Pendular States Research Articles

Quantum gate control of polar molecules with machine learning.

We propose a scheme for achieving basic quantum gates using ultracold polar molecules in pendular states. The qubits are encoded in the YbF molecules trapped in an electric field with a certain gradient and coupled by the dipole-dipole interaction. The time-dependent control sequences consisting of multiple pulses are considered to interact with the pendular qubits. To achieve high-fidelity quantum gates, we map the control problem for the coupled molecular system into a Markov decision process and deal with it using the techniques of deep reinforcement learning (DRL). By training the agents over multiple episodes, the optimal control pulse sequences for the two-qubit gates of NOT, controlled NOT, and Hadamard are discovered with high fidelities. Moreover, the population dynamics of YbF molecules driven by the discovered gate sequences are analyzed in detail. Furthermore, by combining the optimal gate sequences, we successfully simulate the quantum circuit for entanglement. Our findings could offer new insights into efficiently controlling molecular systems for practical molecule-based quantum computing using DRL.

Implementation of three-qubit Deutsch-Jozsa algorithm with pendular states of polar molecules by optimal control

Ultracold polar molecules have gained much attention as a potential candidate for quantum information processing due to their long coherence time and strong dipole–dipole interaction. In the present study, we explore the dynamics of three polar molecules that are mutually coupled and arranged in an equilateral triangle configuration within a gradient electric field. By employing the pendular states of polar molecules as qubits, we simulate the three-qubit Deutsch-Jozsa algorithm via multi-target optimal control. Through the design of optimal microwave pulses with multiple iterations, our approach can accomplish the operations required to complete the algorithm in a single operational step with high fidelity and large transition probability. Furthermore, we compare and analyze the fidelity and average transition probability with respect to iteration numbers for each unitary operation Uf pulse. It is found that by combining the optimized X, H⊗H⊗H, Uf, and H⊗H gate pulses, the Deutsch-Jozsa algorithm in the three-dipole system can be performed well for distinguishing between constant and balanced functions. Our findings could shed some light on the physical realization of multi-particle quantum algorithm based on polar molecules in external electric fields.

Simulation of quantum walks on a circle with polar molecules via optimal control.

Quantum walks are the quantum counterpart of classical random walks and have various applications in quantum information science. Polar molecules have rich internal energy structure and long coherence time and thus are considered as a promising candidate for quantum information processing. In this paper, we propose a theoretical scheme for implementing discrete-time quantum walks on a circle with dipole-dipole coupled SrO molecules. The states of the walker and the coin are encoded in the pendular states of polar molecules induced by an external electric field. We design the optimal microwave pulses for implementing quantum walks on a four-node circle and a three-node circle by multi-target optimal control theory. To reduce the accumulation of decoherence and improve the fidelity, we successfully realize a step of quantum walk with only one optimal pulse. Moreover, we also encode the walker into a three-level molecular qutrit and a four-level molecular ququart and design the corresponding optimal pulses for quantum walks, which can reduce the number of molecules used. It is found that all the quantum walks on a circle in our scheme can be achieved via optimal control fields with high fidelities. Our results could shed some light on the implementation of discrete-time quantum walks and high-dimensional quantum information processing with polar molecules.

A thermodynamics-based micro-macro elastoplastic micropolar continuum model for granular materials

A micro–macro elastoplastic micropolar continuum model for granular materials in the dry and pendular states is proposed on the basis of thermodynamics. The independent rotational degrees of freedom are considered besides the translational degrees of freedom for particles among the discrete particle system, which is described by the equivalent micropolar continuum. In the framework of the micropolar continuum, the elastic part and yield locus at macroscale are firstly rigorously deduced from the general elastic constitutive relation and Coulomb-type yield criterion at inter-particle contacts, respectively. Furthermore, the micro–macro elastoplastic micropolar continuum model is proposed, in which the model parameters have clear physical meanings. Subsequently, a return mapping algorithm for the integration of the micropolar elastoplastic model is presented. Finally, the proposed model, coded into ABAQUS software, is validated by comparisons of test and discrete element method results in terms of the stress–strain relation and strain localization phenomenon. The stress–strain relation and shear band modes are well reproduced, and the effects of the confining pressure and the partially saturated state on granular materials can also be correctly predicted by the proposed model.

