Abstract

Adiabatic quantum control is a very important approach for quantum physics and quantum information processing (QIP). It holds the advantage with robustness to experimental imperfections but accumulates more decoherence due to the long evolution time. Here, we propose a universal protocol for fast and robust quantum control in multimode interactions of a quantum system by using shortcuts to adiabaticity. The results show this protocol can speed up the evolution of a multimode quantum system effectively, and it can also keep the robustness very good while adiabatic quantum control processes cannot. We apply this protocol for the quantum state transfer in QIP in the photon-phonon interactions in an optomechanical system, showing a perfect result. These good features make this protocol have the capability of improving effectively the feasibility of the practical applications of multimode interactions in QIP in experiment.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  9. M. Demirplak and S. A. Rice, “Assisted adiabatic passage revisited,” J. Phys. Chem. B 109, 6838 (2005).
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  11. X. Chen, I. Lizuain, A. Ruschhaupt, D. Guéry-Odelin, and J. G. Muga, “Shortcut to adiabatic passage in two- and three-Level atoms,” Phys. Rev. Lett. 105, 123003 (2010).
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  32. Y. X. Du, Z. T. Liang, Y. C. Li, X. X. Yue, Q. X. Lv, W. Huang, X. Chen, H. Yan, and S. L. Zhu, “Experimental realization of stimulated Raman shortcut-to-adiabatic passage with cold atoms,” Nat. Commun. 7, 12479 (2016).
    [Crossref] [PubMed]
  33. S. An, D. Lv, A. del Campo, and K. Kim, “Shortcuts to adiabaticity by counterdiabatic driving for trapped-ion displacement in phase space,” Nat. Commun. 7, 12999 (2016).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
  38. F. C. Lei, M. Gao, C. G. Du, Q. L. Jing, and G. L. Long, “Three-pathway electromagnetically induced transparency in coupled-cavity optomechanical system,” Opt. Express 23, 11508–11517 (2015).
    [Crossref] [PubMed]
  39. X. Jiang, M. Wang, M. C. Kuzyk, T. Oo, G. L. Long, and H. Wang, “Chip-based silica microspheres for cavity optomechanics,” Opt. Express 23, 27260–27265 (2015).
    [Crossref] [PubMed]
  40. R. Riedinger, A. Wallucks, I. Marinković, C. Löschnauer, M. Aspelmeyer, S. Hong, and S. Gröblacher, “Remote quantum entanglement between two micromechanical oscillators,” Nature 556, 473 (2018).
    [Crossref] [PubMed]
  41. C. Dong, V. Fiore, M. C. Kuzyk, and H. Wang, “Optomechanical dark mode,” Science 338, 1609–1613 (2012).
    [Crossref] [PubMed]
  42. Y. D. Wang and A. A. Clerk, “Using interference for high fidelity quantum state transfer in optomechanics,” Phys. Rev. Lett. 108, 153603 (2012).
    [Crossref] [PubMed]
  43. L. Tian, “Adiabatic state conversion and pulse transmission in optomechanical systems,” Phys. Rev. Lett. 108, 153604 (2012).
    [Crossref] [PubMed]
  44. L. Tian, “Robust photon entanglement via quantum interference in optomechanical interfaces,” Phys. Rev. Lett. 110, 233602 (2013).
    [Crossref] [PubMed]
  45. Y. D. Wang and A. A. Clerk, “Reservoir-engineered entanglement in optomechanical systems,” Phys. Rev. Lett. 110, 253601 (2013).
    [Crossref] [PubMed]
  46. Q. Lin, J. Rosenberg, D. Chang, R. Camacho, M. Eichenfield, K. J. Vahala, and O. Painter, “Coherent mixing of mechanical excitations in nano-optomechanical structures,” Nat. Photon. 4, 236 (2010).
    [Crossref]
  47. F. Massel, S. U. Cho, J.-M. Pirkkalainen, P. J. Hakonen, T. T. Heikkilä, and M. A. Sillanpää, “Multimode circuit optomechanics near the quantum limit,” Nat. Commun. 3, 987 (2012).
    [Crossref] [PubMed]
  48. N. Spethmann, J. Kohler, S. Schreppler, L. Buchmann, and D. M. Stamper-Kurn, “Cavity-mediated coupling of mechanical oscillators limited by quantum back-action,” Nat. Phys. 12, 27 (2016).
    [Crossref]
  49. M. C. Kuzyk and H. Wang, “Controlling multimode optomechanical interactions via interference,” Phys. Rev. A 96, 023860 (2017).
    [Crossref]
  50. G. Vasilev, A. Kuhn, and N. Vitanov, “Optimum pulse shapes for stimulated Raman adiabatic passage,” Phys. Rev. A 80, 013417 (2009).
    [Crossref]
  51. J. I. Cirac, P. Zoller, H. J. Kimble, and H. Mabuchi, “Quantum state transfer and entanglement distribution among distant nodes in a quantum network,” Phys. Rev. Lett. 78, 3221 (1997).
    [Crossref]
  52. H. K. Li, X. X. Ren, Y. C. Liu, and Y. F. Xiao, “Photon-photon interactions in a largely detuned optomechanical cavity,” Phys. Rev. A 88, 053850 (2013).
    [Crossref]

