## Publications

114 results found

Ho C, Wright S, Sauer B,
et al., 2023, Systematic errors arising from polarization imperfections in measurements of the electron’s electric dipole moment, *Physical Review Research*, Vol: 5, ISSN: 2643-1564

The electron’s electric dipole moment (eEDM) can be determined by polarizing the spin of an atom or a molecule and then measuring the spin precession frequency in an applied electric field. Radiation is used to polarize the spin and then analyze the precession angle, and the measurement is often sensitive to the polarization of this radiation. We show how systematic errors can arise when both the polarization of the radiation and the magnitude of the electric field are imperfectly controlled. We derive approximate analytical expressions for these errors, confirm their accuracy numerically, and show how they can be corrected empirically. We consider spin manipulation using single-photon pulses, Raman pulses, and Stimulated Raman Adiabatic Passage (STIRAP), and show that STIRAP provides better immunity to these systematic errors. An experimental study of these errors partly supports our findings but also reveals another potential error that is not captured by this analysis.

Mukherjee B, Frye MD, Le Sueur CR,
et al., 2023, Shielding collisions of ultracold CaF molecules with static electric fields, *Physical Review Research*, Vol: 5, ISSN: 2643-1564

We study collisions of ultracold CaF molecules in strong static electric fields. These fields allow the creationof long-range barriers in the interaction potential, effectively preventing the molecules from reaching theshort-range region where inelastic and other loss processes are likely to occur. We carry out coupled-channelcalculations of rate coefficients for elastic scattering and loss. We develop an efficient procedure for includingenergetically well-separated rotor functions in the basis set via a Van Vleck transformation. We show thatshielding is particularly efficient for CaF and allows the rate of two-body loss processes to be reduced by a factorof 107 or more at a field of 23 kV/cm. The loss rates remain low over a substantial range of fields. Electron andnuclear spins cause strong additional loss in some small ranges of field, but have little effect elsewhere. Theseresults pave the way for evaporative cooling of CaF towards quantum degeneracy

Bird RC, Tarbutt MR, Hutson JM, 2023, Tunable Feshbach resonances in collisions of ultracold molecules in ²∑ states with alkali-metal atoms, *Physical Review Research*, Vol: 5, ISSN: 2643-1564

We consider the magnetically tunable Feshbach resonances that may exist in ultracold mixtures of moleculesin 2 states and alkali-metal atoms. We focus on Rb+CaF as a prototype system. There are likely to be Feshbachresonances analogous to those between pairs of alkali-metal atoms. We investigate the patterns of near-thresholdstates and the resonances that they cause, using coupled-channel calculations of the bound states and low-energyscattering on model interaction potentials. We explore the dependence of the properties on as-yet-unknownpotential parameters. There is a high probability that resonances will exist at magnetic fields below 1000 G,and that these will be broad enough to control collisions and form triatomic molecules by magnetoassociation.We consider the effects of CaF rotation and anisotropy of the interaction potential, and conclude that they mayproduce additional resonances but should not affect the existence of rotation-free resonances.

Ho C, Lim J, Sauer B,
et al., 2023, Measuring the nuclear magnetic quadrupole moment in heavy polar molecules, *Frontiers in Physics*, Vol: 11, Pages: 1-10, ISSN: 2296-424X

Theories that extend the Standard Model of particle physics often introduce new interactions that violate charge-parity (CP) symmetry. CP-violating effects within an atomic nucleus can be probed by measuring its nuclear magnetic quadrupole moment (MQM). The sensitivity of such a measurement is enhanced when using a heavy polar molecule containing a nucleus with quadrupole deformation. We determine how the energy levels of a molecule are shifted by the MQM and how those shifts can be measured. The measurement scheme requires molecules in a superposition of magnetic sub-levels that differ by many units of angular momentum. We develop a generic scheme for preparing these states. Finally, we consider the sensitivity that can be reached, showing that this method can reduce the current uncertainties on several CP-violating parameters.

Zhang C, Tarbutt M, 2022, Quantum computation in a hybrid array of molecules and Rydberg atoms, *PRX Quantum*, Vol: 3, Pages: 1-17, ISSN: 2691-3399

We show that an array of polar molecules interacting with Rydberg atoms is a promising hybrid system for scalable quantum computation. Quantum information is stored in long-lived hyperfine or rotational states of molecules which interact indirectly through resonant dipole-dipole interactions with Rydberg atoms. A two-qubit gate based on this interaction has a duration of 1 μs and an achievable fidelity of 99.9%. The gate has little sensitivity to the motional states of the particles – the molecules can be in thermal states, the atoms do not need to be trapped during Rydberg excitation, the gate does not heat the molecules, and heating of the atoms has a negligible effect. Within a large, static array, the gate can be applied to arbitrary pairs of molecules separated by tens of micrometres, making the scheme highly scalable. The molecule-atom interaction can also be used for rapid qubit initialization and efficient, non-destructive qubit readout, without driving any molecular transitions. Single qubit gates are driven using microwave pulses alone, exploiting the strong electric dipole transitions between rotational states. Thus, all operations required for large scale quantum computation can be done without moving the molecules or exciting them out of their ground electronic states.

