Controlling the hyperfine state of rovibronic ground-state polar molecules

Two-axis twisting using Floquet-engineered XYZ spin models with polar molecules

Polar molecules confined in an optical lattice are a versatile platform to explore spin-motion dynamics based on strong, long-range dipolar interactions1,2. The precise tunability3 of Ising and spin-exchange interactions with both microwave and d.c. electric fields makes the molecular system particularly suitable for engineering complex many-body dynamics4-6. Here we used Floquet engineering7 to realize new quantum many-body systems of polar molecules. Using a spin encoded in the two lowest rotational states of ultracold 40K87Rb molecules, we mutually validated XXZ spin models tuned by a Floquet microwave pulse sequence against those tuned by a d.c. electric field through observations of Ramsey contrast dynamics. This validation sets the stage for the realization of Hamiltonians inaccessible with static fields. In particular, we observed two-axis twisting8 mean-field dynamics, generated by a Floquet-engineered XYZ model using itinerant molecules in two-dimensional layers. In the future, Floquet-engineered Hamiltonians could generate entangled states for molecule-based precision measurement9 or could take advantage of the rich molecular structure for quantum simulation of multi-level systems10,11.

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 control of field-free molecular orientation

Generating field-free (non-stationary) orientation of molecules in space has been a longstanding goal in the field of quantum control of molecular rotation, which has significant applications in physical chemistry, chemical physics, strong-field physics, and quantum information science. In this Perspective, we review and examine several representative control schemes developed in recent years and implemented in theoretical and experimental areas for generating field-free orientation of molecules. By conducting numerical simulations of different control schemes on the same molecular system, we demonstrate that quantum coherent control, specifically targeting a limited number of the lowest-lying rotational levels to achieve an optimal superposition, can result in a high degree of orientation. To this end, we provide an overview of our latest developed analytical method, which enables the precise design of terahertz field parameters through resonant excitation. This design approach facilitates the attainment of desired field-free orientations by optimizing the amplitudes and phases of rotational wave functions for the selected rotational levels. Finally, we outlook the significance of such progress in multiple frontier research fields, highlighting its potential applications in ultracold physics, quantum computation, quantum simulation, and quantum metrology.

General Classification of Qubit Encodings in Ultracold Diatomic Molecules

Owing to their rich internal structure and significant long-range interactions, ultracold molecules have been widely explored as carriers of quantum information. Several different schemes for encoding qubits into molecular states, both bare and field-dressed, have been proposed. At the same time, the rich internal structure of molecules leaves many unexplored possibilities for qubit encodings. We show that all molecular qubit encodings can be classified into four classes by the type of the effective interaction between the qubits. In the case of polar molecules, the four classes are determined by the relative magnitudes of matrix elements of the dipole moment operator in the single-molecule basis. We exemplify our classification scheme by considering the encoding of the effective spin-1/2 system into nonadjacent rotational states (e.g., N = 0 and 2) of polar and nonpolar molecules with the same nuclear spin projection. Our classification scheme is designed to inform the optimal choice of molecular qubit encoding for quantum information storage and processing applications, as well as for dynamical generation of many-body entangled states and for quantum annealing.

Robust Nuclear Spin Entanglement via Dipolar Interactions in Polar Molecules

We propose a general protocol for on-demand generation of robust entangled states of nuclear and/or electron spins of ultracold ^{1}Σ and ^{2}Σ polar molecules using electric dipolar interactions. By encoding a spin-1/2 degree of freedom in a combined set of spin and rotational molecular levels, we theoretically demonstrate the emergence of effective spin-spin interactions of the Ising and XXZ forms, enabled by efficient magnetic control over electric dipolar interactions. We show how to use these interactions to create long-lived cluster and squeezed spin states.

Observation of Vibrational Dynamics of Orientated Rydberg-Atom-Ion Molecules

Vibrational dynamics in conventional molecules usually takes place on a timescale of picoseconds or shorter. A striking exception are ultralong-range Rydberg molecules, for which dynamics is dramatically slowed down as a consequence of the huge bond length of up to several micrometers. Here, we report on the direct observation of vibrational dynamics of a recently observed Rydberg-atom-ion molecule. By applying a weak external electric field of a few millivolts per centimeter, we are able to control the orientation of the photoassociated ultralong-range Rydberg molecules and induce vibrational dynamics by quenching the electric field. A high resolution ion microscope allows us to detect the molecule's orientation and its temporal vibrational dynamics in real space. Our study opens the door to the control of molecular dynamics in Rydberg molecules.

