Dynamic research between spin and carbon nanotube resonator under strong coupling

Abstract

Abstract: The dynamic behavior of system which influenced by the coupling between the single electron spin and carbon nanotube mechanical resonator is theoretically analyzed.By means of a master equation, average phonon occupation number as functions of the frequency detuning under the case with and without qubit-oscillator coupling is investigated via a semiclassical approach、the variation of average phonon occupation number as functions of the frequency detuning under the case with and without rotating-wave approximation is compared for different coupling strength. For coupling system, average phonon occupation number occurs a splitting phenomenmon when resonance, simultaneously, a bistable state is observed near the splitting peak. By analysing the average phonon occupation number of the carbon nanotubes resonator, it finds that rotating-wave approximation and non-rotating-wave approximation can coincide with each other very well under the weak coupling strength . However, the non-rotating-wave approximation term must be considered in the ultrastrong coupling system due to the rotating-wave approximation is no longer effective.

Key words: quantum optics, average phonon possession number, rotating-wave approximation, non-rotating-wave approximation

CLC Number:

O431.2

LI Xiu-hong, MI Xian-wu. Dynamic research between spin and carbon nanotube resonator under strong coupling [J]. J4, 2013, 30(6): 703-709.

References

[1] Hanson R, Kouwenhoven L P, Petta J R, et al. Spins in few-electron quantum dots [J]. Rev. Mod. Phy , 2007, 79: 1217–1265. [2] Palyi A, Struck P R, Rudner M, et al. Spin-orbit-induced strong coupling of a single spin to a nanomechanical resonator [J]. Phys.Rev.Lett.., 2012, 108: 206811. [3] Zheng H, Zhu S Y, Zubairy M S, et al. Zeno and Anti-Zeno effects: without rotating wave approximation [J]. Phys. Rev. Lett.., 2008, 101:200404-200408. [4] Ai Q, Li Y, Zheng H, et al. Quantum anti-Zeno effect without rotating wave approximation [J]. Phys. Rev. A, 2010, 81:042116-042127. [5] Zhang Y W, Chen G, Yu L X, et al. Analytical ground state for the Jaynes-Cummings model with ultrastrong coupling [J]. Phys.Rev.A, 2011, 83:065802-065805. [6] Beaudoin F , Gambetta J M , Blais A, et al. Dissipation and ultrastrong coupling in circuit QED [J]. Phys.Rev.A, 2011, 84:043832-043846. [7] Chen Q H, Yang Y, Liu T, et al. Quantum discord dynamics of two qubits in the single-mode cavities [J]. Phys.Rev.A, 2010, 82: 052306-052313. [8] Anappara A A, Liberato S D, Tredicucci A, et al. Signatures of the ultrastrong light-matter coupling [J]. Phys. Rev. B, 2009, 79: 201303-201313. [9] Todorov Y, Andrews A M, Colombelli R, et al. Ultrastrong Light-Matter Coupling Regime with Polariton Dots [J]. Phys. Rev. Lett., 2010, 105:196402-196405. [10] Fedorov A, Feofanov A K, Macha P, et al. Strong Coupling of a Quantum Oscillator to a Flux Qubit at its Symmetry Point [J]. Phys. Rev. Lett., 2010, 105:060503-060506. [11] Nataf P , Ciuti C. Protected Quantum Computation with Multiple Resonators in Ultrastrong Coupling Circuit QED [J]. Phys. Rev. Lett., 2011, 107: 190402-190405. [12] Lizuain I, Casanova J, García-Ripoll J J, et al. Zeno physics in ultrastrong circuit QED [J]. Phys. Rev. A, 2010, 81:062131 – 062139. [13] Huettel A K ,Steele G A, Witkamp B, et al. Carbon nanotubes as ultrahigh quality factor mechanical resonators [J]. Science, 2009, 325: 1103 . [14] Palyi A, Struck P R, Rudner M, et al. Supplementary electronic material for: Spin-orbit-induced strong coupling of a single spin to a nanomechanical resonator [J]. Phys.Rev.Lett., 2012, 108 :206811. [15] Jaynes E T , Cummings F W. Comparison of quantum and semiclassical radiation theories with application to the beam maser [J]. Proc. IEEE, 1963, 51: 89 . [16] Bulaev D V , Loss D. Spin-orbit-mediated coupling of electron spin dynamics [J]. Phys. Rev. B, 2008, 77: 235-301 . [17] Rugar D, Budakian R, Mamin H, et al. Single spin detection by magnetic resonance force microscopy [J]. Nature (London), 2004, 430: 329 . [18] Rabl P, Cappellaro P, Gurudev Dutt M V, et al. Strong magnetic coupling between an electronic spin qubit and a mechanical resonator [J]. Phys. Rev. B, 2009, 79: 041302(R) . [19] Rabl P, Kolkowitz S J, Koppens F H L, et al. A quantum spin transducer based on nanoelectromecha- nical resonator arrays [J]. Nature Phys., 2010, 6: 602 . [20] Ando T. Spin-Orbit Interaction in Carbon Nanotubes [J]. J. Phys. Soc. Jpn, 2000 , 691: 757 . [21] Schulz A, Martino A D, Egger R. Spin-orbit coupling and spectral function of interacting electrons in carbon nanotubes [J]. Phys. Rev. B, 2009, 80: 075409. [22] Wataru I, Kentaro S, Riichiro S. Spin–Orbit Interaction in Single Wall Carbon Nanotubes: Symmetry Adapted Tight-Binding Calculation and Effective Model Analysis [J]. J. Phys. Soc. Jpn, 2009, 78: 074707 . [23] Klinovaja J, Schmidt M J, Braunecker B, et al. Helical modes in carbon nanotubes generated by strong electric fields [J]. Phys. Rev. Lett., 2011, 106: 156809 . [24] Yang H, E.ltkis M, Moriya R, et al. Nonlocal spin transport in single walled carbon nanotube networks [J].Nature Phys., 2011 , 7: 348 . [25] Alsing P, Carmichael H J. Spontaneous dressed-state polarization of a coupled atom and cavity mode [J].Quantum Opt., 1991, 3: 13. [26] Bishop L S, Ginossar E, Girvin S M. Response of the strongly driven Jaynes-Cummings oscillator [J]. Phys. Rev.Lett., 2010, 105: 100505 . [27] Reed M D, DiCarlo L, Johnson B R, et al. High-Fidelity Readout in Circuit Quantum Electrodynamics Using the Janyes-Cummings Nonlinearity [J]. Phys. Rev.Lett.., 2010, 105: 173601 .