Prediction of Feshbach resonances using an analytical quantum-defect matrix

Abstract

We present a theoretical model for describing ultracold atomic collision based on the multichannel quantumdefect theory. An analytical expression for the quantum-defect matrix Y is derived for the truncated 1/R 6 model potential, and threshold behaviors of the quantum-defect parameters are discussed. The model allows us to predict the Feshbach resonances when the singlet and triplet scattering lengths are known or to fit the scattering lengths when a couple of Feshbach resonances is located experimentally. As an illustrative example, we investigate the 6 Li-40 K scattering. The theoretical results agree quite well with experimental values.

Quantum defect theory for the van der Waals plus dipole-dipole interaction

“…When the electric field is absent, the long-range interaction potential between two polar molecules reduces to a pure van der Waals potential and R 0 is determined by the scattering length a of this potential [27].…”

“…[18], andā 0 = 0.4779888 is the mean scattering length [27]. For a particle moving in the model potential V l (R) from the asymptotic region into the inner region, t oi l,m l represents the amplitude tunneling through the long-range potential.…”

Simple model for predicting and analyzing magnetically induced Feshbach resonances

“…For convenience, we use a = (2/aC6/ / r ) l/4 ande = h2/Ifia2 as the length and energy units, respectively, as done in Refs. [28,29,33,34], In a MQDT, the coupled-channel equation (2) can be solved in the long-range region separated from the shortrange region [17,18], In the long-range region, the coupling interactions between different channels vanish and W (/?) can be replaced by N uncoupled reference potentials having the same asymptotic form as Eq.…”

“…The theoretical studies of FRs have been performed by using coupled-channel (CC) theory [10,11 ] as well as some approximate models, such as effective-range theory [12,13], the asymptotic bound-state model [14,15], and multichannel quantum-defect theory (MQDT) [16][17][18][19][20][21][22][23][24][25][26][27][28][29]. MQDT is computa tionally both accurate and economical, thus it has been widely applied to the investigation of cold and ultracold collisions in not only atom-atom [19] and atom-ion [20] systems, but also atom-molecule [21] and molecule-molecule [22] systems.…”

“…In recent years, MQDT has been extended to describe more complex issues such as high-partial problems [23,24] and reaction collisions [25,26]. Based on MQDT, researchers proposed several simple expressions used for predicting and analyzing FRs [27][28][29].…”