Weakly bound molecules have physical properties without atomic analogues, even as the bond length approaches dissociation. In particular, the internal symmetries of homonuclear diatomic molecules result in formation of two-body superradiant and subradiant excited states. While superradiance [1][2][3] has been demonstrated in a variety of systems, subradiance [4][5][6] is more elusive due to the inherently weak interaction with the environment. Here we characterize the properties of deeply subradiant molecular states with intrinsic quality factors exceeding 10 13 via precise optical spectroscopy with the longest molecule-light coherent interaction times to date. We find that two competing effects limit the lifetimes of the subradiant molecules, with different asymptotic behaviors. The first is radiative decay via weak magnetic-dipole and electric-quadrupole interactions. We prove that its rate increases quadratically with the bond length, confirming quantum mechanical predictions. The second is nonradiative decay through weak gyroscopic predissociation, with a rate proportional to the vibrational mode spacing and sensitive to short-range physics. This work bridges the gap between atomic and molecular metrology based on lattice-clock techniques [7], yielding new understanding of long-range interatomic interactions and placing ultracold molecules at the forefront of precision measurements.Simple molecules provide a wealth of opportunities for precision measurements. Their richer internal structure compared to atoms enables experiments that push the boundaries in determinations of the electric dipole moment of the electron [8], the electron-to-proton mass ratio and its variations [9,10], and parity violation [11]. Diatomic molecules are moving to the forefront of manybody science [12] and quantum chemistry [13], providing glimpses into fundamental laws [14]. However, this attractive complexity of molecular structure has historically posed difficulties for manipulation and modeling [15]. This work removes many of these barriers by employing techniques of optical lattice atomic clocks [16,17] to control the quantum states of weakly bound homonuclear diatomic strontium molecules, in particular by using state-insensitive optical lattices [18] for molecular transitions with three types of optical transition moments. We observe strongly forbidden optical transitions in this asymptotic diatomic system, an ideal regime for studying the breakdown of the ubiquitous dipole approximation where the size of the quantum particle is a significant fraction of the resonant wavelength. We explain these observations with a state-of-the-art ab initio molecular model [19] and asymptotic scaling laws. The results prove that the quantum mechanical effect of subradiance can be exploited for precision spectroscopy, and demonstrate the promise of combining precise state control, coherent manipulation, and accurate ab initio calculations with recently available ultracold molecular systems.We create Sr 2 molecules by photoassociation [20] from ...

We have produced large samples of stable ultracold 88 Sr2 molecules in the electronic ground state in an optical lattice. The fast, all-optical method of molecule creation involves a nearintercombination-line photoassociation pulse followed by spontaneous emission with a near-unity Franck-Condon factor. The detection uses excitation to a weakly bound electronically excited vibrational level corresponding to a very large dimer and yields a high-Q molecular vibronic resonance. This is the first of two steps needed to create deeply bound 88 Sr2 for frequency metrology and ultracold chemistry.PACS numbers: 67.85. 34.50.Rk, 37.10.Jk, 37.10.Pq The rapid progress in laser cooling has given rise to many new fields of research. One important example is the study of ultracold, dense clouds of molecules. The molecules can exhibit new physical phenomena near quantum degeneracy [1][2][3]. For example, long-range anisotropic interactions are expected between heteronuclear polar molecules. Such molecules have also been explored as a paradigm for quantum information and computation [4]. On the other hand, homonuclear molecular dimers without a dipole moment present a metrological interest, for example in constraining the variation of the electron-proton mass ratio [5,6] or complementing atomic clocks by serving as time standards in the terahertz regime [6]. These molecules also provide an excellent testing ground for many possible approaches to creating large ultracold samples, trapping them to allow long interrogation times, and precisely controlling their quantum states. The four promising routes toward trapped neutral molecules [1] are direct control of polar molecule dynamics via electric fields; buffer gas cooling of magnetic species; direct laser cooling of a suitable class of molecules [7]; and using magnetic or optical fields to combine laser cooled atoms into dimers [8][9][10][11][12]. The latter process typically results in molecules with relatively small binding energies but nonetheless has played a major role in the study of new phenomena. These dimers are also most promising for quantum control, since they are routinely produced at sub-µK temperatures.In this Letter, we describe optical production of 88 Sr 2 in the electronic ground state in an optical lattice. In contrast to alkali-metal atoms, Sr atoms possess no electronic spin and cannot be combined into molecules via the magnetic Feshbach resonance technique [13]. However, Sr has the advantage of the intercombination (spinforbidden) transition from the ground state, 1 S 0 − 3 P 1 (7 kHz linewidth [14], 689 nm wavelength), which allows Doppler cooling to < 1 µK [15] and provides several features that enable efficient photoassociation (PA) into molecules [14,16]. The unusually fast time scale (0.25 s) of ultracold molecule production is particularly important for establishing a short duty cycle in metrological applications. Furthermore, there is active interest in exploring molecules of alkaline-earth-metal (and the isoelectronic Yb) atoms in various combina...

Anomalously large linear and quadratic Zeeman shifts are measured for weakly bound ultracold 88Sr2 molecules near the intercombination-line asymptote. Nonadiabatic Coriolis coupling and the nature of long-range molecular potentials explain how this effect arises and scales roughly cubically with the size of the molecule. The linear shifts yield nonadiabatic mixing angles of the molecular states. The quadratic shifts are sensitive to nearby opposite f-parity states and exhibit fourth-order corrections, providing a stringent test of a state-of-the-art ab initio model.

Chemical reactions at ultracold temperatures are expected to be dominated by quantum mechanical effects. Although progress towards ultracold chemistry has been made through atomic photoassociation, Feshbach resonances and bimolecular collisions, these approaches have been limited by imperfect quantum state selectivity. In particular, attaining complete control of the ground or excited continuum quantum states has remained a challenge. Here we achieve this control using photodissociation, an approach that encodes a wealth of information in the angular distribution of outgoing fragments. By photodissociating ultracold (88)Sr2 molecules with full control of the low-energy continuum, we access the quantum regime of ultracold chemistry, observing resonant and nonresonant barrier tunnelling, matter-wave interference of reaction products and forbidden reaction pathways. Our results illustrate the failure of the traditional quasiclassical model of photodissociation and instead are accurately described by a quantum mechanical model. The experimental ability to produce well-defined quantum continuum states at low energies will enable high-precision studies of long-range molecular potentials for which accurate quantum chemistry models are unavailable, and may serve as a source of entangled states and coherent matter waves for a wide range of experiments in quantum optics.

For atoms or molecules in optical lattices, conventional thermometry methods are often unsuitable due to low particle numbers or a lack of cycling transitions. However, a differential spectroscopic light shift can map temperature onto the line shape with a low sensitivity to trap anharmonicity. We study narrow molecular transitions to demonstrate precise frequency-based lattice thermometry, as well as carrier cooling. This approach should be applicable down to nanokelvin temperatures. We also discuss how the thermal light shift can affect the accuracy of optical lattice clocks.