Dipolar physics: a review of experiments with magnetic quantum gases

Since the achievement of quantum degeneracy in gases of chromium atoms in 2004, the experimental investigation of ultracold gases made of highly magnetic atoms has blossomed. The field has yielded the observation of many unprecedented phenomena, in particular those in which long-range and anisotropic dipole-dipole interactions (DDIs) play a crucial role. In this review, we aim to present the aspects of the magnetic quantum-gas platform that make it unique for exploring ultracold and quantum physics as well as to give a thorough overview of experimental achievements. Highly magnetic atoms distinguish themselves by the fact that their electronic ground-state configuration possesses a large electronic total angular momentum. This results in a large magnetic moment and a rich electronic transition spectrum. Such transitions are useful for cooling, trapping, and manipulating these atoms. The complex atomic structure and large dipolar moments of these atoms also lead to a dense spectrum of resonances in their two-body scattering behaviour. These resonances can be used to control the interatomic interactions and, in particular, the relative importance of contact over dipolar interactions. These features provide exquisite control knobs for exploring the few- and many-body physics of dipolar quantum gases. The study of dipolar effects in magnetic quantum gases has covered various few-body phenomena that are based on elastic and inelastic anisotropic scattering. Various many-body effects have also been demonstrated. These affect both the shape, stability, dynamics, and excitations of fully polarised repulsive Bose or Fermi gases. Beyond the mean-field instability, strong dipolar interactions competing with slightly weaker contact interactions between magnetic bosons yield new quantum-stabilised states, among which are self-bound droplets, droplet assemblies, and supersolids. Dipolar interactions also deeply affect the physics of atomic gases with an internal degree of freedom as these interactions intrinsically couple spin and atomic motion. Finally, long-range dipolar interactions can stabilise strongly correlated excited states of 1D gases and also impact the physics of lattice-confined systems, both at the spin-polarised level (Hubbard models with off-site interactions) and at the spinful level (XYZ models). In the present manuscript, we aim to provide an extensive overview of the various related experimental achievements up to the present.

Realization of Heisenberg models of spin systems with polar molecules in pendular states

Ultra-cold polar diatomic or linear molecules, oriented in an external electric field and mutually coupled by dipole–dipole interactions, can be used to realize the exact Heisenberg XYZ, XXZ and XY models without invoking any approximation.

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.

Full-Dimensional Global Potential Energy Surface for the KRb + KRb → K2Rb2* → K2 + Rb2 Reaction with Accurate Long-Range Interactions and Quantum Statistical Calculation of the Product State Distribution under Ultracold Conditions

A full-dimensional global potential energy surface (PES) for the KRb + KRb → K₂Rb₂* → K₂ + Rb₂ reaction is reported based on high-level ab initio calculations. The short-range part of the PES is fit with the permutationally invariant polynomial-neural network method, while the long-range parts of the PES in both the reactant and product asymptotes are represented by an asymptotically correct form. The long- and short-range parts are connected with intermediate-range parts to make them smooth. Within a statistical quantum model, this PES reproduces both the measured loss rates of ultracold KRb molecules and the K₂ and Rb₂ product state distributions, underscoring the important role of tunneling in ultracold chemistry. The PES also correctly predicts the lifetime of the K₂Rb₂* intermediate complex within the Rice-Ramsperger-Kassel-Marcus limit. It thus provides a reliable platform for future dynamical studies of the prototypical reaction.

Realizing Hopf Insulators in Dipolar Spin Systems

The Hopf insulator is a weak topological insulator characterized by an insulating bulk with conducting edge states protected by an integer-valued linking number invariant. The state exists in three-dimensional two-band models. We demonstrate that the Hopf insulator can be naturally realized in lattices of dipolar-interacting spins, where spin exchange plays the role of particle hopping. The long-ranged, anisotropic nature of the dipole-dipole interactions allows for the precise detail required in the momentum-space structure, while different spin orientations ensure the necessary structure of the complex phases of the hoppings. Our model features robust gapless edge states at both smooth edges, as well as sharp edges obeying a certain crystalline symmetry, despite the breakdown of the two-band picture at the latter. In an accompanying paper [T. Schuster et al., Phys. Rev. A 103, AW11986 (2021)PLRAAN2469-9926] we provide a specific experimental blueprint for implementing our proposal using ultracold polar molecules of ^{40}K^{87}Rb.

