Laser cooling and trapping of atoms and atomic ions has led to numerous advances including the observation of exotic phases of matter [1,2], development of exquisite sensors [3] and state-of-the-art atomic clocks [4]. The same level of control in molecules could also lead to profound developments such as controlled chemical reactions and sensitive probes of fundamental theories [5], but the vibrational and rotational degrees of freedom in molecules pose a formidable challenge for controlling their quantum mechanical states. Here, we use quantumlogic spectroscopy (QLS) [6] for preparation and nondestructive detection of quantum mechanical states in molecular ions [7]. We develop a general technique to enable optical pumping and preparation of the molecule into a pure initial state. This allows for the observation of high-resolution spectra in a single ion (here CaH + ) and coherent phenomena such as Rabi flopping and Ramsey fringes. The protocol requires a single, far-off resonant laser, which is not specific to the molecule, so that many other molecular ions, including polyatomic species, could be treated with the same methods in the same apparatus by changing the molecular source. Combined with long interrogation times afforded by ion traps, a broad range of molecular ions could be studied with unprecedented control and precision, representing a critical step towards proposed applications, such as precision molecular spectroscopy, stringent tests of fundamental physics, quantum computing, and precision control of molecular dynamics [8].Significant progress has been made in recent years toward the goals of controlling the quantum mechanical states of ultracold molecules [9,10] (also see Methods). For a molecular ion, its charge provides a means of trapping and sympathetically cooling via its Coulomb interaction with a co-trapped atomic ion that is readily laser-cooled [11]. Cooling of vibrational [12] and rotational [13][14][15][16] states has also been realized in heteronuclear molecular ions. Preparation in specific vibrational and rotational states was achieved via threshold photoionization [17] and optical pumping into individual hyperfine states has been demonstrated [18]. In the context of QLS, state detection of a single molecular ion in a particular subset of states in a rotational manifold has been achieved [7]. Many of these experiments rely on fortuitous molecular properties [9,13], dedicated multi-laser systems [9,14,15,18] or sophisticated laser cooling techniques [10]. Coherent control of pure quantum states of a molecular ion, crucial to precision experiments, has not yet been accomplished. 2Here, we demonstrate a general protocol for coherent manipulation of trapped molecular ions in their electronic and vibrational ground states based on QLS [6] and stimulated Raman transitions (SRTs) driven by a far-detuned laser source [19][20][21]. Because the rotational motion is not cooled, our approach relies on probabilistically preparing a particular rotational state via a projective measurement [22]. We...

Spectroscopy is a powerful tool for studying molecules and is commonly performed on large thermal molecular ensembles that are perturbed by motional shifts and interactions with the environment and one another, resulting in convoluted spectra and limited resolution. Here, we use generally applicable quantum-logic techniques to prepare a trapped molecular ion in a single quantum state, drive terahertz rotational transitions with an optical frequency comb, and read out the final state non-destructively, leaving the molecule ready for further manipulation. We resolve rotational transitions to 11 significant digits and derive the rotational constant of 40 CaH + to be B R = 142 501 777.9(1.7) kHz. Our approach suits a wide range of molecular ions, including polyatomics and species relevant for tests of fundamental physics, chemistry, and astrophysics.Precision molecular spectroscopy produces information that is essential to understand molecular properties and functions, which underpin chemistry and biology. In particular, microwave rotational spectroscopy can precisely determine various aspects of molecular structure, such as bond lengths and angles, and help identify molecules. However, even in a dilute gas, where the interaction with surrounding molecules is reduced, spectroscopic experiments often fall short of the ultimate resolution set by the natural linewidth of the transitions. This is due to effects that crowd and blur molecular spectra, such as uncontrolled nuclear, rotational, vibrational, and electronic states, line shifts and broadening from external fields, reduced interaction time from time-of-flight, and the Doppler effect. These limitations have motivated efforts toward trapping molecules and cooling them close to absolute zero temperature. Laser cooling and trapping [1-3], which revolutionized atomic physics, have enabled formation of molecules from cold atoms [4] and precision molecular spectroscopy [5]. Direct laser cooling of molecules shows promise for species with advantageous level structures that only require a few laser wavelengths [6-8], but is infeasible for the vast majority of molecules.Furthermore, even with trapped and cooled molecules [9], commonly used detection methods, such as state-dependent photo-dissociation or ionization [10,11], destroy the molecules under study, making them unavailable for further manipulation.In this work, we perform high resolution spectroscopy on rotational states of a molecular ion using methods that are generally applicable to a broad range of molecular ions, which are readily trapped in electromagnetic potentials [12] and cooled by coupling to co-trapped atomic ions amenable to laser cooling [13,14]. The long interrogation times and low translational temperature enabled by trapping and sympathetic cooling lead to high resolution [15], which has, among other advances, enabled the most stringent test of fundamental theory carried out by molecular ions [16]. We prepare a trapped 40 CaH + molecular ion at rest in a single, known quantum state and coherently ...

A quantum network combines the benefits of quantum systems regarding secure information transmission and calculational speed-up by employing quantum coherence and entanglement to store, transmit and process information. A promising platform for implementing such a network are atom-based quantum memories and processors, interconnected by photonic quantum channels. A crucial building block in this scenario is the conversion of quantum states between single photons and single atoms through controlled emission and absorption. Here we present an experimental protocol for photon-to-atom quantum state conversion, whereby the polarization state of an absorbed photon is mapped onto the spin state of a single absorbing atom with 495% fidelity, while successful conversion is heralded by a single emitted photon. Heralded high-fidelity conversion without affecting the converted state is a main experimental challenge, in order to make the transferred information reliably available for further operations. We record 480 s À 1 successful state transfer events out of 18,000 s À 1 repetitions.

We report on the efficient generation of single photons, making use of spontaneous Raman scattering in a single trapped ion. The photons are collected through in-vacuum high-numerical-aperture objectives. Photon frequency, polarization and temporal shape are controlled through appropriate laser parameters, allowing for photons in a pure quantum state. These photons are suitable heralds for single-photon absorption in a single-ion quantum memory.Quantum networks allow for quantum communication between distant locations (nodes) where local quantum information processing is carried out. The key ingredient for this kind of network architecture is to establish entanglement between network nodes [1]. Its scalability is facilitated by employing quantum repeaters [2,3].Different platforms are pursued for implementing quantum networks, and various schemes exist to generate entanglement between their nodes. In the field of trapped single atoms and ions as nodes [4], one approach is to use pairs of entangled photons, split them up and have them absorbed by two separate atoms, thus transferring the photonic entanglement onto

We establish a heralded interaction between two remotely trapped single (40)Ca(+) ions through the exchange of single photons. In the sender ion, we release single photons with a controlled temporal shape on the P(3/2) to D(5/2) transition and transmit them to the distant receiver ion. Individual absorption events in the receiver ion are detected by quantum jumps. For continuously generated photons, the absorption reduces significantly the lifetime of the long-lived D(5/2) state. For triggered single-photon transmission, we observe a coincidence between the emission at the sender and quantum jump events at the receiver.