2018 (2)

H. L. Mortensen, J. J. W. H. Sørensen, K. Mølmer, and J. F. Sherson, “Fast state transfer in a Λ-system: a shortcut-to-adiabaticity approach to robust and resource optimized control,” New J. Phys. 20, 025009 (2018).
[Crossref]

R. Riedinger, A. Wallucks, I. Marinković, C. Löschnauer, M. Aspelmeyer, S. Hong, and S. Gröblacher, “Remote quantum entanglement between two micromechanical oscillators,” Nature 556, 473 (2018).
[Crossref] [PubMed]

2017 (3)

B. B. Zhou, A. Baksic, H. Ribeiro, C. G. Yale, F. J. Heremans, P. C. Jerger, A. Auer, G. Burkard, A. A. Clerk, and D. D. Awschalom, “Accelerated quantum control using superadiabatic dynamics in a solid-state lambda system,” Nat. Phys. 13, 330–334 (2017).
[Crossref]

M. C. Kuzyk and H. Wang, “Controlling multimode optomechanical interactions via interference,” Phys. Rev. A 96, 023860 (2017).
[Crossref]

J. L. Wu, X. Ji, and S. Zhang, “Shortcut to adiabatic passage in a three-level system via a chosen path and its application in a complicated system,” Opt. Express 25, 21084–21093 (2017).
[Crossref] [PubMed]

2016 (10)

N. Spethmann, J. Kohler, S. Schreppler, L. Buchmann, and D. M. Stamper-Kurn, “Cavity-mediated coupling of mechanical oscillators limited by quantum back-action,” Nat. Phys. 12, 27 (2016).
[Crossref]

Y. X. Du, Z. T. Liang, Y. C. Li, X. X. Yue, Q. X. Lv, W. Huang, X. Chen, H. Yan, and S. L. Zhu, “Experimental realization of stimulated Raman shortcut-to-adiabatic passage with cold atoms,” Nat. Commun. 7, 12479 (2016).
[Crossref] [PubMed]

S. An, D. Lv, A. del Campo, and K. Kim, “Shortcuts to adiabaticity by counterdiabatic driving for trapped-ion displacement in phase space,” Nat. Commun. 7, 12999 (2016).
[Crossref] [PubMed]

S. He, S. L. Su, D. Y. Wang, W. M. Sun, C. H. Bai, A. D. Zhu, H. F. Wang, and S. Zhang, “Efficient shortcuts to adiabatic passage for three-dimensional entanglement generation via transitionless quantum driving,” Sci. Rep. 6, 30929 (2016).
[Crossref] [PubMed]

A. C. Santos, R. D. Silva, and M. S. Sarandy, “Shortcut to adiabatic gate teleportation,” Phys. Rev. A 93, 012311 (2016).
[Crossref]

X. K. Song, H. Zhang, Q. Ai, J. Qiu, and F. G. Deng, “Shortcuts to adiabatic holonomic quantum computation in decoherence-free subspace with transitionless quantum driving algorithm,” New J. Phys. 18, 023001 (2016).
[Crossref]