Zhang C, Zhang C, Cheng L,
et al., 2022, Inner-shell excitation in the YbF molecule and its impact on laser cooling, *Journal of Molecular Spectroscopy*, Vol: 386, ISSN: 0022-2852

The YbF molecule is a sensitive system for measuring the electron’s electric dipole moment. The precision ofthis measurement can be improved by direct laser cooling of the molecules to ultracold temperature. However,low-lying electronic states arising from excitation of a 4f electron may hinder laser cooling. One set of these ‘‘4fhole’’ states lies below the 𝐴2𝛱1∕2 excited state used for laser cooling, and radiative decay to these intermediatelevels, even with branching ratios as small as 10−5, can be a hindrance. Other 4f hole states lie very close tothe 𝐴2𝛱1∕2 state, and a perturbation results in states of mixed character that are involved in the laser coolingcycle. This perturbation may enhance the loss of molecules to states outside of the laser cooling cycle. Wemodel the perturbation of the 𝐴2𝛱1∕2 state to determine the strength of the coupling between the states, thede-perturbed potential energy curves, and the radiative branching ratios to various vibrational levels of theground state, 𝑋2𝛴+. We use electronic structure calculations to characterize the 4f hole states and the strengthsof transitions between these states and the 𝐴2𝛱1∕2 and 𝑋2𝛴+ states. We identify a leak out of the cooling cyclewith a branching ratio of roughly 5 × 10−4, dominated by the contribution of the ground state configurationin a 4f hole state. Finally, we assess the impact of these results for laser cooling of YbF and molecules withsimilar structure.

Barontini G, Blackburn L, Boyer V, et al., 2021, Measuring the stability of fundamental constants with a network of clocks, Publisher: arXiv

The detection of variations of fundamental constants of the Standard Modelwould provide us with compelling evidence of new physics, and could lift theveil on the nature of dark matter and dark energy. In this work, we discuss howa network of atomic and molecular clocks can be used to look for suchvariations with unprecedented sensitivity over a wide range of time scales.This is precisely the goal of the recently launched QSNET project: A network ofclocks for measuring the stability of fundamental constants. QSNET will includestate-of-the-art atomic clocks, but will also develop next-generation molecularand highly charged ion clocks with enhanced sensitivity to variations offundamental constants. We describe the technological and scientific aims ofQSNET and evaluate its expected performance. We show that in the range ofparameters probed by QSNET, either we will discover new physics, or we willimpose new constraints on violations of fundamental symmetries and a range oftheories beyond the Standard Model, including dark matter and dark energymodels.

Alauze X, Lim J, Trigatzis MA,
et al., 2021, An ultracold molecular beam for testing fundamental physics, *QUANTUM SCIENCE AND TECHNOLOGY*, Vol: 6, ISSN: 2058-9565

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- Citations: 13

Jurgilas S, Chakraborty A, Rich C,
et al., 2021, Collisions in a dual-species magneto-optical trap of molecules and atoms, *New Journal of Physics*, Vol: 23, ISSN: 1367-2630

We study inelastic collisions between CaF molecules and ⁸⁷Rb atoms in a dual-species magneto-optical trap. The presence of atoms increases the loss rate of molecules from the trap. By measuring the loss rates and density distributions, we determine a collisional loss rate coeﬃcient k₂ = (1.43 ± 0.29) × 10‾¹⁰cm³/s at a temperature of 2.4 mK. We show that this is not substantially changed by light-induced collisions or by varying the populations of excited-state atoms and molecules. The observed loss rate is close to the universal rate expected in the presence of fast loss at short range, and can be explained by rotation-changing collisions in the ground electronic state.

