Entanglement of polar symmetric top molecules as candidate qubits

An optical tweezer array of ultracold polyatomic molecules

Polyatomic molecules have rich structural features that make them uniquely suited to applications in quantum information science1-3, quantum simulation4-6, ultracold chemistry7 and searches for physics beyond the standard model8-10. However, a key challenge is fully controlling both the internal quantum state and the motional degrees of freedom of the molecules. Here we demonstrate the creation of an optical tweezer array of individual polyatomic molecules, CaOH, with quantum control of their internal quantum state. The complex quantum structure of CaOH results in a non-trivial dependence of the molecules' behaviour on the tweezer light wavelength. We control this interaction and directly and non-destructively image individual molecules in the tweezer array with a fidelity greater than 90%. The molecules are manipulated at the single internal quantum state level, thus demonstrating coherent state control in a tweezer array. The platform demonstrated here will enable a variety of experiments using individual polyatomic molecules with arbitrary spatial arrangement.

Quantum control of trapped polyatomic molecules for eEDM searches

Ultracold polyatomic molecules are promising candidates for experiments in quantum science and precision searches for physics beyond the Standard Model. A key requirement is the ability to achieve full quantum control over the internal structure of the molecules. In this work, we established coherent control of individual quantum states in calcium monohydroxide (CaOH) and demonstrated a method for searching for the electron electric dipole moment (eEDM). Optically trapped, ultracold CaOH molecules were prepared in a single quantum state, polarized in an electric field, and coherently transferred into an eEDM-sensitive state where an electron spin precession measurement was performed. To extend the coherence time, we used eEDM-sensitive states with tunable, near-zero magnetic field sensitivity. Our results establish a path for eEDM searches with trapped polyatomic molecules.

Intensity-Borrowing Mechanisms Pertinent to Laser Cooling of Linear Polyatomic Molecules

A study of the intensity-borrowing mechanisms important to optical cycling transitions in laser-coolable polyatomic molecules arising from non-adiabatic coupling, contributions beyond the Franck-Condon approximation, and Fermi resonances is reported. It has been shown to be necessary to include non-adiabatic coupling to obtain computational accuracy that is sufficient to be useful for laser cooling of molecules. The predicted vibronic branching ratios using perturbation theory based on the non-adiabatic mechanisms have been demonstrated to agree well with those obtained from variational discrete variable representation calculations for representative molecules including CaOH, SrOH, and YbOH. The electron-correlation and basis-set effects on the calculated transition properties, including the vibronic coupling constants, the spin-orbit coupling matrix elements, and the transition dipole moments, and on the calculated branching ratios have been thoroughly studied. The vibronic branching ratios predicted using the present methodologies demonstrate that RaOH is a promising radioactive molecule candidate for laser cooling.

Optical Trapping of a Polyatomic Molecule in an ℓ-Type Parity Doublet State

We report optical trapping of a polyatomic molecule, calcium monohydroxide (CaOH). CaOH molecules from a magneto-optical trap are sub-Doppler laser cooled to 20(3)  μK in free space and loaded into an optical dipole trap. We attain an in-trap molecule number density of 3(1)×10^{9}  cm^{-3} at a temperature of 57(8)  μK. Trapped CaOH molecules are optically pumped into an excited vibrational bending mode, whose ℓ-type parity doublet structure is a potential resource for a wide range of proposed quantum science applications with polyatomic molecules. We measure the spontaneous, radiative lifetime of this bending mode state to be ∼0.7  s.

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.

Quantum machine learning for chemistry and physics

Machine learning (ML) has emerged as a formidable force for identifying hidden but pertinent patterns within a given data set with the objective of subsequent generation of automated predictive behavior. In recent years, it is safe to conclude that ML and its close cousin, deep learning (DL), have ushered in unprecedented developments in all areas of physical sciences, especially chemistry. Not only classical variants of ML, even those trainable on near-term quantum hardwares have been developed with promising outcomes. Such algorithms have revolutionized materials design and performance of photovoltaics, electronic structure calculations of ground and excited states of correlated matter, computation of force-fields and potential energy surfaces informing chemical reaction dynamics, reactivity inspired rational strategies of drug designing and even classification of phases of matter with accurate identification of emergent criticality. In this review we shall explicate a subset of such topics and delineate the contributions made by both classical and quantum computing enhanced machine learning algorithms over the past few years. We shall not only present a brief overview of the well-known techniques but also highlight their learning strategies using statistical physical insight. The objective of the review is not only to foster exposition of the aforesaid techniques but also to empower and promote cross-pollination among future research in all areas of chemistry which can benefit from ML and in turn can potentially accelerate the growth of such algorithms.