Y. H. Kang, Y. H. Chen, Q. C. Wu, B. H. Huang, Y. Xia, and J. Song, “Reverse engineering of a Hamiltonian by designing the evolution operators,” Sci. Rep. 6, 30151 (2016).
[Crossref] [PubMed]

X. K. Song, Q. Ai, J. Qiu, and F. G. Deng, “Physically feasible three-level transitionless quantum driving with multiple Schrödinger dynamics,” Phys. Rev. A 93, 052324 (2016).
[Crossref]

Y. H. Chen, Y. Xia, Q. C. Wu, B. H. Huang, and J. Song, “Method for constructing shortcuts to adiabaticity by a substitute of counterdiabatic driving terms,” Phys. Rev. A 93, 052109 (2016).
[Crossref]

A. Baksic, H. Ribeiro, and A. A. Clerk, “Speeding up adiabatic quantum state transfer by using dressed states,” Phys. Rev. Lett. 116, 230503 (2016).
[Crossref] [PubMed]

2015 (6)

A. C. Santos and M. S. Sarandy, “Superadiabatic controlled evolutions and universal quantum computation,” Sci. Rep. 5, 15775 (2015).
[Crossref] [PubMed]

Y. H. Chen, Y. Xia, Q. Q. Chen, and J. Song, “Fast and noise-resistant implementation of quantum phase gates and creation of quantum entangled states,” Phys. Rev. A 91, 012325 (2015).
[Crossref]

Y. Liang, Q. C. Wu, S. L. Su, X. Ji, and S. Zhang, “Shortcuts to adiabatic passage for multiqubit controlled-phase gate,” Phys. Rev. A 91, 032304 (2015).
[Crossref]

F. C. Lei, M. Gao, C. G. Du, Q. L. Jing, and G. L. Long, “Three-pathway electromagnetically induced transparency in coupled-cavity optomechanical system,” Opt. Express 23, 11508–11517 (2015).
[Crossref] [PubMed]

X. Jiang, M. Wang, M. C. Kuzyk, T. Oo, G. L. Long, and H. Wang, “Chip-based silica microspheres for cavity optomechanics,” Opt. Express 23, 27260–27265 (2015).
[Crossref] [PubMed]

M. Gao, F. C. Lei, C. G. Du, and G. L. Long, “Self-sustained oscillation and dynamical multistability of optomechanical systems in the extremely-large-amplitude regime,” Phys. Rev. A 91, 013833 (2015).
[Crossref]

2014 (5)

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86, 1391 (2014).
[Crossref]

Y. H. Chen, Y. Xia, Q. Q. Chen, and J. Song, “Efficient shortcuts to adiabatic passage for fast population transfer in multiparticle systems,” Phys. Rev. A 89, 033856 (2014).
[Crossref]

M. Lu, Y. Xia, L. T. Shen, J. Song, and N. B. An, “Shortcuts to adiabatic passage for population transfer and maximum entanglement creation between two atoms in a cavity,” Phys. Rev. A 89, 012326 (2014).
[Crossref]

M. Lu, Y. Xia, L. T. Shen, and J. Song, “An effective shortcut to adiabatic passage for fast quantum state transfer in a cavity quantum electronic dynamics system,” Laser Phys. 24, 105201 (2014).
[Crossref]

S. Martínez-Garaot, E. Torrontegui, X. Chen, and J. G. Muga, “Shortcuts to adiabaticity in three-level systems using Lie transforms,” Phys. Rev. A 89, 053408 (2014).
[Crossref]

2013 (6)

A. del Campo, “Shortcuts to adiabaticity by counterdiabatic driving,” Phys. Rev. Lett. 111, 100502 (2013).
[Crossref]

E. Torrontegui, S. Ibáñez, S. Martínez-Garaot, M. Modugno, A. del Campo, D. Guéry-Odelin, A. Ruschhaupt, X. Chen, and J. G. Muga, “Shortcuts to adiabaticity,” Adv. Atom. Mol. Opt. Phys. 62, 117 (2013).
[Crossref]

J. Zhang, J. H. Shim, I. Niemeyer, T. Taniguchi, T. Teraji, H. Abe, S. Onoda, T. Yamamoto, T. Ohshima, J. Isoya, and D. Suter, “Experimental implementation of assisted quantum adiabatic passage in a single spin,” Phys. Rev. Lett. 110, 240501 (2013).
[Crossref] [PubMed]