Microwave-assisted coherent control of ultracold polar molecules in a ladder-type configuration of rotational states

We demonstrate microwave-assisted coherent control of ultracold 85Rb133Cs molecules in a ladder-type configuration of rotational states. Specifically, we use a probe and a control MW field to address the transitions between the J = 1 → 2 and J = 2 → 3 rotational states of the X1Σ+(v = 0) vibrational level, respectively, and use the control field to modify the response of the probe MW transition by coherently reducing the population of the intermediate J = 2 state. We observe that an increased Rabi frequency of the control field leads to broadening of the probe spectrum splitting and a shift of the central frequency. We apply Akaike's information criterion (AIC) to conclude that the observed coherent spectral response appears across the crossover regime between electromagnetically induced transparency and Aulter-Townes splitting. Our work is a significant development in microwave-assisted quantum control of ultracold polar molecules with multilevel configuration.

Rotational Doppler cooling and heating

Doppler cooling is a widely used technique to laser cool atoms, molecules, and nanoparticles by exploiting the Doppler shift associated with translational motion. The rotational Doppler effect arising from rotational coordinate transformation should similarly enable optical manipulation of the rotational motion of nanosystems. Here, we show that rotational Doppler cooling and heating (RDC and RDH) effects embody rich and unexplored physics, including an unexpected strong dependence on particle morphology. For geometrically constrained particles, cooling and heating are observed at red- or blue-detuned laser frequencies relative to particle resonances. In contrast, for nanosystems that can be modeled as solid particles, RDH appears close to resonant illumination, while detuned frequencies produce cooling of rotation. We further predict that RDH can lead to optomechanical spontaneous chiral symmetry breaking, where an achiral particle under linearly polarized illumination starts spontaneously rotating. Our results open up new exciting possibilities to control the rotational motion of nanosystems.

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.

Collective Dissipative Molecule Formation in a Cavity

We propose a mechanism to realize high-yield molecular formation from ultracold atoms. Atom pairs are continuously excited by a laser, and a collective decay into the molecular ground state is induced by a coupling to a lossy cavity mode. Using a combination of analytical and numerical techniques, we demonstrate that the molecular yield can be improved by simply increasing the number of atoms, and can overcome efficiencies of state-of-the-art association schemes. We discuss realistic experimental setups for diatomic polar and nonpolar molecules, opening up collective light matter interactions as a tool for quantum state engineering, enhanced molecule formation, collective dynamics, and cavity mediated chemistry.

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.

Tune-Out and Magic Wavelengths for Ground-State ^{23}Na^{40}K Molecules

We demonstrate a versatile, state-dependent trapping scheme for the ground and first excited rotational states of ^{23}Na^{40}K molecules. Close to the rotational manifold of a narrow electronic transition, we determine tune-out frequencies where the polarizability of one state vanishes while the other remains finite, and a magic frequency where both states experience equal polarizability. The proximity of these frequencies of only 10 GHz allows for dynamic switching between different trap configurations in a single experiment, while still maintaining sufficiently low scattering rates.

Microwave coherent control of ultracold ground-state molecules formed by short-range photoassociation

We report the observation of microwave coherent control of rotational states of ultracold ⁸⁵Rb¹³³Cs molecules formed in their vibronic ground state by short-range photoassociation. Molecules are formed in the single rotational state X(v = 0, J = 1) by exciting pairs of atoms to the short-range state (2)³Π_0^-(v = 11, J = 0), followed by spontaneous decay. We use depletion spectroscopy to record the dynamic evolution of the population distribution and observe clear Rabi oscillations while irradiating on a microwave transition between coupled neighbouring rotational levels. A density-matrix formalism that accounts for longitudinal and transverse decay times reproduces both the dynamic evolution during the coherent process and the equilibrium population. The coherent control reported here is valuable both for investigating coherent quantum effects and for applications of cold polar molecules produced by continuous short-range photoassociation.

