Abstract

The interaction of a two-level atom with a single-mode quantized field is one of the simplest models in quantum optics. Under the rotating wave approximation, it is known as the Jaynes-Cummings model and without it as the Rabi model. Real-world realizations of the Jaynes-Cummings model include cavity, ion trap and circuit quantum electrodynamics. The Rabi model can be realized in circuit quantum electrodynamics. As soon as nonlinear couplings are introduced, feasible experimental realizations in quantum systems are drastically reduced. We propose a set of two photonic lattices that classically simulates the interaction of a single two-level system with a quantized field under field nonlinearities and nonlinear couplings as long as the quantum optics model conserves parity. We describe how to reconstruct the mean value of quantum optics measurements, such as photon number and atomic energy excitation, from the intensity and from the field, such as von Neumann entropy and fidelity, at the output of the photonic lattices. We discuss how typical initial states involving coherent or displaced Fock fields can be engineered from recently discussed Glauber-Fock lattices. As an example, the Buck-Sukumar model, where the coupling depends on the intensity of the field, is classically simulated for separable and entangled initial states.

© 2013 OSA

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  34. M. Abdel-Aty, S. Furuichi, and A.-S. F. Obada, “Entanglement degree of a nonlinear multiphoton Jaynes-Cummings model,” J. Opt. B: Quantum Semiclass. Opt.4, 37–43 (2002).
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    [CrossRef]
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  47. E. A. Tur, “Energy spectrum of the Hamiltonian of the Jaynes-Cummings model without rotating-wave approximation,” Opt. Spectrosc.91, 899–902 (2001).
    [CrossRef]
  48. J. Casanova, G. Romero, I. Lizuain, J. J. García-Ripoll, and E. Solano, “Deep strong coupling regime of the Jaynes-Cummings model,” Phys. Rev. Lett.105, 263603 (2010).
    [CrossRef]
  49. B. M. Rodríguez-Lara and H. M. Moya-Cessa, “Exact solution of generalized Dicke models via Susskind-Glogower operators,” J. Phys. A: Math. Theor.46, 095301 (2013).
    [CrossRef]
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  51. S. Longhi, “Photonic analog of zitterbewegung in binary waveguide arrays,” Opt. Lett.35, 235–237 (2010).
    [CrossRef] [PubMed]
  52. C. Thompson, G. Vemuri, and G. S. Agarwal, “Quantum physics inspired optical effects in tight-binding lattices: Phase-controlled photonic transport,” Phys. Rev. B84, 214302 (2011).
    [CrossRef]
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    [CrossRef]
  54. 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] [PubMed]

2013 (4)

B. M. Rodríguez-Lara, A. Z. Cárdenas, F. Soto-Eguibar, and H. M. Moya-Cessa, “A photonic crystal realization of a phase driven two-level atom,” Opt. Commun.292, 87–91 (2013).
[CrossRef]

B. M. Rodríguez-Lara and H. M. Moya-Cessa, “Exact solution of generalized Dicke models via Susskind-Glogower operators,” J. Phys. A: Math. Theor.46, 095301 (2013).
[CrossRef]

A. Perez-Leija, R. Keil, A. Kay, H. Moya-Cessa, S. Nolte, L.-C. Kwek, B.M. Rodríguez-Lara, A. Szameit, and D. Christodoulides, “Coherent quantum transport in photonic lattices,” Phys. Rev. A87, 012309 (2013).
[CrossRef]

B. M. Rodríguez-Lara and H. Moya-Cessa, “Photon transport in binary photonic lattices,” Phys. Scr.87, 038116 (2013).
[CrossRef]

2012 (7)

S. Longhi, “Many-body dynamic localization of strongly correlated electrons in ac-driven hubbard lattices,” J. Phys.: Condens. Matter24, 435601 (2012).
[CrossRef]

S. Longhi and G. Della Valle, “Photonic realization of 𝔓 𝔗-symmetric quantum field theories,” Phys. Rev. A85, 012112 (2012).
[CrossRef]

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, “Light propagation an localization in modulated photonic lattices and waveguides,” Phys. Rep518, 1–79 (2012).
[CrossRef]

O. de los Santos-Sanchez and J. Récamier, “The f-deformed Jaynes-Cummings model and its nonlinear coherent states,” J. Phys. B: At. Mol. Opt. Phys.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. A85, 013848 (2012).
[CrossRef]

H. Moya-Cessa, F. Soto-Eguibar, J. M. Vargas-Martínez, R. Juárez-Amaro, and A. Zúñiga Segundo, “Ion-laser interactions: The most complete solution,” Physics Reports513, 229–261 (2012).
[CrossRef]

