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Acta Physica Sinica

Tripartite quantum correlations of polar molecules in pendular states

Yan-Jie Li, Liu Jin-Ming

Published Jan 1, 2014• 9 citations
Publisher

Abstract

Cold polar molecules have long coherence time and strong dipole-dipole interaction and thus are regarded as a promising quantum carrier for quantum information processing. In this paper, by employing the pendular states of polar molecules as qubit, we investigate the properties of three types of tripartite quantum correlations for three linear polar molecules and numerically analyze the relations of tripartite negativity, measurement-induced disturbance (MID), and tripartite quantum discord (TQD) to three dimensionless reduced variables that relate to external field strength, dipole moment, rotational constant, dipole-dipole coupling, and temperature. The result shows that if the values of the other parameters are fixed, the three quantum correlations decrease with the increase of the field strength, and the three quantum correlations first increase to their respective maxima and then diminish gradually as the dipole-dipole coupling becomes larger. Moreover, as the temperature increases, both tripartite negativity and TQD become small, but with the variation of temperature there exhibit different evolution tendencies for MID between the influence of the electric field strength and that of the dipole-dipole coupling. In addition, the three quantum correlations of polar molecules in pendular state can be manipulated by tuning the external electric field strength, dipole-dipole coupling, and temperature.

DOI
10.7498/aps.63.200302

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Cold polar molecules have long coherence time and strong dipole-dipole interaction and thus are regarded as a promising quantum carrier for quantum information processing. In this paper, by employing the pendular states of polar molecules as qubit, we investigate the properties of three types of tripartite quantum correlations for three linear polar molecules and numerically analyze the relations of tripartite negativity, measurement-induced disturbance (MID), and tripartite quantum discord (TQD) to three dimensionless reduced variables that relate to external field strength, dipole moment, rotational constant, dipole-dipole coupling, and temperature. The result shows that if the values of the other parameters are fixed, the three quantum correlations decrease with the increase of the field strength, and the three quantum correlations first increase to their respective maxima and then diminish gradually as the dipole-dipole coupling becomes larger. Moreover, as the temperature increases, both tripartite negativity and TQD become small, but with the variation of temperature there exhibit different evolution tendencies for MID between the influence of the electric field strength and that of the dipole-dipole coupling. In addition, the three quantum correlations of polar molecules in pendular state can be manipulated by tuning the external electric field strength, dipole-dipole coupling, and temperature.
Abstract 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.
An array of ultracold polar molecules trapped in an external electric field is regarded as a promising carrier of quantum information. Under the action of this field, molecules are compelled to undergo pendular oscillations by the Stark effect. Particular attention has been paid to the influence of intrinsic decoherence on the model of linear polar molecular pendular states, thereby we evaluate the tripartite entanglement with negativity, as well as fidelity of bipartite quantum systems for input and output signals using electric dipole moments of polar molecules as qubits. According to this study, we consider three typical initial states for both systems, respectively, and investigate the temporal evolution with variable values of the external field intensity, the intrinsic decoherence factor, and the dipole-dipole interaction. Thus, we demonstrate the sound selection of these three main parameters to obtain the best entanglement degree and fidelity.
In proposals for quantum computers using arrays of trapped ultracold polar molecules as qubits, a strong external field with appreciable gradient is imposed in order to prevent quenching of the dipole moments by rotation and to distinguish among the qubit sites. That field induces the molecular dipoles to undergo pendular oscillations, which markedly affect the qubit states and the dipole-dipole interaction. We evaluate entanglement of the pendular qubit states for two linear dipoles, characterized by pairwise concurrence, as a function of the molecular dipole moment and rotational constant, strengths of the external field and the dipole-dipole coupling, and ambient temperature. We also evaluate a key frequency shift, △ω, produced by the dipole-dipole interaction. Under conditions envisioned for the proposed quantum computers, both the concurrence and △ω become very small for the ground eigenstate. In principle, such weak entanglement can be sufficient for operation of logic gates, provided the resolution is high enough to detect the △ω shift unambiguously. In practice, however, for many candidate polar molecules it appears a challenging task to attain adequate resolution. Simple approximate formulas fitted to our numerical results are provided from which the concurrence and △ω shift can be obtained in terms of unitless reduced variables.
In proposals for quantum computers using arrays of trapped ultracold polar molecules as qubits, a strong external field with appreciable gradient is imposed in order to prevent quenching of the dipole moments by rotation and to distinguish among the qubit sites. That field induces the molecular dipoles to undergo pendular oscillations, which markedly affect the qubit states and the dipole-dipole interaction. We evaluate entanglement of the pendular qubit states for two linear dipoles, characterized by pairwise concurrence, as a function of the molecular dipole moment and rotational constant, strengths of the external field and the dipole-dipole coupling, and ambient temperature. We also evaluate a key frequency shift, △ω, produced by the dipole-dipole interaction. Under conditions envisioned for the proposed quantum computers, both the concurrence and △ω become very small for the ground eigenstate. In principle, such weak entanglement can be sufficient for operation of logic gates, provided the resolution is high enough to detect the △ω shift unambiguously. In practice, however, for many candidate polar molecules it appears a challenging task to attain adequate resolution. Simple approximate formulas fitted to our numerical results are provided from which the concurrence and △ω shift can be obtained in terms of unitless reduced variables.
We investigate the characteristics of three kinds of quantum correlations, measured by pairwise quantum discord (QD), geometric measure of quantum discord (GMQD), and measurement-induced disturbance (MID), in the systems of three- and four-dipole arrays. The influence of the temperature on the three quantum correlations and entanglement of the systems is also analyzed numerically. It is found that novel quantum correlation switches called QD, GMQD, and MID respectively can be constructed with the qubits consisting of electric dipoles coupled by the dipole—dipole interaction and oriented along or against the external electric field. Moreover, with the increase of temperature, QD, GMQD, and MID are more robust than entanglement against the thermal environment. It is also found that for each dipole pair of the three- and four-dipole arrangements, the MID is always the largest and the GMQD the smallest.
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 WWW 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.