All-optical control of pendular qubit states with nonresonant two-color laser pulses

Practical methodologies for qubit controls are established by two prerequisites, i.e., preparation of a well-defined initial quantum state and coherent control of that quantum state. Here we propose a quantum control method, realized by irradiating nonresonant nanosecond two-color (ω and 2ω) laser pulses to molecules in the pendular (field-dressed) ground state. The two-color field nonadiabatically splits the initial pendular ground state |tilde{0},tilde{0}rangle to a superposition state of |tilde{0},tilde{0}rangle and |tilde{1},tilde{0}rangle , whose relative probability amplitudes can be controlled by the peak intensity of one wavelength component (ω) while the peak intensity of the other component (2ω) is fixed. The splitting of the quantum paths is evidenced by observing degrees of orientation of ground-state-selected OCS molecules by the velocity map imaging technique. This quantum control method is highly advantageous because any polar molecule can be controlled regardless of the molecular energy structures.

Optimization two-qubit quantum gate by two optical control methods in molecular pendular states

Implementation of quantum gates are important for quantum computations in physical system made of polar molecules. We investigate the feasibility of implementing gates based on pendular states of the molecular system by two different quantum optical control methods. Firstly, the Multi-Target optimal control theory and the Multi-Constraint optimal control theory are described for optimizing control fields and accomplish the optimization of quantum gates. Numerical results show that the controlled NOT gate (CNOT) can be realized under the control of above methods with high fidelities (0.975 and 0.999) respectively. In addition, in order to examine the dependence of the fidelity on energy difference in the same molecular system, the SWAP gate in the molecular system is also optimized with high fidelity (0.999) by the Multi-Constraint optimal control theory with the zero-area and constant-fluence constraints.

Creation of high-dimensional entanglement of polar molecules via optimal control fields

Quantum entanglement in high-dimensional Hilbert space offers broad prospects for quantum information science. Polar molecules have a rich internal structure and long coherence time, serving as an attractive candidate for quantum information processing. In this paper, we propose a theoretical scheme for creating high-dimensional entangled states based on ultracold SrO molecules. Qudits are encoded in the pendular states induced by an external electric field and coupled by the dipole-dipole interaction. With the assistance of optimal control theory, a series of optimal microwave fields is designed for the generation of an entangled qutrit-qubit state, qutrit-qutrit state, and ququart-ququart state through numerical iterations. We detail the relation of the fidelity and entanglement of the systemic final states with the number of iteration steps after the control fields are applied and analyze the population dynamics of the field-driven wave functions during time evolution. Moreover, three coupled SrO molecules arranged in an equilateral triangle configuration are employed as pendular qubits, and the trimolecular $W$ and Greenberger-Horne-Zeilinger states are realized with high fidelities by optimal control. The specific molecule and experimental parameters used in our theoretical studies are chosen for computational convenience, but we include a discussion of how our results can be applied to realistic situations as well. In principle, our results could be extended to a situation with more pendular qudits, providing a significant step toward the achievement of high-dimensional quantum information processing with arrays of polar molecules.

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

We show that 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. The two lowest lying excited pendular states coupled by microwave or radio-frequency fields are used to encode the pseudo-spin. We map out the general features of the models by evaluating the models constants as functions of the molecular dipole moment, rotational constant, strength and direction of the external field as well as the distance between molecules. We calculate the phase diagram for a linear chain of polar molecules based on the Heisenberg models and discuss their drawbacks, advantages, and potential applications.

Temporal dynamics of photonic stop-band in volatile solvent infiltrated opals

The effect of the infiltration of volatile solvents in photonic crystals is experimentally studied. Silica particles were synthesized and the opal structures were fabricated by self-assembly technique. Solutions containing various concentrations of methanol in ethanol were infiltrated in the opals and its effect on the temporal dynamics of the photonic stop-band during the evaporation process are studied. The recovery time of the solvent infiltrated opals is found to depend on the vapour pressure of the infiltrated solvent. The fabricated opal structures exhibit recovery time of ~2.8 s and 1.5 s for ethanol and methanol solvents respectively, with good repeatability. A model is proposed to understand the behaviour of volatile solvents in opals, and the observations made in the reflectance spectra are ascribed to the formation of saturated, funicular and pendular states. A comparative study of volatile solvents such as acetone, methanol, ethanol and 2-propanol is also performed and the effect of evaporation rates on the photonic stop-band is studied.