Electric-Field-Controlled Cold Dipolar Collisions between Trapped CH_{3}F Molecules

Reaching high densities is a key step toward cold-collision experiments with polyatomic molecules. We use a cryofuge to load up to 2×10^{7} CH_{3}F molecules into a boxlike electric trap, achieving densities up to 10^{7}/cm^{3} at temperatures around 350 mK where the elastic dipolar cross section exceeds 7×10^{-12}  cm^{2}. We measure inelastic rate constants below 4×10^{-8}  cm^{3}/s and control these by tuning a homogeneous electric field that covers a large fraction of the trap volume. Comparison to ab initio calculations gives excellent agreement with dipolar relaxation. Our techniques and findings are generic and immediately relevant for other cold-molecule collision experiments.

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.

Accurate prediction and measurement of vibronic branching ratios for laser cooling linear polyatomic molecules

We report a generally applicable computational and experimental approach to determine vibronic branching ratios in linear polyatomic molecules to the 10^-5 level, including for nominally symmetry-forbidden transitions. These methods are demonstrated in CaOH and YbOH, showing approximately two orders of magnitude improved sensitivity compared with the previous state of the art. Knowledge of branching ratios at this level is needed for the successful deep laser cooling of a broad range of molecular species.

1D Magneto-Optical Trap of Polyatomic Molecules

We demonstrate a 1D magneto-optical trap of the polar free radical calcium monohydroxide (CaOH). A quasiclosed cycling transition is established to scatter ∼10^{3} photons per molecule, predominantly limited by interaction time. This enables radiative laser cooling of CaOH while compressing the molecular beam, leading to a significant increase in on axis beam brightness and reduction in temperature from 8.4 to 1.4 mK.

Spin-momentum entanglement in a Bose–Einstein condensate

Mechanisms including two types of Raman laser coupling (Ω₁ & Ω₂) and rf field coupling (Ω_rf) are applied to drive transitions between different hyperfine spin states. We investigated the entanglement between the spin and momentum degrees of freedom.

Optical control of entanglement and coherence for polar molecules in pendular states

Quantum entanglement and coherence are both essential physical resources in quantum theory. Cold polar molecules have long coherence time and strong dipole-dipole interaction and thus have been suggested as a platform for quantum information processing. In this paper, we employ the pendular states of the polar molecules trapped in static electric fields as the qubits, and put forward several theoretical schemes to generate the entanglement and coherence for two coupled dipoles by using optimal control theory. Through the designs of appropriate laser pulses, the transitions from the ground state to the Bell state and maximally coherent state can be realized with high fidelities 0.9906 and 0.9943 in the two-dipole system, respectively. Meanwhile, we show that the degrees of entanglement and coherence between the two pendular qubits are effectively enhanced with the help of optimized control fields. Furthermore, our schemes are generalized to the preparation of the Hardy state and even to the creation of arbitrary two-qubit states. Our findings can shed some light on the implementation of quantum information tasks with the molecular pendular states.

Entangling non planar molecules via inversion doublet transition with negligible spontaneous emission

We analyze theoretically the entanglement between two non-planar and light identical molecules (e.g., pyramidal NH3) that present inversion doubling due to the internal spatial inversion of their nuclear conformations by tunneling. The peculiarity of this system lies in the simplicity of this type of molecular system in which two near levels can be connected by an allowed electric dipole transition with considerable value of the dipole moment transition and negligible spontaneous emission because the transition is in the microwave or far-infrared range. These properties give place to entanglement states oscillating by free evolution with frequency determined by the dipole-dipole interaction and negligible spontaneous decay, which allows consideration of an efficient quantum Zeno effect by frequent measurements of one of the entangled states. If the molecules are initially both in the upper (or lower) eigenstate, the system evolves under an external radiation field, which can induce oscillations of the generated entangled states, with frequency of the order of the Rabi frequency of the field. For a certain detuning, a symmetric entangled state, which is an eigenstate of the collective system, can be populated, and given its negligible spontaneous emission, could be maintained for a time limited only by external decoherence processes, which could be minimized. Although the data used are those of the NH3 molecule, other molecules could present the same advantageous features.