Fitch N, Tarbutt M, 2021, Laser-cooled molecules, *Advances in Atomic Molecular and Optical Physics*, ISSN: 1049-250X

Jurgilas S, Chakraborty A, Rich CJH,
et al., 2021, Collisions between Ultracold Molecules and Atoms in a Magnetic Trap, *PHYSICAL REVIEW LETTERS*, Vol: 126, ISSN: 0031-9007

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- Citations: 25

Caldwell L, Tarbutt M, 2021, General approach to state-dependent optical tweezer traps for polar molecules, *Physical Review Research*, Vol: 3, ISSN: 2643-1564

State-dependent optical tweezers can be used to trap a pair of molecules with a separation much smaller than the wavelength of the trapping light, greatly enhancing the dipole-dipole interaction between them. Here we describe a general approach to producing these state-dependent potentials using the tensor part of the ac Stark shift and show how it can be used to carry out two-qubit gates between pairs of molecules. The method is applicable to broad classes of molecules including bialkali molecules produced by atom association and those amenable to direct laser cooling.

Fitch NJ, Lim J, Hinds EA,
et al., 2021, Methods for measuring the electron's electric dipole moment using ultracold YbF molecules, *QUANTUM SCIENCE AND TECHNOLOGY*, Vol: 6, ISSN: 2058-9565

Caldwell L, Tarbutt MR, 2020, Enhancing dipolar interactions between molecules using state-dependent optical tweezer traps, *Physical Review Letters*, Vol: 125, Pages: 243201 – 1-243201 – 6, ISSN: 0031-9007

We show how state-dependent optical potentials can be used to trap a pair of molecules in different internal states at a separation much smaller than the wavelength of the trapping light. This close spacing greatly enhances thedipole-dipole interaction and we show how it can be used to implement two-qubit gates between molecules that are 100 times faster than existing protocols and than rotational coherence times already demonstrated. We analyze complications due to hyperfine structure, tensor light shifts, photon scattering and collisional loss, and conclude that none is a barrier to implementing the scheme.

Hughes M, Frye MD, Sawant R,
et al., 2020, Robust entangling gate for polar molecules using magnetic and microwave fields, *Physical Review A*, Vol: 101, Pages: 062308-1-062308-12, ISSN: 2469-9926

Polar molecules are an emerging platform for quantum technologies based on their long-range electric dipole–dipole interactions, which open new possibilities for quantum information processing and the quantum simulation of strongly correlated systems. Here, we use magnetic and microwave fields to design a fast entangling gate with >0.999 fidelity and which is robust with respect to fluctuations in the trapping and control fields and to small thermal excitations. These results establish the feasibility to build a scalable quantum processor with a broad range of molecular species in optical-lattice and optical-tweezers setups.

Ho C, Devlin JA, Rabey I,
et al., 2020, New techniques for a measurement of the electron's electric dipole moment, *New Journal of Physics*, Vol: 22, ISSN: 1367-2630

The electric dipole moment of the electron (eEDM) can be measured with high precision using heavy polar molecules. In this paper, we report on a series of new techniques that have improved the statistical sensitivity of the YbF eEDM experiment. We increase the number of molecules participating in the experiment by an order of magnitude using a carefully designed optical pumping scheme. We also increase the detection efficiency of these molecules by another order of magnitude using an optical cycling scheme. In addition, we show how to destabilise dark states and reduce backgrounds that otherwise limit the efficiency of these techniques. Together, these improvements allow us to demonstrate a statistical sensitivity of 1.8 x 10⁻²⁸ e cm after one day of measurement, which is 1.2 times the shot-noise limit. The techniques presented here are applicable to other high-precision measurements using molecules.

Ho C, Devlin J, Rabey I,
et al., 2020, New techniques for a measurement of the electron's electric dipole moment, *New Journal of Physics*, ISSN: 1367-2630

The electric dipole moment of the electron (eEDM) can be measured with high precision using heavy polar molecules. In this paper, we report on a series of new techniques that have improved the statistical sensitivity of the YbF eEDM experiment. We increase the number of molecules participating in the experiment by an order of magnitude using a carefully designed optical pumping scheme. We also increase the detection efficiency of these molecules by another order of magnitude using an optical cycling scheme. In addition, we show how to destabilise dark states and reduce backgrounds that otherwise limit the efficiency of these techniques. Together, these improvements allow us to demonstrate a statistical sensitivity of 1.8 x 10⁻²⁸ e cm after one day of measurement, which is 1.2 times the shot-noise limit. The techniques presented here are applicable to other high-precision measurements using molecules.

