Quantum superpositions and schrödinger cat states in quantum optics

American Journal of Physics

Volumn 65, Issue 10, 1997, Pages 964-974

  Gerry, C C ^a,b   Knight, P L ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

^b POLYTECHNIC UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040091895     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.18698     Document Type: Article

References (42)

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2. An excellent review of this and other interpretations is given by H. C. Ohanian, Principles of Quantum Mechanics (Prentice-Hall, Englewood Cliffs, NJ, 1990), Chap. 12.
3. W. H. Zurek, "'Decoherence and the Transition from Quantum to Classical," Phys. Today 36-44 (1991), and references therein.
4. It is not enough that we have superpositions of states with "large" quantum numbers of other parameters; the states should be sufficiently distinguishable from each other in some macroscopic way.
5. E. Schrödinger, "Die gegenwartige Situation in der Quantenmechanik," Naturwissensheften 23, 807-812, 823-828, 844-849 (1935); an English translation can be found in Quantum Theory of Measurement, edited by J. A. Wheeler and W. H. Zurek (Princeton U.P. Princeton, 1983), pp. 152-167.
6. E. Schrödinger, "Die gegenwartige Situation in der Quantenmechanik," Naturwissensheften 23, 807-812, 823-828, 844-849 (1935); an English translation can be found in Quantum Theory of Measurement, edited by J. A. Wheeler and W. H. Zurek (Princeton U.P. Princeton, 1983), pp. 152-167.
7. A. Einstein, B. Podolsky, and N. Rosen, "Can the Quantum-Mechanical Description of Physical reality be Considered Complete?," Phys. Rev. 47, 777-780 (1935).
8. A. J. Leggett, "Schrödinger's Cat and Her Laboratory Cousins," Contemp. Phys. 25, 583-598 (1984).
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13. R. Loudon, Quantum Theory of Light (Oxford U.P., Oxford, 1983), 2nd ed.; M. Sargent III, M. O. Scully, and W. E. Lamb Jr., Laser Physics (Addison-Wesley, Reading, MA, 1975); P. Meystre and M. Sargent III, Elements of Quantum Optics (Springer-Verlag, Berlin, 1990); D. F. Walls and G. J. Milburn, Quantum Optics (Springer-Verlag, Berlin, 1994); L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U.P., Cambridge, 1995).
14. R. Loudon, Quantum Theory of Light (Oxford U.P., Oxford, 1983), 2nd ed.; M. Sargent III, M. O. Scully, and W. E. Lamb Jr., Laser Physics (Addison-Wesley, Reading, MA, 1975); P. Meystre and M. Sargent III, Elements of Quantum Optics (Springer-Verlag, Berlin, 1990); D. F. Walls and G. J. Milburn, Quantum Optics (Springer-Verlag, Berlin, 1994); L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U.P., Cambridge, 1995).
15. R. Loudon, Quantum Theory of Light (Oxford U.P., Oxford, 1983), 2nd ed.; M. Sargent III, M. O. Scully, and W. E. Lamb Jr., Laser Physics (Addison-Wesley, Reading, MA, 1975); P. Meystre and M. Sargent III, Elements of Quantum Optics (Springer-Verlag, Berlin, 1990); D. F. Walls and G. J. Milburn, Quantum Optics (Springer-Verlag, Berlin, 1994); L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U.P., Cambridge, 1995).
16. R. Loudon, Quantum Theory of Light (Oxford U.P., Oxford, 1983), 2nd ed.; M. Sargent III, M. O. Scully, and W. E. Lamb Jr., Laser Physics (Addison-Wesley, Reading, MA, 1975); P. Meystre and M. Sargent III, Elements of Quantum Optics (Springer-Verlag, Berlin, 1990); D. F. Walls and G. J. Milburn, Quantum Optics (Springer-Verlag, Berlin, 1994); L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U.P., Cambridge, 1995).
17. L. Susskind and J. Glogower, "Quantum Mechanical Phase and Time Operator," Physics 1, 49-61 (1964); S. M. Barnett and D. T. Pegg, "Quantum Optical Phase," J. Mod. Opt. 44, 225-264 (1997).
18. L. Susskind and J. Glogower, "Quantum Mechanical Phase and Time Operator," Physics 1, 49-61 (1964); S. M. Barnett and D. T. Pegg, "Quantum Optical Phase," J. Mod. Opt. 44, 225-264 (1997).
19. See G. S. Agarwal, S. Chaturvedi, K. Tara, and V. Srinivasan, "Classical Phase Changes in Nonlinear Processes and their Quantum Counter Parts," Phys. Rev. A 45, 4904-4910 (1992).
