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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 40Ca19F and 87Rb133Cs, which are examples of molecules with 2 and 1 electronic ground states, respectively. In each case we identify a subset of levels within a single rotational manifold suitable to implement a four-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 87 Rb 133 Cs 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. Ultracold polar molecules are an excellent platform for quantum science but experiments so far see fast trap losses that are poorly understood. Here the authors investigate collisional losses of nonreactive RbCs, and show they are consistent with the sticky collision hypothesis, but are slower than the universal rate.

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 in the dark 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.

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, to reach the longest possible coherence times. Here we fully characterize the dominant mechanisms of decoherence for 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 a subtle 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 polarized trap light and the applied magnetic field to a magic angle of arccos(1/3)≈55∘. This leads to a coherence time exceeding 5.6 s at the 95% confidence level.The hyperfine states of ultracold polar molecules are a strong candidate for storing quantum information. Identifying and eliminating all detectable causes of decoherence has extended the qubit coherence time beyond 5.6 s in RbCs molecules.

We present a study on the optical losses of Fabry-Pérot cavities subject to realistic transverse mirror misalignment. We consider mirrors of the two most prevalent surface forms: idealised spherical depressions, and Gaussian profiles generated by laser ablation. We first describe the mode mixing phenomena seen in the spherical mirror case and compare to the frequently-used clipping model, observing close agreement in the predicted diffraction loss, but with the addition of protective mode mixing at transverse degeneracies. We then discuss the Gaussian mirror case, detailing how the varying surface curvature across the mirror leads to complex variations in round trip loss and mode profile. In light of the severe mode distortion and strongly elevated loss predicted for many cavity lengths and transverse alignments when using Gaussian mirrors, we suggest that the consequences of mirror surface profile are carefully considered when designing cavity experiments.

In the design optimisation of ion-cavity interfaces for quantum networking applications, difficulties occur due to the many competing figures of merit and highly interdependent design constraints, many of which present `soft-limits', amenable to improvement at the cost of engineering time. In this work we present a systematic approach to this problem which offers a means to identify efficient and robust operating regimes, and to elucidate the trade-offs involved in the design process, allowing engineering efforts to be focused on the most sensitive and critical parameters. We show that in many relevant cases it is possible to approximately separate the geometric aspects of the cooperativity from those associated with the atomic system and the mirror surfaces themselves, greatly simplifying the optimisation procedure. Although our approach to optimisation can be applied to most operating regimes, here we consider cavities suitable for typical ion trapping experiments, and with substantial transverse misalignment of the mirrors. We find that cavities with mirror misalignments of many micrometres can still offer very high photon extraction efficiencies, offering an appealing route to the scalable production of ion-cavity interfaces for large scale quantum networks.

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.

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.

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.

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.