Abstract
A general overview of quantum nondemolition measurements is provided and illustrated with a few examples from quantum optics. Also given are basic principles and theoretical fundament.
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Quantum Theory and Measurement, Eds. J. A. Wheeler and W. H. Zurek (Princeton University, Princeton, NJ, 1983).
One may also have a goal oriented more to a preparation rather than to measurement. Here the repeated measurements can be used in a feedback loop, where the variable of interest is measured and then corrected towards a desirable value by an active device. Such cases as well as any other active intervention into the quantum system are left beyond the scope of this lecture.
V. B. Braginsky and Y. I. Vorontsov, “Quantum-mechanical limitations in macroscopic experiments and modern experimental technique” Usp. Fiz. Nauk 114, 41–53 (1974) [Sov. Phys. Usp. 17, 644–650 (1975)]; V. B. Braginsky, Y. I. Vorontsov, and F. Y. Khalili “Quantum singularities of a ponderomotive meter of electromagnetic energy” Zh. Eksp. Teor. Fiz. 73, 1340–1343 (1977) [Sov. Phys. JETP 46, 705–706 (1977)].
P. D. Drummond, R. M. Shelby, S. R. Friberg, and Y. Yamamoto, “Quantum solitons in optical fibres”, Nature (London) 365, 307–313 (1993); P. Grangier, J. A. Levenson, and J.-P. Poizat, “Quantum non-demolition measurements in optics”, Nature (London) 396, 537–542 (1998); A. Sizmann and G. Leuchs, in “Progress in Optics” vol. XXXIX, ed. by E. Wolf, (Elsevier, NY) 1999, p.373.
V. B. Braginsky and F. Ya. Khalili, Quantum measurement (Cambridge Univ. Press, 1992).
H. A. Haus, Electromagnetic noise and quantum optical measurements (Springer, Berlin, 2000).
G. Nogues, A. Rauschenbeutel, S. Osnaghi, M. Brune, J. M. Raimond, and S. Haroche, “Seeing a single photon without destroying it”, Nature 400, 239–242 (1999).
B.-G. Englert, N. Sterpi, and H. Walther, “Parity states in the one-atom maser”, Opt. Commun. 100, 526–535 (1993).
This theoretical treatment is after V.V. Kozlov and J.H. Eberly (unpublished).
L. Allen and J. H. Eberly, Optical resonance and two-level atoms (Dover, New-York, 1987).
M. Brune, S. Haroche, J. M. Raimond, L. Davidovich, N. Zaury, “Manipulation of photons in a cavity by dispersive atom-field coupling: quantum non-demolition measurements and generation of Schrodinger cat states”, Phys. Rev. A 45, 5193–5214 (1992).
B. T. H. Varcoe, S. Brattke, M. Weidinger, and H. Walther, “Preparing pure photon number states of the radiation field”, Nature (London) 403, 743–746 (2000).
K. S. Thorne, R. W. P. Drever, C. M. Caves, M. Zimmermann, and V. D. Sandberg “Quantum nondemolition measurements of harmonic oscillators” Phys. Rev. Lett. 40, 667–671 (1978); W. G. Unruh “Quantum nondemolition and gravity-wave detection” Phys. Rev. B 19, 2888–2896 (1979); C. M. Caves, K. S. Thorne, R. W. P. Drever, V. D. Sandberg, and M. Zimmermann, “On the measurement of a weak classical force coupled to a quantum-mechanical oscillator. I. Issues of principles” Rev. Mod. Phys. 52, 341–392 (1980).
V. B. Braginsky and F. Ya. Khalili, “Quantum nondemolition measurements: the route from toys to tools”, Rev. Mod. Phys. 68, pp. 1–11 (1996).
N. Imoto, H. A. Haus, and Y. Yamamoto, “Quantum nondemolition measurement of the photon number via the optical Kerr effect”, Phys. Rev. A 32, pp. 2287–2292 (1985).
P. Carruthers and M. M. Nieto, “Coherent states and the number-phase uncertainty relation”, Phys. Rev. Lett. 14, pp. 387–389 (1965).
The sine operator Eq. (50) is used as a substitute for the phase operator. The definition of the last has a controversial history, see for instance a special issue on this subject in Physica Scripta, 48 (1993), “Quantum phase and phase dependent measurements”, Eds. W. P. Schleich and S. M. Barnett. The sine operator is however a well defined object and fits well the context of our problem. What is equally important, the operator can be measured directly in an optical experiment, see J. W. Noh, A. Fougeres, and L. Mandel, “Measurement of the quantum phase by photon counting”, Phys. Rev. Lett. 67, 1426–1429 (1991).
V. E. Zakharov and A. B. Shabat, “Exact theory of three-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media”, Soviet Physics JETP 34, 62–69 (1972) [Zh. Eksp. Teor. Fiz. 61, 118–134 (1971)].
see H. A. Haus, K. Watanabe, and Y. Yamamoto, “Quantum-nondemolition measurement of optical solitons”, J. Opt. Soc. Am. B6, 1138–1148 (1989), for the first proposal of the QND measurements of optical solitons. See also S. R. Friberg, S. Machida, and Y. Yamamoto, “Quantum-nondemolition measurement of the photon number of an optical soliton”, Phys. Rev. Lett. 69, 3165–3168 (1992), for the first QND experiment with optical solitons.
V. V. Kozlov and D. A. Ivanov, “Accurate quantum nondemolition measurements of optical solitons”, Phys. Rev. A 65, 023812 (2002).
D. J. Kaup, J. Math. Phys. 16, 2036 (1975).
H. A. Haus and Y. Lai, “Quantum theory of soliton squeezing: a linearized approach”, J. Opt. Soc. Am. B7, 386–392 (1990).
P.D. Drummond, J. Breslin, R.M. Shelby, “Quantum-nondemolition measurements with coherent soliton probes”, Phys. Rev. Lett. 73, 2837–2840 (1994).
V. V. Kozlov and A. B. Matsko, “Second-quantized models for optical solitons in nonlinear fibers: Equal-time versus equal-space commutation relations”, Phys. Rev. A 62, 033811 (2000).
V. V. Kozlov and A. B. Matsko, “Einstein-Podolsky-Rosen paradox with quantum solitons in optical fibers”, Europhys. Lett., 54, 592–598 (2001).
V. V. Kozlov and M. Freyberger, “High-bit-rate quantum communication”, Opt. Commun. 206, 287–294 (2002).
Ch. Silberhorn, T. C. Ralph, N. Lütkenhaus, and G. Leuchs, “Continuous variable quantum cryptography: beating the 3 dB loss limit”, Phys. Rev. Lett. 89, 167901 (2002).
J.-M. Courty, S. Spälter, F. König, A. Sizmann, and G. Leuchs, “Noise-free quantum-nondemolition measurement using optical solitons”, Phys. Rev. A 58, 1501 (1998).
V. V. Kozlov and A. B. Matsko, “Cancellation of the Gordon-Haus effect in optical transmission system with resonant medium”, J. Opt. Soc. Am. B. 16, 519–522 (1999).
A. B. Matsko, V. V. Kozlov, and M. O. Scully, “Back-action cancellation in quantum nondemolition measurement of optical solitons”, Phys. Rev. Lett. 82, 3244–3247 (1999).
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Kozlov, V.V. (2003). Lecture Notes on Quantum-Nondemolition Measurements in Optics. In: Shumovsky, A.S., Rupasov, V.I. (eds) Quantum Communication and Information Technologies. NATO Science Series, vol 113. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0171-7_5
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