Reaction interferometry with ultracold molecules.

We propose to coherently control the ultracold 2KRb → K2 + Rb2 reaction product state distribution via quantum interference. By leveraging that the nuclear spin degrees of freedom in the reaction maintain coherence, which was demonstrated in Liu, Zhu et al., arXiv, 2023, arXiv:2310.07620, https://doi.org/10.48550/arXiv.2310.07620, we explore the concept of a "reaction interferometer". Such an interferometer involves splitting one KRb molecular cloud into two, imprinting a well-defined relative phase between them, recombining the clouds for reactions, and measuring the product state distribution. We show that the interference patterns provide a mechanism to coherently control the product states, and specific product channels also serve as an entanglement witness of the atoms in the reactant KRb molecule.

Quantum interference in atom-exchange reactions.

Chemical reactions, in which bonds break and form, are highly dynamic quantum processes. A fundamental question is whether coherence can be preserved in chemical reactions and then harnessed to generate entangled products. Here we investigated this question by studying the 2KRb [Formula: see text][Formula: see text] + Rb2 reaction at 500 nanokelvins, focusing on the nuclear spin degrees of freedom. We prepared the initial nuclear spins in KRb (potassium-rubidium) in an entangled state by lowering the magnetic field to where the spin-spin interaction dominates and characterized the preserved coherence in nuclear spin wave function after the reaction. We observed an interference pattern that is consistent with full coherence at the end of the reaction, suggesting that entanglement prepared within the reactants could be redistributed through the atom-exchange process.

Dipolar spin-exchange and entanglement between molecules in an optical tweezer array.

Ultracold polar molecules are promising candidate qubits for quantum computing and quantum simulations. Their long-lived molecular rotational states form robust qubits, and the long-range dipolar interaction between molecules provides quantum entanglement. In this work, we demonstrate dipolar spin-exchange interactions between single calcium monofluoride (CaF) molecules trapped in an optical tweezer array. We realized the spin-[Formula: see text] quantum XY model by encoding an effective spin-[Formula: see text] system into the rotational states of the molecules and used it to generate a Bell state through an iSWAP operation. Conditioned on the verified existence of molecules in both tweezers at the end of the measurement, we obtained a Bell state fidelity of 0.89(6). Using interleaved tweezer arrays, we demonstrate single-site molecular addressability.

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.

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 µK, 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.

Rotational Coherence Times of Polar Molecules in Optical Tweezers.

Qubit coherence times are critical to the performance of any robust quantum computing platform. For quantum information processing using arrays of polar molecules, a key performance parameter is the molecular rotational coherence time. We report a 93(7) ms coherence time for rotational state qubits of laser cooled CaF molecules in optical tweezer traps, over an order of magnitude longer than previous systems. Inhomogeneous broadening due to the differential polarizability between the qubit states is suppressed by tuning the tweezer polarization and applied magnetic field to a "magic" angle. The coherence time is limited by the residual differential polarizability, implying improvement with further cooling. A single spin-echo pulse is able to extend the coherence time to nearly half a second. The measured coherence times demonstrate the potential of polar molecules as high fidelity qubits.

Observation of microwave shielding of ultracold molecules.

Harnessing the potential wide-ranging quantum science applications of molecules will require control of their interactions. Here, we used microwave radiation to directly engineer and tune the interaction potentials between ultracold calcium monofluoride (CaF) molecules. By merging two optical tweezers, each containing a single molecule, we probed collisions in three dimensions. The correct combination of microwave frequency and power created an effective repulsive shield, which suppressed the inelastic loss rate by a factor of six, in agreement with theoretical calculations. The demonstrated microwave shielding shows a general route to the creation of long-lived, dense samples of ultracold polar molecules and evaporative cooling.

Precision test of statistical dynamics with state-to-state ultracold chemistry.

Chemical reactions represent a class of quantum problems that challenge both the current theoretical understanding and computational capabilities1. Reactions that occur at ultralow temperatures provide an ideal testing ground for quantum chemistry and scattering theories, because they can be experimentally studied with unprecedented control2, yet display dynamics that are highly complex3. Here we report the full product state distribution for the reaction 2KRb → K2 + Rb2. Ultracold preparation of the reactants allows us complete control over their initial quantum degrees of freedom, whereas state-resolved, coincident detection of both products enables the probability of scattering into each of the 57 allowed rotational state-pairs to be measured. Our results show an overall agreement with a state-counting model based on statistical theory4-6, but also reveal several deviating state-pairs. In particular, we observe a strong suppression of population in the state-pair closest to the exoergicity limit as a result of the long-range potential inhibiting the escape of products. The completeness of our measurements provides a benchmark for quantum dynamics calculations beyond the current state of the art.

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.

Nuclear spin conservation enables state-to-state control of ultracold molecular reactions.

Quantum-state control of reactive systems has enabled microscopic probes of underlying interaction potentials and the alteration of reaction rates using quantum statistics. However, extending such control to the quantum states of reaction outcomes remains challenging. Here, we realize this goal by utilizing the conservation of nuclear spins throughout the reaction. Using resonance-enhanced multiphoton ionization spectroscopy to investigate the products formed in bimolecular reactions between ultracold KRb molecules we find that the system retains a near-perfect memory of the reactants' nuclear spins, manifested as a strong parity preference for the rotational states of the products. We leverage this effect to alter the occupation of these product states by changing the coherent superposition of initial nuclear spin states with an external magnetic field. In this way, we are able to control both the inputs and outputs of a reaction with quantum-state resolution. The techniques demonstrated here open up the possibilities to study quantum entanglement between reaction products and ultracold reaction dynamics at the state-to-state level.

