Abstract

We cast the phase state as a SU(1,1) nonlinear coherent state to support the idea that the SU(1,1) representation of the electromagnetic field may be helpful in some instances and to bring forward that it may relate to the phase state problem. We also construct nonlinear coherent states related to the exponential phase operator and provide their corresponding nonlinear annihilation operators. Finally, we discuss the propagation of classical fields through arrays of coupled waveguides that are solved through the use of nonlinear coherent states of SU(1,1) or the exponential phase operator.

© 2014 Optical Society of America

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  35. W. Schleich, R. J. Horowicz, and S. Varro, “Bifurcation in the phase probability distribution of a highly squeezed state,” Phys. Rev. A 40, 7405–7408 (1989).
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  38. V. Bužek, “Light squeezing in the Jaynes–Cummings model with intensity-dependent coupling,” J. Mod. Opt. 36, 1151–1162 (1989).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  48. A. Perez-Leija, R. Keil, A. Szameit, A. F. Abouraddy, H. Moya-Cessa, and D. N. Christodoulides, “Tailoring the correlation and anticorrelation behavior of path-entangled photons in Glauber–Fock lattices,” Phys. Rev. A 85, 013848 (2012).
    [Crossref]
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    [Crossref]
  51. K. G. Makris and D. N. Christodoulides, “Method of images in optical discrete systems,” Phys. Rev. E 73, 036616 (2006).
    [Crossref]
  52. R. de J. León-Montiel and H. Moya-Cessa, “Modeling non-linear coherent states in fiber arrays,” Int. J. Quantum. Inform. 9, 349–355 (2011).
    [Crossref]

2014 (2)

2013 (1)

O. de los Santos-Sánchez and J. Récamier, “Morse-like squeezed coherent states and some of their properties,” J. Phys. A Math. Theor. 46, 375303 (2013).
[Crossref]

2012 (2)

O. de los Santos-Sanchez and J. Récamier, “The f-deformed Jaynes–Cummings model and its nonlinear coherent states,” J. Phys. B 45, 015502 (2012).
[Crossref]

A. Perez-Leija, R. Keil, A. Szameit, A. F. Abouraddy, H. Moya-Cessa, and D. N. Christodoulides, “Tailoring the correlation and anticorrelation behavior of path-entangled photons in Glauber–Fock lattices,” Phys. Rev. A 85, 013848 (2012).
[Crossref]

2011 (6)

R. de J. León-Montiel and H. Moya-Cessa, “Modeling non-linear coherent states in fiber arrays,” Int. J. Quantum. Inform. 9, 349–355 (2011).
[Crossref]

A. Perez-Leija, H. Moya-Cessa, F. Soto-Eguibar, O. Aguilar-Loreto, and D. N. Christodoulides, “Classical analogues to quantum nonlinear coherent states in photonic lattices,” Opt. Commun. 284, 1833–1836 (2011).
[Crossref]

S. Longhi, “Classical simulation of relativistic quantum mechanics in periodic optical structures,” Appl. Phys. B 104, 453–468 (2011).
[Crossref]

R. Keil, A. Perez-Leija, F. Dreisow, M. Heinrich, H. Moya-Cessa, S. Nolte, D. N. Christodoulides, and A. Szameit, “Classical analogue of displaced Fock states and quantum correlations in Glauber–Fock photonic lattices,” Phys. Rev. Lett. 107, 103601 (2011).
[Crossref]

B. M. Rodrguez-Lara, “Exact dynamics of finite Glauber–Fock photonic lattices,” Phys. Rev. A 84, 053845 (2011).
[Crossref]

R. de J. León-Montiel, H. Moya-Cessa, and F. Soto-Eguibar, “Nonlinear coherent states for the Susskind–Glogower operators,” Rev. Mex. Fis. S 57, 133–147 (2011).

2009 (1)

S. Longhi, “Quantum-optical analogies using photonic structures,” Laser Photonics Rev. 3, 243–261 (2009).
[Crossref]

2008 (1)

J. Recamier, M. Gorayeb, W. L. Mochán, and J. L. Paz, “Nonlinear coherent states and some of their properties,” Int. J. Theor. Phys. 47, 673–683 (2008).
[Crossref]

2006 (2)

H. A. Kastrup, “Quantization of the canonically conjugate pair angle and orbital angular momentum,” Phys. Rev. A 73, 052104 (2006).
[Crossref]

K. G. Makris and D. N. Christodoulides, “Method of images in optical discrete systems,” Phys. Rev. E 73, 036616 (2006).
[Crossref]

2004 (1)

M. Rasetti, “A fully consistent Lie algebraic representation of quantum phase and number operators,” J. Phys. A: Math. Gen. 37, L479–L487 (2004).
[Crossref]

2003 (2)

H. A. Kastrup, “Quantization of the optical phase space S2={φ mod 2π,I>0}; in terms of the group SO↑(1,2),” Fortschr. Phys. 51, 975–1134 (2003).
[Crossref]

R. Chakrabarti and S. Vasan, “Entanglement via Barut–Girardello coherent state for suq(1,1) quantum algebra: bipartite composite system,” Phys. Lett. A 312, 287–295 (2003).
[Crossref]

2002 (1)

S. Sivakumar, “Interpolating coherent states for Heisenberg–Weyl and single-photon SU(1,1) algebras,” J. Phys. A: Math. Gen. 35, 6755–6766 (2002).
[Crossref]

2000 (1)

