Atomic lattice clocks have spurred numerous ideas for tests of fundamental physics, detection of general relativistic effects, and studies of interacting many-body systems. On the other hand, molecular structure and dynamics offer rich energy scales that are at the heart of new protocols in precision measurement and quantum information science. Here we demonstrate a fundamentally distinct type of lattice clock that is based on vibrations in diatomic molecules, and present coherent Rabi oscillations between weakly and deeply bound molecules that persist for 10's of milliseconds. This control is made possible by a state-insensitive magic lattice trap that weakly couples to molecular vibronic resonances and enhances the coherence time between molecules and light by several orders of magnitude. The achieved quality factor Q = 8 × 10 11 results from 30-Hz narrow resonances for a 25-THz clock transition in Sr2. Our technique of extended coherent manipulation is applicable to long-term storage of quantum information in qubits based on ultracold polar molecules, while the vibrational clock enables precise probes of interatomic forces, tests of Newtonian gravitation at ultrashort range, and model-independent searches for electron-to-proton mass ratio variations.

We report on the observation of quantum coherence of Bose-Einstein condensed photons in an optically pumped, dye-filled microcavity. We find that coherence is long-range in space and time above condensation threshold, but short-range below threshold, compatible with thermalequilibrium theory. Far above threshold, the condensate is no longer at thermal equilibrium and is fragmented over non-degenerate, spatially overlapping modes. A microscopic theory including cavity loss, molecular structure and relaxation shows that this multimode condensation is similar to multimode lasing induced by imperfect gain clamping. BEC means that interferometry is one of the most urgent measurements to be made with a condensate [4,5]. Where thermal equilibrium is not completely reached, coherence is the defining characteristic of non-BEC quantum condensation, e.g for semiconductor exciton-polaritons [6-9] and organic polaritons [10,11]. In nonideal Bose gases, such as ultracold atoms, interactions tend to reduce but not destroy the coherence [12][13][14].The long range coherence behaviour of two-dimensional (2D) microcavity condensates is currently an open question. The coherence of interacting, equilibrium 2D Bose gases decays with a power law at large distances. The exponent is no greater than 1/4, which is reached at the threshold for the Berezinskii-Kosterlitz-Thouless transition [15]. It is known that the equation of motion for the local phase of a non-equilibrium drivendissipative 2D condensate is in the universality class of the Kardar-Parisi-Zhang (KPZ) equation [16], and nonpower-law decays are possible. Since the long-range coherence only shows non-equilibrium behaviour for systems which are very large compared to interaction length scales (such as the healing length), it has proven difficult to observe the true long-range behaviour, mainly due to unavoidable pumping inhomogeneities [17].Photon condensates in dye-filled microcavities are weakly interacting [18][19][20][21], inhomogeneous [22, 23], dissipative Bose gases close to thermal equilibrium at room temperature [24][25][26][27][28]. It is worth noting that the physical system has some similarities to a dye laser, with the decisive difference being that lasing is necessarily a non-equilibrium effect whereas photons can also undergo BEC in thermal equilibrium. Consequently BEC implies macroscopic occupation of the ground state independently of the loss and gain properties, whereas a laser is characterised by a large occupation of exactly the mode that has the most gain [29].Unique among physical realisations of BEC, in dye-microcavity photon BEC the particles thermalise only with a bath and not directly among themselves. This implies that the establishment of phase coherence in the OPEN ACCESS RECEIVED

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