Long-range interaction of the 39K(4s)+39K(4p) asymptote by photoassociative spectroscopy. I. The g− pure long-range state and the long-range potential constants

Abstract

Long-range interaction of the 39K(4s)+39K(4p) asymptote by photoassociative spectroscopy. I. The 0g− pure long-range state and the long-range potential constants This paper reports on a comprehensive study of the long-range interaction of the 39 K(4s) ϩ 39 K(4p) asymptotic system. We present a detailed discussion of the R-dependent angular momentum couplings and correlation between the Hund's case ͑a͒ and case ͑c͒ molecular states. Analytical expressions for the 16 adiabatic Hund's case ͑c͒ long-range potential curves are derived including the higher order dispersion forces and the effects of retardation. Experimentally, six Hund's case ͑c͒ long-range molecular states ͑0 u ϩ , 1 g , and 0 g Ϫ dissociating to the 4 2 S 1/2 ϩ4 2 P 3/2 asymptote and 0 u ϩ , 1 g , and 0 g Ϫ to the 4 2 S 1/2 ϩ4 2 P 1/2 limit͒ are observed with rovibrational resolution by photoassociative spectroscopy of ultracold 39 K atoms in a high density magneto-optical trap ͑MOT͒. Among the six observed long-range states, the upper 0 g Ϫ ''pure long-range'' state has negligible short-range chemical exchange contributions and the measured molecular binding energies (vϭ0 -26) are used to precisely determine the long-range potential constants of the 4sϩ4 p interaction. We determine: C 3 ⌸ ϭ8.436(14) a.u., C 3 ⌺ ϭ16.872(28) a.u., C 6 ⌸ ϭ6272(94) a.u., and C 6 ⌺ ϭ9365(141) a.u.. Molecular constants for the three special pure long-range states, the 0 g Ϫ and 1 u ͑dissociating to the 4 2 P 3/2 limit and with potential minimum͒ and the 1 u ͑dissociating to the 4 2 P 1/2 and with potential maximum͒, are reported. The internal consistency of the theoretical model used in this work is confirmed by the excellent agreement between the long-range potential curve of the 1 g state obtained in present work ͑from the 0 g Ϫ state͒ and the long-range portion of the RKR potential curve of the 1 1 ⌸ g state previously determined by conventional molecular spectroscopy. The radiative lifetime of the K 4 p state derived from the dipole-dipole interaction constant C 3 ⌸ is also in excellent agreement with a recent fast-beam measurement.

Short-pulse photoassociation in rubidium below theD1line

“…When including the spinorbit interaction (see e.g. [28]), the respective 0, 1 and 2 (Hund's case (c)) potentials are obtained. Five of these are correlated to the 5S + 5P 1/2 asymptote, i.e.…”

“…For the 0 + u states, the spin-orbit coupling has resonant character [29,30,31] and leads to an avoided crossing between 0 + u (P 1/2 ) and 0 + u (P 3/2 ) at short internuclear distance. The spin-orbit coupling therefore needs to be included explicitly: The Hund's case (c) potentials are obtained by diagonalizing the Hamiltonian containing the Hund's case (a) potentials on the diagonal and the spin-orbit coupling on the off-diagonal [28]. The corresponding unitary transformation leads to off-diagonal elements of the kinetic energy which usually are neglected.…”

Polarization spectroscopy and magnetically-induced dichroism of the potassium D_2 lines

“…For higher intensities, power broadening should lead to an increase in Γ, which would cause the signal amplitude to saturate and the slope to roll over. In a two-level approximation without transit-time effects, the relevant scale is set by the saturation intensity I sat which is equal to 1.75 mW/cm 2 for the F = 2 → F ′ = 3 cycling transition [15,17]. In Fig.…”

“…Since the natural half-width at half-maximum (HWHM) for potassium γ = 2π × 3.017 MHz [15] is on the order of the excited-state splittings, neighboring transitions tend to overlap and significant off-resonant excitation can occur. Additionally, the isotope shifts and ground-state splittings are smaller than the Doppler width.…”

Measurement of a Wavelength of Light for Which the Energy Shift for an Atom Vanishes

“…In comparison, our measurement of R has an uncertainty of 0.20%. State lifetimes can also be derived from molecular or photoassociation spectroscopy [17,18]. However, these spectroscopy experiments [17,18] do not distinguish between the 4p 1/2 and 4p 3/2 state lifetimes (they depend on an average) so they cannot be used to determine R nor λ zero .…”