Caldwell L, Tarbutt MR, 2020, Sideband cooling of molecules in optical traps, Publisher: AMER PHYSICAL SOC

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- Citations: 24

Caldwell L, Tarbutt M, 2020, Sideband cooling of molecules in optical traps, *Physical Review & Research*, Vol: 2, ISSN: 2643-1564

Sideband cooling is a popular method for cooling atoms to the ground state of an optical trap. Applying the same method to molecules requires a number of challenges to be overcome. Strong tensor Stark shifts in molecules cause the optical trapping potential, and corresponding trap frequency, to depend strongly on rotational, hyper fine and Zeeman state. Consequently, transition frequencies depend on the motional quantum number and there are additional heating mechanisms, either of which can be fatal for an eff ective sideband cooling scheme. We develop the theory of sideband cooling in state-dependent potentials, and derive an expression for the heating due to photon scattering. We calculate the ac Stark shifts of molecular states in the presence of a magnetic field, and for any polarization. We show that the complexity of sideband cooling can be greatly reduced by applying a large magnetic fi eld to eliminate electron- and nuclear-spin degrees of freedom from the problem. We consider how large the magnetic field needs to be, show that heating can be managedsuffi ciently well, and present a simple recipe for cooling to the ground state of motion.

Caldwell L, Williams H, Fitch N,
et al., 2020, Long rotational coherence times of molecules in a magnetic trap, *Physical Review Letters*, Vol: 124, ISSN: 0031-9007

Polar molecules in superpositions of rotational states exhibit long-range dipolar interactions, but maintaining their coherence in a trapped sample is a challenge. We present calculations that show many laser-coolable molecules have convenient rotational transitions that are exceptionally insensitive to magnetic fi elds. We verify this experimentally for CaF where we find a transition with sensitivity below 5 HzG‾¹ and use it to demonstrate a rotational coherence time of 6.4(8) ms in a magnetic trap. Simulations suggest it is feasible to extend this to > 1 s using a smaller cloud in abiased magnetic trap.

Sawant R, Blackmore JA, Gregory PD,
et al., 2020, Ultracold polar molecules as qudits, *New Journal of Physics*, Vol: 22, Pages: 1-12, ISSN: 1367-2630

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 2Σ and 1Σ 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.

Wright S, Wall T, Tarbutt M, 2019, Microwave trap for atoms and molecules, *Physical Review Research*, Vol: 1, ISSN: 2643-1564

We demonstrate a trap that confines polarizable particles around the antinode of a standing-wave microwave field. The trap relies only on the polarizability of the particles far from any resonances, so can trap a wide variety of atoms and molecules in a wide range of internal states, including the ground state. The trap has a volume of about 10 cm³, and a depth approaching 1K for many polarmolecules. We measure the trap properties using ⁷Li atoms, showing that when the input microwave power is 610W, the atoms remain trapped with a 1/e lifetime of 1.76(12) s, oscillating with an axial frequency of 28.55(5) Hz and a radial frequency of 8.81(8) Hz. The trap could be loaded with slowmolecules from a range of available sources, and is particularly well suited to sympathetic cooling and evaporative cooling of molecules.

Caldwell L, Devlin J, Williams H,
et al., 2019, Deep Laser Cooling and Efficient Magnetic Compression of Molecules, *Physical Review Letters*, Vol: 123, ISSN: 0031-9007

We introduce a scheme for deep laser cooling of molecules based on robust dark states at zero velocity. By simulating this scheme, we show it to be a widely applicable method that can reach the recoil limit or below. We demonstrate and characterise the method experimentally, reachinga temperature of 5.4(7) μK. We solve a general problem of measuring low temperatures for large clouds by rotating the phase-space distribution and then directly imaging the complete velocity distribution. Using the same phase-space rotation method, we rapidly compress the cloud. Applying the cooling method a second time, we compress both the position and velocity distributions.

Tarbutt MR, 2019, Laser cooling of molecules, *Contemporary Physics*, Vol: 59, Pages: 356-376, ISSN: 0010-7514

Recently, laser cooling methods have been extended from atoms to molecules. The complex rotational and vibrational energy level structure of molecules makes laser cooling difficult, but these difficulties have been overcome and molecules have now been cooled to a few microkelvin and trapped for several seconds. This opens many possibilities for applications in quantum science and technology, controlled chemistry, and tests of fundamental physics. This article explains how molecules can be decelerated, cooled and trapped using laser light, reviews the progress made in recent years, and outlines some future applications.

Blackmore JA, Caldwell L, Gregory PD,
et al., 2019, Ultracold molecules for quantum simulation: rotational coherences in CaF and RbCs, *Quantum Science and Technology*, Vol: 4, ISSN: 2058-9565

Polar molecules offer a new platform for quantum simulation of systems with long-range interactions, based on the electrostatic interaction between their electric dipole moments. Here, we report the development of coherent quantum state control using microwave fields in 40Ca19F and 87Rb133Cs molecules, a crucial ingredient for many quantum simulation applications. We perform Ramsey interferometry measurements with fringe spacings of ~1 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 40Ca19F we use a magnetically insensitive transition and observe a coherence time of 0.61(3) ms. For optically trapped 87Rb133Cs we exploit an avoided crossing in the AC Stark shifts and observe a maximum coherence time of 0.75(6) ms.

