1
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Smucker J, Pérez-Ríos J. Alignment transport between ultracold polar molecules. Phys Chem Chem Phys 2024; 26:21513-21519. [PMID: 39081230 DOI: 10.1039/d4cp01956c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/15/2024]
Abstract
We propose an array of ultracold polar molecules as a platform to study alignment transport between molecules. We envision a polar molecule being aligned with an intense off-resonant laser field whose alignment migrates to a nearby molecule due to dipole-dipole interactions. Our results show that the transport of the alignment is due to a complex interplay between electric field-driven excitations and dipole-dipole interactions. All mechanisms for alignment transfer are elucidated and analyzed. Using NaCs as a prototype molecule, we find that the time for alignment transfer is (10 μs), which makes the phenomena readily observable in the lab.
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Affiliation(s)
- Jonathan Smucker
- Department of Physics and Astronomy, Stony Brook University, Stony Brook, 11790, USA.
| | - Jesus Pérez-Ríos
- Department of Physics and Astronomy, Stony Brook University, Stony Brook, 11790, USA.
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2
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Zhang ZY, Hu JR, Fang YY, Li JF, Liu JM, Huang X, Sun Z. Quantum gate control of polar molecules with machine learning. J Chem Phys 2024; 161:034102. [PMID: 39007369 DOI: 10.1063/5.0216013] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2024] [Accepted: 06/26/2024] [Indexed: 07/16/2024] Open
Abstract
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.
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Affiliation(s)
- Zuo-Yuan Zhang
- College of Physical Science and Technology, Yangzhou University, Yangzhou 225009, China
| | - Jie-Ru Hu
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200241, China
| | - Yu-Yan Fang
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200241, China
| | - Jin-Fang Li
- Department of Physics and Electronic Engineering, Xianyang Normal University, Shaanxi 712000, China
| | - Jin-Ming Liu
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200241, China
- Chongqing Key Laboratory of Precision Optics, Chongqing Institute of East China Normal University, Chongqing 401120, China
| | - Xinning Huang
- College of Physical Science and Technology, Yangzhou University, Yangzhou 225009, China
| | - Zhaoxi Sun
- Changping Laboratory, Beijing 102206, China
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3
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Zhang ZY, Sun Z, Duan T, Ding YK, Huang X, Liu JM. Entanglement Generation of Polar Molecules via Deep Reinforcement Learning. J Chem Theory Comput 2024; 20:1811-1820. [PMID: 38320113 DOI: 10.1021/acs.jctc.3c01214] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/08/2024]
Abstract
Polar molecules are a promising platform for achieving scalable quantum information processing because of their long-range electric dipole-dipole interactions. Here, we take the coupled ultracold CaF molecules in an external electric field with gradient as qubits and concentrate on the creation of intermolecular entanglement with the method of deep reinforcement learning (RL). After sufficient training episodes, the educated RL agents can discover optimal time-dependent control fields that steer the molecular systems from separate states to two-qubit and three-qubit entangled states with high fidelities. We analyze the fidelities and the negativities (characterizing entanglement) of the generated states as a function of training episodes. Moreover, we present the population dynamics of the molecular systems under the influence of control fields discovered by the agents. Compared with the schemes for creating molecular entangled states based on optimal control theory, some conditions (e.g., molecular spacing and electric field gradient) adopted in this work are more feasible in the experiment. Our results demonstrate the potential of machine learning to effectively solve quantum control problems in polar molecular systems.
