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Many experimental platforms for quantum science depend on state control via laser fields. Frequently, however, the control fidelity is limited by optical phase noise. This is exacerbated in stabilized laser systems where high-frequency phase noise is an unavoidable consequence of feedback. Here we implement an optical feedforward technique to suppress laser phase noise in the STIRAP state transfer of ultracold RbCs molecules, across 114 THz, from a weakly bound Feshbach state to the rovibrational ground state. By performing over 100 state transfers on single molecules, we measure a significantly enhanced transfer efficiency of 98.7(1)% limited only by available laser intensity.

We report on the transport of ultracold cesium and rubidium atoms over $37.2\,$cm in under $25\,$ms using an optical conveyor belt formed by two counter-propagating beams with a controllable frequency difference that generate a movable optical lattice. By carefully selecting the waists and focus positions, we are able to use two static Gaussian beams for the transport, avoiding the need for a Bessel beam or vari-focus lenses. We characterize the transport efficiency for both species, including a comparison of different transport trajectories, gaining insight into the loss mechanisms and finding the minimum jerk trajectory to be optimum. Using the optimized parameters, we are able to transport up to $7 \times 10^6$ cesium or rubidium atoms with an efficiency up to $75\,$%. To demonstrate the viability of our transport scheme for experiments employing quantum gas microscopy, we produce Bose-Einstein condensates of either species after transport and present measurements of the simultaneous transport of both species., Comment: 15 pages, 10 figures

Ultracold polar molecules uniquely combine a rich structure of long-lived internal states with access to controllable long-range, anisotropic dipole-dipole interactions. In particular, the rotational states of polar molecules confined in optical tweezers or optical lattices may be used to encode interacting qubits for quantum computation or pseudo-spins for simulating quantum magnetism. As with all quantum platforms, the engineering of robust coherent superpositions of states is vital. However, for optically trapped molecules, the coherence time between rotational states is typically limited by inhomogeneous light shifts. Here we demonstrate a rotationally-magic optical trap for RbCs molecules that supports a Ramsey coherence time of 0.78(4) seconds in the absence of dipole-dipole interactions. This extends to >1.4 seconds at the 95% confidence level using a single spin-echo pulse. In our magic trap, dipolar interactions become the dominant mechanism by which Ramsey contrast is lost for superpositions that generate oscillating dipoles. By changing the states forming the superposition, we tune the effective dipole moment and show that the coherence time is inversely proportional to the strength of the dipolar interaction. Our work unlocks the full potential of the rotational degree of freedom in molecules for quantum computation and quantum simulation., Comment: 12 pages, 7 figures (main text and supplementary information combined)

We identify a route for the production of $^{87}$Rb$^{133}$Cs molecules in the $\textrm{X} \, ^1\Sigma^+$ rovibronic ground state that is compatible with efficient mixing of the atoms in optical lattices. We first construct a model for the excited-state structure using constants found by fitting to spectroscopy of the relevant $\textrm{a} \, ^3\Sigma^+ \rightarrow \textrm{b} \, ^3\Pi_1$ transitions at 181.5 G and 217.1 G. We then compare the predicted transition dipole matrix elements from this model to those found for the transitions that have been successfully used for STIRAP at 181.5 G. We form molecules by magnetoassociation on a broad interspecies Feshbach resonance at 352.7 G and explore the pattern of Feshbach states near 305 G. This allows us to navigate to a suitable initial state for STIRAP by jumping across an avoided crossing with radiofrequency radiation. We identify suitable transitions for STIRAP at 305 G. We characterize these transitions experimentally and demonstrate STIRAP to a single hyperfine level of the ground state with a one-way efficiency of 85(4)%., Comment: 21 pages, 8 figures

We present a computer program to calculate the quantised rotational and hyperfine energy levels of $^{1}\Sigma $ diatomic molecules in the presence of dc electric, dc magnetic, and off-resonant optical fields. Our program is applicable to the bialkali molecules used in ongoing state-of-the-art experiments with ultracold molecular gases. We include functions for the calculation of space-fixed electric dipole moments, magnetic moments and transition dipole moments.

