Collisional properties of trapped cold chromium atoms

Abstract

We report on calculations of the elastic cross section and thermalization rate for collision between two maximally spin-polarized chromium atoms in the cold and ultracold regimes, relevant to buffergas and magneto-optical cooling of chromium atoms. We calculate ab initio potential energy curves for Cr2 and the van der Waals coefficient C6, and construct interaction potentials between two colliding Cr atoms. We explore the effect of shape resonances on elastic cross section, and find that they dramatically affect the thermalization rate. Our calculated value for the s-wave scattering length is compared in magnitude with a recent measurement at ultracold temperatures.Collisions of atoms at ultracold temperatures have received considerable attention because of their importance in cooling and trapping of atoms [1] and their role in high precision spectroscopy [2] and Bose-Einstein condensation [3]. Processes occurring in the cold regime are sensitive to the details of the interaction potentials between the colliding systems over an extended range of internuclear separations. Recent experiments with chromium [4,5,6,7] emphasize the need for theoretical studies of Cr scattering properties. The interest in cooling Cr stems from its particular properties; in its ground state 7 S 3 , it possesses a very large magnetic moment, 6 µ B (µ B : Bohr magneton), making it an ideal atom for buffer-cooling in a purely magnetic trap [7], as well as for magneto-optical trapping [4]. In addition, anisotropic long-range interactions, such as chromium's magnetic dipole-dipole interactions, may lead to novel phenomena in BECs [9,10]. The existence of a stable fermionic isotope, 53 Cr, opens the possibility of obtaining fermionic degenerate gas using sympathetic cooling. Chromium was also used in a new cooling scheme [5], where ultracold chromium atoms were loaded from a MOT into an Ioffe-Pritchard magnetic trap, and cooled below 100µK. However, a not so-desirable byproduct of large-spin collision is inelastic "bad" scattering rates that deplete the trap.On the theoretical front, the electronic spectrum of the Cr 2 dimer poses a considerable numerical challenge. Chromium is the first atom in the periodic table with a half-filled d shell (the ground electronic configuration is Cr(3d 5 4s, 7 S)) and the Cr 2 dimer is one of the most extreme cases of multiple metal-metal bonding. To date, the best attempt to calculate its interaction potential curves is a multiconfiguration second-order perturbation theory with complete active space self-consistent field (CASSCF/CASPT2) [11,12]. While some information on the spectroscopy of the ground electronic state ( 1 Σ + g molecular symmetry) exists, there is no data available for the interaction of two maximally spin-stretched Cr atoms in the 13 Σ + g molecular symmetry, i.e. total spin, S = 6. In this communication, we explore the collisional properties of Cr atoms in the cold and ultracold temperature regimes by revisiting the electronic structure of the dimer. More accurate Born-Oppenheimer potenti...

The CIPT2 method: Coupling of multi-reference configuration interaction and multi-reference perturbation theory. Application to the chromium dimer

“…To accurately account for these effects has proven to be an intricate computational task. Many different theoretical methods have been used in the past in attempts to reproduce the spectroscopic quantities experimentally measured: generalized valence bond [1,2], density functional theory [3][4][5][6][7][8][9][10][11][12], coupled cluster methods [3], multi-reference perturbation theory [13][14][15][16][17][18][19][20][21][22], multi-reference configuration interaction (MRCI), and its variants like multi-reference average coupled-pair functionals (MRACPF) [23][24][25]. For the specific purpose of this paper the studies that use multi-reference configuration interaction and multireference perturbation theory are of particular interest.…”

“…The ground-state potential energy curve of Cr 2 has recently been calculated [13][14][15][16][17] using a complete active space self-consistent-field reference wave function [26,27] (CASSCF) and subsequent multi-reference second-order perturbation theory [28][29][30][31] (CASPT2). The aim was not only to check whether the complexity of the hextuple bond in Cr 2 could be accurately described using perturbation theory, but also to test the efficiency of real [14] and imaginary [15] level shifts to remove intruder states, which appear for this specific molecule even on the ground-state curve.…”

Low-energy universality and scaling of van der Waals forces

“…(17). Alternatively, and discarding the exceptional outliers for α 0 [24,25,26] (Li-Li,Na-Na), [27] (Cs-Cs), [28] (Na-Rb), [29] (Be-Be), [30] (Cs-Rb), [31] (Cr-Cr), [32] (Fr-Fr), [33,34,35,36] (H-H), [36] (He-He). The line corresponds to Eq.…”

CrRb: A molecule with large magnetic and electric dipole moments

“…The summation is understood to also include integration over continuum. Our calculated value of C 6 for the Cr + Rb system, 1770 a.u., which we believe to be accurate within 3%, is obtained from the highly-accurate values of the Rb dynamic polarizability at imaginary frequencies [11] and the recently accurate values for the Cr dipole polarizability [12,13]. This should be compared to the values of C 6 (Rb 2 ) = 4691 a.u.…”

“…Our vdW coefficient is sufficiently accurate to describe the potentials at large separations. In the short range repulsive wall region, we shift the potential energy curves, according to the prescription in our earlier work [12], and the results for the elastic cross sections are shown in Fig. 2.…”