Cournol A, Manceau M, Pierens M,
et al., 2019, A new experiment to test parity symmetry in cold chiral molecules using vibrational spectroscopy, *QUANTUM ELECTRONICS*, Vol: 49, Pages: 288-292, ISSN: 1063-7818

Devlin J, Tarbutt M, 2018, Laser cooling and magneto-optical trapping of molecules analyzed using optical Bloch equations and the Fokker-Planck-Kramers equation, *Physical Review A*, Vol: 98, ISSN: 1050-2947

We study theoretically the behavior of laser-cooled calcium monofluoride (CaF) molecules in an optical molasses and magneto-optical trap (MOT), and compare our results to recent experiments. We use multilevel optical Bloch equations to estimate the force and the diffusion constant, followed by a Fokker-Planck-Kramers equation to calculate the time evolution of the velocity distribution. The calculations are done in three dimensions, and we include all the relevant energy levels of the molecule and all the relevant frequency components of the light. Similar to simpler model systems, the velocity-dependent force curve exhibits Doppler and polarization-gradient forces of opposite signs. We show that the temperature of the MOT is governed mainly by the balance of these two forces. Our calculated MOT temperatures and photon scattering rates are in broad agreement with those measured experimentally over a wide range of parameters. In a blue-detuned molasses, the temperature is determined by the balance of polarization-gradient cooling, and heating due to momentum diffusion, with no significant contribution from Doppler heating. In the molasses, we calculate a damping rate similar to the measured one, and steady-state temperatures that have the same dependence on laser intensity and applied magnetic field as measured experimentally, but are consistently a few times smaller than measured. We attribute the higher temperatures in the experiments to fluctuations of the dipole force which are not captured by our model. We show that the photon scattering rate is strongly influenced by the presence of dark states in the system, but that the scattering rate does not go to zero even for stationary molecules because of the transient nature of the dark states.

Jarvis K, Sauer B, Tarbutt M, 2018, Characteristics of unconventional Rb magneto-optical traps, *Physical Review A*, Vol: 98, ISSN: 1050-2947

We study several new magneto-optical trapping configurations in ⁸⁷Rb. These unconventional MOTs all use type-II transitions, where the angular momentum of the ground state is greater than or equal to that of the excited state. Some use red-detuned light, and others blue-detuned light. The properties of these MOTs are strongly influenced by the balance between opposing Doppler and Sisyphus forces, and vary widely from one configuration to another. In the blue-detuned MOT, Sisyphus cooling dominates over Doppler heating for all relevant speeds and magnetic fields. We measure the capture velocity of this MOT as a function of intensity and detuning, finding a maximum of 3.8 ± 0.1 m/s. Atomic densities are particularly high in the blue-detuned MOT, and its lifetime is limited by collisions between the trapped atoms. We present measurements of the loss rate due to these ultracold collisions as a function of laser intensity and detuning. In the red-detuned MOTs, Sisyphus heating dominates at low speeds and Doppler cooling at higher speeds. Consequently, temperatures in the red-detuned MOTs are up to a thousand times higher than in the blue-detuned MOTs. One MOT forms large ring structures, with no density at the centre, showing how atoms driven towards a non-zero equilibrium speed remain trapped by orbiting around the centre. Another MOT demonstrates that magnetic mixing of the excited-state hyperfine levels can be an important mechanism in type-II MOTs.

Williams HJ, Caldwell L, Fitch NJ,
et al., 2018, Magnetic trapping and coherent control of laser-cooled molecules, *Physical Review Letters*, Vol: 120, ISSN: 0031-9007

We demonstrate coherent microwave control of the rotational, hyperfine and Zeeman states of ultracold CaF molecules, and the magnetic trapping of these molecules in a single, selectable quantum state. We trap about 5 X 10³ molecules for almost 2s at a temperature of 70(8) μK and a density of 1.2 X 10⁵ cm⁻³. We measure the state-specific loss rate due to collisions with background helium.

Lim J, Almond J, Trigatzis M,
et al., 2018, Laser cooled YbF molecules for measuring the electron's electric dipole moment, *Physical Review Letters*, Vol: 120, ISSN: 0031-9007

We demonstrate one-dimensional sub-Doppler laser cooling of a beam of YbF molecules to 100 μK. This is a key step towards a measurement of the electron's electric dipole moment using ultracold molecules. We compare the effectiveness of magnetically-assisted and polarization-gradient sub-Doppler cooling mechanisms. We model the experiment and fi nd good agreement with our data.

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