K. M. Ng, C. F. Lo, and K. L. Liu, “Exact eigenstates of the intensity-dependent Jaynes–Cummings model with the counter-rotating term,” Phys. A 275, 463–474 (2000).
[Crossref]

1999 (2)

C. F. Lo, K. L. Liu, and K. M. Ng, “The multiquantum intensity-dependent Jaynes–Cummings model with the counterrotating terms,” Phys. A 265, 557–564 (1999).
[Crossref]

E. Celeghini, “A new definition of bosons,” Int. J. Mod. Phys. B 13, 2909–2913 (1999).
[Crossref]

1998 (1)

E. Celeghini and M. Rasetti, “Generalized bosons and coherent states,” Phys. Rev. Lett. 80, 3424–3427 (1998).
[Crossref]

1997 (1)

G. Breitenbach and S. Schiller, “Homodyne tomography of classical and non-classical light,” J. Mod. Opt. 44, 2207–2225 (1997).
[Crossref]

1996 (1)

E. Celeghini and M. Rasetti, “Many-particle quantum statistics and co-algebra,” Int. J. Mod. Phys. B 10, 1625–1636 (1996).
[Crossref]

1995 (1)

E. Celeghini, M. Rasetti, and G. Vitiello, “Identical particles and permutation group,” J. Phys. A: Math. Gen. 28, L239–L244 (1995).
[Crossref]

1993 (1)

1992 (1)

M. Ban, “su(1,1) Lie algebraic approach to linear dissipative processes in quantum optics,” J. Math. Phys. 33, 3213–3228 (1992).
[Crossref]

1990 (1)

V. Bužek, “SU(1,1) squeezing of SU(1,1) generalized coherent states,” J. Mod. Opt. 37, 303–316 (1990).
[Crossref]

1989 (3)

W. Schleich, R. J. Horowicz, and S. Varro, “Bifurcation in the phase probability distribution of a highly squeezed state,” Phys. Rev. A 40, 7405–7408 (1989).
[Crossref]

V. Bužek, “Light squeezing in the Jaynes–Cummings model with intensity-dependent coupling,” J. Mod. Opt. 36, 1151–1162 (1989).
[Crossref]

M. G. Rasetti, G. D’Ariano, and A. Montorsi, “Coherent states and infinite-dimensional Lie algebras: an outlook,” Nuovo Cimento D 11, 19–29 (1989).
[Crossref]

1987 (1)

C. C. Gerry, “Application of su(1,1) coherent states to the interaction of squeezed light in an anharmonic oscillator,” Phys. Rev. A 35, 2146–2149 (1987).
[Crossref]

1985 (3)

C. C. Gerry, “Dynamics of su(1,1) coherent states,” Phys. Rev. A 31, 2721–2723 (1985).
[Crossref]

K. Wódkiewicz and J. H. Eberly, “Coherent states, squeezed fluctuations, and the SU(2) and SU(1,1) groups in quantum-optics applications,” J. Opt. Soc. Am. B 2, 458–466 (1985).
[Crossref]

G. D’Ariano, M. Rasetti, and M. Vadacchino, “Stability of coherent states,” J. Phys. A: Math. Gen. 18, 1295–1307 (1985).
[Crossref]

1981 (1)

B. Buck and C. V. Sukumar, “Exactly soluble model of atom–phonon coupling showing periodic decay and revival,” Phys. Lett. 81, 132–135 (1981).
[Crossref]

1975 (1)

M. Rasetti, “Generalized definition of coherent states and dynamical groups,” Int. J. Theor. Phys. 13, 425–430 (1975).
[Crossref]

1972 (1)

A. M. Perelomov, “Coherent states for arbitrary Lie group,” Commun. Math. Phys. 26, 222–236 (1972).
[Crossref]

1971 (1)

A. O. Barut and L. Girardello, “New “coherent” states associated with non-compact groups,” Commun. Math. Phys. 21, 41–55 (1971).
[Crossref]

1968 (1)

P. Carruthers and M. M. Nieto, “Phase and angle variables in quantum mechanics,” Rev. Mod. Phys. 40, 411–440 (1968).
[Crossref]

1964 (1)

L. Susskind and J. Glogower, “Quantum mechanical phase and time operator,” Physics 1, 49–61 (1964).

1963 (2)

E. C. G. Sudarshan, “Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams,” Phys. Rev. Lett. 10, 277–279 (1963).
[Crossref]

R. J. Glauber, “Coherent and incoherent states of the radiation field,” Phys. Rev. 131, 2766–2788 (1963).
[Crossref]

1927 (2)

F. London, “Winkervariable und kanonische transformationen in der undulationsmechanik,” Z. Phys. 40, 193–210 (1927).
[Crossref]

P. A. M. Dirac, “The quantum theory of the emission and absorption of radiation,” Proc. R. Soc. A 114, 243–265 (1927).
[Crossref]

1926 (2)

F. London, “Über die Jacobischen transformationen der quantenmechanik,” Z. Phys. 37, 915–925 (1926).
[Crossref]

E. Schrödinger, “Der stetige übergang von der mikro- zur makromechanik,” Naturwissenschaften 14, 664–666 (1926).
[Crossref]

Abouraddy, A. F.

A. Perez-Leija, R. Keil, A. Szameit, A. F. Abouraddy, H. Moya-Cessa, and D. N. Christodoulides, “Tailoring the correlation and anticorrelation behavior of path-entangled photons in Glauber–Fock lattices,” Phys. Rev. A 85, 013848 (2012).
[Crossref]

Aguilar-Loreto, O.

