Abstract
We study, in this chapter, the various approaches to the problem of the Quantum Phase.
Dirac was the first one to postulate the existence of a Hermitian phase variable in the early days of Quantum Electrodynamics [1].
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Dirac, P.A.M.: The quantum theory of the emission and absorption of radiation. Proc. Roy. Soc. Lond. A 114, 243 (1927)
Susskind, L., Glogower, I.: Quantum mechanical phase and time operator. Physics 1 49 (1964)
Louisell, W.H.: Amplitude and phase uncertainty relations. Phys. Lett. 7, 60 (1963)
Vogel, W., Welsch, D.G.: Lectures on Quantum Optics. Akademic, Berlin (1994)
Carruthers, P., Nieto, M.M.: Coherent states and the number-phase uncertainty relation. Phys. Rev. Lett. 14, 387 (1965)
London, F.: Uber die Jacobischen Transformationen der Quantenmechanik. Z. Phys. 37, 915 (1926)
London, F.: Winkelvariable und kanonische Transformationen in der Undulationsmechanik. Z. Phys. 40, 193 (1926)
Lerner, E.C.: Harmonic oscillator phase operators. Nuovo Cimento B 56, 183 (1968)
Zak, J.: Angle and phase coordinates in quantum mechanics. Phys. Rev. 187, 1803 (1969)
Turski, L.A.: The velocity operator for many-boson systems. Physics 57, 432 (1972)
Paul, H.: Phase of a microscopic electromagnetic field and its measurement. Forts. d. Physik 22, 657 (1974)
Schubert, M., Vogel, W.: Field fluctuations of two-photon coherent states. Phys. Lett. 68A, 321 (1978)
Barnett, S.M., Pegg, D.T.: Phase in quantum optics. J. Phys. A 19, 3849 (1986)
Barnett, S.M., Pegg, D.T.: On the Hermitian optical phase operator. J. Mod. Opt. 36, 7 (1989)
Pegg, D.T., Barnett, S.M.: Unitary phase operator in quantum mechanics. Europhys. Lett. 6, 483 (1988)
Pegg, D.T., Barnett, S.M.: Phase properties of the quantized single-mode electromagnetic field. Phys. Rev. A 39, 1665 (1986)
Lynch, R.: Fluctuation of the Barnett-Pegg phase operator in a coherent state. Phys. Rev. A 41, 2841 (1990)
Shapiro, J.H., Shepard, S.R., Wong, N.C.: Ultimate quantum limits on phase measurement. Phys. Rev. Lett. 62, 2377 (1989)
Schleich, W., Horowitz, R.J., Varro, S.: Bifurcation in the phase probability distribution of a highly squeezed state. Phys. Rev. A 40, 7405 (1989)
Bandilla, A., Paul, H., Ritze, H.H.: Realistic quantum states of light with minimum phase uncertainty. Quant. Opt. 3, 267 (1991)
Vogel, W., Schleich, W.: Phase distribution of a quantum state without using phase states. Phys. Rev. A 44, 7642 (1991)
Noh, J.W., Fougieres, A., Mandel, L.: Measurement of the quantum phase by photon counting. Phys. Rev. Lett. 67, 1426 (1991)
Noh, J.W., Fougieres, A., Mandel, L.: Operational approach to the phase of a quantum field. Phys. Rev. A 45, 424 (1992a)
Noh, J.W., Fougieres, A., Mandel, L.: Further investigations of the operationally defined quantum phase. Phys. Rev. A 46, 2840 (1992b)
Noh, J.W., Fougieres, A., Mandel, L.: Measurements of the probability distribution of the operationally defined quantum phase difference. Phys. Rev. Lett. 71, 2579 (1993)
Orszag, M., Saavedra, C.: Phase fluctuations in a laser with atomic memory effects. Phys. Rev. A 43, 554 (1991)
Barnett, S., Vaccaro, J.A.: The Quantum Phase Operator. Taylor & Francis, New York (2007); Perinova, V., Luks, A., Perinova, J.: Phase in Optics. World Scientific, Singapore (1998)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Orszag, M. (2016). Quantum Phase. In: Quantum Optics. Springer, Cham. https://doi.org/10.1007/978-3-319-29037-9_15
Download citation
DOI: https://doi.org/10.1007/978-3-319-29037-9_15
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-29035-5
Online ISBN: 978-3-319-29037-9
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)