(45-3) 09 * << * >> * Русский * English * Содержание * Все выпуски

Non-Markovian decoherence of a two-level system in a Lorentzian bosonic reservoir and a stochastic environment with finite correlation time
V.A. Mikhailov 1, N.V. Troshkin 1

Samara National Research University, 443086, Samara, Russia, Moskovskoye Shosse 34

 PDF, 1642 kB

DOI: 10.18287/2412-6179-CO-776

Страницы: 372-381.

Язык статьи: English

Аннотация:
In this paper we investigate non-Markovian evolution of a two-level system (qubit) in a bosonic bath under influence of an external classical fluctuating environment. The interaction with the bath has the Lorentzian spectral density, and the fluctuating environment (stochastic field) is represented by a set of Ornstein-Uhlenbeck processes. Each of the subenvironments of the composite environment is able to induce non-Markovian dynamics of the two-level system. By means of the numerically exact method of hierarchical equations of motion, we study steady states of the two-level system, evolution of the reduced density matrix and the equilibrium emission spectra in dependence on the frequency cutoffs and the coupling strengths of the subenvironments. Additionally, we investigate the impact of the rotating wave approximation (RWA) for the interaction with the bath on accuracy of the results.

Ключевые слова:
non-Markovian evolution, bosonic reservoir, stochastic field, two-level system.

Citation:
Mikhailov VA, Troshkin NV. Non-Markovian decoherence of a two-level system in a Lorentzian bosonic reservoir and a stochastic environment with finite correlation time. Computer Optics 2021; 45(3): 372-381. DOI: 10.18287/2412-6179-CO-776.

Литература:

  1. Koch CP. Controlling open quantum systems: tools, achievements, and limitations. J Phys Condens Matter 2016; 28(21): 213001. DOI: 10.1088/0953-8984/28/21/213001.
  2. Khurana D, Agarwalla BK, Mahesh TS. Experimental emulation of quantum non-Markovian dynamics and coherence protection in the presence of information backflow. Phys Rev A 2019; 99: 022107. DOI: 10.1103/PhysRevA.99.022107.
  3. D’Arrigo A, Falci G, Paladino E. Quantum zeno and anti-zeno effect on a two-qubit gate by dynamical decoupling. Eur Phys J Spec Top 2019; 227(15): 2189-2194. DOI: 10.1140/epjst/ e2018-800081-0.
  4. Jing J, Wu L-A. Decoherence and control of a qubit in spin baths: an exact master equation study. Sci Rep 2018; 8(1): 1471. DOI: 10.1038/s41598-018-19977-9.
  5. Ban M. Decoherence of a two-qubit system interacting with initially correlated random telegraph noises. Quantum Inf Process 2020; 19(2): 46. DOI: 10.1007/s11128-019-2539-4.
  6. Moreira S, Marques B, Paiva R, Cruz L, Soares-Pinto D, Semião F. Enhancing quantum transport efficiency by tuning non-Markovian dephasing. Phys Rev A 2020; 101(1): 012123. DOI: 10.1103/PhysRevA.101.012123.
  7. Maier C, Brydges T, Jurcevic P, Trautmann N, Hempel C, Lanyon B, Hauke P, Blatt R, Roos C. Environment-assisted quantum transport in a 10-qubit network. Phys Rev Lett 2019; 122(5): 050501. DOI: 10.1103/PhysRevLett.122.050501.
  8. Breuer H-P, Petruccione F, et al. The theory of open quantum systems. Oxford: Oxford University Press; 2002.
  9. Rivas A, Huelga SF, Plenio MB. Quantum non-markovianity: characterization, quantification and detection. Rep Progr Phys 2014; 77(9): 094001. DOI: 10.1088/0034-4885/77/9/094001.
  10. Lindblad G. On the generators of quantum dynamical semigroups. Commun Math Phys 1976; 48(2): 119-130. DOI: 10.1007/ BF01608499.
  11. de Vega I, Alonso D. Dynamics of non-Markovian open quantum systems. Rev Mod Phys 2017; 89: 015001. DOI: 10.1103/RevModPhys.89.015001.
  12. Wu J, Chen S, Seeds A, Liu H. Quantum dot optoelectronic devices: lasers, photodetectors and solar cells. J Phys D Appl Phys 2015; 48(36): 363001. DOI: 10.1088/0022-3727/48/36/363001.
  13. Meden V. The Anderson–Josephson quantum dot—a theory perspective. J Phys Cond Matter 2019; 31(16): 163001. DOI: 10. 1088/1361-648x/aafd6a.
  14. Tahara H, Ogawa Y, Minami F, Akahane K, Sasaki M. Long-time correlation in non-Markovian dephasing of an exciton-phonon system in inas quantum dots. Phys Rev Lett 2014; 112: 147404. DOI: 10.1103/PhysRevLett.112.147404.
  15. Bera D, Qian L, Tseng T-K, Holloway P. Quantum dots and their multimodal applications: A review. Materials 2010; 3(4): 2260-2345. DOI: 10.3390/ma3042260.
  16. Aspelmeyer M, Kippenberg T, Marquardt F. Cavity optomechanics. Rev Mod Phys 2014; 86(4): 1391-1452. DOI: 10.1103/ RevModPhys.86.1391.
  17. Gröblacher S, Trubarov A, Prigge N, Cole GD, Aspelmeyer M, Eisert J. Observation of non-Markovian micromechanical brownian motion. Nat Commun 2015; 6(1): 7606. DOI: 10.1038/ncomms8606.
  18. Andersson G, Suri B, Guo L, Aref T, Delsing P. Non-exponential decay of a giant artificial atom. Nature Phys 2019; 15(11): 1123-1127. DOI: 10.1038/s41567-019-0605-6.
  19. Potočnik A, Bargerbos A, Schröder FAYN, Khan SA, Collodo MC, Gasparinetti S, Salathé Y, Creatore C, Eichler C, Türeci HE, Chin AW, Wallraff A. Studying light-harvesting models with superconducting circuits. Nature Commun 2018; 9(1): 904. DOI: 10.1038/s41467-018-03312-x.
  20. Yu D, Dumke R. Open ising model perturbed by classical colored noise. Phys Rev A 2019; 100(2): 022124. DOI: 10.1103/PhysRevA.100.022124.
  21. Pfalzgraff W, Montoya-Castillo A, Kelly A, Markland T. Efficient construction of generalized master equation memory kernels for multi-state systems from nonadiabatic quantum-classical dynamics. J Chem Phys 2019; 150(24): 244109. DOI: 10.1063/1.5095715.
  22. Hwang-Fu Y-H, Chen W, Cheng Y-C. A coherent modified redfield theory for excitation energy transfer in molecular aggregates. Chem Phys 2015; 447: 46-53. DOI: 10.1016/j.chemphys.2014.11.026.
  23. Chin AW, Prior J, Rosenbach R, Caycedo-Soler F, Huelga SF, Plenio MB. The role of non-equilibrium vibrational structures in electronic coherence and recoherence in pigment-protein complexes. Nat Phys 2013; 9(2): 113-118. DOI: 10.1038/nphys2515.
  24. Lee MK, Huo P, Coker DF. Semiclassical path integral dynamics: Photosynthetic energy transfer with realistic environment interactions. Annu Rev Phys Chem 2016; 67(1): 639-668. DOI: 10.1146/annurev-physchem-040215-112252.