A. Perez-Leija, H. Moya-Cessa, F. Soto-Eguibar, O. Aguilar-Loreto, and D. N. Christodoulides, “Classical analogues to quantum nonlinear coherent states in photonic lattices,” Opt. Commun. 284, 1833–1836 (2011).
[Crossref]

Ban, M.

M. Ban, “Decomposition formulas for su(1,1) and su(2,2) Lie algebras and their applications in quantum optics,” J. Opt. Soc. Am. B 10, 1347–1359 (1993).
[Crossref]

M. Ban, “su(1,1) Lie algebraic approach to linear dissipative processes in quantum optics,” J. Math. Phys. 33, 3213–3228 (1992).
[Crossref]

Barut, A. O.

A. O. Barut and L. Girardello, “New “coherent” states associated with non-compact groups,” Commun. Math. Phys. 21, 41–55 (1971).
[Crossref]

Breitenbach, G.

G. Breitenbach and S. Schiller, “Homodyne tomography of classical and non-classical light,” J. Mod. Opt. 44, 2207–2225 (1997).
[Crossref]

Buck, B.

B. Buck and C. V. Sukumar, “Exactly soluble model of atom–phonon coupling showing periodic decay and revival,” Phys. Lett. 81, 132–135 (1981).
[Crossref]

Bužek, V.

V. Bužek, “SU(1,1) squeezing of SU(1,1) generalized coherent states,” J. Mod. Opt. 37, 303–316 (1990).
[Crossref]

V. Bužek, “Light squeezing in the Jaynes–Cummings model with intensity-dependent coupling,” J. Mod. Opt. 36, 1151–1162 (1989).
[Crossref]

Carruthers, P.

P. Carruthers and M. M. Nieto, “Phase and angle variables in quantum mechanics,” Rev. Mod. Phys. 40, 411–440 (1968).
[Crossref]

Celeghini, E.

E. Celeghini, “A new definition of bosons,” Int. J. Mod. Phys. B 13, 2909–2913 (1999).
[Crossref]

E. Celeghini and M. Rasetti, “Generalized bosons and coherent states,” Phys. Rev. Lett. 80, 3424–3427 (1998).
[Crossref]

E. Celeghini and M. Rasetti, “Many-particle quantum statistics and co-algebra,” Int. J. Mod. Phys. B 10, 1625–1636 (1996).
[Crossref]

E. Celeghini, M. Rasetti, and G. Vitiello, “Identical particles and permutation group,” J. Phys. A: Math. Gen. 28, L239–L244 (1995).
[Crossref]

Chakrabarti, R.

R. Chakrabarti and S. Vasan, “Entanglement via Barut–Girardello coherent state for suq(1,1) quantum algebra: bipartite composite system,” Phys. Lett. A 312, 287–295 (2003).
[Crossref]

Christodoulides, D. N.

A. Perez-Leija, R. Keil, A. Szameit, A. F. Abouraddy, H. Moya-Cessa, and D. N. Christodoulides, “Tailoring the correlation and anticorrelation behavior of path-entangled photons in Glauber–Fock lattices,” Phys. Rev. A 85, 013848 (2012).
[Crossref]

A. Perez-Leija, H. Moya-Cessa, F. Soto-Eguibar, O. Aguilar-Loreto, and D. N. Christodoulides, “Classical analogues to quantum nonlinear coherent states in photonic lattices,” Opt. Commun. 284, 1833–1836 (2011).
[Crossref]

R. Keil, A. Perez-Leija, F. Dreisow, M. Heinrich, H. Moya-Cessa, S. Nolte, D. N. Christodoulides, and A. Szameit, “Classical analogue of displaced Fock states and quantum correlations in Glauber–Fock photonic lattices,” Phys. Rev. Lett. 107, 103601 (2011).
[Crossref]

K. G. Makris and D. N. Christodoulides, “Method of images in optical discrete systems,” Phys. Rev. E 73, 036616 (2006).
[Crossref]

D’Ariano, G.

M. G. Rasetti, G. D’Ariano, and A. Montorsi, “Coherent states and infinite-dimensional Lie algebras: an outlook,” Nuovo Cimento D 11, 19–29 (1989).
[Crossref]

G. D’Ariano, M. Rasetti, and M. Vadacchino, “Stability of coherent states,” J. Phys. A: Math. Gen. 18, 1295–1307 (1985).
[Crossref]

de J. León-Montiel, R.

R. de J. León-Montiel, H. Moya-Cessa, and F. Soto-Eguibar, “Nonlinear coherent states for the Susskind–Glogower operators,” Rev. Mex. Fis. S 57, 133–147 (2011).

R. de J. León-Montiel and H. Moya-Cessa, “Modeling non-linear coherent states in fiber arrays,” Int. J. Quantum. Inform. 9, 349–355 (2011).
[Crossref]

de los Santos-Sanchez, O.

O. de los Santos-Sanchez and J. Récamier, “The f-deformed Jaynes–Cummings model and its nonlinear coherent states,” J. Phys. B 45, 015502 (2012).
[Crossref]

de los Santos-Sánchez, O.

O. de los Santos-Sánchez and J. Récamier, “Morse-like squeezed coherent states and some of their properties,” J. Phys. A Math. Theor. 46, 375303 (2013).
[Crossref]

Dirac, P. A. M.

