Abstract
Measurements proceed by establishing correlations between a system and a meter. In a quantum description, these correlations are established by quantum fluctuations of the meter exciting the system. We observe such measurement-induced quantum correlations in the interferometric measurement of position.
Correlations have physical reality; that which they correlate does not. And that’s all there is to it, the rest is commentary.
David Mermin
Notes
- 1.
We have omitted a term proportional to the correlation between the two conjugate quadratures; such a term is strictly zero when the angle fluctuations are uncorrelated with the quadrature fluctuations, which is indeed the typical case.
- 2.
This is only an upper-bound because in practice, thermo-mechanical motion could be transduced into the amplitude quadrature by dissipative optomechanical coupling [24].
- 3.
- 4.
References
V.B. Braginsky, F.Y. Khalili, Quantum Measurement (Cambridge University Press, Cambridge, 1992)
H.M. Wiseman, G.J. Milburn, Quantum Measurement and Control (Cambridge University Press, Cambridge, 2010)
D.W.C. Brooks, T. Botter, S. Schreppler, T.P. Purdy, N. Brahms, D.M. Stamper-Kurn, Nature 488, 476 (2012)
A.H. Safavi-Naeini, S. Gröblacher, J.T. Hill, J. Chan, M. Aspelmeyer, O. Painter, Nature 500, 185 (2013)
T.P. Purdy, R.W. Peterson, C. Regal, Science 339, 801 (2013)
V. Sudhir, D.J. Wilson, R. Schilling, H. Schütz, A. Ghadimi, A. Nunnenkamp, T.J. Kippenberg, Phys. Rev. X 7, 011001 (2017)
F. Khalili, H. Miao, H. Yang, A. Safavi-Naeini, O. Painter, Y. Chen, Phys. Rev. A 86, 033840 (2012)
A. Weinstein, C. Lei, E. Wollman, J. Suh, A. Metelmann, A. Clerk, K. Schwab, Phys. Rev. X 4, 041003 (2014)
T.P. Purdy, P.-L. Yu, N.S. Kampel, R.W. Peterson, K. Cicak, R.W. Simmonds, C.A. Regal, Phys. Rev. A 92, 031802 (2015)
M. Underwood, D. Mason, D. Lee, H. Xu, L. Jiang, A.B. Shkarin, K. Børkje, S.M. Girvin, J.G.E. Harris, Phys. Rev. A 92, 061801 (2015)
J.H. Shapiro, IEEE, J. Quant. Elec. 21, 237 (1985)
V.B. Braginsky, M.L. Gorodetsky, F.Y. Khalili, A.B. Matsko, K.S. Thorne, S.P. Vyatchanin, Phys. Rev. D 67, 082001 (2003)
C. Fabre, M. Pinard, S. Bourzeix, A. Heidmann, E. Giacobino, S. Reynaud, Phys. Rev. A 49, 1337 (1994)
S. Mancini, P. Tombesi, Phys. Rev. A 49, 4055 (1994)
H.J. Carmichael, J. Opt. Soc. Am. B 4, 1588 (1987)
R. Loudon, P.L. Knight, J. Mod. Opt. 34, 709 (1987)
A.H. Safavi-Naeini, J. Chan, J.T. Hill, T.P.M. Alegre, A. Krause, O. Painter, Phys. Rev. Lett. 108, 033602 (2012)
I. Wilson-Rae, N. Nooshi, W. Zwerger, T.J. Kippenberg, Phys. Rev. Lett. 99, 093901 (2007)
F. Marquardt, J. Chen, A.A. Clerk, S.M. Girvin, Phys. Rev. Lett. 99, 093902 (2007)
M.S. Taubman, H. Wiseman, D.E. McClelland, H.-A. Bachor, J. Opt. Soc. Am. B 12, 1792 (1995)
R.W. Peterson, T.P. Purdy, N.S. Kampel, R.W. Andrews, K.W. Yu, P.-L. Lehnert, C.A. Regal, Phys. Rev. Lett 116, 063601 (2016)
R. Schilling, H. Schütz, A. Ghadimi, V. Sudhir, D. Wilson, T. Kippenberg, Phys. Rev. Appl. 5, 054019 (2016)
S. Steinlechner, B.W. Barr, A.S. Bell, S.L. Danilishin, A. Gläfke, C. Gräf, J.-S. Hennig, E.A. Houston, S.H. Huttner, S.S. Leavey, D. Pascucci, B. Sorazu, A. Spencer, K.A. Strain, J. Wright, S. Hild, Phys. Rev. D 92, 072009 (2015)
A. Sawadsky, H. Kaufer, R. Moghadas-Nia, S. Tarabrin, F. Khalili, K. Hammerer, R. Schnabel, Phys. Rev. Lett. 114, 043601 (2015)
H.M. Wiseman, J. Opt. B 1, 459 (1999)
A.A. Clerk, M.H. Devoret, S.M. Girvin, F. Marquardt, R.J. Schoelkopf, Rev. Mod. Phys. 82, 1155 (2010)
A.M. Jayich, J.C. Sankey, K. Børkje, D. Lee, C. Yang, M. Underwood, L. Childress, A. Petrenko, S.M. Girvin, J.G.E. Harris, New J. Phys. 14, 115018 (2012)
A.H. Safavi-Naeini, J. Chan, J.T. Hill, S. Gröblacher, H. Miao, Y. Chen, M. Aspelmeyer, O. Painter, New J. Phys. 15, 035007 (2013)
K. Vahala, C. Harder, A. Yariv, Appl. Phys. Lett. 42, 211 (1983)
M. van Exeter, W. Hamel, J.P. Woerdman, B. Zeijlmans, IEEE, J. Quant. Elec. 28, 1470 (1992)
C.E. Wieman, L. Hollberg, Rev. Sci. Instru. 62, 1 (1991)
T.J. Kippenberg, A. Schliesser, M.L. Gorodetsky, New J. Phys 15, 015019 (2013)
C.W. Gardiner, A.S. Parkins, M.J. Collett, J. Opt. Soc. Am. B 4, 1617 (1987)
M.L. Gorodetsky, I.S. Grudinin, J. Opt. Soc. Am. B 21, 697 (2004)
A. Gillespie, F. Raab, Phys. Lett. A 178, 357 (1993)
V.B. Braginsky, M.L. Gorodetsky, F.Y. Khalili, K.S. Thorne, Phys. Rev. D 61, 044002 (2000)
H. Cramer, Mathematical Methods of Statistics (Princeton University Press, Princeton, 1946)
C. Sayrin, I. Dotsenko, X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi, H. Amini, M. Brune, J.-M. Raimond, S. Haroche, Nature 477, 73 (2011)
D. Ristè, M. Dukalski, C.A. Watson, G. de Lange, M.J. Tiggelman, Y.M. Blanter, K.W. Lehnert, R.N. Schouten, L. DiCarlo, Nature 502, 350 (2013)
Y. Liu, S. Shankar, N. Ofek, M. Hatridge, A. Narla, K. Sliwa, L. Frunzio, R. Schoelkopf, M. Devoret, Phys. Rev. X 6, 011022 (2016)
K.C. Cox, G.P. Greve, J.M. Weiner, J.K. Thompson, Phys. Rev. Lett. 116, 093602 (2016)
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Sudhir, V. (2018). Observation of Quantum Correlations Using Feedback. In: Quantum Limits on Measurement and Control of a Mechanical Oscillator. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-69431-3_7
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