  25. Segal D, Agarwalla BK. Vibrational heat transport in molecular junctions. Annu Rev Phys Chem 2016; 67(1): 185-209. doi: 10.1146/annurev-physchem-040215-112103.
  26. Plenio MB, Almeida J, Huelga SF. Origin of long-lived oscillations in 2d-spectra of a quantum vibronic model: Electronic versus vibrational coherence. J Chem Phys 2013; 139(23): 235102. DOI: 10.1063/1.4846275.
  27. Coish W, Baugh J. Nuclear spins in nanostructures. Phys Status Solidi B Basic Res 2009; 246(10): 2203-2215. doi: 10.1002/pssb. 200945229.
  28. Barford W. Electronic and optical properties of conjugated polymers. Oxford: Oxford University Press; 2013.
  29. Latune CL, Sinayskiy I, Petruccione F. Quantum force estimation in arbitrary non-Markovian gaussian baths. Phys Rev A 2016; 94: 052115. doi: 10.1103/PhysRevA.94.052115.
  30. Bylicka B, Chruscinski D, Maniscalco S. Non-Markovianity and reservoir memory of quantum channels: a quantum information theory perspective. Sci Rep 2014; 4(1): 5720. DOI: 10.1038/srep05720.
  31. Xiang G-Y, Hou Z-B, Li C-F, Guo G-C, Breuer H-P, Laine E-M, Piilo J. Entanglement distribution in optical fibers assisted by nonlocal memory effects, EPL 2014; 107(5): 54006. DOI: 10.1209/0295-5075/107/54006.
  32. McCutcheon DPS, Dattani NS, Gauger EM, Lovett BW, Nazir A. A general approach to quantum dynamics using a variational master equation: Application to phonon-damped rabi rotations in quantum dots. Phys Rev B 2011; 84: 081305. DOI: 10.1103/PhysRevB.84.081305.
  33. Jang S. Theory of coherent resonance energy transfer for coherent initial condition. J Chem Phys 2009; 131(16): 164101. DOI: 10.1063/1.3247899.
  34. Garraway BM. Nonperturbative decay of an atomic system in a cavity. Phys Rev A 1997; 55: 2290-2303. DOI: 10.1103/PhysRevA.55.2290.
  35. Mascherpa F, Smirne A, Somoza AD, Fernández-Acebal P, Donadi S, Tamascelli D, Huelga SF, Plenio MB. Optimized auxiliary oscillators for the simulation of general open quantum systems. Phys Rev A 2020; 101: 052108. DOI: 10.1103/PhysRevA.101.052108.
  36. Tamascelli D, Smirne A, Huelga SF, Plenio MB. Nonperturbative treatment of non-Markovian dynamics of open quantum systems. Phys Rev Lett 2018; 120: 030402. DOI: 10.1103/PhysRevLett.120.030402.
  37. Makri N, Makarov DE. Tensor propagator for iterative quantum time evolution of reduced density matrices. I. Theory. J Chem Phys 1995; 102(11): 4600-4610. DOI: 10.1063/1.469508.
  38. Makri N, Makarov DE. Tensor propagator for iterative quantum time evolution of reduced density matrices. II. Numerical methodology. J Chem Phys 1995; 102(11): 4611-4618. DOI: 10.1063/1. 469509.
  39. Strathearn A, Kirton P, Kilda D, Keeling J, Lovett BW. Efficient non-Markovian quantum dynamics using time-evolving matrix product operators. Nat Commun 2018; 9(1): 3322. DOI: 10.1038/ s41467-018-05617-3.
  40. Prior J, Chin AW, Huelga SF, Plenio MB. Efficient simulation of strong system-environment interactions. Phys Rev Lett 2010; 105: 050404. DOI: 10.1103/PhysRevLett.105.050404.
  41. Tamascelli D, Smirne A, Lim J, Huelga SF, Plenio MB. Efficient simulation of finite-temperature open quantum systems. Phys Rev Lett 2019; 123: 090402. DOI: 10.1103/PhysRevLett.123.090402.
  42. Nüßeler A, Dhand I, Huelga SF, Plenio MB. Efficient simulation of open quantum systems coupled to a fermionic bath. Phys Rev B 2020; 101: 155134. DOI: 10.1103/PhysRevB.101.155134.
  43. Tanimura Y. Stochastic Liouville, Langevin, Fokker–Planck, and master equation approaches to quantum dissipative systems. J Phys Soc Japan 2006; 75(8): 082001. DOI: 10.1143/JPSJ.75.082001.
  44. Tanimura Y, Kubo R. Time evolution of a quantum system in contact with a nearly Gaussian-Markoffian noise bath. J Phys Soc Japan 1989; 58(1): 101-114. DOI: 10.1143/JPSJ.58.101.
  45. Tanimura Y. Reduced hierarchical equations of motion in real and imaginary time: Correlated initial states and thermodynamic quantities. J Chem Phys 2014; 141(4): 044114. DOI: 10.1063/1. 4890441.
  46. Semin V, Sinayskiy I, Petruccione F. Arbitrary spin in a spin bath: Exact dynamics and approximation techniques, Phys Rev A 2014; 89: 012107. DOI: 10.1103/PhysRevA.89.012107.
  47. Rossi MAC, Paris MGA. Non-Markovian dynamics of single- and two-qubit systems interacting with Gaussian and non-Gaussian fluctuating transverse environments. J Chem Phys 2016; 144(2): 024113. DOI: 10.1063/1.4939733.
