Single-photon Kerr nonlinearities do not help quantum computation

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 73, Issue 6, 2006, Pages

  Shapiro, Jeffrey H ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATION THEORY; NONLINEAR OPTICS; OPTICAL KERR EFFECT; PHASE MODULATION; PHOTONS;

CROSS-PHASE MODULATION; QUANTUM COMPUTATION; RESPONSE FUNCTIONS; SINGLE-PHOTON KERR NONLINEARITIES;

QUANTUM THEORY;

EID: 33744958512     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.73.062305     Document Type: Article

References (29)

1. C. Santori, M. Pelton, G. Solomon, Y. Dale, and Y. Yamamoto, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.1502 86, 1502 (2000);
2. S. Noda, A. Chutinan, and M. Imada, Nature (London) NATUAS 0028-0836 10.1038/35036532 407, 608 (2000);
3. A. Beveratos, R. Brouri, T. Gacoin, J.-Ph. Poizat, and P. Grangier, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.64.061802 64, 061802 (R) (2001);
4. M. Keller, B. Lange, K. Hayasaka, W. Lange, and H. Walther, Nature (London) NATUAS 0028-0836 10.1038/nature02961 431, 1075 (2004).
5. R. M. Stevenson, R. J. Young, P. Atkinson, K. Cooper, D. A. Ritchie, and A. J. Shields, Nature (London) NATUAS 0028-0836 10.1038/nature04446 439, 179 (2006);
6. R. J. Young, R. M. Stevenson, P. Atkinson, K. Cooper, D. A. Ritchie, and A. J. Shields, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/8/2/029 8, 29 (2006).
7. M. Fiorentino, G. Messin, C. E. Kuklewicz, F. N. C. Wong, and J. H. Shapiro, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.041801 69, 041801 (R) (2004);
8. T. Kim, M. Fiorentino, and F. N. C. Wong, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.012316 73, 012316 (2006).
9. I. L. Chuang and Y. Yamamoto, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.52.3489 52, 3489 (1995).
10. E. Knill, R. Laflamme, and G. J. Milburn, Nature (London) NATUAS 0028-0836 10.1038/35051009 409, 46 (2001).
11. C. R. Myers and R. Laflamme, e-print quant-ph/0512104.
12. L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, Nature (London) NATUAS 0028-0836 10.1038/17561 397, 594 (1999).
13. M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.66.055601 66, 055601 (R) (2002);
14. M. Soljacic, C. Luo, J. D. Joannopoulos, and S. Fan, Opt. Lett. OPLEDP 0146-9592 28, 637 (2003);
15. M. F. Yanik, S. Fan, M. Soljacic, and J. D. Joannopoulos, Opt. Lett. OPLEDP 0146-9592 28, 2506 (2003);
16. M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, Opt. Express OPEXFF 1094-4087 10.1364/OPEX.13.002678 13, 2678 (2005).
17. M. Soljacic, E. Lidorikis, J. D. Joannopoulos, and L. V. Hau, Appl. Phys. Lett. APPLAB 0003-6951 10.1063/1.1900956 86, 171101 (2005).
18. M. Kitagawa and Y. Yamamoto, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.34.3974 34, 3974 (1986).
19. L. G. Joneckis and J. H. Shapiro, J. Opt. Soc. Am. B JOBPDE 0740-3224 10, 1102 (1993);
20. J. H. Shapiro and L. Boivin, Opt. Lett. OPLEDP 0146-9592 20, 925 (1995).
21. J. H. Shapiro and R. S. Bondurant, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.022301 73, 022301 (2006).
22. Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.75.4710 75, 4710 (1995).
23. L. Boivin, F. X. Kärtner, and H. A. Haus, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.73.240 73, 240 (1994).
24. That the input-output relation for Fig. 1 must impose a nonzero response time on the XPM interaction follows from the same consideration presented in L. G. Joneckis and J. H. Shapiro, J. Opt. Soc. Am. B JOBPDE 0740-3224 10, 1102 (1993); see the discussion of Eq. 12 below. That Eqs. 2 3 4 5 constitute a commutator-preserving set can be shown, for example, by evaluating the output field operators' commutators in the representations associated with the continuous-time eigenkets of their respective photon-flux operators, E□ K† (t) E□ K (t) for K=A,B.
25. J. H. Shapiro, Quantum Semiclassic. Opt. QUSOEC 1355-5111 10, 567 (1998).
26. We have previously used this underdamped impulse response-with appropriate choices for κ, ω0, and γ -as a coarse approximation to the Raman response of fused silica fiber. See J. H. Shapiro and A. Shakeel, J. Opt. Soc. Am. B JOBPDE 0740-3224 14, 232 (1997).
27. Q. A. Turchette, Ph.D. thesis, California Institute of Technology, 1997.
28. W. J. Munro, K. Nemoto, and T. P. Spiller, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/7/1/137 7, 137 (2005).
29. T. P. Spiller, K. Nemoto, S. L. Braunstein, W. J. Munro, P. van Loock, and G. J. Milburn, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/8/2/030 8, 30 (2006).