A. Crespi, S. Longhi, and R. Osellame, “Photonic realization of the quantum Rabi model,” Phys. Rev. Lett.108, 163601 (2012).
[CrossRef] [PubMed]

2011 (7)

B. M. Rodríguez-Lara, “Exact dynamics of finite Glauber-Fock photonic lattices,” Phys. Rev. A84, 053845 (2011).
[CrossRef]

S. Cordero and J. Récamier, “Selective transition and complete revivals of a single two-level atom in the Jaynes-Cummings Hamiltonian with an additional Kerr medium,” J. Phys. B: At. Mol. Opt. Phys.44, 135502 (2011).
[CrossRef]

C. Thompson, G. Vemuri, and G. S. Agarwal, “Quantum physics inspired optical effects in tight-binding lattices: Phase-controlled photonic transport,” Phys. Rev. B84, 214302 (2011).
[CrossRef]

S. Longhi, “Classical simulation of relativistic quantum mechanics in periodic optical structures,” Appl. Phys. B104, 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] [PubMed]

S. Longhi, “Photonic Bloch oscillations of correlated particles,” Opt. Lett.36, 3248–3250 (2011).
[CrossRef] [PubMed]

S. Longhi, “Jaynes-Cummings photonic superlattices,” Opt. Lett.36, 3407–3409 (2011).
[CrossRef] [PubMed]

2010 (7)

S. Longhi, “Photonic analog of zitterbewegung in binary waveguide arrays,” Opt. Lett.35, 235–237 (2010).
[CrossRef] [PubMed]

A. Perez-Leija, H. Moya-Cessa, A. Szameit, and D. N. Christodoulides, “Glauber-Fock photonic lattices,” Opt. Lett.35, 2409–2411 (2010).
[CrossRef] [PubMed]

J. Casanova, G. Romero, I. Lizuain, J. J. García-Ripoll, and E. Solano, “Deep strong coupling regime of the Jaynes-Cummings model,” Phys. Rev. Lett.105, 263603 (2010).
[CrossRef]

T. Esslinger, “Fermi-Hubbard Physics with atoms in an optical lattice,” Annu. Rev. Condens. Matter Phys.1, 129–152 (2010).
[CrossRef]

Y. Lahini, Y. Bromberg, D. N. Christodoulides, and Y. Silberberg, “Quantum correlations in two-particle Anderson localization,” Phys. Rev. Lett.105, 163905 (2010).
[CrossRef]

F. Dreisow, M. Heinrich, R. Keil, A. Tunnermann, S. Nolte, S. Longhi, and A. Szameit, “Classical simulation of relativistic zitterbewegung in photonic lattices,” Phys. Rev. Lett.105, 143902 (2010).
[CrossRef]

S. Longhi, “Klein tunneling in binary photonic superlattices,” Phys. Rev. B81, 075102 (2010).
[CrossRef]

2009 (3)

Y. Bromberg, Y. Lahini, R. Morandotti, and Y. Silberberg, “Quantum and classical correlations in waveguide lattices,” Phys. Rev. Lett.102, 253904 (2009).
[CrossRef] [PubMed]

F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, A. Tunnermann, and S. Longhi, “Bloch-Zener oscillations in binary superlattices,” Phys. Rev. Lett.102, 076802 (2009).
[CrossRef] [PubMed]

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

2008 (2)

H. B. Perets, Y. Lahini, F. Pozzi, M. Sorel, R. Morandotti, and Y. Silberberg, “Realization of quantum walks with negligible decoherence in waveguide lattices,” Phys. Rev. Lett.100, 170506 (2008).
[CrossRef] [PubMed]

G. Della Valle, M. Ornigotti, T. T. Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, “Adiabatic light transfer via dressed states in optical waveguide arrays,” Appl. Phys. Lett.92, 011106 (2008).
[CrossRef]

2006 (1)

S. Longhi, “Nonexponential decay via tunneling in tight-binding lattices and the optical Zeno effect,” Phys. Rev. Lett.97, 110402 (2006).
[CrossRef] [PubMed]

2005 (1)

M. H. Naderi, M. Soltanolkotabi, and R. Roknizadeh, “A theoretical scheme for generation of nonlinear coherent states in a micromaser under intensity-dependent Jaynes-Cummings model,” Eur. Phys. J. D32, 397–408 (2005).
[CrossRef]

2002 (1)

M. Abdel-Aty, S. Furuichi, and A.-S. F. Obada, “Entanglement degree of a nonlinear multiphoton Jaynes-Cummings model,” J. Opt. B: Quantum Semiclass. Opt.4, 37–43 (2002).
[CrossRef]

2001 (2)

