for our cases with a completely anisotropic trap, only the equation for the ground-state energy of some cases has been derived (J. Liang and C. Zhang, Phys. Scr. 77, 025302 (2008)). Our results in this work are applicable for arbitrary eigen-energy of this system, and can be used for the studies of dynamics and thermal-dynamics of interacting ultracold atoms in this trap, e.g., the calculation of the 2nd virial coefficient or the evolution of two-body wave functions. In addition, our approach for the derivation of the above equations can also be used for other two-body problems of ultracold atoms.
arXiv comment15 pages, 8 figures
References in corpus (45)
- Observation of two-orbital spin-exchange interactions with ultracold SU(N)-symmetric fermions
- From Few to Many: Observing the Formation of a Fermi Sea One Atom at a Time
- Ultracold heteronuclear molecules in a 3D optical lattice
- An Optical Tweezer Array of Ultracold Molecules
- Molecules of Fermionic Atoms in an Optical Lattice
- Building one molecule from a reservoir of two atoms
- Alkaline earth atoms in optical tweezers
- Microscopic control and detection of ultracold strontium in optical-tweezer arrays
- Few-body physics with ultracold atomic and molecular systems in traps
- Direct observation of coherent inter-orbital spin-exchange dynamics
- Virial expansion for a strongly correlated Fermi gas
- Localized magnetic moments with tunable spin exchange in a gas of ultracold fermions
- Analytical solutions for the dynamics of two trapped interacting ultracold atoms
- Universal Fermi gases in mixed dimensions
- Virial expansion for a strongly correlated Fermi system and its application to ultracold atomic Fermi gases
- Precision Measurements on a Tunable Mott Insulator of Ultracold Atoms
- Energetics and Structural Properties of Trapped Two-Component Fermi Gases
- Two atoms in an anisotropic harmonic trap
- Three-dimensional strong localization of matter waves by scattering from atoms in a lattice with a confinement-induced resonance
- Coherent molecule formation in anharmonic potentials near confinement-induced resonances
- Precision Test of the Limits to Universality in Few-Body Physics
- Near-ground-state cooling of atoms optically trapped 300nm away from a hot surface
- Energy spectrum of harmonically trapped two-component Fermi gases: Three- and Four-Particle Problem
- Observation of ultra-strong spin-motion coupling for cold atoms in optical microtraps
- Three s-wave interacting fermions under anisotropic harmonic confinement: Dimensional crossover of energetics and virial coefficients
- Preparation of a Heteronuclear Two-atom System in the 3D Motional Ground State in an Optical Tweezer
- Exact theoretical description of two ultracold atoms in a single site of a 3D optical lattice using realistic interatomic interaction potentials
- Three particles in an external trap: Nature of the complete J=0 spectrum
- Multichannel interactions of two atoms in an optical tweezer
- Theory of inelastic confinement-induced resonances due to the coupling of center-of-mass and relative motion
- Theoretical description of two ultracold atoms in finite 3D optical lattices using realistic interatomic interaction potentials
- Quantum dynamics of two trapped bosons following infinite interaction quenches
- Density Oscillations Induced by Individual Ultracold Two-Body Collisions
- Trapped unitary two-component Fermi gases with up to ten particles
- Coherent Manipulation of Orbital Feshbach Molecules of Two-Electron Atoms
- Quench Dynamics of Two One-Dimensional Harmonically Trapped Bosons Bridging Attraction and Repulsion
- Analytical treatment of the interaction quench dynamics of two bosons in a two-dimensional harmonic trap
- Few-body perspective of a quantum anomaly in two-dimensional Fermi gases
- Harmonically Trapped Four-Boson System
- Universal and non-universal effective -body interactions for ultracold harmonically-trapped few-atom systems
- Two ultracold atoms in a completely anisotropic trap
- Tight-Binding Kondo Model and Spin-Exchange Collision Rate of Alkaline-Earth Atoms in a Mixed-Dimensional Optical Lattice
- Virial expansion of a harmonically trapped Fermi gas across a narrow Feshbach resonance
- Confinement Induced Resonance with Weak Bare Interaction in a Quasi 3+0 Dimensional Ultracold Gas
- Confinement-Induced Resonance with Weak Background Interaction
Cited by in corpus (6)
- Quantum Register of Fermion Pairs
- Stationary and dynamical properties of two harmonically trapped bosons in the crossover from two dimensions to one
- Floquet-driven crossover from density-assisted tunneling to enhanced pair tunneling
- Analytical solutions of the Schrödinger equation for two confined atoms with van der Waals interaction
- Exploring the Strongly-Interacting Regime of Effective Multi-Body Interactions in a Trapped Ultracold Atom System
- Molecular excited state in the interaction quench dynamics of two different atoms in a two-dimensional anisotropic trap