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.

Observation of Collisions between Two Ultracold Ground-State CaF Molecules.

We measure inelastic collisions between ultracold CaF molecules by combining two optical tweezers, each containing a single molecule. We observe collisions between ^{2}Σ CaF molecules in the absolute ground state |X,v=0,N=0,F=0⟩, and in excited hyperfine and rotational states. In the absolute ground state, we find a two-body loss rate of 7(4)×10^{-11} cm^{3}/s, which is below, but close to, the predicted universal loss rate.

Forming a Single Molecule by Magnetoassociation in an Optical Tweezer.

We demonstrate the formation of a single NaCs molecule in an optical tweezer by magnetoassociation through an s-wave Feshbach resonance at 864.11(5) G. Starting from single atoms cooled to their motional ground states, we achieve conversion efficiencies of 47(1)%, and measure a molecular lifetime of 4.7(7) ms. By construction, the single molecules are predominantly [77(5)%] in the center-of-mass motional ground state of the tweezer. Furthermore, we produce a single p-wave molecule near 807 G by first preparing one of the atoms with one quantum of motional excitation. Our creation of a single weakly bound molecule in a designated internal state in the motional ground state of an optical tweezer is a crucial step towards coherent control of single molecules in optical tweezer arrays.

Probing ultracold chemistry using ion spectrometry.

Rapid progress in atomic, molecular, and optical (AMO) physics techniques enabled the creation of ultracold samples of molecular species and opened opportunities to explore chemistry in the ultralow temperature regime. In particular, both the external and internal quantum degrees of freedom of the reactant atoms and molecules are controlled, allowing studies that explored the role of the long-range potential in ultracold reactions. The kinetics of these reactions have typically been determined using the loss of reactants as proxies. To extend such studies into the short-range, we developed an experimental apparatus that combines the production of quantum-state-selected ultracold KRb molecules with ion mass and kinetic energy spectrometry, and directly observed KRb + KRb reaction intermediates and products [M.-G. Hu and Y. Liu, et al., Science, 2019, 366, 1111]. Here, we present the apparatus in detail. For future studies that aim for detecting the quantum states of the reaction products, we demonstrate a photodissociation based scheme to calibrate the ion kinetic energy spectrometer at low energies.

An optical tweezer array of ultracold molecules.

Ultracold molecules have important applications that range from quantum simulation and computation to precision measurements probing physics beyond the Standard Model. Optical tweezer arrays of laser-cooled molecules, which allow control of individual particles, offer a platform for realizing this full potential. In this work, we report on creating an optical tweezer array of laser-cooled calcium monofluoride molecules. This platform has also allowed us to observe ground-state collisions of laser-cooled molecules both in the presence and absence of near-resonant light.

Dipolar exchange quantum logic gate with polar molecules.

We propose a two-qubit gate based on dipolar exchange interactions between individually addressable ultracold polar molecules in an array of optical dipole traps. Our proposal treats the full Hamiltonian of the 1Σ+ molecule NaCs, utilizing a pair of nuclear spin states as storage qubits. A third rotationally excited state with rotation-hyperfine coupling enables switchable electric dipolar exchange interactions between two molecules to generate an iSWAP gate. All three states are insensitive to external magnetic and electric fields. Impacts on gate fidelity due to coupling to other molecular states, imperfect ground-state cooling, blackbody radiation and vacuum spontaneous emission are small, leading to potential fidelity above 99.99% in a coherent quantum system that can be scaled by purely optical means.

Elliptical polarization for molecular Stark shift compensation in deep optical traps.

In optical dipole traps, the excited rotational states of a molecule may experience a very different light shift than the ground state. For particles with two polarizability components (parallel and perpendicular), such as linear 1Σ molecules, the differential shift can be nulled by choice of elliptical polarization. When one component of the polarization vector is ±i2 times the orthogonal component, the light shift for a sublevel of excited rotational states ±approaches that of the ground state at high optical intensity. In this case, fluctuating trap intensity need not limit coherence between ground and excited rotational states.

A low-temperature external cavity diode laser for broad wavelength tuning.

We report on the design and characterization of a low-temperature external cavity diode laser (ECDL) system for broad wavelength tuning. The performance achieved with multiple diode models addresses the scarcity of commercial red laser diodes below 633 nm, which is a wavelength range relevant to the spectroscopy of many molecules and ions. Using a combination of multiple-stage thermoelectric cooling and water cooling, the operating temperature of a laser diode is lowered to -64 °C, more than 85 °C below the ambient temperature. The laser system integrates temperature and diffraction grating feedback tunability for coarse and fine wavelength adjustments, respectively. For two different diode models, single-mode operation is achieved with 38 mW output power at 616.8 nm and 69 mW at 622.6 nm, more than 15 nm below their ambient temperature free-running wavelengths. The ECDL design can be used for diodes of any available wavelength, allowing individual diodes to be tuned continuously over tens of nanometers and extending the wavelength coverage of commercial laser diodes.