L. Tian, “Robust photon entanglement via quantum interference in optomechanical interfaces,” Phys. Rev. Lett. 110, 233602 (2013).
[Crossref] [PubMed]

Y. D. Wang and A. A. Clerk, “Reservoir-engineered entanglement in optomechanical systems,” Phys. Rev. Lett. 110, 253601 (2013).
[Crossref] [PubMed]

H. K. Li, X. X. Ren, Y. C. Liu, and Y. F. Xiao, “Photon-photon interactions in a largely detuned optomechanical cavity,” Phys. Rev. A 88, 053850 (2013).
[Crossref]

2012 (6)

F. Massel, S. U. Cho, J.-M. Pirkkalainen, P. J. Hakonen, T. T. Heikkilä, and M. A. Sillanpää, “Multimode circuit optomechanics near the quantum limit,” Nat. Commun. 3, 987 (2012).
[Crossref] [PubMed]

C. Dong, V. Fiore, M. C. Kuzyk, and H. Wang, “Optomechanical dark mode,” Science 338, 1609–1613 (2012).
[Crossref] [PubMed]

Y. D. Wang and A. A. Clerk, “Using interference for high fidelity quantum state transfer in optomechanics,” Phys. Rev. Lett. 108, 153603 (2012).
[Crossref] [PubMed]

L. Tian, “Adiabatic state conversion and pulse transmission in optomechanical systems,” Phys. Rev. Lett. 108, 153604 (2012).
[Crossref] [PubMed]

M. G. Bason, M. Viteau, N. Malossi, P. Huillery, E. Arimondo, D. Ciampini, R. Fazio, V. Giovannetti, R. Mannella, and O. Morsch, “High-fidelity quantum driving,” Nat. Phys. 8, 147–152 (2012).
[Crossref]

S. Ibáñez, X. Chen, E. Torrontegui, J. G. Muga, and A. Ruschhaupt, “Multiple Schrödinger pictures and dynamics in shortcuts to adiabaticity,” Phys. Rev. Lett. 109, 100403 (2012).
[Crossref]

2011 (1)

X. Chen, E. Torrontegui, and J. G. Muga, “Lewis-Riesenfeld invariants and transitionless quantum driving,” Phys. Rev. A 83, 062116 (2011).
[Crossref]

2010 (2)

X. Chen, I. Lizuain, A. Ruschhaupt, D. Guéry-Odelin, and J. G. Muga, “Shortcut to adiabatic passage in two- and three-Level atoms,” Phys. Rev. Lett. 105, 123003 (2010).
[Crossref] [PubMed]

Q. Lin, J. Rosenberg, D. Chang, R. Camacho, M. Eichenfield, K. J. Vahala, and O. Painter, “Coherent mixing of mechanical excitations in nano-optomechanical structures,” Nat. Photon. 4, 236 (2010).
[Crossref]

2009 (2)

G. Vasilev, A. Kuhn, and N. Vitanov, “Optimum pulse shapes for stimulated Raman adiabatic passage,” Phys. Rev. A 80, 013417 (2009).
[Crossref]

M. V. Berry, “Transitionless quantum driving,” J. Phys. A: Math. Theor. 42, 365303 (2009).
[Crossref]

2005 (1)

M. Demirplak and S. A. Rice, “Assisted adiabatic passage revisited,” J. Phys. Chem. B 109, 6838 (2005).
[Crossref]

2003 (1)

M. Demirplak and S. A. Rice, “Adiabatic population transfer with control fields,” J. Phys. Chem. A 107, 9937 (2003).
[Crossref]

2001 (1)

N. V. Vitanov, T. Halfmann, B. W. Shore, and K. Bergmann, “Laser-induced population transfer by adiabatic passage techniques,” Annu. Rev. Phys. Chem. 52, 763 (2001).
[Crossref] [PubMed]

1998 (1)

K. Bergmann, H. Theuer, and B. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70, 1003 (1998).
[Crossref]

1997 (1)