Photoinduced Two-Body Loss of Ultracold Molecules

The lifetime of nonreactive ultracold bialkali gases was conjectured to be limited by sticky collisions amplifying three-body loss. We show that the sticking times were previously overestimated and do not support this hypothesis. We find that electronic excitation of NaK+NaK collision complexes by the trapping laser leads to the experimentally observed two-body loss. We calculate the excitation rate with a quasiclassical, statistical model employing ab initio potentials and transition dipole moments. Using longer laser wavelengths or repulsive box potentials may suppress the losses.

Observation of Interference between Resonant and Detuned stirap in the Adiabatic Creation of ^{23}Na^{40}K Molecules

Stimulated Raman adiabatic passage (stirap) allows efficiently transferring the populations between two discrete quantum states and has been used to prepare molecules in their rovibrational ground state. In realistic molecules, a well-resolved intermediate state is usually selected to implement the resonant stirap. Because of the complex molecular level structures, the detuned stirap always coexists with the resonant stirap and may cause unexpected interference phenomenon. However, it is generally accepted that the detuned stirap can be neglected if compared with the resonant stirap. Here we report on the first observation of interference between the resonant and detuned stirap in the adiabatic creation of ^{23}Na^{40}K ground-state molecules. The interference is identified by observing that the number of Feshbach molecules after a round-trip stirap oscillates as a function of the hold time, with a visibility of about 90%. This occurs even if the intermediate excited states are well resolved, and the single-photon detuning of the detuned stirap is about 1 order of magnitude larger than the linewidth of the excited state and the Rabi frequencies of the stirap lasers. Moreover, the observed interference indicates that if more than one hyperfine level of the ground state is populated, the stirap prepares a coherent superposition state among them, but not an incoherent mixed state. Further, the purity of the hyperfine levels of the created ground state can be quantitatively determined by the visibility of the oscillation.

Extending Rotational Coherence of Interacting Polar Molecules in a Spin-Decoupled Magic Trap

Superpositions of rotational states in polar molecules induce strong, long-range dipolar interactions. Here we extend the rotational coherence by nearly 1 order of magnitude to 8.7(6) ms in a dilute gas of polar ^{23}Na^{40}K molecules in an optical trap. We demonstrate spin-decoupled magic trapping, which cancels first-order and reduces second-order differential light shifts. The latter is achieved with a dc electric field that decouples nuclear spin, rotation, and trapping light field. We observe density-dependent coherence times, which can be explained by dipolar interactions in the bulk gas.

Signature of the s-Wave Regime High above Ultralow Temperatures

Resonant exchange is a general process playing a key role in many-body dynamics and transport phenomena, such as spin, charge, or excitation diffusion. The underlying process is described by the resonant exchange cross section. We show that the s-wave scattering, generally thought to contribute mainly in the ultracold (or Wigner) regime, dictates the overall cross section over a broad range of energies. We derive an analytical expression and explain its applicability high above the Wigner regime. In particular, we demonstrate its relationship to the classical capture (Langevin) cross section and apply it to three very different resonant processes: namely, resonant charge transfer, spin flip, and excitation exchange. This expression explains large variations for different isotopes that cannot otherwise be accounted for by the small change in mass. The s-wave signature also allows us to gain information about the Wigner regime from data obtained at much higher temperatures, which is especially advantageous for systems where the ultracold regime is not reachable.

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.

A dynamical process of optically trapped singlet ground state 85Rb133Cs molecules produced via short-range photoassociation

We investigate the dynamical process of optically trapped X¹Σ⁺ (v'' = 0) state ⁸⁵Rb¹³³Cs molecules distributed in J'' = 1 and J'' = 3 rotational states. The considered molecules, formed from short-range photoassociation of mixed cold atoms, are subsequently confined in a crossed optical dipole trap. Based on a phenomenological rate equation, we provide a detailed study of the dynamics of ⁸⁵Rb¹³³Cs molecules during the loading and holding processes. The inelastic collisions of ⁸⁵Rb¹³³Cs molecules in the X¹Σ⁺ (v'' = 0, J'' = 1 and J'' = 3) states with ultracold ⁸⁵Rb (or ¹³³Cs) atoms are measured to be 1.0 (2) × 10^-10 cm³ s^-1 (1.2 (3) × 10^-10 cm³ s^-1). Our work provides a simple and generic procedure for studying the dynamical process of trapped cold molecules in the singlet ground states.

