利用双通道级联型原子库实现辐射场双模压缩真空态
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摘要
本文研究了利用双级联型四能级原子实现高纯度、强的双模腔场压缩纠缠态。考虑将四能级联型原子注入至一个双模腔中,腔场与原子能级形成共振的相互作用。在原子-腔场弱相互作用下,若原子自发辐射速率远大于腔场的衰减速率,在腔场相干时间内将原子视为腔场的外部环境库,我们推导出腔场所满足的主方程。通过分析主方程并发现:在不考虑腔场真空耗散的情况下,腔场等效地与一个双模压缩真空库耦合,因此在稳态区域处于纯的双模压缩真空态,并且压缩程度只依赖于原子初始上能级的布居;在考虑腔场耗散的情况下,耗散对其纯度的影响大于对纠缠的影响;与单通道原子库情况比较,利用双通道的原子库可以有效地提高腔场的纠缠和纯度。
In this paper,we investigate the generation of stationary entangled state of a two-mode cavity field via injecting into the cavity a beam of four-level atoms with two channels of two-photon cascaded transition.By treating the atomic beam as the external reservoir for the cavity field in weak cavity-atom interactions,we find that a two-mode squeezed vacuum reservoir of the cavity field can be achieved by using the atomic system.Therefore,in the steady-state regime,the cavity field can be driven into the two-mode squeezed vacuum when neglecting the cavity dissipation.The squeezing degree only depends on the initial population of the atomic upper level and thus strong squeezing can be generated in principle.We also reveal that the entanglement between the two cavity fields is less affected by the cavity damping than the purity of the entangled cavity field state.In addition,our two-channel scheme can effectively improve the entanglement and purity of the entangled cavity field,compared to the previous single-channel proposals.
In this paper,we investigate the generation of stationary entangled state of a two-mode cavity field via injecting into the cavity a beam of four-level atoms with two channels of two-photon cascaded transition.By treating the atomic beam as the external reservoir for the cavity field in weak cavity-atom interactions,we find that a two-mode squeezed vacuum reservoir of the cavity field can be achieved by using the atomic system.Therefore,in the steady-state regime,the cavity field can be driven into the two-mode squeezed vacuum when neglecting the cavity dissipation.The squeezing degree only depends on the initial population of the atomic upper level and thus strong squeezing can be generated in principle.We also reveal that the entanglement between the two cavity fields is less affected by the cavity damping than the purity of the entangled cavity field state.In addition,our two-channel scheme can effectively improve the entanglement and purity of the entangled cavity field,compared to the previous single-channel proposals.
引文
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[21]Li G,Tan H,Wu S,et al.Entanglement for Excitons in Two Quantum Dots Placed in Two Separate Single-mode Cavities[J].Phys Rev A,2004,70:034307.DOI:https:∥doi.org/10.1103/PhysRevA.70.034307.
[22]Wang F,Nie W,Feng X,et al.Steady-state Entanglement of Harmonic Oscillators Via Dissipation in a Single Superconducting Artificial Atom[J].Phys Rev A,2016,94:012330.DOI:https:∥doi.org/10.1103/PhysRevA.94.012330.
[23]Pielawa S,Morigi G,Vitali D,et al.Generation of Einstein-Podolsky-Rosen-Entangled Radiation through an Atomic Reservoir[J].Phys Rev Lett,2007,98:240401.DOI:https:∥doi.org/10.1103/PhysRevLett.98.240401.
[24]Scully M O,Zubairy M S.Quantum Optics[M].1997,出版社:Cambridge University.
[25]Duan L M,Giedke G,Cirac J I,et al.Inseparability Criterion for Continuous Variable Systems[J].Phys Rev Lett,2000:84,2722.DOI:https:∥doi.org/10.1103/PhysRevLett.84.2722.
[2]Einstein A,Podolsky B,Rosen N.Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?[J].Phys Rev,1935,47:777-780.DOI:https:∥doi.org/10.1103/PhysRev.47.777.
[3]Reid M D.Demonstration of the Einstein-Podolsky-Rosen Paradox using Nondegenerate Parametric Amplification[J].Phys Rev A,1989,40:913-923.DOI:https:∥doi.org/10.1103/PhysRevA.40.913.
[4]Braunstein S L,Loock P V.Quantum Information with Continuous Variables[J].Rev Mod Phys,2005,77:513-577.DOI:https:∥doi.org/10.1103/RevModPhys.77.513.
[5]Ou Z Y,Pereira S F,Kimble H J,et al.Realization of the Einstein-Podolsky-Rosen Paradox for Continuous Variables[J].Phys Rev Lett,1992,68:3663-3666.DOI:https:∥doi.org/10.1103/PhysRevLett.68.3663.
[6]Serra R M,Villas-Boas C J,de Almeida N G,et al.Frequency Up-and Down-conversions in Two-mode Cavity Quantum Electrodynamics[J].Phys Rev A,2005,71:045802.DOI:https:∥doi.org/10.1103/PhysRevA.71.045802.