J. I. Cirac, P. Zoller, H. J. Kimble, and H. Mabuchi, “Quantum state transfer and entanglement distribution among distant nodes in a quantum network,” Phys. Rev. Lett. 78, 3221 (1997).
[Crossref]

1977 (1)

J. T. Hwang and P. Pechukas, “The adiabatic theorem in the complex plane and the semiclassical calculation of nonadiabatic transition amplitudes,” J. Chem. Phys. 67, 4640 (1977).
[Crossref]

1976 (1)

J. P. Davis and P. Pechukas, “Nonadiabatic transitions induced by a time-dependent Hamiltonian in the semiclassical/adiabatic limit: the two-state case,” J. Chem. Phys. 64, 3129 (1976).
[Crossref]

1969 (1)

H. R. Lewis and W. B. Riesenfeld, “An exact quantum theory of the time-dependent harmonic oscillator and of a charged particle in a time-dependent electromagnetic field,” J. Math. Phys. 10, 1458 (1969).
[Crossref]

1928 (1)

M. Born and V. A. Fock, “Beweis des Adiabatensatzes,” Z. Phys. 51, 165 (1928).
[Crossref]

Abe, H.

J. Zhang, J. H. Shim, I. Niemeyer, T. Taniguchi, T. Teraji, H. Abe, S. Onoda, T. Yamamoto, T. Ohshima, J. Isoya, and D. Suter, “Experimental implementation of assisted quantum adiabatic passage in a single spin,” Phys. Rev. Lett. 110, 240501 (2013).
[Crossref] [PubMed]

Ai, Q.

X. K. Song, H. Zhang, Q. Ai, J. Qiu, and F. G. Deng, “Shortcuts to adiabatic holonomic quantum computation in decoherence-free subspace with transitionless quantum driving algorithm,” New J. Phys. 18, 023001 (2016).
[Crossref]

X. K. Song, Q. Ai, J. Qiu, and F. G. Deng, “Physically feasible three-level transitionless quantum driving with multiple Schrödinger dynamics,” Phys. Rev. A 93, 052324 (2016).
[Crossref]

An, N. B.

M. Lu, Y. Xia, L. T. Shen, J. Song, and N. B. An, “Shortcuts to adiabatic passage for population transfer and maximum entanglement creation between two atoms in a cavity,” Phys. Rev. A 89, 012326 (2014).
[Crossref]

An, S.

S. An, D. Lv, A. del Campo, and K. Kim, “Shortcuts to adiabaticity by counterdiabatic driving for trapped-ion displacement in phase space,” Nat. Commun. 7, 12999 (2016).
[Crossref] [PubMed]

Arimondo, E.

M. G. Bason, M. Viteau, N. Malossi, P. Huillery, E. Arimondo, D. Ciampini, R. Fazio, V. Giovannetti, R. Mannella, and O. Morsch, “High-fidelity quantum driving,” Nat. Phys. 8, 147–152 (2012).
[Crossref]

Aspelmeyer, M.

R. Riedinger, A. Wallucks, I. Marinković, C. Löschnauer, M. Aspelmeyer, S. Hong, and S. Gröblacher, “Remote quantum entanglement between two micromechanical oscillators,” Nature 556, 473 (2018).
[Crossref] [PubMed]

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86, 1391 (2014).
[Crossref]

Auer, A.

B. B. Zhou, A. Baksic, H. Ribeiro, C. G. Yale, F. J. Heremans, P. C. Jerger, A. Auer, G. Burkard, A. A. Clerk, and D. D. Awschalom, “Accelerated quantum control using superadiabatic dynamics in a solid-state lambda system,” Nat. Phys. 13, 330–334 (2017).
[Crossref]

Awschalom, D. D.