Communication: General variational approach to nuclear-quadrupole coupling in rovibrational spectra of polyatomic molecules

A general algorithm for computing the quadrupole-hyperfine effects in the rovibrational spectra of polyatomic molecules is presented for the case of ammonia (NH₃). The method extends the general variational approach TROVE [J. Mol. Spectrosc. 245, 126-140 (2007)] by adding the extra term in the Hamiltonian that describes the nuclear quadrupole coupling, with no inherent limitation on the number of quadrupolar nuclei in a molecule. We applied the new approach to compute the nitrogen-nuclear-quadrupole hyperfine structure in the rovibrational spectrum of NH314. These results agree very well with recent experimental spectroscopic data for the pure rotational transitions in the ground vibrational and ν₂ states and the rovibrational transitions in the ν₁, ν₃, 2ν₄, and ν₁ + ν₃ bands. The computed hyperfine-resolved rovibrational spectrum of ammonia will be beneficial for the assignment of experimental rovibrational spectra, further detection of ammonia in interstellar space, and studies of the proton-to-electron mass variation.

Long-Lived Ultracold Molecules with Electric and Magnetic Dipole Moments

We create fermionic dipolar ^{23}Na^{6}Li molecules in their triplet ground state from an ultracold mixture of ^{23}Na and ^{6}Li. Using magnetoassociation across a narrow Feshbach resonance followed by a two-photon stimulated Raman adiabatic passage to the triplet ground state, we produce 3×10^{4} ground state molecules in a spin-polarized state. We observe a lifetime of 4.6 s in an isolated molecular sample, approaching the p-wave universal rate limit. Electron spin resonance spectroscopy of the triplet state was used to determine the hyperfine structure of this previously unobserved molecular state.

Cold molecules: Progress in quantum engineering of chemistry and quantum matter

Cooling atoms to ultralow temperatures has produced a wealth of opportunities in fundamental physics, precision metrology, and quantum science. The more recent application of sophisticated cooling techniques to molecules, which has been more challenging to implement owing to the complexity of molecular structures, has now opened the door to the longstanding goal of precisely controlling molecular internal and external degrees of freedom and the resulting interaction processes. This line of research can leverage fundamental insights into how molecules interact and evolve to enable the control of reaction chemistry and the design and realization of a range of advanced quantum materials.

Coherent Microwave Control of Ultracold ^{23}Na^{40}K Molecules

We demonstrate coherent microwave control of rotational and hyperfine states of trapped, ultracold, and chemically stable ^{23}Na^{40}K molecules. Starting with all molecules in the absolute rovibrational and hyperfine ground state, we study rotational transitions in combined magnetic and electric fields and explain the rich hyperfine structure. Following the transfer of the entire molecular ensemble into a single hyperfine level of the first rotationally excited state, J=1, we observe lifetimes of more than 3 s, comparable to those in the rovibrational ground state, J=0. Long-lived ensembles and full quantum state control are prerequisites for the use of ultracold molecules in quantum simulation, precision measurements, and quantum information processing.

Ultracold Nonreactive Molecules in an Optical Lattice: Connecting Chemistry to Many-Body Physics

We derive effective lattice models for ultracold bosonic or fermionic nonreactive molecules (NRMs) in an optical lattice, analogous to the Hubbard model that describes ultracold atoms in a lattice. In stark contrast to the Hubbard model, which is commonly assumed to accurately describe NRMs, we find that the single on-site interaction parameter U is replaced by a multichannel interaction, whose properties we elucidate. Because this arises from complex short-range collisional physics, it requires no dipolar interactions and thus occurs even in the absence of an electric field or for homonuclear molecules. We find a crossover between coherent few-channel models and fully incoherent single-channel models as the lattice depth is increased. We show that the effective model parameters can be determined in lattice modulation experiments, which, consequently, measure molecular collision dynamics with a vastly sharper energy resolution than experiments in a free-space ultracold gas.

Long-range interactions between polar bialkali ground-state molecules in arbitrary vibrational levels

We have calculated the isotropic C6 coefficients characterizing the long-range van der Waals interaction between two identical heteronuclear alkali-metal diatomic molecules in the same arbitrary vibrational level of their ground electronic state X(1)Σ(+). We consider the ten species made up of (7)Li, (23)Na, (39)K, (87)Rb, and (133)Cs. Following our previous work [Lepers et al., Phys. Rev. A 88, 032709 (2013)], we use the sum-over-state formula inherent to the second-order perturbation theory, composed of the contributions from the transitions within the ground state levels, from the transition between ground-state and excited state levels, and from a crossed term. These calculations involve a combination of experimental and quantum-chemical data for potential energy curves and transition dipole moments. We also investigate the case where the two molecules are in different vibrational levels and we show that the Moelwyn-Hughes approximation is valid provided that it is applied for each of the three contributions to the sum-over-state formula. Our results are particularly relevant in the context of inelastic and reactive collisions between ultracold bialkali molecules in deeply bound or in Feshbach levels.