We perform a measurement of the tune-out wavelength, $\lambda_{0}$, between the $D_{1}$, $6^2S_{1/2}\rightarrow6^2P_{1/2}$, and $D_{2}$, $6^2S_{1/2}\rightarrow6^2P_{3/2}$, transitions for $^{133}$Cs in the ground hyperfine state $(F=3, m_{F}=+3)$. At $\lambda_{0}$, the frequency-dependent scalar polarizability is zero leading to a zero scalar ac Stark shift. We measure the polarizability as a function of wavelength using Kapitza-Dirac scattering of a $^{133}$Cs Bose-Einstein condensate in a one-dimensional optical lattice, and determine the tune-out wavelength to be $\lambda_{0}=880.21790(40)_{\textrm{stat}}(8)_{\textrm{sys}}$ nm. From this measurement we determine the ratio of reduced matrix elements to be $\left|\left<{6P_{3/2}\| d\|6S_{1/2}}\right>\right|^{2}\left|\left<{6P_{1/2}\| d\|6S_{1/2}}\right>\right|^{2}=1.9808(2)$. This represents an improvement of a factor of 10 over previous results derived from excited-state lifetime measurements. We use the present measurement as a benchmark test of high-precision theory.

Understanding ultracold collisions involving molecules is of fundamental importance for current experiments, where inelastic collisions typically limit the lifetime of molecular ensembles in optical traps. Here we present a broad study of optically trapped ultracold RbCs molecules in collisions with one another, in reactive collisions with Rb atoms, and in nonreactive collisions with Cs atoms. For experiments with RbCs alone, we show that by modulating the intensity of the optical trap, such that the molecules spend 75% of each modulation cycle in the dark, we partially suppress collisional loss of the molecules. This is evidence for optical excitation of molecule pairs mediated via sticky collisions. We find that the suppression is less effective for molecules not prepared in the spin-stretched hyperfine ground state. This may be due either to longer lifetimes for complexes or to laser-free decay pathways. For atom-molecule mixtures, RbCs+Rb and RbCs+Cs, we demonstrate that the rate of collisional loss of molecules scales linearly with the density of atoms. This indicates that, in both cases, the loss of molecules is rate-limited by two-body atom-molecule processes. For both mixtures, we measure loss rates that are below the thermally averaged universal limit., Comment: 21 pages, 9 figures

Quantum states with long-lived coherence are essential for quantum computation, simulation and metrology. The nuclear spin states of ultracold molecules prepared in the singlet rovibrational ground state are an excellent candidate for encoding and storing quantum information. However, it is important to understand all sources of decoherence for these qubits, and then eliminate them, in order to reach the longest possible coherence times. Here, we fully characterise the dominant mechanisms for decoherence of a storage qubit in an optically trapped ultracold gas of RbCs molecules using high-resolution Ramsey spectroscopy. Guided by a detailed understanding of the hyperfine structure of the molecule, we tune the magnetic field to where a pair of hyperfine states have the same magnetic moment. These states form a qubit, which is insensitive to variations in magnetic field. Our experiments reveal an unexpected differential tensor light shift between the states, caused by weak mixing of rotational states. We demonstrate how this light shift can be eliminated by setting the angle between the linearly polarised trap light and the applied magnetic field to a magic angle of $\arccos{(1/\sqrt{3})}\approx55^{\circ}$. This leads to a coherence time exceeding 6.9 s (90% confidence level). Our results unlock the potential of ultracold molecules as a platform for quantum computation., Comment: 19 pages, 12 figures

We explore coherent multi-photon processes in $^{87}$Rb$^{133}$Cs molecules using 3-level lambda and ladder configurations of rotational and hyperfine states, and discuss their relevance to future applications in quantum computation and quantum simulation. In the lambda configuration, we demonstrate the driving of population between two hyperfine levels of the rotational ground state via a two-photon Raman transition. Such pairs of states may be used in the future as a quantum memory, and we measure a Ramsey coherence time for a superposition of these states of 58(9) ms. In the ladder configuration, we show that we can generate and coherently populate microwave dressed states via the observation of an Autler-Townes doublet. We demonstrate that we can control the strength of this dressing by varying the intensity of the microwave coupling field. Finally, we perform spectroscopy of the rotational states of $^{87}$Rb$^{133}$Cs up to $N=6$, highlighting the potential of ultracold molecules for quantum simulation in synthetic dimensions. By fitting the measured transition frequencies we determine a new value of the centrifugal distortion coefficient $D_v=h\times207.3(2)~$Hz.

