Dynamic quantum tunneling in mesoscopic driven Duffing oscillators

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 84, Issue 1, 2011, Pages

  Guo, Lingzhen ^a,b   Zheng, Zhigang ^a   Li, Xin Qi ^a   Yan, Yijing ^c  

^a BEIJING NORMAL UNIVERSITY   (China)

^b KARLSRUHE INSTITUTE OF TECHNOLOGY   (Germany)

^c HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION POINTS; DRIVING DISTANCE; DUFFING OSCILLATOR; LINEAR SCALING; MESOSCOPICS; QUANTUM TUNNELING; TUNNELING RATES;

BIFURCATION (MATHEMATICS); ELECTRON TUNNELING; OSCILLATORS (MECHANICAL);

SUPERCONDUCTING MATERIALS;

EID: 79961116967     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.84.011144     Document Type: Article

References (36)

1. I. Kozinsky, H. W. C. Postma, O. Kogan, A. Husain, and M. L. Roukes, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.207201 99, 207201 (2007). (Pubitemid 350113505)
2. I. Siddiqi, R. Vijay, F. Pierre, C.A M. Wilson, M. Metcalfe, C. Rigetti, L. Frunzio, and M. H. Devoret, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.207002 93, 207002 (2004);
3. I. Siddiqi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94. 027005 94, 027005 (2005). (Pubitemid 40620176)
4. I. Siddiqi, R. Vijay, M.A Metcalfe, E. Boaknin, L. Frunzio, R. J. Schoelkopf, and M. H. Devoret, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.73.054510 73, 054510 (2006). (Pubitemid 43291114)
5. V. E. Manucharyan, E. Boaknin, M. Metcalfe, R. Vijay, I.A Siddiqi, and M. Devoret, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.76.014524 76, 014524 (2007).
6. A. Lupascu, Nat. Phys. PRLTAO 1745-2473 10.1038/nphys509 3, 119 (2007).
7. I. Katz, A. Retzker, R. Straub, and R.A Lifshitz, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.040404 99, 040404 (2007); (Pubitemid 47173787)
8. I. Katz, R. Lifshitz, A. Retzker, and R.A Straub, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/10/12/125023 10, 125023 (2008).
9. V. Peano and M. Thorwart, Phys. Rev. B NJOPFM 1098-0121 10.1103/PhysRevB.70.235401 70, 235401 (2004); (Pubitemid 40270790)
10. V. Peano and M. Thorwart, Chem. Phys. CMPHC2 0301-0104 10.1016/j.chemphys.2005.06.047 322, 135 (2006);
11. V. Peano and M. Thorwart, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/8/2/021 8, 21 (2006). (Pubitemid 43670272)
12. M. I. Dykman, I. B. Schwartz, and M. Shapiro, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.72.021102 72, 021102 (2005). (Pubitemid 41520830)
13. M. Marthaler and M. I. Dykman, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.042108 73, 042108 (2006). (Pubitemid 43671414)
14. M. I. Dykman, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.75.011101 75, 011101 (2007). (Pubitemid 46134204)
15. I. Serban and F. K. Wilhelm, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.137001 99, 137001 (2007). (Pubitemid 47480011)
16. M. A. Armen and H. Mabuchi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.063801 73, 063801 (2006). (Pubitemid 43837728)
17. N. Gronbech-Jensen, M. G. Castellano, F. Chiarello, M. Cirillo, C. Cosmelli, L. V. Filippenko, R. Russo, and G. Torrioli, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.107002 93, 107002 (2004).
18. N. Gronbech-Jensen and M. Cirillo, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.067001 95, 067001 (2005). (Pubitemid 41506096)
19. M. G. Castellano, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 98.177002 98, 177002 (2007). (Pubitemid 46659440)
20. N. Gronbech-Jensen, J. E. Marchese, M. Cirillo, and J. A. Blackburn, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.105.010501 105, 010501 (2010).
21. Actually, in our numerical simulations, about "18" bound states will be involved in the nonlinear dynamics. We noticed that in Ref., about "60" states are involved in the dynamics, corresponding to a quasiclassical limit. While in the papers by Peano and Thorwart, where the nonlinear term of the potential is positive and, thus, can support an arbitrary number of bound states, only a few numbers of states (about "8") are involved in the dynamics, implying a "deep quantum regime." The term "mesoscopic" we used in our work basically means that the number of relevant (bound) states in the dynamics is in an intermediate range, i.e., between "a few" and "a large" number of states.
22. In this work, following Ref., we use the term "dynamic quantum tunneling" to describe the quantum transition between the metastable states in the bistable region. For a driven dynamic system, the phase space can have classically forbidden areas even in the absence of potential barriers. Quantum mechanically, however, these areas can be crossed in a process called dynamical tunneling (see and references therein). As a matter of fact, this is exactly the same process as studied in Ref., where the term "quantum activation" is employed, noting that it also describes the escape from a metastable state due to quantum fluctuations that lead to diffusion away from the metastable state and, ultimately, to transition over the classical "barrier", that is, the boundary of the basin of attraction to the metastable state.
23. U. Weiss, Quantum Dissipative Systems, 2nd ed. (World Scientific, Singapore, 1999).
24. L. Z. Guo, Z. G. Zheng, and X. Q. Li, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/90/10011 90, 10011 (2010).
25. D. Kohen, C. C. Marston, and D. J. Tannor, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.474887 107, 5236 (1997).
26. Y. J. Yan, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.58.2721 58, 2721 (1998);
27. R. X. Xu and Y. J. Yan, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.75.016108 75, 031107 (2007). (Pubitemid 46174723)
28. A. Shnirman and G. Schön, Phys. Rev. B PLRAAN 1098-0121 10.1103/PhysRevB.57.15400 57, 15400 (1998);
29. Yu.A Makhlin, G. Schön, and A. Shnirman, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.73.357 73, 357 (2001).
30. E. Joos, Decoherence and the Appearance of a Classical World in Quantum Theory, 2nd ed. (Springer-Verlag, Berlin Heidelberg New York, 2003), p.A 332.
31. C. Gerry and P. Knight, Introductory Quantum Optics (Cambridge University Press, Cambridge, 2005), p. 208.
32. K. V. Kheruntsyan, J. Opt. B: Quantum Semiclass. Opt. JOBOFD 1464-4266 10.1088/1464-4266/1/2/005 1, 225 (1999). (Pubitemid 30559523)
33. That the SAS is an approximate coherent state can be understood as follows. For a dissipative harmonic oscillator described by a Lindblad master equation, e.g., a damping optical cavity under laser driving, the stationary state is exactly a coherent state. An elegant proof for this can be found in the Ref.. For the DDO problem, since the SAS is near the bottom of the potential well where the anharmonicity is negligible, we can then expect that the SAS is an approximate coherent state.
34. C. Stambaugh and H. B. Chan, Phys. Rev. B JOBOFD 1098-0121 10.1103/PhysRevB.73.172302 73, 172302 (2006). (Pubitemid 43782045)
35. I. Siddiqi, R. Vijay, F. Pierre, C. M. Wilson, M. Metcalfe, C. Rigetti, L.A Frunzio, and M. H. Devoret, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett. 93.207002 93, 207002 (2004);
36. I. Siddiqi, R. Vijay, F. Pierre, C. M. Wilson, L. Frunzio, M. Metcalfe, C. Rigetti, and M. H. Devoret, Quantum Computing in Solid State Systems (Springer Science + Business Media, Inc., New York, 2006), p.A 28-36.