Quantum measurements without macroscopic superpositions

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 77, Issue 5, 2008, Pages

  Spehner, Dominique ^a   Haake, Fritz ^b  

^a INSTITUT FOURIER   (France)

^b UNIVERSITY OF DUISBURG ESSEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; MARKOV PROCESSES; OHMIC CONTACTS; QUANTUM COMPUTERS;

OBJECT-POINTER DYNAMICS; POINTER-BATH COUPLING; QUANTUM MEASUREMENTS;

QUANTUM ENTANGLEMENT;

EID: 44149112323     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.77.052114     Document Type: Article

References (56)

1. J. A. Wheeler and W. H. Zurek, Quantum Theory and Measurement (Princeton University Press, Princeton, NJ, 1983).
2. J. von Neumann, Mathematical Foundations of Quantum Mechanics (Princeton University Press, Princeton, NJ, 1955).
3. D. Giulini, E. Joos, C. Kiefer, J. Kupsch, I.-O. Stamatescu, and H. D. Zeh, Decoherence and the Appearance of a Classical Word in Quantum Theory (Springer, Berlin, 1996).
4. W. H. Zurek, Phys. Rev. D PRVDAQ 0556-2821 10.1103/PhysRevD.24.1516 24, 1516 (1981).
5. W. H. Zurek, Phys. Today PHTOAD 0031-9228 44 (10), 36 (1991)
6. e-print arXiv:quant-ph/0306072 (updated version).
7. W. H. Zurek, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.75.715 75, 715 (2003).
8. M. B. Plenio and P. L. Knight, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.70.101 70, 101 (1998), and references therein.
9. M. C. Fischer, B. Gutierrez-Medina, and M. G. Raizen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.040402 87, 040402 (2001).
10. P. E. Toschek and C. Wunderlich, Eur. Phys. J. D EPJDF6 1434-6060 10.1007/s100530170207 14, 387 (2001).
11. M. Brune, E. Hagley, J. Dreyer, X. Maître, A. Maali, C. Wunderlich, J.-M. Raimond, and S. Haroche, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77.4887 77, 4887 (1996).
12. C. J. Myatt, B. E. King, Q. A. Turchette, C. A. Sackett, D. Kielpinski, W. M. Itano, C. Monroe, and D. J. Wineland, Nature (London) NATUAS 0028-0836 10.1038/35002001 403, 269 (2000).
13. P. Borri, W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.157401 87, 157401 (2001)
14. A. Vagov, V. M. Axt, T. Kuhn, W. Langbein, P. Borri, and U. Woggon, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.70.201305 70, 201305 (R) (2004).
15. G. Ithier, E. Collin, P. Joyez, P. J. Meeson, D. Vion, D. Esteve, F. Chiarello, A. Shnirman, Y. Makhlin, J. Schriefl, and G. Schön, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.72.134519 72, 134519 (2005).
16. J. Claudon, A. Fay, L. P. Lévy, and O. Buisson, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.73.180502 73, 180502 (R) (2006).
17. K. Hornberger, S. Uttenthaler, B. Brezger, L. Hackermüller, M. Arndt, and A. Zeilinger, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 90.160401 90, 160401 (2003).
18. P. Sonnentag and F. Hasselbach, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.200402 98, 200402 (2007).
19. F. Haake and M. Zukowski, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.47.2506 47, 2506 (1993).
20. A. E. Allahverdyan, R. Balian, and T. M. Nieuwenhuizen, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.64.032108 64, 032108 (2001).
21. A. E. Allahverdyan, R. Balian, and T. M. Nieuwenhuizen, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2003-00150-y 61, 452 (2003).
22. E. Wigner, Am. J. Phys. AJPIAS 0002-9505 10.1119/1.1969254 31, 6 (1963).
23. D. Braun, F. Haake, and W. T. Strunz, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.2913 86, 2913 (2001)
24. W. T. Strunz, F. Haake, and D. Braun, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67.022101 67, 022101 (2003).
25. M. Ohya and D. Petz, Quantum Entropy and Its Use (Springer-Verlag, Berlin, 1993).
26. A. F. Verbeure, in Encyclopedia of Mathematical Physics, edited by, J.-P. Françoise, G. L. Naber, and, T. S. Tsou, (Elsevier, Amsterdam, 2006), Vol. 4, p. 130.