Ultracold Dipolar Gas of Fermionic 23Na40 K Molecules in Their Absolute Ground State

We report on the creation of an ultracold dipolar gas of fermionic 23Na40 K molecules in their absolute rovibrational and hyperfine ground state. Starting from weakly bound Feshbach molecules, we demonstrate hyperfine resolved two-photon transfer into the singlet X 1Σ+|v=0,J=0⟩ ground state, coherently bridging a binding energy difference of 0.65 eV via stimulated rapid adiabatic passage. The spin-polarized, nearly quantum degenerate molecular gas displays a lifetime longer than 2.5 s, highlighting NaK's stability against two-body chemical reactions. A homogeneous electric field is applied to induce a dipole moment of up to 0.8 D. With these advances, the exploration of many-body physics with strongly dipolar Fermi gases of 23Na40K molecules is within experimental reach.

Ultracold dense samples of dipolar RbCs molecules in the rovibrational and hyperfine ground state

We produce ultracold dense trapped samples of ^{87}Rb^{133}Cs molecules in their rovibrational ground state, with full nuclear hyperfine state control, by stimulated Raman adiabatic passage (STIRAP) with efficiencies of 90%. We observe the onset of hyperfine-changing collisions when the magnetic field is ramped so that the molecules are no longer in the hyperfine ground state. A strong quadratic shift of the transition frequencies as a function of applied electric field shows the strongly dipolar character of the RbCs ground-state molecule. Our results open up the prospect of realizing stable bosonic dipolar quantum gases with ultracold molecules.

Many-body dynamics of dipolar molecules in an optical lattice

We use Ramsey spectroscopy to experimentally probe the quantum dynamics of disordered dipolar-interacting ultracold molecules in a partially filled optical lattice, and we compare the results to theory. We report the capability to control the dipolar interaction strength. We find excellent agreement between our measurements of the spin dynamics and theoretical calculations with no fitting parameters, including the dynamics' dependence on molecule number and on the dipolar interaction strength. This agreement verifies the microscopic model expected to govern the dynamics of dipolar molecules, even in this strongly correlated beyond-mean-field regime, and represents the first step towards using this system to explore many-body dynamics in regimes that are inaccessible to current theoretical techniques.

Role of quantum fluctuations in the hexatic phase of cold polar molecules

Two-dimensional crystals melt via an intermediate hexatic phase, which is characterized by an anomalous scaling of spatial and orientational correlation functions and the absence of an attraction between dislocations. We propose a protocol to study the effect of quantum fluctuations on the nature of this phase with a model system of strongly correlated ultracold polar molecules. Dislocations can be located in experiment from local energy differences which induce internal stark shifts in the molecules. We present a criterion to identify the hexatic phase from the statistics of the end points of topological defect strings and find a hexatic phase, which is dominated by quantum fluctuations, between the crystal and superfluid phases.

Fourier-transform spectroscopy of (4)1Σ+ → A1Σ+ - b3Π, A1Σ+ - b3Π → X1Σ+, and (1)3Δ1→b3Π(0±) transitions in KCs and deperturbation treatment of A1Σ+ and b3Π states