We investigate the effects of static electric and magnetic fields on the differential ac Stark shifts for microwave transitions in ultracold bosonic $^{87}$Rb$^{133}$Cs molecules, for light of wavelength $\lambda = 1064~\mathrm{nm}$. Near this wavelength we observe unexpected two-photon transitions that may cause trap loss. We measure the ac Stark effect in external magnetic and electric fields, using microwave spectroscopy of the first rotational transition. We quantify the isotropic and anisotropic parts of the molecular polarizability at this wavelength. We demonstrate that a modest electric field can decouple the nuclear spins from the rotational angular momentum, greatly simplifying the ac Stark effect. We use this simplification to control the ac Stark shift using the polarization angle of the trapping laser.

We show that the lifetime of ultracold ground-state $^{87}$Rb$^{133}$Cs molecules in an optical trap is limited by fast optical excitation of long-lived two-body collision complexes. We partially suppress this loss mechanism by applying square-wave modulation to the trap intensity, such that the molecules spend 75% of each modulation cycle in the dark. By varying the modulation frequency, we show that the lifetime of the collision complex is $0.53\pm0.06$ ms in the dark. We find that the rate of optical excitation of the collision complex is $3^{+4}_{-2}\times10^{3}$ W$^{-1}$ cm$^2$ s$^{-1}$ for $\lambda = 1550$ nm, leading to a lifetime of <100 ns for typical trap intensities. These results explain the two-body loss observed in experiments on nonreactive bialkali molecules., Comment: 6 pages, 4 figures

We discuss how the internal structure of ultracold molecules, trapped in the motional ground state of optical tweezers, can be used to implement qudits. We explore the rotational, fine and hyperfine structure of $^{40}$Ca$^{19}$F and $^{87}$Rb$^{133}$Cs, which are examples of molecules with $^2\Sigma$ and $^1\Sigma$ electronic ground states, respectively. In each case we identify a subset of levels within a single rotational manifold suitable to implement a 4-level qudit. Quantum gates can be implemented using two-photon microwave transitions via levels in a neighboring rotational manifold. We discuss limitations to the usefulness of molecular qudits, arising from off-resonant excitation and decoherence. As an example, we present a protocol for using a molecular qudit of dimension $d=4$ to perform the Deutsch algorithm.

Understanding and controlling collisions is crucial to the burgeoning field of ultracold molecules. All experiments so far have observed fast loss of molecules from the trap. However, the dominant mechanism for collisional loss is not well understood when there are no allowed 2-body loss processes. Here we experimentally investigate collisional losses of nonreactive ultracold RbCs molecules, and compare our findings with the sticky collision hypothesis that pairs of molecules form long-lived collision complexes. We demonstrate that loss of molecules occupying their rotational and hyperfine ground state is best described by second-order rate equations, consistent with the expectation for complex-mediated collisions, but that the rate is lower than the limit of universal loss. The loss is insensitive to magnetic field but increases for excited rotational states. We demonstrate that dipolar effects lead to significantly faster loss for an incoherent mixture of rotational states., Comment: 15 pages, 7 figures, 1 table

We explore the uses of ultracold molecules as a platform for future experiments in the field of quantum simulation, focusing on two molecular species, $^{40}$Ca$^{19}$F and $^{87}$Rb$^{133}$Cs. We report the development of coherent quantum state control using microwave fields in both molecular species; this is a crucial ingredient for many quantum simulation applications. We demonstrate proof-of-principle Ramsey interferometry measurements with fringe spacings of $\sim 1~\rm kHz$ and investigate the dephasing time of a superposition of $N=0$ and $N=1$ rotational states when the molecules are confined. For both molecules, we show that a judicious choice of molecular hyperfine states minimises the impact of spatially varying transition-frequency shifts across the trap. For magnetically trapped $^{40}$Ca$^{19}$F we use a magnetically insensitive transition and observe a coherence time of 0.61(3) ms. For optically trapped $^{87}$Rb$^{133}$Cs we exploit an avoided crossing in the AC Stark shift and observe a maximum coherence time of 0.75(6) ms., Comment: Accepted for publication in Quantum Science and Technology