Coherent Bichromatic Force Deflection of Molecules

We demonstrate the effect of the coherent optical bichromatic force on a molecule, the polar free radical strontium monohydroxide (SrOH). A dual-frequency retroreflected laser beam addressing the X[over ˜]^{2}Σ^{+}↔A[over ˜]^{2}Π_{1/2} electronic transition coherently imparts momentum onto a cryogenic beam of SrOH. This directional photon exchange creates a bichromatic force that transversely deflects the molecules. By adjusting the relative phase between the forward and counterpropagating laser beams we reverse the direction of the applied force. A momentum transfer of 70ℏk is achieved with minimal loss of molecules to dark states. Modeling of the bichromatic force is performed via direct numerical solution of the time-dependent density matrix and is compared with experimental observations. Our results open the door to further coherent manipulation of molecular motion, including the efficient optical deceleration of diatomic and polyatomic molecules with complex level structures.

EPR steering of polar molecules in pendular states and their dynamics under intrinsic decoherence

The EPR steering of two coupled polar molecules in pendular states is investigated and their dynamics under intrinsic decoherence are analyzed.

Quantum Correlations and Coherence of Polar Symmetric Top Molecules in Pendular States

We consider two ultracold polar symmetric top molecules coupled by dipole-dipole interaction in an external electric field with appreciable intensity gradient, serving as the physical carrier of quantum information. Each molecule is induced to undergo pendular oscillations under the strong static electric field. Based on the pendular states of polar symmetric top molecules as candidate qubits, we investigate the bipartite quantum correlations of the two polar molecular system for the thermal equilibrium states, characterized by negativity and quantum discord, and then analyze the corresponding coherence, measured by relative entropy and l₁ norm. Furthermore, we also examine the dynamics of the entanglement and coherence of the system in the presence of intrinsic decoherence, and explore the relations of their temporal evolution with various physical system parameters for two different initial Bell states. It is found that quantum correlations and coherence of the two polar molecules in pendular states can be manipulated by adjusting appropriate reduced variables including external electric field, dipole-dipole interaction, ambient temperature and decoherence factor. Our findings could be used for molecular quantum computing based on rotational 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.

Precision Measurement of Time-Reversal Symmetry Violation with Laser-Cooled Polyatomic Molecules

Precision searches for time-reversal symmetry violating interactions in polar molecules are extremely sensitive probes of high energy physics beyond the standard model. To extend the reach of these probes into the PeV regime, long coherence times and large count rates are necessary. Recent advances in laser cooling of polar molecules offer one important tool-optical trapping. However, the types of molecules that have been laser cooled so far do not have the highly desirable combination of features for new physics searches, such as the ability to fully polarize and the existence of internal comagnetometer states. We show that by utilizing the internal degrees of freedom present only in molecules with at least three atoms, these features can be attained simultaneously with molecules that have simple structure and are amenable to laser cooling and trapping.

Adsorbed molecules in external fields: Effect of confining potential

We study the rotational excitation of a molecule adsorbed on a surface. As is well known the interaction potential between the surface and the molecule can be modeled in number of ways, depending on the molecular structure and the geometry under which the molecule is being adsorbed by the surface. We explore the effect of change of confining potential on the excitation, which is largely controlled by the static electric fields and continuous wave laser fields. We focus on dipolar molecules and hence we restrict ourselves to the first order interaction in field-molecule interaction potential either through permanent dipole moment or/and the molecular polarizability parameter. It is shown that confining potential shapes, strength of the confinement, strongly affect the excitation. We compare our results for different confining potentials.