P. A. M. Dirac, “The quantum theory of the emission and absorption of radiation,” Proc. R. Soc. A 114, 243–265 (1927).
[Crossref]

Dreisow, F.

R. Keil, A. Perez-Leija, F. Dreisow, M. Heinrich, H. Moya-Cessa, S. Nolte, D. N. Christodoulides, and A. Szameit, “Classical analogue of displaced Fock states and quantum correlations in Glauber–Fock photonic lattices,” Phys. Rev. Lett. 107, 103601 (2011).
[Crossref]

Eberly, J. H.

Fernández C., D. J.

Gerry, C. C.

C. C. Gerry, “Application of su(1,1) coherent states to the interaction of squeezed light in an anharmonic oscillator,” Phys. Rev. A 35, 2146–2149 (1987).
[Crossref]

C. C. Gerry, “Dynamics of su(1,1) coherent states,” Phys. Rev. A 31, 2721–2723 (1985).
[Crossref]

Girardello, L.

A. O. Barut and L. Girardello, “New “coherent” states associated with non-compact groups,” Commun. Math. Phys. 21, 41–55 (1971).
[Crossref]

Glauber, R. J.

R. J. Glauber, “Coherent and incoherent states of the radiation field,” Phys. Rev. 131, 2766–2788 (1963).
[Crossref]

Glogower, J.

L. Susskind and J. Glogower, “Quantum mechanical phase and time operator,” Physics 1, 49–61 (1964).

Gorayeb, M.

J. Recamier, M. Gorayeb, W. L. Mochán, and J. L. Paz, “Nonlinear coherent states and some of their properties,” Int. J. Theor. Phys. 47, 673–683 (2008).
[Crossref]

Gutiérrez, C. G.

Heinrich, M.

R. Keil, A. Perez-Leija, F. Dreisow, M. Heinrich, H. Moya-Cessa, S. Nolte, D. N. Christodoulides, and A. Szameit, “Classical analogue of displaced Fock states and quantum correlations in Glauber–Fock photonic lattices,” Phys. Rev. Lett. 107, 103601 (2011).
[Crossref]

Horowicz, R. J.

W. Schleich, R. J. Horowicz, and S. Varro, “Bifurcation in the phase probability distribution of a highly squeezed state,” Phys. Rev. A 40, 7405–7408 (1989).
[Crossref]

Kastrup, H. A.

H. A. Kastrup, “Quantization of the canonically conjugate pair angle and orbital angular momentum,” Phys. Rev. A 73, 052104 (2006).
[Crossref]

H. A. Kastrup, “Quantization of the optical phase space S2={φ mod 2π,I>0}; in terms of the group SO↑(1,2),” Fortschr. Phys. 51, 975–1134 (2003).
[Crossref]

Keil, R.

A. Perez-Leija, R. Keil, A. Szameit, A. F. Abouraddy, H. Moya-Cessa, and D. N. Christodoulides, “Tailoring the correlation and anticorrelation behavior of path-entangled photons in Glauber–Fock lattices,” Phys. Rev. A 85, 013848 (2012).
[Crossref]

R. Keil, A. Perez-Leija, F. Dreisow, M. Heinrich, H. Moya-Cessa, S. Nolte, D. N. Christodoulides, and A. Szameit, “Classical analogue of displaced Fock states and quantum correlations in Glauber–Fock photonic lattices,” Phys. Rev. Lett. 107, 103601 (2011).
[Crossref]

Liu, K. L.

K. M. Ng, C. F. Lo, and K. L. Liu, “Exact eigenstates of the intensity-dependent Jaynes–Cummings model with the counter-rotating term,” Phys. A 275, 463–474 (2000).
[Crossref]

C. F. Lo, K. L. Liu, and K. M. Ng, “The multiquantum intensity-dependent Jaynes–Cummings model with the counterrotating terms,” Phys. A 265, 557–564 (1999).
[Crossref]

Lo, C. F.

K. M. Ng, C. F. Lo, and K. L. Liu, “Exact eigenstates of the intensity-dependent Jaynes–Cummings model with the counter-rotating term,” Phys. A 275, 463–474 (2000).
[Crossref]

C. F. Lo, K. L. Liu, and K. M. Ng, “The multiquantum intensity-dependent Jaynes–Cummings model with the counterrotating terms,” Phys. A 265, 557–564 (1999).
[Crossref]

London, F.

F. London, “Winkervariable und kanonische transformationen in der undulationsmechanik,” Z. Phys. 40, 193–210 (1927).
[Crossref]

F. London, “Über die Jacobischen transformationen der quantenmechanik,” Z. Phys. 37, 915–925 (1926).
[Crossref]

Longhi, S.

S. Longhi, “Classical simulation of relativistic quantum mechanics in periodic optical structures,” Appl. Phys. B 104, 453–468 (2011).
[Crossref]

S. Longhi, “Quantum-optical analogies using photonic structures,” Laser Photonics Rev. 3, 243–261 (2009).
[Crossref]

Loudon, R.

R. Loudon, The Quantum Theory of Light (Oxford University, 1973).

Makris, K. G.

K. G. Makris and D. N. Christodoulides, “Method of images in optical discrete systems,” Phys. Rev. E 73, 036616 (2006).
[Crossref]

Mochán, W. L.

J. Recamier, M. Gorayeb, W. L. Mochán, and J. L. Paz, “Nonlinear coherent states and some of their properties,” Int. J. Theor. Phys. 47, 673–683 (2008).
[Crossref]

Montorsi, A.

