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In physics, specifically in quantum mechanics, a coherent state is the specific quantum state of the quantum harmonic oscillator, often described as a state which has dynamics most closely resembling the oscillatory behavior of a classical harmonic oscillator. It was the first example of quantum dynamics when Erwin Schrödinger derived it in 1926, while searching for solutions of the Schrödinger equation that satisfy the correspondence principle. The quantum harmonic oscillator and hence, the coherent states arise in the quantum theory of a wide range of physical systems. For instance, a coherent state describes the oscillating motion of a particle confined in a quadratic potential well (for an early reference, see e.g. Schiff's textbook). The coherent state describes a state in a system for which the ground-state wavepacket is displaced from the origin of the system. This state can be related to classical solutions by a particle oscillating with an amplitude equivalent to the displacement. These states, expressed as eigenvectors of the lowering operator and forming an overcomplete family, were introduced in the early papers of John R. Klauder, e.g. . In the quantum theory of light (quantum electrodynamics) and other bosonic quantum field theories, coherent states were introduced by the work of Roy J. Glauber in 1963. The concept of coherent states has been considerably abstracted; it has become a major topic in mathematical physics and in applied mathematics, with applications ranging from quantization to signal processing and image processing (see Coherent states in mathematical physics). For this reason, the coherent states associated to the quantum harmonic oscillator are sometimes referred to as canonical coherent states (CCS), standard coherent states, Gaussian states, or oscillator states.
References
- G. Breitenbach, S. Schiller, and J. Mlynek, Measurement of the quantum states of squeezed light, Nature 387 (1997) 471-475 http://gerdbreitenbach.de/publications/nature1997.pdf
- J.R. Klauder and B. Skagerstam, Coherent States, World Scientific, Singapore, 1985.
- W-M. Zhang, D. H. Feng, and R. Gilmore, Coherent states: Theory and some applications, Rev. Mod. Phys. 62 (1990) 867-927.
- J-P. Gazeau, Coherent States in Quantum Physics, Wiley-VCH, Berlin, 2009.
- E. Schrödinger, Der stetige Übergang von der Mikro- zur Makromechanik, Naturwissenschaften 14 (1926) 664-666.
- R.J. Glauber, Coherent and incoherent states of radiation field,Phys. Rev. 131 (1963) 2766-2788.
- E.C.G. Sudarshan, Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams, Phys. Rev. Lett. 10 (1963) 277-279.
- J. Schwinger, Theory of quantized fields. III, Phys. Rev. 91 (1953) 728-740
- L. Susskind and J. Glogower, Quantum mechanical phase and time operator,Physics 1 (1963) 49.
- P. Carruthers and M.N. Nieto, Phase and angle variables in quantum mechanics,Rev. Mod. Phys. 40 (1968) 411-440.
- S.M. Barnett and D.T. Pegg, On the Hermitian optical phase operator,J. Mod. Opt. 36 (1989) 7-19.
- P. Busch, M. Grabowski and P.J. Lahti, Who is afraid of POV measures? Unified approach to quantum phase observables, Ann. Phys. (N.Y.) 237 (1995) 1-11.
- V.V. Dodonov, 'Nonclassical' states in quantum optics: a 'squeezed' review of the first 75 years, J. Opt. B: Quantum Semiclass. Opt. 4 (2002) R1-R33.
- V.V. Dodonov and V.I.Man'ko (eds), Theory of Nonclassical States of Light, Taylor \& Francis, London, New York, 2003.
- A. Vourdas, Analytic representations in quantum mechanics, J. Phys. A: Math. Gen. 39 (2006) R65-R141.
- J-P. Gazeau,Coherent States in Quantum Physics, Wiley-VCH, Berlin, 2009.
- Agarwal, G. S.; Tara, K. (1991-01-01). "Nonclassical properties of states generated by the excitations on a coherent state". Physical Review A 43 (1): 492–497. doi:10.1103/PhysRevA.43.492. Bibcode: 1991PhRvA..43..492A. https://link.aps.org/doi/10.1103/PhysRevA.43.492.
- J. Oz-Vogt, A. Mann and M. Revzen, Thermal coherent states and thermal squeezed states, J. Mod. Opt., 1991, VOL . 38, 2339-2347
- G. J. Hyland, G. Rowlands, and F. W. Cummings, A proposal for an experimental determination of the equilibrium condensate fraction in superfluid helium, Phys. Lett. 31A (1970) 465-466.
- J. Mayers, The Bose–Einstein condensation, phase coherence, and two-fluid behavior in He-4, Phys. Rev. Lett. 92 (2004) 135302.
- J. Mayers, The Bose–Einstein condensation and two-fluid behavior in He-4, Phys. Rev. B 74 (2006) 014516.
- A.C. Olinto, Condensate fraction in superfluid He-4, Phys. Rev. B 35 (1986) 4771-4774.
- O. Penrose and L. Onsager, Bose–Einstein condensation and liquid Helium, Phys. Rev. 104(1956) 576-584.
- C. N. Yang, Concept of Off-Diagonal Long-Range Order and the quantum phases of liquid He and superconductors, Rev. Mod Phys. 34 (1962) 694-704.
- Yang, C. N. (1962). Concept of off-diagonal long-range order and the quantum phases of liquid He and of superconductors. Reviews of Modern Physics, 34(4), 694.
- [see John Bardeen's chapter in: Cooperative Phenomena, eds. H. Haken and M. Wagner (Springer-Verlag, Berlin, Heidelberg, New York, 1973)]
- J. Bardeen, L.N. Cooper and J. R. Schrieffer, Phys. Rev. 108, 1175 (1957)
- A. M. Perelomov, Coherent states for arbitrary Lie groups, Commun. Math. Phys. 26 (1972) 222-236; arXiv: math-ph/0203002. https://arxiv.org/abs/math-ph/0203002
- A. Perelomov, Generalized coherent states and their applications, Springer, Berlin 1986.
- R. Gilmore, Geometry of symmetrized states, Ann. Phys. (NY) 74 (1972) 391-463.
- R. Gilmore, On properties of coherent states, Rev. Mex. Fis. 23 (1974) 143-187.
- G. Kaiser, Quantum Physics, Relativity, and Complex Spacetime: Towards a New Synthesis, North-Holland, Amsterdam, 1990.
- S.T. Ali, J-P. Antoine, and J-P. Gazeau, Coherent States, Wavelets and Their Generalizations, Springer-Verlag, New York, Berlin, Heidelberg, 2000.
- C. Anastopoulos, Generalized Coherent States for Spinning Relativistic Particles, J. Phys. A: Math. Gen. 37 (2004) 8619-8637
- A. Ashtekar, J. Lewandowski, D. Marolf, J. Mourão and T. Thiemann, Coherent state transforms for spaces of connections, J. Funct. Anal. 135 (1996) 519-551.
- H. Sahlmann, T. Thiemann and O. Winkler, Coherent states for canonical quantum general relativity and the infinite tensor product extension, Nucl. Phys. B 606 (2001) 401-440.
