We present a multiscale quantum-defect theory for two identical atoms in a symmetric harmonic trap that combines the quantum-defect theory for the van der Waals interaction [B. Gao, Phys. Rev. A 64, 010701(R) (2001)] at short distances with a quantum-defect theory for the harmonic trapping potential at large distances. The theory provides a systematic understanding of two atoms in a trap, from deeply bound molecular states and states of different partial waves, to highly excited trap states. It shows, e.g., that a strong $p$ -wave pairing can lead to a lower energy state around the threshold than a $s$ -wave pairing.We present a multiscale quantum-defect theory for two identical atoms in a symmetric harmonic trap that combines the quantum-defect theory for the van der Waals interaction [B. Gao, Phys. Rev. A 64, 010701(R) (2001)] at short distances with a quantum-defect theory for the harmonic trapping potential at large distances. The theory provides a systematic understanding of two atoms in a trap, from deeply bound molecular states and states of different partial waves, to highly excited trap states. It shows, e.g., that a strong $p$-wave pairing can lead to a lower energy state around the threshold than a $s$-wave pairing.

arXiv:cond-mat/0701384Physical Review AMay 3, 200720 citations

Interacting atoms under strong quantum confinement

Carl J. Williams, Eite Tiesinga, Éric Charron +2 more

APSJun 1, 20000 citations

Analytic solution for a class of multiscale long-range potentials

Haixiang Fu, Xiaoji Zhou, Mingzhe Li

We present a unified exact analytic solution of the radial Schrödinger equation with a class of four long-range potentials, three of which are two-scale. The physics of different potentials are encapsulated in the solution variable and parameters. Based on this solution and its asymptotic behaviors, we generalize Bo Gao’s formulation of quantum defect theory for single-scale potentials to two-scale regime. As an application of this two-scale quantum defect theory, we propose a concept of harmonic oscillator quantum defect of energy levels in a spherical harmonic trap, which characterizes the effect of the two-body interactions on their trap states. This concept is a generalization of the standard quantum defect for Coulomb potential, with a distinct feature that the equations followed by the two types of quantum defects induced by the potentials under study are formally the same yet with different parameters. Examples of these two quantum defects are illustrated for Rb and Cs atoms.We present a unified exact analytic solution of the radial Schrödinger equation with a class of four long-range potentials, three of which are two-scale. The physics of different potentials are encapsulated in the solution variable and parameters. Based on this solution and its asymptotic behaviors, we generalize Bo Gao’s formulation of quantum defect theory for single-scale potentials to two-scale regime. As an application of this two-scale quantum defect theory, we propose a concept of harmonic oscillator quantum defect of energy levels in a spherical harmonic trap, which characterizes the effect of the two-body interactions on their trap states. This concept is a generalization of the standard quantum defect for Coulomb potential, with a distinct feature that the equations followed by the two types of quantum defects induced by the potentials under study are formally the same yet with different parameters. Examples of these two quantum defects are illustrated for Rb and Cs atoms.

Physical Review ResearchSep 17, 20250 citations

Variance minimization variational Monte Carlo method

Imran Khan, Bo Gao

We present a variational Monte Carlo (VMC) method that works equally well for the ground and the excited states of a quantum system. The method is based on the minimization of the variance of energy, as opposed to the energy itself in standard methods. As a test, it is applied to the investigation of the universal spectrum at the van der Waals length scale for two identical Bose atoms in a symmetric harmonic trap, with results compared to the basically exact results obtained from a multiscale quantum-defect theory.We present a variational Monte Carlo (VMC) method that works equally well for the ground and the excited states of a quantum system. The method is based on the minimization of the variance of energy, as opposed to the energy itself in standard methods. As a test, it is applied to the investigation of the universal spectrum at the van der Waals length scale for two identical Bose atoms in a symmetric harmonic trap, with results compared to the basically exact results obtained from a multiscale quantum-defect theory.

arXiv:physics/0701223APSJan 19, 20070 citations

Probing decoherence at an atom-defect quantum interface

Xue Han, Alec Cao, Alec Jenkins +5 more

Bulletin of the American Physical SocietyMar 6, 20190 citations

p

-wave pairing can lead to a lower energy state around the threshold than a

s

-wave pairing.