  48. Mwalaba M, Sinayskiy I, Petruccione F. Dynamics and thermalization in a simple mesoscopic fermionic bath. Phys Rev A 2019; 99: 052102. DOI: 10.1103/PhysRevA.99.052102.
  49. Pavelev A, Semin V. Investigation of non-Markovian dynamics of two dipole-dipole interacting Qubits based on numerical solution of the non-linear stochastic Schrödinger equation. Computer Optics 2019; 43(2): 168-173. DOI: 10.18287/2412-6179-2019-43-2-168-173.
  50. Vasilev D, Semin V. Qubit dynamics in extern laser field. Computer Optics 2019; 43(4): 562-566. DOI: 10.18287/ 2412-6179-2019-43-4-562-566.
  51. Iles-Smith J, Lambert N, Nazir A. Environmental dynamics, correlations, and the emergence of noncanonical equilibrium states in open quantum systems. Phys Rev A 2014; 90: 032114. DOI: 10.1103/PhysRevA.90.032114.
  52. De Santis D, Johansson M, Bylicka B, Bernardes NK, Acín A. Correlation measure detecting almost all non-markovian evolutions. Phys Rev A 2019; 99: 012303. DOI: 10.1103/PhysRevA.99.012303.
  53. Ali MM, Lo P-Y, Tu MW-Y, Zhang W-M. Non-Markovianity measure using two-time correlation functions. Phys Rev A 2015; 92: 062306. DOI: 10.1103/PhysRevA.92.062306.
  54. McCutcheon DPS. Optical signatures of non-Markovian behavior in open quantum systems. Phys Rev A 2016; 93: 022119. DOI: 10.1103/ PhysRevA.93.022119.
  55. Fleming C, Cummings NI, Anastopoulos C, Hu BL. The rotating-wave approximation: consistency and applicability from an open quantum system analysis. J Phys A Math Theor 2010; 43(40): 405304. DOI: 10.1088/1751-8113/43/40/405304.
  56. Mäkelä H, Möttönen M. Effects of the rotating-wave and secular approximations on non-Markovianity. Phys Rev A 2013; 88: 052111. DOI: 10.1103/PhysRevA.88.052111.
  57. Eastham PR, Kirton P, Cammack HM, Lovett BW, Keeling J. Bath-induced coherence and the secular approximation. Phys Rev A 2016; 94: 012110. DOI: 10.1103/PhysRevA.94.012110.
  58. Jing J, Yu T, Lam C-H, You JQ, Wu L-A. Control relaxation via dephasing: A quantum-state-diffusion study. Phys Rev A 2018; 97: 012104. DOI: 10.1103/PhysRevA.97.012104.
  59. Jing J, Li R, You JQ, Yu T. Nonperturbative stochastic dynamics driven by strongly correlated colored noise. Phys Rev A 2015; 91: 022109. DOI: 10.1103/PhysRevA.91.022109.
  60. Jing J, Wu L-A. Control of decoherence with no control, Sci Rep 2013; 3(1): 2746. DOI: 10.1038/srep02746.
  61. Brian Walton D, Visscher K. Noise suppression and spectral decomposition for state-dependent noise in the presence of a stationary fluctuating input. Phys Rev E 2004; 69: 051110. DOI: 10.1103/PhysRevE.69.051110.
  62. Wang ZH, Ji YJ, Li Y, Zhou DL. Dissipation and decoherence induced by collective dephasing in a coupled-qubit system with a common bath. Phys Rev A 2015; 91: 013838. DOI: 10.1103/PhysRevA.91.013838.
  63. Semin V. Non-Markovian relaxation of a three-level atom in two laser fields with noise. Laser Phys 2020; 30(2): 025204. DOI: 10.1088/1555-6611/ab65c3.
  64. Biercuk MJ, Doherty AC, Uys H. Dynamical decoupling sequence construction as a filter-design problem. J Phys B-At Mol Opt 2011; 44(15): 154002. DOI: 10.1088/0953-4075/44/15/154002.
  65. Wu W, Lin H-Q. Quantum zeno and anti-zeno effects in quantum dissipative systems. Phys Rev A 2017; 95: 042132. DOI: 10.1103/PhysRevA.95.042132.
  66. Wu W. Realization of hierarchical equations of motion from stochastic perspectives. Phys Rev A 2018; 98: 012110. DOI: 10.1103/PhysRevA.98.012110.
  67. Li J-G, Zou J, Shao B. Non-Markovianity of the damped jaynescummings model with detuning. Phys Rev A 2010; 81: 062124. DOI: 10.1103/PhysRevA.81.062124.
  68. Mikhailov VA, Troshkin NV. Non-Markovian dynamics of a two-level system in a bosonic bath and a gaussian fluctuating environment with finite correlation time. Phys Rev A 2021; 103: 012208. DOI: 10.1103/PhysRevA.103.012208.
  69. Mikhailov VA, Troshkin NV. Master equation averaged over stochastic process realizations for the description of a three-level atom relaxation. Computer Optics 2016; 40(5): 649-653. DOI: 10.18287/2412-6179-2016-40-5-649-653.
  70. Risken H, Frank T. The Fokker-Planck equation. Berlin, Heidelberg: Springer-Verlag; 1996. DOI: 10.1007/978-3-642-61544-3.

© 2009, IPSI RAS
Россия, 443001, Самара, ул. Молодогвардейская, 151; электронная почта: journal@computeroptics.ru; тел: +7 (846) 242-41-24 (ответственный секретарь), +7 (846) 332-56-22 (технический редактор), факс: +7 (846) 332-56-20