Forming a Single Molecule by Magnetoassociation in an Optical Tweezer

Entanglement and iSWAP gate between molecular qubits

Quantum computation and simulation rely on long-lived qubits with controllable interactions. Trapped polar molecules have been proposed as a promising quantum computing platform, offering scalability and single-particle addressability while still leveraging inherent complexity and strong couplings of molecules1-5. Recent progress in the single quantum state preparation and coherence of the hyperfine-rotational states of individually trapped molecules allows them to serve as promising qubits6-11, with intermolecular dipolar interactions creating entanglement12,13. However, universal two-qubit gates have not been demonstrated with molecules. Here we harness intrinsic molecular resources to implement a two-qubit iSWAP gate using individually trapped X1Σ+ NaCs molecules. By allowing the molecules to interact for 664 μs at a distance of 1.9 μm, we create a maximally entangled Bell state with a fidelity of 94(3)% in trials in which both molecules are present. Using motion-rotation coupling, we measure residual excitation of the lowest few motional states along the axial trapping direction and find them to be the primary source of decoherence. Finally, we identify two non-interacting hyperfine states within the ground rotational level in which we encode a qubit. The interaction is toggled by transferring between interacting and non-interacting states to realize an iSWAP gate. We verify the gate performance by measuring its logical truth table.

Magnetically Tunable Electric Dipolar Interactions of Ultracold Polar Molecules in the Quantum Ergodic Regime

By leveraging the hyperfine interaction between the rotational and nuclear spin degrees of freedom, we demonstrate extensive magnetic control over the electric dipole moments, electric dipolar interactions, and ac Stark shifts of ground-state alkali-dimer molecules such as KRb(X^{1}Σ^{+}). The control is enabled by narrow avoided crossings and the highly ergodic character of molecular eigenstates at low magnetic fields, offering a general and robust way of continuously tuning the intermolecular electric dipolar interaction for applications in quantum simulation, quantum sensing, and dipolar spinor physics.

Extended Rotational Coherence of Polar Molecules in an Elliptically Polarized Trap

We demonstrate long rotational coherence of individual polar molecules in the motional ground state of an optical trap. In the present, previously unexplored regime, the rotational eigenstates of molecules are dominantly quantized by trapping light rather than static fields, and the main source of decoherence is differential light shift. In an optical tweezer array of NaCs molecules, we achieve a three-orders-of-magnitude reduction in differential light shift by changing the trap's polarization from linear to a specific "magic" ellipticity. With spin-echo pulses, we measure a rotational coherence time of 62(3) ms (one pulse) and 250(40) ms (up to 72 pulses), surpassing the projected duration of resonant dipole-dipole entangling gates by orders of magnitude.

Imaging a ^{6}Li Atom in an Optical Tweezer 2000 Times with Λ-Enhanced Gray Molasses

We have imaged lithium-6 thousands of times in an optical tweezer using Λ-enhanced gray molasses cooling light. Despite being the lightest alkali metal, with a recoil temperature of 3.5  μK, we achieve an imaging survival of 0.999 50(2), which sets the new benchmark for low-loss imaging of neutral atoms in optical tweezers. Lithium is loaded directly from a magneto-optical trap into a tweezer with an enhanced loading rate of 0.7. We cool the atom to 70  μK and present a new cooling model that accurately predicts steady-state temperature and scattering rate in the tweezer. These results pave the way for ground state preparation of lithium en route to the assembly of the LiCs molecule in its ground state.

Bichromatic Imaging of Single Molecules in an Optical Tweezer Array

We report on a novel bichromatic fluorescent imaging scheme for background-free detection of single CaF molecules trapped in an optical tweezer array. By collecting fluorescence on one optical transition while using another for laser cooling, we achieve an imaging fidelity of 97.7(2)% and a nondestructive detection fidelity of 95.5(6)%. Notably, these fidelities are achieved with a modest photon budget, suggesting that the method could be extended to more complex laser-coolable molecules with less favorable optical cycling properties. We also report on a framework and new methods to characterize various loss mechanisms that occur generally during fluorescent detection of trapped molecules, including two-photon decay and admixtures of higher excited states that are induced by the trapping light. In particular, we develop a novel method to dispersively measure transition matrix elements between electronically excited states. The method could also be used to measure arbitrarily small Franck-Condon factors between electronically excited states, which could significantly aid in ongoing efforts to laser cool complex polyatomic molecules.