Study of grain-scale effects in bulk handling using discrete element simulations

Industrial granular flow issues are affected by the particle properties and environmental conditions of the materials. To understand the impact of grain-scale effects on flowability, experimental testing should be complemented with particle-based modelling. In this study, we simulate the effects of particle size, shape, and hygroscopicity by the discrete element method (DEM) for different bulk handling problems. We examine a granular column collapse set-up, comparing flow propagation of dry, mono-sized sphere packings to granular systems with particle size dispersity, prolate spheroidal particles, and liquid contents in pendular capillary states. Our results corroborate the experimental observations of evolving height profiles, velocity fields, energy balance, and particle orientation. We also analyse different hopper design alternatives dealing with particle size segregation in an industrial case study of the filling operation. This study illustrates the usability of the DEM as an effective support tool to characterise complex granular flows and improve bulk handling technology.

Protonation isomers of highly charged protein ions can be separated in FAIMS-MS

High-field asymmetric waveform ion mobility spectrometry-mass spectrometry (FAIMS-MS) can resolve over an order of magnitude more conformers for a given protein ion than alternative methods. Such an expansion in separation space results, in part, from protein ions with masses of >29 kDa undergoing dipole alignment in the high electric field of FAIMS, and the resolution of ions that adopt pendular vs free rotor states. In this study, FAIMS-MS, collision-induced dissociation (CID), and travelling wave (TW) IMS-MS were used to investigate the pendular and free rotor states of protonated carbonic anhydrase II (CAII, 29 kDa). The electrospray ionization additive 1,2-butylene carbonate was used to increase protein charge states and ensure extended ion conformations were formed. For relatively high charge states in which dipole alignment occurs (30–38+), FAIMS-MS can baseline resolve the isobaric pendular and free rotor ion populations. For TWIMS-MS, these same charge states resulted in monomodal arrival time distributions with collision cross sections corresponding to highly extended ion conformations. Interestingly, CID of FAIMS-selected pendular and free rotor ion populations resulted in significantly different fragmentation patterns. For example, CID of the dipole aligned CAII 37+ resulted in cleavages C-terminal to residue 183, 192 and 196, whereas cleavage sites for the free rotor population occurred near residues 12 and 238. Given that the cleavage sites are ’directed’ by protonation sites in the CID of protein ions, and highly charged protein ions adopt extended conformations with the same or very similar collision cross sections, these results indicate that the pendular and free rotor populations separated in FAIMS can be attributed to protonation isomers. Moreover, the extent of protein ion charging in FAIMS-MS decreased substantially as the carrier gas flow rate decreased, indicating that ion charging in FAIMS-MS can be limited by proton-transfer reactions. Given that the total mass of proton charge carriers corresponds to less than 0.2% the mass of CAII, we anticipate that FAIMS-MS can be used to separate intact isobaric proteoforms with masses of at least ∼29 kDa that result from alternative sites of post-translational modifications.

Discrete-element simulation of drying effect on the volume and equivalent effective stress of kaolinite

The effect of the drying path on the porosity and equivalent effective stress of unsaturated kaolinite is investigated using the discrete-element method. An unsaturated model is developed to determine the distribution of water and calculate the capillary forces between the platy clay particles. Non-flexible and flexible clay particles are simulated and the results are compared with laboratory data to investigate the influence of particle flexibility on the accuracy of the results. Simulations with flexible particles were found to be more accurate than simulations with non-flexible particles. The effect of the pore water characteristics of cation valence, cation concentration and initial porosity on the drying process is also examined. A range of water contents for kaolinite was selected for pendular and partially pendular states. The results showed that, as the cation valence and concentration increased, porosity decreased and the equivalent effective stress increased. It was shown that a decrease in sample porosity increased the equivalent effective stress.

