Photoassociation spectroscopy ofSr88: Reconstruction of the wave function near the last node

Abstract

We have investigated photoassociation ͑PA͒ spectra of ultracold 88 Sr atoms near the 5s 2 1 S 0 +5s5p 1 P 1 atomic asymptote. The intensity modulation of the PA lines was used to reconstruct the ground-state scattering wave function, whose last nodal point was determined to be r 0 = 3.78͑18͒ nm. The PA lines also determined a precise lifetime of the 1 P 1 state to be 5.263͑4͒ ns.Precise knowledge of atom-atom interactions is of significant importance in the creation and manipulation of ultracold atoms or molecules as well as in their application to precision measurements. Investigations on light-induced atom losses in magneto-optical traps ͑MOTs͒, where collision processes are altered by the presence of near resonant photons ͓1͔, have triggered an emerging field of cold collisions with laser cooled atoms ͓2͔. The stability and dynamics of the Bose-Einstein condensates ͑BECs͒ are governed by the ultracold collisional properties ͓3-6͔. Their tunability via magnetic or optical method is utilized to produce ultracold molecules as well as molecular BECs ͓7-10͔. From a metrological point of view, atomic collisions introduce unwanted frequency shifts that critically limit the performance of the state-of-the-art atomic fountain clocks ͓11͔ and optical clocks ͓12͔.A two-body collision problem is most simplified for ultracold atoms. The ground-state wave function for the angular momentum l =0 ͑s-wave͒ state can be written as R͑r͒ = u g ͑r͒ / r with u g ͑r͒ the solution of an ordinary onedimensional ͑1D͒ Schrödinger equation and r the interatomic separation. The interaction is characterized by a single parameter, the s-wave scattering length a, which is associated with the last node of the scattering wave function u g ͑r͒ ͓13͔.One of the most versatile experimental techniques for probing the wave function, especially its last node, is the photoassociation ͑PA͒ spectroscopy ͓14͔ that measures the intensity modulation of the PA lines ͓15-17͔. Since the demonstration of the technique in laser-cooled Na ͓18͔ and Rb ͓19͔ atoms, there have been extensive theoretical as well as experimental studies in alkali-metal systems ͓2͔. However, analysis of these PA lines are not easy because the hyperfine structure in their ground state as well as the excited state gives rise to complicated molecular potentials. In contrast, alkaline-earth-metal system offers the simplest energy structures, i.e., the 1 S 0 ground state and the 1 P 1 excited state, which allows straightforward interpretation of PA spectra. Recently a PA line profile was obtained for Ca, which determined the possible range of the scattering length ͓20͔. A predissociation process was revealed through the broadening of the PA line profiles in Yb atoms ͓21͔. PA spectra near the dissociation limit was investigated for Sr, which determined the 1 P 1 excited state lifetime ͓22͔.In this Rapid Communication we report on the determination of the last node of the scattering wave function for the 5s 2 1 S 0 state of 88 Sr atoms by reconstructing the wave function through PA spectroscop...

Magic wavelengths for terahertz clock transitions

“…However, typically the literature gives the total transition rate A T from a given excited state to the fine structure manifold states below. So we need establish the relation [25], b [26], c [27], d [28], e [29], f [30], g [31]. [33].…”

“…After calculating magic wavelengths for Sr and Ca optical clock transitions and comparing them to the experimental values, we calculate the polarizability of terahertz transition with data collection mainly from Ref. [20,[25][26][27][28][29][30][31][32].…”

Tune-out wavelengths for the alkaline-earth-metal atoms

“…An experimental value was used for the 5s 2 1 S e -5s5p 1 P o matrix element [20] and the energy differences for the low-lying excitations were set to the experimental energies. This matrix element set was used to calculate dispersion coefficients between two strontium atoms, and also between strontium and the rare gases [13].…”

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

“…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].…”

“…In particular, if the Wigner's threshold laws (17-18) apply (ie if the temperature is not too high), the photoassociation rate is given by the standard expression: (32) where E = 2 k 2 2µ . The term kl opt is responsible for the socalled power-broadening by the laser.…”