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Adv. Atom. Mol. Opt. Phys. (1)

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Annu. Rev. Phys. Chem. (1)

N. V. Vitanov, T. Halfmann, B. W. Shore, and K. Bergmann, “Laser-induced population transfer by adiabatic passage techniques,” Annu. Rev. Phys. Chem. 52, 763 (2001).
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Figures (6)

Fig. 1
Fig. 1 Schematic diagram for universal multimode interactions in a quantum system. Each mode can be represented by a harmonic oscillator. a3 is a intermediate mode for connecting two others.
Fig. 2
Fig. 2 Simulation of two quantum control approaches for the quantum state transfer in multimode interactions. The initial state is prepared in mode a1 with the Fock state |1〉. All the labels for curves with different colors are given in the last figures of every row. p1, p2 and p3 are the populations for the modes a1, a2 and a3, respectively. (a)–(c) are the variation of coupling strengths. (d)–(f) are the corresponding adiabatic quantum control processes. (g)–(i) are the corresponding fast and robust quantum control processes. The parameter changes as follow: (a) ν = 0.5; (b) ν = 1; (c) ν = 2.
Fig. 3
Fig. 3 (a) Practical schematic diagram for photon-phonon-photon interactions induced by the optomechanical system composed of two cavities and a membrane. The two cavity walls and the middle membrane are fixed, but the membrane can be vibrated. (b) Schematic diagram for phonon-phonon-phonon interactions. Two cavity walls are fixed on cantilevers.
Fig. 4
Fig. 4 Simulation of the quantum state transfer by using our fast and robust quantum control in optomechanical interactions. (a) The shape of new coupling strengths with the parameters ν = 2 MHz and δ = 40 MHz. (b) The process of the population transfer by using the coupling in (a). P1, P2 and P3 are the populations for the optical modes 1, 2 and the mechanical mode, respectively. The population of the phonon is amplified in the insert. (c) Variation of the maximal average phonon number with detuning. The insert is the variation of the maximal average phonon number vs the rate between detuning and the maximal coupling strength.
Fig. 5
Fig. 5 Fidelities for the parameter time deviation Δt. The range of the time interval is [−0.60, 0.60]. The positive and negative values represent the time delay and advance, respectively. G1 (G2) is the result from changing G1 (G2) and keeping G2 (G1) unchanged. The parameters are chosen to be ν = 2 MHz and δ = 40 MHz.
Fig. 6
Fig. 6 Fidelity of the TQD process in the present of different dissipations κ in optomechanical interactions. (a) Fidelities for the adiabatic quantum control. Here, we choose ν = 0.5 MHz. (b) Fidelities for the fast quantum control process. Parameters are chosen as γm = 500 Hz and nth = 100.

Equations (13)

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H ^ 1 = g 1 a ^ 1 a ^ 3 + g 2 a ^ 2 a ^ 3 + H . c . ,
i d v ( t ) / d t = M ( t ) v ( t ) ,
M ( t ) = [ 0 g 1 ( t ) 0 g 1 ( t ) 0 g 2 ( t ) 0 g 2 ( t ) 0 ] .
M 1 ( t ) = i n | ψ n ( t ) t ψ n ( t ) | ,
M 1 ( t ) = i n = 1 3 ψ ˙ n ψ n = [ 0 0 i G 0 0 0 i G 0 0 ] ,
g 1 ( t ) = g 0 sin ( θ ( t ) ) , g 2 ( t ) = g 0 cos ( θ ( t ) ) , θ ( t ) = π 2 1 1 + e ν ( t 5 / ν ) .
H ^ 2 = ω m b ^ b ^ + i = 1 , 2 [ Δ i a ^ i a ^ i + G i ( a ^ i + a ^ i ) ( b ^ + b ^ ) ] ,
H ^ 3 = i = 1 , 2 δ i a ^ i a ^ i + G i ( a ^ i b ^ m + b ^ m a ^ i ) ,
i d v o p ( t ) / d t = M o p ( t ) v o p ( t ) ,
H ^ 4 = i = 1 , 2 ( δ i + Ω i ) a ^ i a ^ i + Ω ( a ^ 1 a ^ 2 + a ^ 2 a ^ 1 ) ,
M 2 ( t ) = [ 0 0 G 1 G 2 δ 0 0 0 G 1 G 2 δ 0 0 ] .
G 1 G 2 δ = g 1 g ˙ 2 g ˙ 1 g 2 g 0 2 .
d ρ ^ d t = i [ ρ ^ , H ^ s ( t ) ] + κ 1 L ^ [ a ^ 1 ] ρ ^ + κ 2 L ^ [ a ^ 2 ] ρ ^ + γ m D ^ [ b ^ m ] ρ ^ ,

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