27. A. O. Caldeira and A. J. Leggett, Ann. Phys. ANPYA2 0003-3804 10.1016/0003-4916(83)90202-6 149, 374 (1983)
28. A. O. Caldeira and A. J. Leggett, Physica A PHYADX 0378-4371 10.1016/0378-4371(83)90013-4 121, 587 (1983).
29. U. Weiss, Quantum Dissipative Systems (World Scientific, Singapore, 1993).
30. D. Spehner and F. Haake, J. Phys. A JPHAC5 0305-4470 41, 072002 (2008).
31. W. H. Zurek, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90. 120404 90, 120404 (2003).
32. M. Gross and S. Haroche, Phys. Rep. PRPLCM 0370-1573 10.1016/0370- 1573(82)90102-8 93, 301 (1982).
33. D. Polder, M. F. H. Schuurmans, and Q. H. F. Vrehen, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.19.1192 19, 1192 (1979).
34. F. Haake, H. King, G. Schröder, J. Haus, and R. Glauber, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.20.2047 20, 2047 (1979).
35. A. Peres, Quantum Theory: Concepts and Methods (Kluwer Academic, Dordrecht, 1995).
36. S. J. Freedman and J. F. Clauser, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.28.938 28, 938 (1972).
37. A. Aspect, J. Dalibard, and G. Roger, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.49.1804 49, 1804 (1982).
38. S. Gröblacher, T. Paterek, R. Kaltenbaek, C. Brukner, M. Zukowski, M. Aspelmeyer, and A. Zeilinger, Nature (London) NATUAS 0028-0836 10.1038/nature05677 446, 871 (2007).
39. Our calculations can be generalized to a Hamiltonian HPB of the form Bf (X), where f is a nice real function. In particular, a cutoff function at large distances can be introduced by choosing f (x) 0 for large x 's and f (x) xα otherwise, so that the pointer coupling agent f (X) remains bounded.
40. L. S. Schulman, Techniques and Applications of Path Integration (Wiley, New York, 1996).
41. T. Gorin, C. Pineda, and T. H. Seligman, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.240405 99, 240405 (2007).
42. E. Lutz and H. A. Weidenmüller, Physica A PHYADX 0378-4371 10.1016/S0378-4371(99)00022-9 267, 354 (1999)
43. E. Lutz, Physica E (Amsterdam) PELNFM 1386-9477 10.1016/S1386-9477(00) 00230-7 9, 369 (2001).
44. D. Bohm, Quantum Theory (Prentice-Hall, Englewood Cliffs, NJ, 1951).
45. F. Haake and R. Reibold, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.32.2462 32, 2462 (1985).
46. D. A. Lidar and K. B. Whaley, in Irreversible Quantum Dynamics, edited by, F. Benatti, and, R. Floreanini, Lecture Notes in Physics, Vol. 622 (Springer, Berlin, 2003), p. 83
47. D. A. Lidar and K. B. Whaley, e-print arXiv:quant-ph/0301032.
48. To show that the constant is uniform in time, it must be proven that for all 0≤a,b≤α one has supt0 t2α-a-b Ia,b,t / Iα,α,t < with Ia,b,t = 0t d τ1 0t d τ2 τ1a τ2b Reh (τ1 - τ2). This can be done by using the asymptotic analysis developed in Secs. 6 6.
49. An upper bound tdec ≤ t dec may be obtained by substituting tent (s, s′) in 44 by its maximum value tent =Δ/ (δs), cα (s, s′) by its minimum value cα min, and tdec (s, s′) by t dec. Indeed, as the right-hand side of 44 increases with tdec (s, s′) the solution t dec obtained after these substitutions is larger than tdec.
50. In fact, the small-time behavior 50 can be obtained directly, without relying on our previous general results, by setting H= HPS + HPB in 8 and determining the dynamics in a similar way as in Ref..
51. K. Hepp and E. H. Lieb, Helv. Phys. Acta HPACAK 0018-0238 46, 573 (1973).
52. V. Gorini and A. Kossakowski, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.523057 17, 1298 (1976).
53. O. Bratteli and D. W. Robinson, Operator Algebras and Quantum Statistical Mechanics (Springer, Berlin, 1997), Vol. 2.
54. G. M. Palma, K.-A. Suominen, and A. K. Ekert, Proc. R. Soc. London, Ser. A PRLAAZ 0950-1207 10.1098/rspa.1996.0029 452, 567 (1996).
55. D. Spehner and F. Haake, J. Phys.: Conf. Ser. JPCSDZ 1742-6588 10.1088/1742-6596/84/1/012018 84, 012018 (2007).
56. C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-photon Interactions: Basic Processes and Applications (Wiley, New York, 1992).