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22. E. P. Wigner, "On the Quantum Correction for Thermodynamic Equilibrium," Phys. Rev. A 10, 749-759 (1932); M. Hillery, R. F. O'Connell, M. O. Scully, and E. P. Wigner, "Distribution Functions in Physics: Fundamentals," Phys. Rep. 106, 121-167 (1984).
23. R. L. Hudson, "When is the Wigner quasi-probability density non-negative," Rep. Math. Phys. 6, 249 (1974).
24. Of course, one should not forget that on hearing of the death of President Calvin Coolidge Dorothy Parker remarked "How can they tell?"
25. B. Yurke and D. Stoler, "Generating Quantum Mechanical Superpositions of Macroscopically Distinguishable States via Amplitude Dispersion," Phys. Rev. Lett. 57, 13-16 (1986).
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27. R. Loudon and P. L. Knight, "Squeezed Light," J. Mod. Opt. 34, 209-759 (1987); A. K. Ekert and P. L. Knight, "Correlations and Squeezing of two-mode oscillations," Am. J. Phys. 57, 692-697 (1989); D. F. Walls, "Squeezed States of Light," Nature 306, 141-146 (1983).
28. R. Loudon and P. L. Knight, "Squeezed Light," J. Mod. Opt. 34, 209-759 (1987); A. K. Ekert and P. L. Knight, "Correlations and Squeezing of two-mode oscillations," Am. J. Phys. 57, 692-697 (1989); D. F. Walls, "Squeezed States of Light," Nature 306, 141-146 (1983).
29. R. Loudon and P. L. Knight, "Squeezed Light," J. Mod. Opt. 34, 209-759 (1987); A. K. Ekert and P. L. Knight, "Correlations and Squeezing of two-mode oscillations," Am. J. Phys. 57, 692-697 (1989); D. F. Walls, "Squeezed States of Light," Nature 306, 141-146 (1983).
30. W. H. Louisell, Quantum Statistical Properties of Radiation (Wiley, New York, 1974).
31. G. J. Milburn and D. F. Walls, "Effect of Dissipation on Interference in Phase-Space," Phys. Rev. A 38, 1087-1090 (1988); B. Garraway and P. L. Knight, "Quantum Superpositions in dissipative environments: Decoherence and deconstruction," in Proceedings of the 44th Scottish Universities Summer School in Physics, edited by G. L. Oppo, S. M. Barnett, E. Riis, and M. Wilkinson (IOPP, Bristol, 1996), pp. 199-238; for an exactly solvable model of coherence within a dissipative environment see G. J. Milbum and C. A. Holmes, "Dissipative quantum and classical Lionville mechanics of the anharmonic oscillator," Phys. Rev. Lett. 56, 2237-2240 (1986).
32. G. J. Milburn and D. F. Walls, "Effect of Dissipation on Interference in Phase-Space," Phys. Rev. A 38, 1087-1090 (1988); B. Garraway and P. L. Knight, "Quantum Superpositions in dissipative environments: Decoherence and deconstruction," in Proceedings of the 44th Scottish Universities Summer School in Physics, edited by G. L. Oppo, S. M. Barnett, E. Riis, and M. Wilkinson (IOPP, Bristol, 1996), pp. 199-238; for an exactly solvable model of coherence within a dissipative environment see G. J. Milbum and C. A. Holmes, "Dissipative quantum and classical Lionville mechanics of the anharmonic oscillator," Phys. Rev. Lett. 56, 2237-2240 (1986).
33. G. J. Milburn and D. F. Walls, "Effect of Dissipation on Interference in Phase-Space," Phys. Rev. A 38, 1087-1090 (1988); B. Garraway and P. L. Knight, "Quantum Superpositions in dissipative environments: Decoherence and deconstruction," in Proceedings of the 44th Scottish Universities Summer School in Physics, edited by G. L. Oppo, S. M. Barnett, E. Riis, and M. Wilkinson (IOPP, Bristol, 1996), pp. 199-238; for an exactly solvable model of coherence within a dissipative environment see G. J. Milbum and C. A. Holmes, "Dissipative quantum and classical Lionville mechanics of the anharmonic oscillator," Phys. Rev. Lett. 56, 2237-2240 (1986).
34. J. von Neumann, Mathematical Foundations of Quantum Mechanics (Princeton U.P., Princeton, 1955).