High resolution Fourier-transform spectroscopy data of term values in the spin-orbit (SO) coupled first excited A(1)Σ(+) and b(3)Π states in KCs were obtained from (4)(1)Σ(+) → A(1)Σ(+) - b(3)Π, A(1)Σ(+) - b(3)Π → X(1)Σ(+), and (1)(3)Δ1→b(3)Π(0(±)) spectra of laser-induced fluorescence (LIF). About 3000 new rovibronic term values of the A(1)Σ(+) and b(3)Π(Ω) states were obtained with an uncertainty about 0.01 cm(-1) and added to the previously obtained 3439 term values in Kruzins et al. [Phys. Rev. A 81, 042509 (2010)] and 30 term values of the b(3)Π(0(+)) state levels below the A(1)Σ(+) state in Tamanis et al. [Phys. Rev. A 82, 032506 (2010)]. The data field was extended considerably, going down to vibrational level v(b) = 0 and up in energy to 13,814 cm(-1), as compared to previously achieved v(b) = 14 and E = 13,250 cm(-1). Overall 6431 e-symmetry term values of (39)K(133)Cs were included in 4 × 4 coupled-channel deperturbation analysis. The analytical Morse-Long-Range (MLR) function yielded empirical diabatic potentials for the A(1)Σ(+) and b(3)Π(0(+)) states while the morphing of the SO ab initio points [J. T. Kim et al., J. Mol. Spectrosc. 256, 57 (2009)] provided the empirical diagonal and off-diagonal SO functions. Overall 98.5% of the fitted term values were reproduced with a rms (root mean square) uncertainty of 0.004 cm(-1). The reliability of the model is proved by a good agreement of predicted and measured term values of the (41)K(133)Cs isotopologue, as well as of measured and calculated intensities of (4)(1)Σ(+) → A(1)Σ(+) - b(3)Π LIF progressions. Direct-potential-fit of low-lying v(b) levels of the b(3)Π(0(-)) component yielded the MLR potential which represents the 204 f-symmetry experimental term values with a rms uncertainty of 0.002 cm(-1). The Ω-doubling of the b(3)Π0 sub-state demonstrates a pronounced vb-dependent increase.

Spectroscopy and applications of the 3 3Σ+ electronic state of 39K85Rb

We report new results on the spectroscopy of the 3 (3)Σ(+) electronic state of (39)K(85)Rb. The observations are based on resonance-enhanced multiphoton ionization of ultracold KRb molecules starting in vibrational levels v'' = 18-23 of the a (3)Σ(+) state and ionized via the intermediate 3 (3)Σ(+) state. The a-state ultracold molecules are formed by photoassociation of ultracold (39)K and (85)Rb atoms to the 3(0(+)) state of KRb followed by spontaneous emission. We discuss the potential applications of this state to future experiments, as a pathway for populating the lowest vibrational levels of the a state as well as the X state.

From classical to quantum glasses with ultracold polar molecules

We study the dynamics of a bilayer system of ultracold polar molecules, which exhibits classical and quantum glassy behavior, characterized by long tails in the relaxation time and dynamical heterogeneity. In the proposed setup, quantum fluctuations are of the order of thermal fluctuations and the degree of frustration can be tuned by the interlayer distance. We discuss the possible observation of a glassy anomalous diffusion and dynamical heterogeneity in experiment using internal degrees of freedom of the molecules in combination with optical detection.

Dipolar confinement-induced resonances of ultracold gases in waveguides

We develop a nonperturbative theoretical framework to treat collisions with generic anisotropic interactions in quasi-one-dimensional geometries. Our method avoids the limitations of pseudopotential theory and allows us to include accurately long-range anisotropic interactions. For ultracold dipolar collisions in a harmonic waveguide we predict dipolar confinement-induced resonances (DCIRs) which are attributed to different angular momentum states. The analytically derived resonance condition reveals in detail the interplay of the confinement with the anisotropic nature of the dipole-dipole interactions. The results are in excellent agreement with ab initio numerical calculations confirming the robustness of the presented approach. The exact knowledge of the positions of DCIRs may pave the way for the experimental realization of, e.g., Tonks-Girardeau-like or super-Tonks-Girardeau-like phases in effective one-dimensional dipolar gases.

Quantum gates in hyperfine levels of ultracold alkali dimers by revisiting constrained-phase optimal control design

We simulate the implementation of a 3-qubit quantum Fourier transform gate in the hyperfine levels of ultracold polar alkali dimers in their first two lowest rotational levels. The chosen dimer is (41)K(87)Rb supposed to be trapped in an optical lattice. The hyperfine levels are split by a static magnetic field. The pulses operating in the microwave domain are obtained by optimal control theory. We revisit the problem of phase control in information processing. We compare the efficiency of two optimal fields. The first one is obtained from a functional based on the average of the transition probabilities for each computational basis state but constrained by a supplementary transformation to enforce phase alignment. The second is obtained from a functional constructed on the phase sensitive fidelity involving the sum of the transition amplitudes without any supplementary constrain.