Observation of Rydberg Blockade Due to the Charge-Dipole Interaction between an Atom and a Polar Molecule

We demonstrate Rydberg blockade due to the charge-dipole interaction between a single Rb atom and a single RbCs molecule confined in optical tweezers. The molecule is formed by magnetoassociation of a Rb+Cs atom pair and subsequently transferred to the rovibrational ground state with an efficiency of 91(1)%. Species-specific tweezers are used to control the separation between the atom and molecule. The charge-dipole interaction causes blockade of the transition to the Rb(52s) Rydberg state, when the atom-molecule separation is set to 310(40) nm. The observed excitation dynamics are in good agreement with simulations using calculated interaction potentials. Our results open up the prospect of a hybrid platform where quantum information is transferred between individually trapped molecules using Rydberg atoms.

Formation of Ultracold Molecules by Merging Optical Tweezers

We demonstrate the formation of a single RbCs molecule during the merging of two optical tweezers, one containing a single Rb atom and the other a single Cs atom. Both atoms are initially predominantly in the motional ground states of their respective tweezers. We confirm molecule formation and establish the state of the molecule formed by measuring its binding energy. We find that the probability of molecule formation can be controlled by tuning the confinement of the traps during the merging process, in good agreement with coupled-channel calculations. We show that the conversion efficiency from atoms to molecules using this technique is comparable to magnetoassociation.

Ultracold Gas of Dipolar NaCs Ground State Molecules

We report on the creation of bosonic NaCs molecules in their absolute rovibrational ground state via stimulated Raman adiabatic passage. We create ultracold gases with up to 22 000 dipolar NaCs molecules at a temperature of 300(50) nK and a peak density of 1.0(4)×10^{12}  cm^{-3}. We demonstrate comprehensive quantum state control by preparing the molecules in a specific electronic, vibrational, rotational, and hyperfine state. We measure the ground state ac polarizability at 1064 nm along with the two-body loss rate, which we find to be universal. Employing the tunability and strength of the permanent electric dipole moment of NaCs, we induce dipole moments of up to 2.6 D at a dc electric field of 2.1(2)  kV/cm and demonstrate strong microwave coupling between the two lowest rotational states with a Rabi frequency of 2π×45  MHz. A large electric dipole moment, accessible at relatively small electric fields, makes ultracold gases of NaCs molecules well suited for the exploration of strongly interacting phases of dipolar quantum matter.

Interaction Potential for NaCs for Ultracold Scattering and Spectroscopy

We obtain the interaction potential for NaCs by fitting to experiments on ultracold scattering and spectroscopy in optical tweezers. The central region of the potential has been accurately determined from Fourier transform spectroscopy at higher temperatures, so we focus on adjusting the long-range and short-range parts. We use coupled-channel calculations of binding energies and wave functions to understand the nature of the molecular states observed in ultracold spectroscopy and of the state that causes the Feshbach resonance used to create ultracold NaCs molecules. We elucidate the relationships between the experimental quantities and features of the interaction potential. We establish the combinations of experimental quantities that determine particular features of the potential. We find that the long-range dispersion coefficient C₆ must be increased by about 0.9% to 3256(1)E_ha₀⁶ to fit the experimental results. We use coupled-channel calculations on the final potential to predict bound-state energies and resonance positions.

Defect-Free Arbitrary-Geometry Assembly of Mixed-Species Atom Arrays

Optically trapped mixed-species single atom arrays with arbitrary geometry are an attractive and promising platform for various applications, because tunable quantum systems with multiple components provide extra degrees of freedom for experimental control. Here, we report the first demonstration of two-dimensional 6×4 dual-species atom assembly of ^{85}Rb (^{87}Rb) atoms with a filling fraction of 0.88 (0.89). This mixed-species atomic synthesis is achieved via rearranging initially randomly distributed atoms by a sorting algorithm (heuristic heteronuclear algorithm) which is designed for bottom-up atom assembly with both user-defined geometries and two-species atom number ratios. Our fully tunable hybrid-atom systems with scalable advantages are a good starting point for high-fidelity quantum logic, many-body quantum simulation, and single molecule array formation.

