Quantum theory of transmission line resonator-assisted cooling of a micromechanical resonator

Physical Review B - Condensed Matter and Materials Physics

Volumn 78, Issue 13, 2008, Pages

  Li, Yong ^a,b   Wang, Ying Dan ^a,c   Xue, Fei ^d,e,f   Bruder, C ^a  

^a UNIVERSITY OF BASEL   (Switzerland)

^b UNIVERSITY OF HONG KONG   (Hong Kong)

^c Kashino Diverse Brain Research Laboratory of NTT Communication Science Laboratories   (Japan)

^d JAPAN SCIENCE AND TECHNOLOGY AGENCY   (Japan)

^e INST OF PHYS AND CHEMICAL RESEARCH   (Japan)

^f TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 54449092197     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.78.134301     Document Type: Article

References (71)

1. V. B. Braginsky and A. B. Manukin, Measurement of Weak Forces in Physics Experiments (University of Chicago, Chicago, 1977).
2. C. M. Caves, K. S. Thorne, R. W. P. Drever, V. D. Sandberg, and M. Zimmermann, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.52.341 52, 341 (1980)
3. M. F. Bocko and R. Onofrio, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.68.755 68, 755 (1996)
4. M. D. LaHaye, O. Buu, B. Camarota, and K. C. Schwab, Science SCIEAS 0036-8075 10.1126/science.1094419 304, 74 (2004).
5. K. L. Ekinci, Y. T. Yang, and M. L. Roukes, J. Appl. Phys. JAPIAU 0021-8979 10.1063/1.1642738 95, 2682 (2004).
6. C. M. Caves, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.45.75 45, 75 (1980).
7. B. Abbott, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95. 221101 95, 221101 (2005).
8. S. Mancini, V. Giovannetti, D. Vitali, and P. Tombesi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.120401 88, 120401 (2002).
9. W. Marshall, C. Simon, R. Penrose, and D. Bouwmeester, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.130401 91, 130401 (2003).
10. J. Eisert, M. B. Plenio, S. Bose, and J. Hartley, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.190402 93, 190402 (2004).
11. L. F. Wei, Y.-X. Liu, C. P. Sun, and F. Nori, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.237201 97, 237201 (2006)
12. X. Hu and F. Nori, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 76.2294 76, 2294 (1996)
13. X. Hu and F. Nori, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 79.4605 79, 4605 (1997).
14. F. Xue, L. Zhong, Y. Li, and C. P. Sun, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.75.033407 75, 033407 (2007)
15. F. Xue, Y.-X. Liu, C. P. Sun, and F. Nori, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.76.064305 76, 064305 (2007)
16. F. Xue, Y. D. Wang, C. P. Sun, H. Okamoto, H. Yamaguchi, and K. Semba, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/9/2/035 9, 35 (2007).
17. D. J. Wineland and W. M. Itano, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.20.1521 20, 1521 (1979).
18. I. Martin, A. Shnirman, L. Tian, and P. Zoller, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.69.125339 69, 125339 (2004).
19. P. Zhang, Y. D. Wang, and C. P. Sun, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.097204 95, 097204 (2005).
20. J. Hauss, A. Fedorov, C. Hutter, A. Shnirman, and G. Schön, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.037003 100, 037003 (2008).
21. K. Jaehne, K. Hammerer, and M. Wallquist, arXiv:0804.0603 (unpublished).
22. Y. D. Wang, K. Semba, and H. Yamaguchi, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/10/4/043015 10, 043015 (2008).
23. J. Q. You, Y.-X. Liu, and F. Nori, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.047001 100, 047001 (2008).
24. A. Naik, O. Buu, M. D. LaHaye, A. D. Armour, A. A. Clerk, M. P. Blencowe, and K. C. Schwab, Nature (London) NATUAS 0028-0836 10.1038/nature05027 443, 193 (2006)
25. M. P. Blencowe, J. Imbers, and A. D. Armour, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/7/1/236 7, 236 (2005)
26. A. A. Clerk and S. Bennett, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/7/1/238 7, 238 (2005).
27. I. Wilson-Rae, P. Zoller, and A. Imamoglu, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.075507 92, 075507 (2004).
28. L. Tian and P. Zoller, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.266403 93, 266403 (2004).
29. C. H. Metzger and K. Karrai, Nature (London) NATUAS 0028-0836 10.1038/nature03118 432, 1002 (2004).
30. S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, Nature (London) NATUAS 0028-0836 10.1038/nature05273 444, 67 (2006).
31. O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, and A. Heidmann, Nature (London) NATUAS 0028-0836 10.1038/nature05244 444, 71 (2006).
32. D. Kleckner and D. Bouwmeester, Nature (London) NATUAS 0028-0836 10.1038/nature05231 444, 75 (2006).
33. A. Schliesser, P. Del'Haye, N. Nooshi, K. J. Vahala, and T. J. Kippenberg, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.243905 97, 243905 (2006).
34. T. Corbitt, Y. Chen, E. Innerhofer, H. Muller-Ebhardt, D. Ottaway, H. Rehbein, D. Sigg, S. Whitcomb, C. Wipf, and N. Mavalvala, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.150802 98, 150802 (2007).