Implementation of three-qubit quantum computation with pendular states of polar molecules by optimal control

Ultracold polar molecules have been considered as the possible candidates for quantum information processing due to their long coherence time and strong dipole-dipole interaction. In this paper, we consider three coupled polar molecules arranged in a linear chain and trapped in an electric field with gradient. By employing the pendular states of polar molecules as qubits, we successfully realize three-qubit quantum gates and quantum algorithms via the multi-target optimal control theory. Explicitly speaking, through the designs of the optimal laser pulses with multiple iterations, the triqubit Toffoli gate, the triqubit quantum adders, and the triqubit quantum Fourier transform can be achieved in only one operational step with high fidelities and large transition probabilities. Moreover, by combining the optimized Hadamard, oracle, and diffusion gate pulses, we simulate the Grover algorithm in the three-dipole system and show that the algorithm can perform well for search problems. In addition, the behaviors of the fidelity and the average transition probability with respect to iteration numbers are compared and analyzed for each gate pulse. Our findings could pave the way toward scalability for molecular quantum computing based on the pendular states and could be extended to implement multi-particle gate operation in the molecular system.

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.

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

Einstein–Podolsky–Rosen (EPR) steering gives evidence for the phenomenon called “spooky action at a distance” in quantum mechanics, and provides a useful resource for the implementation of quantum information tasks. In this paper, we consider a pair of ultracold polar molecules trapped in an external electric field as a promising quantum information carrier, and analyze the evolution behavior of EPR steering for the two coupled polar molecules in pendular states. Our results show that the steering of the two linear dipoles is remarkably reliant upon the Stark effect and dipole–dipole interaction. To be specific, the steerability degree is inversely associated with the intensity of the electric field while it is positively correlated with the coupling strength between the two polar molecules. Moreover, it is found that high ambient temperature can lead to a rapid loss of the steerable resource in thermal equilibrium. Further, we put forward an effective strategy to enhance the steerability using the technique of weak measurement reversal (WMR). By taking into account the influence of intrinsic decoherence on the steering dynamics, we found that robust EPR steering preservation can be realized for the initial state being in the Bell state . Our findings may shed some new light on molecular quantum information processing with pendular states.

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.

Anisotropic blockade using pendular long-range Rydberg molecules

SynopsisUltralong-range “butterfly” Rydberg molecules possess large dipole moments which lead to long-range anisotropic interactions between molecules. Their properties are studied using a Hamiltonian that fully includes the electronic and nuclear spin degrees of freedom. Using this more accurate and complete theoretical description, we investigate the intermolecular interaction when the molecules are prepared in pendular states. The anisotropy of this interaction manifests itself strongly in the density of created molecules.

Conditional quasi-exact solvability of the quantum planar pendulum and of its anti-isospectral hyperbolic counterpart

We have subjected the planar pendulum eigenproblem to a symmetry analysis with the goal of explaining the relationship between its conditional quasi-exact solvability (C-QES) and the topology of its eigenenergy surfaces, established in our earlier work [Front. Phys. Chem. Chem. Phys. 2, 1 (2014)]. The present analysis revealed that this relationship can be traced to the structure of the tridiagonal matrices representing the symmetry-adapted pendular Hamiltonian, as well as enabled us to identify many more – 40 in total to be exact – analytic solutions. Furthermore, an analogous analysis of the hyperbolic counterpart of the planar pendulum, the Razavy problem, which was shown to be also C-QES [Am. J. Phys. 48, 285 (1980)], confirmed that it is anti-isospectral with the pendular eigenproblem. Of key importance for both eigenproblems proved to be the topological index κ, as it determines the loci of the intersections (genuine and avoided) of the eigenenergy surfaces spanned by the dimensionless interaction parameters η and ζ. It also encapsulates the conditions under which analytic solutions to the two eigenproblems obtain and provides the number of analytic solutions. At a given κ, the anti-isospectrality occurs for single states only (i.e., not for doublets), like C-QES holds solely for integer values of κ, and only occurs for the lowest eigenvalues of the pendular and Razavy Hamiltonians, with the order of the eigenvalues reversed for the latter. For all other states, the pendular and Razavy spectra become in fact qualitatively different, as higher pendular states appear as doublets whereas all higher Razavy states are singlets.Graphical abstract

Stress–Force–Fabric Relationship for Unsaturated Granular Materials in Pendular States

AbstractThis paper explores the particle-scale origin of the additional shear strength of unsaturated granular materials in pendular states induced by the capillary effect by applying the stress–fo...

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.