We investigate the effect of far-off-resonant trapping light on ultracold bosonic RbCs molecules. We use kHz-precision microwave spectroscopy to measure the differential AC Stark shifts between the ground and first excited rotational levels of the molecule with hyperfine-state resolution. We demonstrate through both experiment and theory that coupling between neighboring hyperfine states manifests in rich structure with many avoided crossings. This coupling may be tuned by rotating the polarization of the linearly polarized trapping light. A combination of spectroscopic and parametric heating measurements allows complete characterization of the molecular polarizability at a wavelength of 1550~nm in both the ground and first excited rotational states., Comment: 5 pages, 4 figures

We demonstrate coherent control of both the rotational and hyperfine state of ultracold, chemically stable $^{87}$Rb$^{133}$Cs molecules with external microwave fields. We create a sample of ~2000 molecules in the lowest hyperfine level of the rovibronic ground state N = 0. We measure the transition frequencies to 8 different hyperfine levels of the N = 1 state at two magnetic fields ~23 G apart. We determine accurate values of rotational and hyperfine coupling constants that agree well with previous calculations. We observe Rabi oscillations on each transition, allowing complete population transfer to a selected hyperfine level of N = 1. Subsequent application of a second microwave pulse allows transfer of molecules back to a different hyperfine level of N = 0., Comment: 6 pages, 3 figures, 2 tables

We report the binding energy of $^{87}$Rb$^{133}$Cs molecules in their rovibrational ground state measured using an offset-free optical frequency comb based on difference frequency generation technology. We create molecules in the absolute ground state using stimulated Raman adiabatic passage (STIRAP) with a transfer efficiency of 88\%. By measuring the absolute frequencies of our STIRAP lasers, we find the energy-level difference from an initial weakly-bound Feshbach state to the rovibrational ground state with a resolution of 5 kHz over an energy-level difference of more than 114 THz; this lets us discern the hyperfine splitting of the ground state. Combined with theoretical models of the Feshbach state binding energies and ground-state hyperfine structure, we determine a zero-field binding energy of $h\times114\,268\,135\,237(5)(50)$ kHz. To our knowledge, this is the most accurate determination to date of the dissociation energy of a molecule., Comment: 8 pages, 7 figures

We present a detailed study of the absolute Doppler-broadened absorption of a probe beam scanned across the potassium D lines in a thermal vapour. Spectra using a weak probe were measured on the 4S $\rightarrow$ 4P transition and compared to the theoretical model of the electric susceptibility detailed by Zentile et al. (2015) in the code named ElecSus. Comparisons were also made on the 4S $\rightarrow$ 5P transition with an adapted version of ElecSus. This is the first experimental test of ElecSus on an atom with a ground state hyperfine splitting smaller than that of the Doppler width. An excellent agreement was found between ElecSus and experimental measurements at a variety of temperatures with rms errors of $\sim 10^{-3}$. We have also demonstrated the use of ElecSus as an atomic vapour thermometry tool, and present a possible new measurement technique of transition decay rates which we predict to have a precision $\sim$ 3 kHz.

We report the creation of a sample of over 1000 ultracold $^{87}$RbCs molecules in the lowest rovibrational ground state, from an atomic mixture of $^{87}$Rb and Cs, by magnetoassociation on an interspecies Feshbach resonance followed by stimulated Raman adiabatic passage (STIRAP). We measure the binding energy of the RbCs molecule to be $h c \times 3811.576(1)$ cm$^{-1}$ and the $|v''=0, J''=0>$ to $|v''=0, J''=2>$ splitting to be $h \times 2940.09(6)$ MHz. Stark spectroscopy of the rovibrational ground state yields an electric dipole moment of 1.225(3)(8) D, where the values in parentheses are the statistical and systematic uncertainties, respectively. We demonstrate that a space-fixed dipole moment of 0.355(2)(4) D is accessible in RbCs, which is substantially higher than in previous work., Comment: 5 pages, 4 figures + supplementary material