M. G. Rasetti, G. D’Ariano, and A. Montorsi, “Coherent states and infinite-dimensional Lie algebras: an outlook,” Nuovo Cimento D 11, 19–29 (1989).
[Crossref]

Moya-Cessa, H.

A. Perez-Leija, R. Keil, A. Szameit, A. F. Abouraddy, H. Moya-Cessa, and D. N. Christodoulides, “Tailoring the correlation and anticorrelation behavior of path-entangled photons in Glauber–Fock lattices,” Phys. Rev. A 85, 013848 (2012).
[Crossref]

R. Keil, A. Perez-Leija, F. Dreisow, M. Heinrich, H. Moya-Cessa, S. Nolte, D. N. Christodoulides, and A. Szameit, “Classical analogue of displaced Fock states and quantum correlations in Glauber–Fock photonic lattices,” Phys. Rev. Lett. 107, 103601 (2011).
[Crossref]

R. de J. León-Montiel and H. Moya-Cessa, “Modeling non-linear coherent states in fiber arrays,” Int. J. Quantum. Inform. 9, 349–355 (2011).
[Crossref]

A. Perez-Leija, H. Moya-Cessa, F. Soto-Eguibar, O. Aguilar-Loreto, and D. N. Christodoulides, “Classical analogues to quantum nonlinear coherent states in photonic lattices,” Opt. Commun. 284, 1833–1836 (2011).
[Crossref]

R. de J. León-Montiel, H. Moya-Cessa, and F. Soto-Eguibar, “Nonlinear coherent states for the Susskind–Glogower operators,” Rev. Mex. Fis. S 57, 133–147 (2011).

Moya-Cessa, H. M.

Ng, K. M.

K. M. Ng, C. F. Lo, and K. L. Liu, “Exact eigenstates of the intensity-dependent Jaynes–Cummings model with the counter-rotating term,” Phys. A 275, 463–474 (2000).
[Crossref]

C. F. Lo, K. L. Liu, and K. M. Ng, “The multiquantum intensity-dependent Jaynes–Cummings model with the counterrotating terms,” Phys. A 265, 557–564 (1999).
[Crossref]

Nieto, M. M.

P. Carruthers and M. M. Nieto, “Phase and angle variables in quantum mechanics,” Rev. Mod. Phys. 40, 411–440 (1968).
[Crossref]

Nolte, S.

R. Keil, A. Perez-Leija, F. Dreisow, M. Heinrich, H. Moya-Cessa, S. Nolte, D. N. Christodoulides, and A. Szameit, “Classical analogue of displaced Fock states and quantum correlations in Glauber–Fock photonic lattices,” Phys. Rev. Lett. 107, 103601 (2011).
[Crossref]

Paz, J. L.

J. Recamier, M. Gorayeb, W. L. Mochán, and J. L. Paz, “Nonlinear coherent states and some of their properties,” Int. J. Theor. Phys. 47, 673–683 (2008).
[Crossref]

Perelomov, A. M.

A. M. Perelomov, “Coherent states for arbitrary Lie group,” Commun. Math. Phys. 26, 222–236 (1972).
[Crossref]

Perez-Leija, A.

A. Perez-Leija, R. Keil, A. Szameit, A. F. Abouraddy, H. Moya-Cessa, and D. N. Christodoulides, “Tailoring the correlation and anticorrelation behavior of path-entangled photons in Glauber–Fock lattices,” Phys. Rev. A 85, 013848 (2012).
[Crossref]

A. Perez-Leija, H. Moya-Cessa, F. Soto-Eguibar, O. Aguilar-Loreto, and D. N. Christodoulides, “Classical analogues to quantum nonlinear coherent states in photonic lattices,” Opt. Commun. 284, 1833–1836 (2011).
[Crossref]

R. Keil, A. Perez-Leija, F. Dreisow, M. Heinrich, H. Moya-Cessa, S. Nolte, D. N. Christodoulides, and A. Szameit, “Classical analogue of displaced Fock states and quantum correlations in Glauber–Fock photonic lattices,” Phys. Rev. Lett. 107, 103601 (2011).
[Crossref]

Puri, R. R.

R. R. Puri, Mathematical Methods of Quantum Optics (Springer, 2001).

Rasetti, M.

M. Rasetti, “A fully consistent Lie algebraic representation of quantum phase and number operators,” J. Phys. A: Math. Gen. 37, L479–L487 (2004).
[Crossref]

E. Celeghini and M. Rasetti, “Generalized bosons and coherent states,” Phys. Rev. Lett. 80, 3424–3427 (1998).
[Crossref]

E. Celeghini and M. Rasetti, “Many-particle quantum statistics and co-algebra,” Int. J. Mod. Phys. B 10, 1625–1636 (1996).
[Crossref]

E. Celeghini, M. Rasetti, and G. Vitiello, “Identical particles and permutation group,” J. Phys. A: Math. Gen. 28, L239–L244 (1995).
[Crossref]

G. D’Ariano, M. Rasetti, and M. Vadacchino, “Stability of coherent states,” J. Phys. A: Math. Gen. 18, 1295–1307 (1985).
[Crossref]

M. Rasetti, “Generalized definition of coherent states and dynamical groups,” Int. J. Theor. Phys. 13, 425–430 (1975).
[Crossref]

Rasetti, M. G.

M. G. Rasetti, G. D’Ariano, and A. Montorsi, “Coherent states and infinite-dimensional Lie algebras: an outlook,” Nuovo Cimento D 11, 19–29 (1989).
[Crossref]

Recamier, J.

