# Lecture Notes on Quantum-Nondemolition Measurements in Optics

Conference paper

## 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.

### Keywords

Microwave Soliton Assure Expense Sine## Preview

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### References

- [1]Quantum Theory and Measurement, Eds. J. A. Wheeler and W. H. Zurek (Princeton University, Princeton, NJ, 1983).Google Scholar
- [2]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.Google Scholar
- [3]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)].CrossRefGoogle Scholar - [4]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.ADSCrossRefGoogle Scholar - [5]V. B. Braginsky and F. Ya. Khalili, Quantum measurement (Cambridge Univ. Press, 1992).Google Scholar
- [6]H. A. Haus, Electromagnetic noise and quantum optical measurements (Springer, Berlin, 2000).MATHCrossRefGoogle Scholar
- [7]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).ADSCrossRefGoogle Scholar - [8]B.-G. Englert, N. Sterpi, and H. Walther, “Parity states in the one-atom maser”, Opt. Commun.
**100**, 526–535 (1993).ADSCrossRefGoogle Scholar - [9]This theoretical treatment is after V.V. Kozlov and J.H. Eberly (unpublished).Google Scholar
- [10]L. Allen and J. H. Eberly, Optical resonance and two-level atoms (Dover, New-York, 1987).Google Scholar
- [11]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).ADSCrossRefGoogle Scholar - [12]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).ADSCrossRefGoogle Scholar - [13]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).ADSCrossRefGoogle Scholar - [14]V. B. Braginsky and F. Ya. Khalili, “Quantum nondemolition measurements: the route from toys to tools”, Rev. Mod. Phys.
**68**, pp. 1–11 (1996).MathSciNetADSCrossRefGoogle Scholar - [15]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).ADSCrossRefGoogle Scholar - [16]P. Carruthers and M. M. Nieto, “Coherent states and the number-phase uncertainty relation”, Phys. Rev. Lett.
**14**, pp. 387–389 (1965).MathSciNetADSMATHCrossRefGoogle Scholar - [17]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).ADSCrossRefGoogle Scholar - [18]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)].MathSciNetADSGoogle Scholar - [19]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.ADSGoogle Scholar - [20]V. V. Kozlov and D. A. Ivanov, “Accurate quantum nondemolition measurements of optical solitons”, Phys. Rev. A
**65**, 023812 (2002).ADSCrossRefGoogle Scholar - [21]D. J. Kaup, J. Math. Phys.
**16**, 2036 (1975).MathSciNetADSCrossRefGoogle Scholar - [22]H. A. Haus and Y. Lai, “Quantum theory of soliton squeezing: a linearized approach”, J. Opt. Soc. Am.
**B7**, 386–392 (1990).ADSGoogle Scholar - [23]P.D. Drummond, J. Breslin, R.M. Shelby, “Quantum-nondemolition measurements with coherent soliton probes”, Phys. Rev. Lett.
**73**, 2837–2840 (1994).ADSCrossRefGoogle Scholar - [24]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).ADSCrossRefGoogle Scholar - [25]V. V. Kozlov and A. B. Matsko, “Einstein-Podolsky-Rosen paradox with quantum solitons in optical fibers”, Europhys. Lett.,
**54**, 592–598 (2001).ADSCrossRefGoogle Scholar - [26]V. V. Kozlov and M. Freyberger, “High-bit-rate quantum communication”, Opt. Commun.
**206**, 287–294 (2002).ADSCrossRefGoogle Scholar - [27]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).ADSCrossRefGoogle Scholar - [28]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).ADSCrossRefGoogle Scholar - [29]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).ADSCrossRefGoogle Scholar - [30]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).ADSCrossRefGoogle Scholar

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