35. J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, Nature (London) NATUAS 0028-0836 10.1038/nature06715 452, 72 (2008).
36. A. Schliesser, R. Rivière, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, Nat. Phys. ZZZZZZ 1745-2473 4, 415 (2008).
37. S. Mancini, D. Vitali, and P. Tombesi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80.688 80, 688 (1998).
38. D. Vitali, S. Mancini, L. Ribichini, and P. Tombesi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.063803 65, 063803 (2002).
39. M. Grajcar, S. Ashhab, J. R. Johansson, and F. Nori, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.78.035406 78, 035406 (2008).
40. M. Paternostro, S. Gigan, M. S. Kim, F. Blaser, H. R. Böhm, and M. Aspelmeyer, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/8/6/107 8, 107 (2006).
41. I. Wilson-Rae, N. Nooshi, W. Zwerger, and T. J. Kippenberg, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.093901 99, 093901 (2007).
42. F. Marquardt, J. P. Chen, A. A. Clerk, and S. M. Girvin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.093902 99, 093902 (2007).
43. M. Bhattacharya and P. Meystre, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.073601 99, 073601 (2007).
44. C. Genes, D. Vitali, P. Tombesi, S. Gigan, and M. Aspelmeyer, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.77.033804 77, 033804 (2008).
45. A. Dantan, C. Genes, D. Vitali, and M. Pinard, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.77.011804 77, 011804 (R) (2008).
46. T. J. Kippenberg and K. J. Vahala, Opt. Express OPEXFF 1094-4087 10.1364/OE.15.017172 15, 17172 (2007).
47. F. Marquardt, A. A. Clerk, and S. M. Girvin, arXiv:0803.1164 (unpublished).
48. D. Wineland, J. Britton, R. Epstein, D. Leibfried, R. Blakestad, K. Brown, J. Jost, C. Langer, R. Ozeri, S. Seidelin, and J. Wesenberg, arXiv:quant-ph/0606180 (unpublished).
49. K. R. Brown, J. Britton, R. J. Epstein, J. Chiaverini, D. Leibfried, and D. J. Wineland, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.137205 99, 137205 (2007).
50. F. Xue, Y. D. Wang, Y.-X. Liu, and F. Nori, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.76.205302 76, 205302 (2007).
51. D. Vitali, P. Tombesi, M. J. Woolley, A. C. Doherty, and G. J. Milburn, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.76.042336 76, 042336 (2007).
52. J. D. Teufel, C. A. Regal, and K. W. Lehnert, arXiv:0803.4007 (unpublished).
53. M. P. Blencowe and E. Buks, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.76.014511 76, 014511 (2007).
54. E. Buks, S. Zaitsev, E. Segev, B. Abdo, and M. P. Blencowe, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.76.026217 76, 026217 (2007).
55. C. A. Regal, J. D. Teufel, and K. W. Lehnert, Nat. Phys. ZZZZZZ 1745-2473 4, 555 (2008).
56. F. Marquardt, Nat. Phys. ZZZZZZ 1745-2473 4, 513 (2008).
57. V. Giovannetti and D. Vitali, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.63.023812 63, 023812 (2001).
58. A. Blais, R.-S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.062320 69, 062320 (2004).
59. Here we assumed the mechanical resonator to be fabricated at the center of the TLR. As a result, the qubit is coupled to the second mode of the TLR, which is an antinode of the voltage in its center as given in Ref..
60. C. W. Gardiner and P. Zoller, Quantum Noise (Springer-Verlag, Berlin, 2000).
61. D. Vitali, S. Gigan, A. Ferreira, H. R. Bohm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.030405 98, 030405 (2007).
62. M. Pinard, A. Dantan, D. Vitali, O. Arcizet, T. Briant, and A. Heidmann, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2005-10317-6 72, 747 (2005).
63. Strictly speaking, ωb eff (ω) ≃ ωb is not always satisfied for arbitrary parameters, but this is the case for the parameters considered in the following discussion.
64. A. Hurwitz, Selected Papers on Mathematical Trends in Control Theory, edited by, R. Bellman, and, R. Kalaba, (Dover, New York, 1964)
65. E. X. DeJesus and C. Kaufman, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.35.5288 35, 5288 (1987).
66. C. Genes, A. Mari, P. Tombesi, and D. Vitali, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.78.032316 78, 032316 (2008).
67. S. D. Bennett and A. A. Clerk, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.74.201301 74, 201301 (R) (2006).
68. D. A. Rodrigues, J. Imbers, and A. D. Armour, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.067204 98, 067204 (2007).
69. M. Ludwig, B. Kubala, and F. Marquardt, arXiv:0803.3714 (unpublished).
70. It is right that γca (ωb) →0 when κ→0 except the scope nearly close to Δ≡ ωb where γca (ωb) →∞ when κ→0. But we will show in Fig. 4 that some correction should be done since it may be beyond the weak-coupling limit.
71. P. K. Day, Henry G. LeDuc, B. A. Mazin, A. Vayonakis, and J. Zmuidzinas, Nature (London) NATUAS 0028-0836 10.1038/nature02037 425, 817 (2003).