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Affiliation(s)
- Zuo-Yuan Zhang
- School of Physical Science and Technology, Yangzhou University, Yangzhou 225009, China
| | - Zhaoxi Sun
- Changping Laboratory, Beijing 102206, China
| | - Tao Duan
- State Key Laboratory of Transient Optics and Photonics, Xi'an Institute of Optics and Precision Mechanics of CAS, Xi'an 710119, China
| | - Yi-Kai Ding
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200241, China
| | - Xinning Huang
- School of Physical Science and Technology, Yangzhou University, Yangzhou 225009, China
| | - Jin-Ming Liu
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200241, China
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4
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Wang W, Liu X, Pérez-Ríos J. AlF-AlF Reaction Dynamics between 200 K and 1000 K: Reaction Mechanisms and Intermediate Complex Characterization. Molecules 2023; 29:222. [PMID: 38202805 PMCID: PMC10780286 DOI: 10.3390/molecules29010222] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/21/2023] [Revised: 12/20/2023] [Accepted: 12/22/2023] [Indexed: 01/12/2024] Open
Abstract
AlF is a relevant molecule in astrochemistry as a tracer of F-bearing molecules. Additionally, AlF presents diagonal Franck-Condon factors and can be created very efficiently in the lab, which makes it a prototypical molecular for laser cooling. However, very little is known about the reaction dynamics of AlF. In this work, we report on the reaction dynamics of AlF-AlF between 200 and 1000 K using ab initio molecular dynamics and a highly efficient active learning approach for the potential energy surface, including all degrees of freedom. As a result, we identify the main reaction mechanisms and the lifetime of the intermediate complex AlF-AlF relevant to astrochemistry environments and regions in buffer gas cells.
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Affiliation(s)
- Weiqi Wang
- Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany; (W.W.); (X.L.)
| | - Xiangyue Liu
- Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany; (W.W.); (X.L.)
| | - Jesús Pérez-Ríos
- Department of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794-3800, USA
- Institute for Advanced Computational Science, Stony Brook University, Stony Brook, NY 11794-3800, USA
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5
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Ding YK, Zhang ZY, Liu JM. Simulation of quantum walks on a circle with polar molecules via optimal control. J Chem Phys 2023; 159:204303. [PMID: 38010330 DOI: 10.1063/5.0174472] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/31/2023] [Accepted: 11/05/2023] [Indexed: 11/29/2023] Open
Abstract
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.
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Affiliation(s)
- Yi-Kai Ding
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200241, China
| | - Zuo-Yuan Zhang
- School of Physical Science and Technology, Yangzhou University, Yangzhou 225009, China
| | - Jin-Ming Liu
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200241, China
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6
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Li JF, Hu JR, Guo QF, He DS. Resonant and non-resonant optimizations by multi-constraint quantum control theory in molecular rotational states. Sci Rep 2022; 12:19210. [DOI: 10.1038/s41598-022-23762-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/18/2022] [Accepted: 11/04/2022] [Indexed: 11/12/2022] Open
Abstract
AbstractIt is a promising research for optimization of quantum gate in the field of quantum computation. We investigate the feasibility of implementing the single-qubit gate (Hadamard) in molecular rotational system. By applying the Multi-constraint quantum optimal control method, the excepted final states can be achieved based on the molecular rotational states both in resonant and non-resonant cases with the control pulses. The permanent electric dipole moment is ignored in non-resonance. Besides, the zero-pulse area constraint and the constant fluence constraint are employed to optimize shapes of control pulses. Finally, we show that the Hadamard gate can be realized with the high fidelity (0.9999) and also examine the dependence of the fidelity on pulse fluence as well as the control pulse.
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7
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Li JF, Hu JR, Wan F, He DS. Optimization two-qubit quantum gate by two optical control methods in molecular pendular states. Sci Rep 2022; 12:14918. [PMID: 36050511 PMCID: PMC9437090 DOI: 10.1038/s41598-022-18967-2] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/26/2022] [Accepted: 08/23/2022] [Indexed: 11/09/2022] Open
Abstract
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.
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Affiliation(s)
- Jin-Fang Li
- Department of Physics and Electronic Engineering, Xianyang Normal University, Shaanxi, 712000, China. .,State Key Laboratory of Precision Spectroscopy, Department of Physics, East China Normal University, Shanghai, 200062, China.
| | - Jie-Ru Hu
- State Key Laboratory of Precision Spectroscopy, Department of Physics, East China Normal University, Shanghai, 200062, China
| | - Feng Wan
- Department of Physics and Electronic Engineering, Xianyang Normal University, Shaanxi, 712000, China
| | - Dong-Shan He
- Department of Physics and Electronic Engineering, Xianyang Normal University, Shaanxi, 712000, China
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8
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Sajjan M, Li J, Selvarajan R, Sureshbabu SH, Kale SS, Gupta R, Singh V, Kais S. Quantum machine learning for chemistry and physics. Chem Soc Rev 2022; 51:6475-6573. [PMID: 35849066 DOI: 10.1039/d2cs00203e] [Citation(s) in RCA: 14] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
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.
