Spectroscopic Determination of thes-Wave Scattering Lengths ofSr86andSr

Abstract

We report the use of photoassociative spectroscopy to determine the ground-state s-wave scattering lengths for the main bosonic isotopes of strontium, 86 Sr and 88 Sr. Photoassociative transitions are driven with a laser red detuned by up to 1400 GHz from the 1 S 0 -1 P 1 atomic resonance at 461 nm. A minimum in the transition amplitude for 86 Sr at ÿ494 5 GHz allows us to determine the scattering lengths 610a 0 < a 86 < 2300a 0 for 86 Sr and a much smaller value of ÿ1a 0 < a 88 < 13a 0 for 88 Sr. DOI: 10.1103/PhysRevLett.95.223002 PACS numbers: 32.80.Pj Photoassociative spectroscopy (PAS) of ultracold gases, in which a laser field resonantly excites colliding atoms to rovibrational states of excited molecular potentials, is a powerful probe of atomic cold collisions [1]. Transition frequencies have been used to obtain dispersion coefficients of molecular potentials, which yield the most accurate value of the atomic excited-state lifetime [2 -5]. Transition amplitudes are related to the wave function for colliding ground-state atoms [6,7] and can be used to determine the ground-state s-wave scattering length [8][9][10][11][12][13].The s-wave scattering length is a crucial parameter for determining the efficiency of evaporative cooling and the stability of a Bose-Einstein condensate (BEC). It also sets the scale for collisional frequency shifts, which can limit the accuracy and stability of atomic frequency standards.The cold collision properties of alkaline-earth atoms such as strontium, calcium, and magnesium, and atoms with similar electronic structure, such as ytterbium, are currently the focus of intense study. These atoms possess narrow optical resonances that have great potential for optical frequency standards [14 -18]. Laser cooling on narrow transitions [19] is an efficient route to high phasespace density [20,21], and a BEC was recently produced with ytterbium [22]. Fundamental interest in alkaline-earth atoms is also high because their simple molecular potentials allow accurate tests of cold collision theory [23][24][25].PAS of calcium [12] and ytterbium [13] was recently used to determine s-wave scattering lengths of these atoms. This Letter reports the use of PAS to determine the groundstate s-wave scattering lengths for the main bosonic isotopes of strontium, 86 Sr and 88 Sr, which have relative abundances of 10% and 83%, respectively. We find a huge scattering length for 86 Sr of 610a 0 < a 86 < 2300a 0 . Appreciable uncertainty comes from the value of C 6 for the ground-state potential. In contrast, for 88 Sr we find ÿ1a 0 < a 88 < 13a 0 . Recently posted [5] PAS results for 88 Sr yielded an improved measurement of the 5s5p 1 P 1 atomic lifetime ( 5:263 0:004 ns), which we use in our analysis. Disagreement between our reported value of a 88 and results of Ref.[5] will be discussed below.For PAS of strontium, atoms are initially trapped in a magneto-optical trap (MOT) operating on the 461 nm 1 S 0 -1 P 1 transition, as described in Refs. [4,26]. We are able to produce pure samples of each iso...

Optical Feshbach resonances of alkaline-earth-metal atoms in a one- or two-dimensional optical lattice

“…In free space, the optical length is usually determined by measuring the rate (32) which is proportional to it. However the rate can typically have a factor of 2 uncertainty as its determination relies on the knowledge of the density of atoms [8,13]. Here we propose a determination of l opt which does not require the knowledge of the density and is is simply based on a spectroscopic measurement: by measuring the position of the line for different intensities, one should observe a shift linear with the intensity I, and deduce the strength of the resonance l opt /I.…”

“…This would bring complementary information to the usual node method [8] which proves to be difficult for large scattering lengths as it requires a very precise knowledge of the long-range part of the potential. However, the typical uncertainties associated to measured rates in current experiments may limit the interest of this idea.…”

“…There is, of course, an indirect dependence through Γ or l opt which contain a Franck-Condon factor involving the ground-state wave function, whose nodal structure depends on the background scattering length. This indirect dependence has been used to infer the background scattering length from photoassociation spectra [8,32].…”

“…Figure 1 shows the effective photoassociation rate at different temperatures for a typical intercombination line of Strontium 88 in free space, 1D lattice, and 2D lattice. The scattering length of Strontium is taken to be 10 Bohr [8] (1 Bohr ≈ 0.0529177 nm) and the spontaneous emission term γ = 15 kHz [13]. The trapping frequency Ω is 2π×50 kHz, and the optical length is set to 1 Bohr.…”

“…Photoassociation, the process of associating pairs of colliding atoms into excited bound states by making them absorb a resonant photon, appears as the best tool to characterize and control these interactions. Indeed, photoassociation can be used as a spectroscopic tool to measure energy levels in excited molecular states [5,6,7] and characterize ground-state atomic interactions [8]. It can also be regarded as an optical Feshbach resonance [9], analogous to magnetic Feshbach resonances in alkali systems, making it possible to alter these interactions [10].…”