J. Recamier, M. Gorayeb, W. L. Mochán, and J. L. Paz, “Nonlinear coherent states and some of their properties,” Int. J. Theor. Phys. 47, 673–683 (2008).
[Crossref]

Récamier, J.

R. Roman-Acheyta, C. G. Gutiérrez, and J. Récamier, “Photon-added nonlinear coherent states for a one-mode field in a Kerr medium,” J. Opt. Soc. Am. B 31, 38–44 (2014).
[Crossref]

O. de los Santos-Sánchez and J. Récamier, “Morse-like squeezed coherent states and some of their properties,” J. Phys. A Math. Theor. 46, 375303 (2013).
[Crossref]

O. de los Santos-Sanchez and J. Récamier, “The f-deformed Jaynes–Cummings model and its nonlinear coherent states,” J. Phys. B 45, 015502 (2012).
[Crossref]

Rodrguez-Lara, B. M.

B. M. Rodrguez-Lara, “Exact dynamics of finite Glauber–Fock photonic lattices,” Phys. Rev. A 84, 053845 (2011).
[Crossref]

B. M. Rodrguez-Lara, “An intensity-dependent quantum Rabi model: spectrum, SUSY partner and optical simulation,” arXiv: 1401.7376 (2014).

Rodríguez-Lara, B. M.

Roman-Acheyta, R.

Schiller, S.

G. Breitenbach and S. Schiller, “Homodyne tomography of classical and non-classical light,” J. Mod. Opt. 44, 2207–2225 (1997).
[Crossref]

Schleich, W.

W. Schleich, R. J. Horowicz, and S. Varro, “Bifurcation in the phase probability distribution of a highly squeezed state,” Phys. Rev. A 40, 7405–7408 (1989).
[Crossref]

Schleich, W. P.

W. P. Schleich, Quantum Optics in Phase State (Wiley-VCH, 2001).

Schrödinger, E.

E. Schrödinger, “Der stetige übergang von der mikro- zur makromechanik,” Naturwissenschaften 14, 664–666 (1926).
[Crossref]

Sivakumar, S.

S. Sivakumar, “Interpolating coherent states for Heisenberg–Weyl and single-photon SU(1,1) algebras,” J. Phys. A: Math. Gen. 35, 6755–6766 (2002).
[Crossref]

Soto-Eguibar, F.

R. de J. León-Montiel, H. Moya-Cessa, and F. Soto-Eguibar, “Nonlinear coherent states for the Susskind–Glogower operators,” Rev. Mex. Fis. S 57, 133–147 (2011).

A. Perez-Leija, H. Moya-Cessa, F. Soto-Eguibar, O. Aguilar-Loreto, and D. N. Christodoulides, “Classical analogues to quantum nonlinear coherent states in photonic lattices,” Opt. Commun. 284, 1833–1836 (2011).
[Crossref]

Sudarshan, E. C. G.

E. C. G. Sudarshan, “Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams,” Phys. Rev. Lett. 10, 277–279 (1963).
[Crossref]

Sukumar, C. V.

B. Buck and C. V. Sukumar, “Exactly soluble model of atom–phonon coupling showing periodic decay and revival,” Phys. Lett. 81, 132–135 (1981).
[Crossref]

Susskind, L.

L. Susskind and J. Glogower, “Quantum mechanical phase and time operator,” Physics 1, 49–61 (1964).

Szameit, A.

A. Perez-Leija, R. Keil, A. Szameit, A. F. Abouraddy, H. Moya-Cessa, and D. N. Christodoulides, “Tailoring the correlation and anticorrelation behavior of path-entangled photons in Glauber–Fock lattices,” Phys. Rev. A 85, 013848 (2012).
[Crossref]

R. Keil, A. Perez-Leija, F. Dreisow, M. Heinrich, H. Moya-Cessa, S. Nolte, D. N. Christodoulides, and A. Szameit, “Classical analogue of displaced Fock states and quantum correlations in Glauber–Fock photonic lattices,” Phys. Rev. Lett. 107, 103601 (2011).
[Crossref]

Vadacchino, M.

G. D’Ariano, M. Rasetti, and M. Vadacchino, “Stability of coherent states,” J. Phys. A: Math. Gen. 18, 1295–1307 (1985).
[Crossref]

Varro, S.

W. Schleich, R. J. Horowicz, and S. Varro, “Bifurcation in the phase probability distribution of a highly squeezed state,” Phys. Rev. A 40, 7405–7408 (1989).
[Crossref]

Vasan, S.

R. Chakrabarti and S. Vasan, “Entanglement via Barut–Girardello coherent state for suq(1,1) quantum algebra: bipartite composite system,” Phys. Lett. A 312, 287–295 (2003).
[Crossref]

Vitiello, G.

E. Celeghini, M. Rasetti, and G. Vitiello, “Identical particles and permutation group,” J. Phys. A: Math. Gen. 28, L239–L244 (1995).
[Crossref]

Wódkiewicz, K.

Zuñiga-Segundo, A.