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Affiliation(s)
- Manas Sajjan
- Department of Chemistry, Purdue University, West Lafayette, IN-47907, USA. .,Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, USA
| | - Junxu Li
- Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, USA.,Department of Physics and Astronomy, Purdue University, West Lafayette, IN-47907, USA
| | - Raja Selvarajan
- Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, USA.,Department of Physics and Astronomy, Purdue University, West Lafayette, IN-47907, USA
| | - Shree Hari Sureshbabu
- Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, USA.,Elmore Family School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN-47907, USA
| | - Sumit Suresh Kale
- Department of Chemistry, Purdue University, West Lafayette, IN-47907, USA. .,Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, USA
| | - Rishabh Gupta
- Department of Chemistry, Purdue University, West Lafayette, IN-47907, USA. .,Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, USA
| | - Vinit Singh
- Department of Chemistry, Purdue University, West Lafayette, IN-47907, USA. .,Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, USA
| | - Sabre Kais
- Department of Chemistry, Purdue University, West Lafayette, IN-47907, USA. .,Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, USA.,Department of Physics and Astronomy, Purdue University, West Lafayette, IN-47907, USA.,Elmore Family School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN-47907, USA
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9
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Yue W, Wei Q, Kais S, Friedrich B, Herschbach D. Realization of Heisenberg models of spin systems with polar molecules in pendular states. Phys Chem Chem Phys 2022; 24:25270-25278. [DOI: 10.1039/d2cp00380e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
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.
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Affiliation(s)
- Wenjing Yue
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai, China
| | - Qi Wei
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai, China
| | - Sabre Kais
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, USA
| | - Bretislav Friedrich
- Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany
| | - Dudley Herschbach
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts, USA
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10
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Huang P, Kain S, de Oliveira-Filho AGS, Odom BC. Protocol for optically pumping AlH + to a pure quantum state. Phys Chem Chem Phys 2020; 22:24423-24430. [PMID: 33084668 DOI: 10.1039/d0cp04036c] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We propose an optical pumping scheme to prepare trapped AlH+ molecules in a pure state, the stretched hyperfine state of the rovibronic ground manifold |X2Σ+, v = 0, N = 0 . Our scheme utilizes linearly-polarized and circularly-polarized fields of a broadband pulsed laser to cool the rotational degree of freedom and drive the population to the hyperfine state, respectively. We simulate the population dynamics by solving a representative system of rate equations that accounts for the laser fields, blackbody radiation, and spontaneous emission. In order to model the hyperfine structure, new hyperfine constants of the A2Π excited state were computed using a RASSCF wavefunction. We find that adding an infrared laser to drive the 1-0 vibrational transition within the X2Σ+ manifold accelerates the cooling process. The results show that, under optimal conditions, the population in the target state of the rovibronic ground manifold can reach 63% after 68 μs (330 ms) and 95% after 25 ms (1.2 s) with (without) the infrared laser.
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Affiliation(s)
- Panpan Huang
- Department of Physics and Astronomy, Northwestern University, Evanston, IL 60208, USA.
| | - Schuyler Kain
- Department of Physics and Astronomy, Northwestern University, Evanston, IL 60208, USA.
| | - Antonio G S de Oliveira-Filho
- Departamento de Química, Laboratório Computacional de Espectroscopia e Cinética, Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto, Universidade de São Paulo, Ribeirão Preto-SP, 14040-901, Brazil
| | - Brian C Odom
- Department of Physics and Astronomy, Northwestern University, Evanston, IL 60208, USA.
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11
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Zhang ZY, Liu JM, Hu Z, Wang Y. Implementation of three-qubit quantum computation with pendular states of polar molecules by optimal control. J Chem Phys 2020; 152:044303. [PMID: 32007056 DOI: 10.1063/1.5139688] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023] Open
Abstract
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.
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Affiliation(s)
- Zuo-Yuan Zhang
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China
| | - Jin-Ming Liu
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China
| | - Zhengfeng Hu
- The Key Laboratory of Quantum Optics, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China
| | - Yuzhu Wang
- The Key Laboratory of Quantum Optics, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China
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12
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Zhang ZY, Liu JM, Hu Z, Wang Y. Optical control of entanglement and coherence for polar molecules in pendular states. OPTICS EXPRESS 2019; 27:26588-26599. [PMID: 31674537 DOI: 10.1364/oe.27.026588] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2019] [Accepted: 08/15/2019] [Indexed: 06/10/2023]
Abstract
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.