[7]Prado F O,de Almeida N G,Moussa M H Y,et al.Bilinear and Quadratic Hamiltonians in Two-mode Cavity Quantum Electrodynamics[J].Phys Rev A,2006,73:043803.DOI:https:∥doi.org/10.1103/PhysRevA.73.043803.
[8]Fani M,Naderi Andm H.Coherent Coupling Between an Optomechanical Membrane and an Interacting Photon BoseEinstein Condensate[J].Journal of Modern Optics,2017,64:1725-1738.DOI:10.1080/09500340.2017.1311957.
[9]Bai C,Wang D,Wang H,et al.Robust Entanglement Between a Movable Mirror and Atomic Ensemble and Entanglement Transfer in Coupled Optomechanical System[J].Scientific Reports,2016,6:33404.DOI:10.1038/srep33404.
[10]Yang Z,Zhang X,Wang M,et al.Generation of an Entangled Traveling Photon-phonon Pair in an Optomechanical Resonator-waveguide System[J].Phys Rev A,2017,96:013805.DOI:https:∥doi.org/10.1103/PhysRevA.96.013805.
[11]Parkins A S,Solano E,Cirac J I.Unconditional Two-Mode Squeezing of Separated Atomic Ensembles[J].Phys Rev Lett,2006,96:053602.DOI:https:∥doi.org/10.1103/PhysRevLett.96.053602.
[12]Kastoryano M J,Reiter F,Srensen A S.Dissipative Preparation of Entanglement in Optical Cavities[J].Phys Rev Lett,2011,106:090502.DOI:https:∥doi.org/10.1103/PhysRevLett.106.090502.
[13]Muschik C A,Polzik E S,Cirac J I.Dissipatively Driven Entanglement of Two Macroscopic Atomic Ensembles[J].Phys Rev A,2011,83:052312.DOI:https:∥doi.org/10.1103/PhysRevA.83.052312.
[14]Krauter H,Muschik C A,Jensen K,et al.Entanglement Generated by Dissipation and Steady State Entanglement of Two Macroscopic Objects[J].Phys Rev Lett,2011,107:080503.DOI:https:∥doi.org/10.1103/PhysRevLett.107.080503.
[15]Wang Y D,Clerk A.Reservoir-Engineered Entanglement in Optomechanical Systems[J].Phys Rev Lett,2013,110:253601.DOI:https:∥doi.org/10.1103/PhysRevLett.110.253601.
[16]Pirkkalainen J M,Damskagg E,Brandt M,et al.Squeezing of Quantum Noise of Motion in a Micromechanical Resonator[J].Phys Rev Lett,2015,115:243601.DOI:https:∥doi.org/10.1103/PhysRevLett.115.243601.
[17]Ockeloen-Korppi C F,Damskagg E,Pirkkalainen J M,et al.Entangled Massive Mechanical Oscillators[J].arXiv,2017:1711.01640v1.
[18]Tan H,Bariani F,Li G,et al.Generation of Macroscopic Quantum Superpositions of Optomechanical Oscillators by Dissipation[J].Phys Rev A,2013,88:023817.DOI:https:∥doi.org/10.1103/PhysRevA.88.023817.
[19]Tan H.Deterministic Quantum Superpositions and Fock States of Mechanical Oscillators Via Quantum Interference in Single-photon Cavity Optomechanics[J].Phys Rev A,2014,89:053829.DOI:https:∥doi.org/10.1103/PhysRevA.89.053829.
[20]Tesfa S.Entanglement Amplification in a Nondegenerate Three-level Cascade Laser[J].Phys Rev A,2006,74:043816.DOI:https:∥doi.org/10.1103/PhysRevA.74.043816.
[21]Li G,Tan H,Wu S,et al.Entanglement for Excitons in Two Quantum Dots Placed in Two Separate Single-mode Cavities[J].Phys Rev A,2004,70:034307.DOI:https:∥doi.org/10.1103/PhysRevA.70.034307.
[22]Wang F,Nie W,Feng X,et al.Steady-state Entanglement of Harmonic Oscillators Via Dissipation in a Single Superconducting Artificial Atom[J].Phys Rev A,2016,94:012330.DOI:https:∥doi.org/10.1103/PhysRevA.94.012330.
[23]Pielawa S,Morigi G,Vitali D,et al.Generation of Einstein-Podolsky-Rosen-Entangled Radiation through an Atomic Reservoir[J].Phys Rev Lett,2007,98:240401.DOI:https:∥doi.org/10.1103/PhysRevLett.98.240401.
[24]Scully M O,Zubairy M S.Quantum Optics[M].1997,出版社:Cambridge University.
[25]Duan L M,Giedke G,Cirac J I,et al.Inseparability Criterion for Continuous Variable Systems[J].Phys Rev Lett,2000:84,2722.DOI:https:∥doi.org/10.1103/PhysRevLett.84.2722.