Appl. Phys. B (1)

S. Longhi, “Classical simulation of relativistic quantum mechanics in periodic optical structures,” Appl. Phys. B 104, 453–468 (2011).
[Crossref]

Commun. Math. Phys. (2)

A. M. Perelomov, “Coherent states for arbitrary Lie group,” Commun. Math. Phys. 26, 222–236 (1972).
[Crossref]

A. O. Barut and L. Girardello, “New “coherent” states associated with non-compact groups,” Commun. Math. Phys. 21, 41–55 (1971).
[Crossref]

Fortschr. Phys. (1)

H. A. Kastrup, “Quantization of the optical phase space S2={φ mod 2π,I>0}; in terms of the group SO↑(1,2),” Fortschr. Phys. 51, 975–1134 (2003).
[Crossref]

Int. J. Mod. Phys. B (2)

E. Celeghini and M. Rasetti, “Many-particle quantum statistics and co-algebra,” Int. J. Mod. Phys. B 10, 1625–1636 (1996).
[Crossref]

E. Celeghini, “A new definition of bosons,” Int. J. Mod. Phys. B 13, 2909–2913 (1999).
[Crossref]

Int. J. Quantum. Inform. (1)

R. de J. León-Montiel and H. Moya-Cessa, “Modeling non-linear coherent states in fiber arrays,” Int. J. Quantum. Inform. 9, 349–355 (2011).
[Crossref]

Int. J. Theor. Phys. (2)

J. Recamier, M. Gorayeb, W. L. Mochán, and J. L. Paz, “Nonlinear coherent states and some of their properties,” Int. J. Theor. Phys. 47, 673–683 (2008).
[Crossref]

M. Rasetti, “Generalized definition of coherent states and dynamical groups,” Int. J. Theor. Phys. 13, 425–430 (1975).
[Crossref]

J. Math. Phys. (1)

M. Ban, “su(1,1) Lie algebraic approach to linear dissipative processes in quantum optics,” J. Math. Phys. 33, 3213–3228 (1992).
[Crossref]

J. Mod. Opt. (3)

V. Bužek, “Light squeezing in the Jaynes–Cummings model with intensity-dependent coupling,” J. Mod. Opt. 36, 1151–1162 (1989).
[Crossref]

V. Bužek, “SU(1,1) squeezing of SU(1,1) generalized coherent states,” J. Mod. Opt. 37, 303–316 (1990).
[Crossref]

G. Breitenbach and S. Schiller, “Homodyne tomography of classical and non-classical light,” J. Mod. Opt. 44, 2207–2225 (1997).
[Crossref]

J. Opt. Soc. Am. B (3)

J. Phys. A Math. Theor. (1)

O. de los Santos-Sánchez and J. Récamier, “Morse-like squeezed coherent states and some of their properties,” J. Phys. A Math. Theor. 46, 375303 (2013).
[Crossref]

J. Phys. A: Math. Gen. (4)

S. Sivakumar, “Interpolating coherent states for Heisenberg–Weyl and single-photon SU(1,1) algebras,” J. Phys. A: Math. Gen. 35, 6755–6766 (2002).
[Crossref]

G. D’Ariano, M. Rasetti, and M. Vadacchino, “Stability of coherent states,” J. Phys. A: Math. Gen. 18, 1295–1307 (1985).
[Crossref]

M. Rasetti, “A fully consistent Lie algebraic representation of quantum phase and number operators,” J. Phys. A: Math. Gen. 37, L479–L487 (2004).
[Crossref]

E. Celeghini, M. Rasetti, and G. Vitiello, “Identical particles and permutation group,” J. Phys. A: Math. Gen. 28, L239–L244 (1995).
[Crossref]

J. Phys. B (1)

O. de los Santos-Sanchez and J. Récamier, “The f-deformed Jaynes–Cummings model and its nonlinear coherent states,” J. Phys. B 45, 015502 (2012).
[Crossref]

Laser Photonics Rev. (1)

S. Longhi, “Quantum-optical analogies using photonic structures,” Laser Photonics Rev. 3, 243–261 (2009).
[Crossref]

Naturwissenschaften (1)

E. Schrödinger, “Der stetige übergang von der mikro- zur makromechanik,” Naturwissenschaften 14, 664–666 (1926).
[Crossref]

Nuovo Cimento D (1)

M. G. Rasetti, G. D’Ariano, and A. Montorsi, “Coherent states and infinite-dimensional Lie algebras: an outlook,” Nuovo Cimento D 11, 19–29 (1989).
[Crossref]

Opt. Commun. (1)

A. Perez-Leija, H. Moya-Cessa, F. Soto-Eguibar, O. Aguilar-Loreto, and D. N. Christodoulides, “Classical analogues to quantum nonlinear coherent states in photonic lattices,” Opt. Commun. 284, 1833–1836 (2011).
[Crossref]

Opt. Express (1)

Phys. A (2)

C. F. Lo, K. L. Liu, and K. M. Ng, “The multiquantum intensity-dependent Jaynes–Cummings model with the counterrotating terms,” Phys. A 265, 557–564 (1999).
[Crossref]

K. M. Ng, C. F. Lo, and K. L. Liu, “Exact eigenstates of the intensity-dependent Jaynes–Cummings model with the counter-rotating term,” Phys. A 275, 463–474 (2000).
[Crossref]

Phys. Lett. (1)

B. Buck and C. V. Sukumar, “Exactly soluble model of atom–phonon coupling showing periodic decay and revival,” Phys. Lett. 81, 132–135 (1981).
[Crossref]

Phys. Lett. A (1)

R. Chakrabarti and S. Vasan, “Entanglement via Barut–Girardello coherent state for suq(1,1) quantum algebra: bipartite composite system,” Phys. Lett. A 312, 287–295 (2003).
[Crossref]

Phys. Rev. (1)