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13
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Gonzalo I, Antón MA. Entangling non planar molecules via inversion doublet transition with negligible spontaneous emission. Phys Chem Chem Phys 2019; 21:10523-10531. [PMID: 31070606 DOI: 10.1039/c8cp07764a] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
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.
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Affiliation(s)
- Isabel Gonzalo
- Departamento de Óptica, Facultad de Ciencias Físicas, Universidad Complutense de Madrid, 28040 Madrid, Spain.
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14
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Zhang ZY, Wei D, Hu Z, Liu JM. EPR steering of polar molecules in pendular states and their dynamics under intrinsic decoherence. RSC Adv 2018; 8:35928-35935. [PMID: 35558491 PMCID: PMC9088734 DOI: 10.1039/c8ra06342g] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2018] [Accepted: 10/11/2018] [Indexed: 02/03/2023] Open
Abstract
The EPR steering of two coupled polar molecules in pendular states is investigated and their dynamics under intrinsic decoherence are analyzed.
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Affiliation(s)
- Zuo-Yuan Zhang
- State Key Laboratory of Precision Spectroscopy
- East China Normal University
- Shanghai
- China
| | - Daxiu Wei
- Department of Physics and Shanghai Key Laboratory of Magnetic Resonance
- East China Normal University
- Shanghai
- China
| | - Zhengfeng Hu
- Key Laboratory of Quantum Optics
- Shanghai Institute of Optics and Fine Mechanics
- Chinese Academy of Science
- Shanghai
- China
| | - Jin-Ming Liu
- State Key Laboratory of Precision Spectroscopy
- East China Normal University
- Shanghai
- China
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15
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Quantum Correlations and Coherence of Polar Symmetric Top Molecules in Pendular States. Sci Rep 2017; 7:17822. [PMID: 29259261 PMCID: PMC5736622 DOI: 10.1038/s41598-017-18148-6] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/08/2017] [Accepted: 12/06/2017] [Indexed: 11/12/2022] Open
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.
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16
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Wei Q, Cao Y, Kais S, Friedrich B, Herschbach D. Quantum Computation using Arrays of N Polar Molecules in Pendular States. Chemphyschem 2016; 17:3714-3722. [PMID: 27767247 DOI: 10.1002/cphc.201600781] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/17/2016] [Revised: 10/10/2016] [Indexed: 11/07/2022]
Abstract
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.
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Affiliation(s)
- Qi Wei
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai, 200062, China
| | - Yudong Cao
- Department of Computer Science, Purdue University, West Lafayette, IN, 47907, USA
| | - Sabre Kais
- Department of Chemistry and Physics, Purdue University, West Lafayette, IN, 47907, USA.,Qatar Environment and Energy Research Institute, HBKU, Qatar Foundation, Doha, Qatar
| | - Bretislav Friedrich
- Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195, Berlin, Germany
| | - Dudley Herschbach
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts, 02138, USA
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17
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Niederprüm T, Thomas O, Eichert T, Lippe C, Pérez-Ríos J, Greene CH, Ott H. Observation of pendular butterfly Rydberg molecules. Nat Commun 2016; 7:12820. [PMID: 27703143 PMCID: PMC5059458 DOI: 10.1038/ncomms12820] [Citation(s) in RCA: 64] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2016] [Accepted: 08/04/2016] [Indexed: 11/09/2022] Open
Abstract
Engineering molecules with a tunable bond length and defined quantum states lies at the heart of quantum chemistry. The unconventional binding mechanism of Rydberg molecules makes them a promising candidate to implement such tunable molecules. A very peculiar type of Rydberg molecules are the so-called butterfly molecules, which are bound by a shape resonance in the electron-perturber scattering. Here we report the observation of these exotic molecules and employ their exceptional properties to engineer their bond length, vibrational state, angular momentum and orientation in a small electric field. Combining the variable bond length with their giant dipole moment of several hundred Debye, we observe counter-intuitive molecules which locate the average electron position beyond the internuclear distance.