Bimolecular Chemistry in the Ultracold Regime

Advances in atomic, molecular, and optical physics techniques allowed the cooling of simple molecules down to the ultracold regime ([Formula: see text]1 mK) and opened opportunities to study chemical reactions with unprecedented levels of control. This review covers recent developments in studying bimolecular chemistry at ultralow temperatures. We begin with a brief overview of methods for producing, manipulating, and detecting ultracold molecules. We then survey experimental works that exploit the controllability of ultracold molecules to probe and modify their long-range interactions. Further combining the use of physical chemistry techniques such as mass spectrometry and ion imaging significantly improved the detection of ultracold reactions and enabled explorations of their dynamics in the short range. We discuss a series of studies on the reaction KRb + KRb → K₂ + Rb₂ initiated below 1 [Formula: see text]K, including the direct observation of a long-lived complex, the demonstration of product rotational state control via conserved nuclear spins, and a test of the statistical model using the complete quantum state distribution of the products. Expected final online publication date for the Annual Review of Physical Chemistry, Volume 73 is April 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Assembly of a Rovibrational Ground State Molecule in an Optical Tweezer

We demonstrate the coherent creation of a single NaCs molecule in its rotational, vibrational, and electronic (rovibronic) ground state in an optical tweezer. Starting with a weakly bound Feshbach molecule, we locate a two-photon transition via the |c^{3}Σ_{1},v^{'}=26⟩ excited state and drive coherent Rabi oscillations between the Feshbach state and a single hyperfine level of the NaCs rovibronic ground state |X^{1}Σ,v^{''}=0,N^{''}=0⟩ with a binding energy of D_{0}=h×147044.63(11)  GHz. We measure a lifetime of 3.4±1.6  s for the rovibronic ground state molecule, which possesses a large molecule-frame dipole moment of 4.6D and occupies predominantly the motional ground state. These long-lived, fully quantum-state-controlled individual dipolar molecules provide a key resource for molecule-based quantum simulation and information processing.

Pair Correlations and Photoassociation Dynamics of Two Atoms in an Optical Tweezer

We investigate the photoassociation dynamics of exactly two laser-cooled ^{85}Rb atoms in an optical tweezer and reveal fundamentally different behavior to photoassociation in many-atom ensembles. We observe nonexponential decay in our two-atom experiment that cannot be described by a single rate coefficient and find its origin in our system's pair correlation. This is in stark contrast to many-atom photoassociation dynamics, which are governed by decay with a single rate coefficient. We also investigate photoassociation in a three-atom system, thereby probing the transition from two-atom dynamics to many-atom dynamics. Our experiments reveal additional reaction dynamics that are only accessible through the control of single atoms and suggest photoassociation could measure pair correlations in few-atom systems. It further showcases our complete control over the quantum state of individual atoms and molecules, which provides information unobtainable from many-atom experiments.

Enhancing Dipolar Interactions between Molecules Using State-Dependent Optical Tweezer Traps

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 the dipole-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.

Reduction of laser intensity noise over 1 MHz band for single atom trapping

We reduce the intensity noise of laser light by using an electro-optic modulator and acousto-optic modulator in series. The electro-optic modulator reduces noise at high frequency (10 kHz to 1 MHz), while the acousto-optic modulator sets the average power of the light and reduces noise at low frequency (up to 10 kHz). The light is then used to trap single sodium atoms in an optical tweezer, where the lifetime of the atoms is limited by parametric heating due to laser noise at twice the trapping frequency. With our noise eater, the noise is reduced by up to 15 dB at these frequencies and the lifetime of the atom in the optical tweezer is increased by an order of magnitude to around 6 seconds. Our technique is general and acts directly on the laser beam, expanding laser options for sensitive optical trapping applications.

Nondestructive dispersive imaging of rotationally excited ultracold molecules

A barrier to realizing the potential of molecules for quantum information science applications is a lack of high-fidelity, single-molecule imaging techniques. Here, we present and theoretically analyze a general scheme for dispersive imaging of electronic ground-state molecules. Our technique relies on the intrinsic anisotropy of excited molecular rotational states to generate optical birefringence, which can be detected through polarization rotation of an off-resonant probe laser beam. Using 23Na87Rb and 87Rb133Cs as examples, we construct a formalism for choosing the molecular state to be imaged and the excited electronic states involved in off-resonant coupling. Our proposal establishes the relevant parameters for achieving degree-level polarization rotations for bulk molecular gases, thus enabling high-fidelity nondestructive imaging. We additionally outline requirements for the high-fidelity imaging of individually trapped molecules.