R. J. Glauber, “Coherent and incoherent states of the radiation field,” Phys. Rev. 131, 2766–2788 (1963).
[Crossref]

Phys. Rev. A (6)

H. A. Kastrup, “Quantization of the canonically conjugate pair angle and orbital angular momentum,” Phys. Rev. A 73, 052104 (2006).
[Crossref]

C. C. Gerry, “Dynamics of su(1,1) coherent states,” Phys. Rev. A 31, 2721–2723 (1985).
[Crossref]

W. Schleich, R. J. Horowicz, and S. Varro, “Bifurcation in the phase probability distribution of a highly squeezed state,” Phys. Rev. A 40, 7405–7408 (1989).
[Crossref]

C. C. Gerry, “Application of su(1,1) coherent states to the interaction of squeezed light in an anharmonic oscillator,” Phys. Rev. A 35, 2146–2149 (1987).
[Crossref]

B. M. Rodrguez-Lara, “Exact dynamics of finite Glauber–Fock photonic lattices,” Phys. Rev. A 84, 053845 (2011).
[Crossref]

A. Perez-Leija, R. Keil, A. Szameit, A. F. Abouraddy, H. Moya-Cessa, and D. N. Christodoulides, “Tailoring the correlation and anticorrelation behavior of path-entangled photons in Glauber–Fock lattices,” Phys. Rev. A 85, 013848 (2012).
[Crossref]

Phys. Rev. E (1)

K. G. Makris and D. N. Christodoulides, “Method of images in optical discrete systems,” Phys. Rev. E 73, 036616 (2006).
[Crossref]

Phys. Rev. Lett. (3)

R. Keil, A. Perez-Leija, F. Dreisow, M. Heinrich, H. Moya-Cessa, S. Nolte, D. N. Christodoulides, and A. Szameit, “Classical analogue of displaced Fock states and quantum correlations in Glauber–Fock photonic lattices,” Phys. Rev. Lett. 107, 103601 (2011).
[Crossref]

E. C. G. Sudarshan, “Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams,” Phys. Rev. Lett. 10, 277–279 (1963).
[Crossref]

E. Celeghini and M. Rasetti, “Generalized bosons and coherent states,” Phys. Rev. Lett. 80, 3424–3427 (1998).
[Crossref]

Physics (1)

L. Susskind and J. Glogower, “Quantum mechanical phase and time operator,” Physics 1, 49–61 (1964).

Proc. R. Soc. A (1)

P. A. M. Dirac, “The quantum theory of the emission and absorption of radiation,” Proc. R. Soc. A 114, 243–265 (1927).
[Crossref]

Rev. Mex. Fis. S (1)

R. de J. León-Montiel, H. Moya-Cessa, and F. Soto-Eguibar, “Nonlinear coherent states for the Susskind–Glogower operators,” Rev. Mex. Fis. S 57, 133–147 (2011).

Rev. Mod. Phys. (1)

P. Carruthers and M. M. Nieto, “Phase and angle variables in quantum mechanics,” Rev. Mod. Phys. 40, 411–440 (1968).
[Crossref]

Z. Phys. (2)

F. London, “Über die Jacobischen transformationen der quantenmechanik,” Z. Phys. 37, 915–925 (1926).
[Crossref]

F. London, “Winkervariable und kanonische transformationen in der undulationsmechanik,” Z. Phys. 40, 193–210 (1927).
[Crossref]

Other (4)

R. R. Puri, Mathematical Methods of Quantum Optics (Springer, 2001).

R. Loudon, The Quantum Theory of Light (Oxford University, 1973).

W. P. Schleich, Quantum Optics in Phase State (Wiley-VCH, 2001).

B. M. Rodrguez-Lara, “An intensity-dependent quantum Rabi model: spectrum, SUSY partner and optical simulation,” arXiv: 1401.7376 (2014).

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Equations (27)

Equations on this page are rendered with MathJax. Learn more.

|ϕ12πj=0eiϕ(j+12)|j,
|ϕ=12πeiϕK^0eK^+|0.
eA+K^+elnA0K^0eAK^=eBK^elnB0K^0eB+K^+
A±=B±B01B+B0B,
A0=B0(1B+B0B)2,
B±=A±1A+A,
B0=(A0A+A)2A0.
|ϕ=12πeeiϕK^+eiϕK^0eeiϕK^|0.
eiϕ^|ϕ=1n^+1a^|ϕ
=1K^0+12K^|ϕ
=eiϕ|ϕ,
|αBG=1I0(2|α|)j=0αjj!|j,
|αBG=1I0(2|α|)eαV^eα*V^|0.
|α=eα(V^V^)|0,αR
=1αj=0(j+1)Jj+1(2α)|j,
C^α=αJn^+1(2α)(n^+2)Jn^+2(2α)n^+1a^,
=αJK^0+12(2α)(K^0+32)JK^0+32(2α)K^,
iddzEj(z)=[(j+1)(j+2)Ej+1+j(j+1)Ej1],
iddz|E=(K^++K^)|E.
|k,α=eαK^+α*K^|k,0
=(1|μ|2)km=0Γ(2k+m)m!Γ(2k)μm|k,m,
Im,0(z)=m|eiz(K^++K^)|0
=sechz(itanhz)m,
iddzEj(z)=Ej+1+Ej1,
iddz|E=(V^+V^)|E.
Im,0(z)=m|eiz(V^+V^)|0
=1zim(m+1)Jm+1(2z),

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