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Affiliation(s)
- Thomas Niederprüm
- Research Center OPTIMAS, Technische Universität Kaiserslautern, 67663 Kaiserslautern, Germany
| | - Oliver Thomas
- Research Center OPTIMAS, Technische Universität Kaiserslautern, 67663 Kaiserslautern, Germany
- Graduate School Materials Science in Mainz, Staudinger Weg 9, 55128 Mainz, Germany
| | - Tanita Eichert
- Research Center OPTIMAS, Technische Universität Kaiserslautern, 67663 Kaiserslautern, Germany
| | - Carsten Lippe
- Research Center OPTIMAS, Technische Universität Kaiserslautern, 67663 Kaiserslautern, Germany
| | - Jesús Pérez-Ríos
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
| | - Chris H. Greene
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
| | - Herwig Ott
- Research Center OPTIMAS, Technische Universität Kaiserslautern, 67663 Kaiserslautern, Germany
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Deng M, Wang H, Wang Q, Yin J. Dependences of Q-branch integrated intensity of linear-molecule pendular spectra on electric-field strength and rotational temperature and its potential applications. Sci Rep 2016; 6:26776. [PMID: 27231057 PMCID: PMC4882541 DOI: 10.1038/srep26776] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/18/2016] [Accepted: 05/06/2016] [Indexed: 12/19/2022] Open
Abstract
We calculate the pendular-state spectra of cold linear molecules, and investigated the dependences of “Q-branch” integrated intensity of pendular spectra on both electric-field strength and molecular rotation-temperature. A new multi-peak structure in the “Q-branch” spectrum is appearing when the Stark interaction strength ω = μE/B equal to or larger than the critical value. Our study shows that the above results can be used not only to measure the electric-field vector and its spatial distribution in some electrostatic devices, such as the Stark decelerator, Stark velocity filter and electrostatic trap and so on, but also to survey the orientation degree of cold linear molecules in a strong electrostatic field.
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Affiliation(s)
- Min Deng
- State Key Laboratory of Precision Spectroscopy, Department of Physics, East China Normal University, Shanghai 200062, P. R. China
| | - Hailing Wang
- State Key Laboratory of Precision Spectroscopy, Department of Physics, East China Normal University, Shanghai 200062, P. R. China
| | - Qin Wang
- State Key Laboratory of Precision Spectroscopy, Department of Physics, East China Normal University, Shanghai 200062, P. R. China
| | - Jianping Yin
- State Key Laboratory of Precision Spectroscopy, Department of Physics, East China Normal University, Shanghai 200062, P. R. China
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19
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Sharma K, Friedrich B. Pair-eigenstates and mutual alignment of coupled molecular rotors in a magnetic field. Phys Chem Chem Phys 2016; 18:13467-77. [PMID: 27126576 DOI: 10.1039/c6cp00390g] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
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.
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Affiliation(s)
- Ketan Sharma
- Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany.
| | - Bretislav Friedrich
- Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany.
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20
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Han JX, Hu Y, Jin Y, Zhang GF. Influence of intrinsic decoherence on tripartite entanglement and bipartite fidelity of polar molecules in pendular states. J Chem Phys 2016; 144:134308. [PMID: 27059571 DOI: 10.1063/1.4945384] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
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.