35. See: L. Davidovich, M. Brune, J. M. Raimond, and S. Haroche, "Mesoscopic Quantum Coherences in Cavity QED: Preparation and Decoherence Monitoring Schemes," Phys. Rev. A 53, 1295-1309 (1996); S. Haroche, M. Brune, J. M. Raimond, and L. Davidovich, "Mesoscopic Quantum Coherences in Cavity QED," in Fundamentals of Quantum Optics, edited by F. Ehlotzky (Springer-Verlag, Berlin, 1989), pp. 223-236; M. Brune, S. Haroche, J. M. Raimond, L. Davidovich, and N. Zagury, "Manipulation of Photons in a Cavity by Dispersive Atom-Field Coupling: Quantum Nondemolition Measurements and Generation of 'Schrödinger Cat' States," Phys. Rev. A 45, 5193-5214 (1992); M. Brune, E. Hagley, J. Dreyel, X. Maitre, A. Maali, C. Wunderlich, J. M. Raimond, and S. Haroche, "Observing the progressive decoherence of the meter in a quantum measurement," Phys. Rev. Lett. 77, 4887-4890 (1996).
36. See: L. Davidovich, M. Brune, J. M. Raimond, and S. Haroche, "Mesoscopic Quantum Coherences in Cavity QED: Preparation and Decoherence Monitoring Schemes," Phys. Rev. A 53, 1295-1309 (1996); S. Haroche, M. Brune, J. M. Raimond, and L. Davidovich, "Mesoscopic Quantum Coherences in Cavity QED," in Fundamentals of Quantum Optics, edited by F. Ehlotzky (Springer-Verlag, Berlin, 1989), pp. 223-236; M. Brune, S. Haroche, J. M. Raimond, L. Davidovich, and N. Zagury, "Manipulation of Photons in a Cavity by Dispersive Atom-Field Coupling: Quantum Nondemolition Measurements and Generation of 'Schrödinger Cat' States," Phys. Rev. A 45, 5193-5214 (1992); M. Brune, E. Hagley, J. Dreyel, X. Maitre, A. Maali, C. Wunderlich, J. M. Raimond, and S. Haroche, "Observing the progressive decoherence of the meter in a quantum measurement," Phys. Rev. Lett. 77, 4887-4890 (1996).
37. See: L. Davidovich, M. Brune, J. M. Raimond, and S. Haroche, "Mesoscopic Quantum Coherences in Cavity QED: Preparation and Decoherence Monitoring Schemes," Phys. Rev. A 53, 1295-1309 (1996); S. Haroche, M. Brune, J. M. Raimond, and L. Davidovich, "Mesoscopic Quantum Coherences in Cavity QED," in Fundamentals of Quantum Optics, edited by F. Ehlotzky (Springer-Verlag, Berlin, 1989), pp. 223-236; M. Brune, S. Haroche, J. M. Raimond, L. Davidovich, and N. Zagury, "Manipulation of Photons in a Cavity by Dispersive Atom-Field Coupling: Quantum Nondemolition Measurements and Generation of 'Schrödinger Cat' States," Phys. Rev. A 45, 5193-5214 (1992); M. Brune, E. Hagley, J. Dreyel, X. Maitre, A. Maali, C. Wunderlich, J. M. Raimond, and S. Haroche, "Observing the progressive decoherence of the meter in a quantum measurement," Phys. Rev. Lett. 77, 4887-4890 (1996).
38. See: L. Davidovich, M. Brune, J. M. Raimond, and S. Haroche, "Mesoscopic Quantum Coherences in Cavity QED: Preparation and Decoherence Monitoring Schemes," Phys. Rev. A 53, 1295-1309 (1996); S. Haroche, M. Brune, J. M. Raimond, and L. Davidovich, "Mesoscopic Quantum Coherences in Cavity QED," in Fundamentals of Quantum Optics, edited by F. Ehlotzky (Springer-Verlag, Berlin, 1989), pp. 223-236; M. Brune, S. Haroche, J. M. Raimond, L. Davidovich, and N. Zagury, "Manipulation of Photons in a Cavity by Dispersive Atom-Field Coupling: Quantum Nondemolition Measurements and Generation of 'Schrödinger Cat' States," Phys. Rev. A 45, 5193-5214 (1992); M. Brune, E. Hagley, J. Dreyel, X. Maitre, A. Maali, C. Wunderlich, J. M. Raimond, and S. Haroche, "Observing the progressive decoherence of the meter in a quantum measurement," Phys. Rev. Lett. 77, 4887-4890 (1996).
39. D. Bohm, Quantum Theory (Prentice-Hall, Englewood Cliffs, NJ, 1951), p. 611.
40. J. Gribbin, In Search of Schrödinger's Cat (Bantam, New York, 1984).
41. N. W. Noel and C. R. Stroud, Jr., "A Radial Wave Packet Schrödinger Cat State," paper presented at The Seventh Rochester Conference on Coherence and Quantum Optics, edited by J. H. Eberly, L. Mandel and E. Wolf (Plenum, New York, 1996), pp. 563-564; N. W. Noel and C. R. Stroud, Jr., "Excitation of an Atomic Electron to a Coherent Superposition of Microscopically Distinct States," Phys. Rev. Lett. 77, 1913-1916 (1996).
42. N. W. Noel and C. R. Stroud, Jr., "A Radial Wave Packet Schrödinger Cat State," paper presented at The Seventh Rochester Conference on Coherence and Quantum Optics, edited by J. H. Eberly, L. Mandel and E. Wolf (Plenum, New York, 1996), pp. 563-564; N. W. Noel and C. R. Stroud, Jr., "Excitation of an Atomic Electron to a Coherent Superposition of Microscopically Distinct States," Phys. Rev. Lett. 77, 1913-1916 (1996).