Quantum Computation using Arrays of N Polar Molecules in Pendular States

We investigate several aspects of realizing quantum computation using entangled polar molecules in pendular states. Quantum algorithms typically start from a product state |00⋯0⟩ and we show that up to a negligible error, the ground states of polar molecule arrays can be considered as the unentangled qubit basis state |00⋯0⟩ . This state can be prepared by simply allowing the system to reach thermal equilibrium at low temperature (<1 mK). We also evaluate entanglement, characterized by concurrence of pendular state qubits in dipole arrays as governed by the external electric field, dipole-dipole coupling and number N of molecules in the array. In the parameter regime that we consider for quantum computing, we find that qubit entanglement is modest, typically no greater than 10^-4 , confirming the negligible entanglement in the ground state. We discuss methods for realizing quantum computation in the gate model, measurement-based model, instantaneous quantum polynomial time circuits and the adiabatic model using polar molecules in pendular states.

Pair-eigenstates and mutual alignment of coupled molecular rotors in a magnetic field

We examine the rotational states of a pair of polar (2)Σ molecules subject to a uniform magnetic field. The electric dipole-dipole interaction between the molecules creates entangled pair-eigenstates of two types. In one type, the Zeeman interaction between the inherently paramagnetic molecules and the magnetic field destroys the entanglement of the pair-eigenstates, whereas in the other type it does not. The pair-eigenstates exhibit numerous intersections, which become avoided for pair-eigenstates comprised of individual states that meet the selection rules ΔJi = 0, ± 1, ΔNi = 2n (n = 0, ±1, ±2,…), and ΔMi = 0, ± 1 imposed by the electric dipole-dipole operator. Here Ji, Ni and Mi are the total, rotational and projection angular momentum quantum numbers of molecules i = 1, 2 in the absence of the electric dipole-dipole interaction. We evaluate the mutual alignment of the pair-eigenstates and find it to be independent of the magnetic field, except for states that undergo avoided crossings, in which case the alignment of the interacting states is interchanged at the magnetic field corresponding to the crossing point. We present an analytic model which provides ready estimates of the pairwise alignment cosine that characterises the mutual alignment of the pair of coupled rotors.

Optoelectrical Cooling of Polar Molecules to Submillikelvin Temperatures

We demonstrate direct cooling of gaseous formaldehyde (H2CO) to the microkelvin regime. Our approach, optoelectrical Sisyphus cooling, provides a simple dissipative cooling method applicable to electrically trapped dipolar molecules. By reducing the temperature by 3 orders of magnitude and increasing the phase-space density by a factor of ∼10(4), we generate an ensemble of 3×10(5) molecules with a temperature of about 420  μK, populating a single rotational state with more than 80% purity.

Quantum Entanglement and Chemical Reactivity

The water molecule and a hydrogenic abstraction reaction are used to explore in detail some quantum entanglement features of chemical interest. We illustrate that the energetic and quantum-information approaches are necessary for a full understanding of both the geometry of the quantum probability density of molecular systems and the evolution of a chemical reaction. The energy and entanglement hypersurfaces and contour maps of these two models show different phenomena. The energy ones reveal the well-known stable geometry of the models, whereas the entanglement ones grasp the chemical capability to transform from one state system to a new one. In the water molecule the chemical reactivity is witnessed through quantum entanglement as a local minimum indicating the bond cleavage in the dissociation process of the molecule. Finally, quantum entanglement is also useful as a chemical reactivity descriptor by detecting the transition state along the intrinsic reaction path in the hypersurface of the hydrogenic abstraction reaction corresponding to a maximally entangled state.

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.

Linear Stark effect for a sulfur atom in strong high-frequency laser fields

Current trends in laser technology have reached the regime of studying atoms stabilized against ionization, going beyond the perturbation theory. In this work, properties of a laser-dressed sulfur atom are examined in this stabilization regime. The electronic structure of a sulfur atom changes dramatically as it interacts with strong high-frequency laser fields. Degenerate molecularlike states are obtained for the ground state triplet of the laser-dressed sulfur atom for high-frequency and moderate intensity laser parameters. The degenerate ground state is obtained for a laser intensity which is smaller by more than one order of magnitude than the intensity required for hydrogen atoms due to many electron screening effects. An infinitesimally weak static field mixes these degenerate states to give rise to asymmetric states with large permanent dipole moments. Hence, a strong linear Stark effect rather than the usual quadratic one is obtained.