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Affiliation(s)
- Jia-Xing Han
- Key Laboratory of Micro-Nano Measurement-Manipulation and Physics (Ministry of Education), School of Physics and Nuclear Energy Engineering, Beihang University, Xueyuan Road No. 37, Beijing 100191, China
| | - Yuan Hu
- Key Laboratory of Micro-Nano Measurement-Manipulation and Physics (Ministry of Education), School of Physics and Nuclear Energy Engineering, Beihang University, Xueyuan Road No. 37, Beijing 100191, China
| | - Yu Jin
- Key Laboratory of Micro-Nano Measurement-Manipulation and Physics (Ministry of Education), School of Physics and Nuclear Energy Engineering, Beihang University, Xueyuan Road No. 37, Beijing 100191, China
| | - Guo-Feng Zhang
- Key Laboratory of Micro-Nano Measurement-Manipulation and Physics (Ministry of Education), School of Physics and Nuclear Energy Engineering, Beihang University, Xueyuan Road No. 37, Beijing 100191, China
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Karra M, Sharma K, Friedrich B, Kais S, Herschbach D. Prospects for quantum computing with an array of ultracold polar paramagnetic molecules. J Chem Phys 2016; 144:094301. [DOI: 10.1063/1.4942928] [Citation(s) in RCA: 50] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Mallikarjun Karra
- Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany
| | - Ketan Sharma
- Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany
| | - Bretislav Friedrich
- Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany
| | - Sabre Kais
- Departments of Chemistry, Physics and Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
| | - Dudley Herschbach
- Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford Street, Cambridge, Massachusetts 02138, USA
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22
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Yang ZX, Shen X, Hou XW. Entanglement and Energy for Vibrationally Localized States in Molecule CS 2. CHINESE J CHEM PHYS 2015. [DOI: 10.1063/1674-0068/28/cjcp1503044] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
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23
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Shyshlov D, Berrios E, Gruebele M, Babikov D. On readout of vibrational qubits using quantum beats. J Chem Phys 2014; 141:224306. [PMID: 25494748 DOI: 10.1063/1.4903055] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Dmytro Shyshlov
- Chemistry Department, Marquette University, Milwaukee, Wisconsin 53201, USA
| | - Eduardo Berrios
- Department of Chemistry, Department of Physics and Center for Biophysics and Computational Biology, University of Illinois, Urbana, Illinois 61801, USA
| | - Martin Gruebele
- Department of Chemistry, Department of Physics and Center for Biophysics and Computational Biology, University of Illinois, Urbana, Illinois 61801, USA
| | - Dmitri Babikov
- Chemistry Department, Marquette University, Milwaukee, Wisconsin 53201, USA
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24
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Li Z, Krems RV, Heller EJ. Collision dynamics of polyatomic molecules containing carbon rings at low temperatures. J Chem Phys 2014; 141:104317. [DOI: 10.1063/1.4894793] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Zhiying Li
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Roman V. Krems
- Department of Chemistry, The University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada
| | - Eric J. Heller
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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25
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Kais S. Introduction to Quantum Information and Computation for Chemistry. ADVANCES IN CHEMICAL PHYSICS 2014. [DOI: 10.1002/9781118742631.ch01] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
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26
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Schmidt B, Friedrich B. Topology of surfaces for molecular Stark energy, alignment, and orientation generated by combined permanent and induced electric dipole interactions. J Chem Phys 2014; 140:064317. [DOI: 10.1063/1.4864465] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Affiliation(s)
- Mikhail Lemeshko
- a ITAMP, Harvard-Smithsonian Center for Astrophysics , Cambridge , MA , 02138 , USA
- b Physics Department , Harvard University , Cambridge , MA , 02138 , USA
- c Kavli Institute for Theoretical Physics , University of California , Santa Barbara , CA , 93106 , USA
| | - Roman V. Krems
- c Kavli Institute for Theoretical Physics , University of California , Santa Barbara , CA , 93106 , USA
- d Department of Chemistry , University of British Columbia , BC V6T 1Z1, Vancouver , Canada
| | - John M. Doyle
- b Physics Department , Harvard University , Cambridge , MA , 02138 , USA
| | - Sabre Kais
- e Departments of Chemistry and Physics , Purdue University , West Lafayette , IN , 47907 , USA
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28
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List of publications of Bretislav Friedrich. Mol Phys 2013. [DOI: 10.1080/00268976.2013.792470] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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29
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Zhu J, Kais S, Wei Q, Herschbach D, Friedrich B. Implementation of quantum logic gates using polar molecules in pendular states. J Chem Phys 2013; 138:024104. [DOI: 10.1063/1.4774058] [Citation(s) in RCA: 52] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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30
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Wei Q, Kais S, Friedrich B, Herschbach D. Entanglement of polar symmetric top molecules as candidate qubits. J Chem Phys 2011; 135:154102. [DOI: 10.1063/1.3649949] [Citation(s) in RCA: 44] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Qi Wei
- Department of Physics, Texas A & M University, College Station, Texas 77843, USA
| | - Sabre Kais
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, USA
| | - Bretislav Friedrich
- Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany
| | - Dudley Herschbach
- Department of Physics, Texas A & M University, College Station, Texas 77843, USA
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