E. A. Tur, “Energy spectrum of the Hamiltonian of the Jaynes-Cummings model without rotating-wave approximation,” Opt. Spectrosc.91, 899–902 (2001).
[CrossRef]

J. W. Chan, T. Huser, S. Risbud, and D. M. Krol, “Structural changes in fused silica after exposure to focused femtosecond laser pulses,” Opt. Lett.26, 1726–1728 (2001).
[CrossRef]

2000 (3)

A. Joshi, “Nonlinear dynamical evolution of the driven two-photon Jaynes-Cummings model,” Phys. Rev. A62, 043812 (2000).
[CrossRef]

E. A. Tur, “Jaynes-Cummings model: Solutions without rotating wave approximation,” Opt. Spectrosc.89, 574–588 (2000).
[CrossRef]

H. Moya-Cessa and P. Tombesi, “Filtering number states of the vibrational motion of an ion,” Phys. Rev. A61, 025401 (2000).
[CrossRef]

1998 (2)

R. J. C. Spreeuw, “A classical analogy of entanglement,” Found. Phys.28, 361–374 (1998).
[CrossRef]

N. J. Cerf, C. Adami, and P. G. Kwiat, “Optical simulation of quantum logic,” Phys. Rev. A57, R1477–R1480 (1998).
[CrossRef]

1997 (1)

X. Yang, Y. Wu, and Y. Li, “Unified and standarized procedure to solve various nonlinear Jaynes-Cummings models,” Phys. Rev. A55, 4545–4551 (1997).
[CrossRef]

1996 (2)

R. L. de Matos Filho and W. Vogel, “Nonlinear coherent states,” Phys. Rev. A54, 4560–4563 (1996).
[CrossRef] [PubMed]

R. L. de Matos Filho and W. Vogel, “Even and Odd Coherent States of the Motion of a Trapped Ion,” Phys. Rev. Lett.76, 608–611 (1996).
[CrossRef] [PubMed]

1995 (1)

W. Vogel and R. L. de Matos Filho, “Nonlinear Jaynes-Cummings dynamics of a trapped ion,” Phys. Rev. A52, 4214–4217 (1995).
[CrossRef] [PubMed]

1994 (1)

G. Benivegna, A. Messina, and A. Napoli, “Canonical dressing in nonlinear Jaynes-Cummings models,” Phys. Lett. A194, 353–357 (1994).
[CrossRef]

1990 (1)

1989 (1)

R. R. Schlicher, “Jaynes-Cummings model with atomic motion,” Opt. Commun.70, 97–102 (1989).
[CrossRef]

1987 (1)

E. A. Kochetov, “Exactly solvable non-linear generalisations of the Jaynes-Cummings model,” J. Phys. A: Math. Gen.20, 2433–2442 (1987).
[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]

1980 (1)

J. H. Eberly, N. B. Narozhny, and J. J. Sanchez-Mondragon, “Periodic spontaneuous collapse and revival in a simple quantum model,” Phys. Rev. Lett.44, 1323–1326 (1980).
[CrossRef]

1963 (1)

E. T. Jaynes and F. W. Cummings, “Comparison of quantum and semiclassical radiation theories with application to the beam maser,” Proc. IEEE51, 89–109 (1963).
[CrossRef]

1954 (1)

R. H. Dicke, “Coherence in spontaneaous radiation processes,” Phys. Rev.93, 99–110 (1954).
[CrossRef]

Abdel-Aty, M.

M. Abdel-Aty, S. Furuichi, and A.-S. F. Obada, “Entanglement degree of a nonlinear multiphoton Jaynes-Cummings model,” J. Opt. B: Quantum Semiclass. Opt.4, 37–43 (2002).
[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. A85, 013848 (2012).
[CrossRef]

Adami, C.

N. J. Cerf, C. Adami, and P. G. Kwiat, “Optical simulation of quantum logic,” Phys. Rev. A57, R1477–R1480 (1998).
[CrossRef]

Agarwal, G. S.

C. Thompson, G. Vemuri, and G. S. Agarwal, “Quantum physics inspired optical effects in tight-binding lattices: Phase-controlled photonic transport,” Phys. Rev. B84, 214302 (2011).
[CrossRef]

Benivegna, G.

G. Benivegna, A. Messina, and A. Napoli, “Canonical dressing in nonlinear Jaynes-Cummings models,” Phys. Lett. A194, 353–357 (1994).
[CrossRef]

Bromberg, Y.

Y. Lahini, Y. Bromberg, D. N. Christodoulides, and Y. Silberberg, “Quantum correlations in two-particle Anderson localization,” Phys. Rev. Lett.105, 163905 (2010).
[CrossRef]

Y. Bromberg, Y. Lahini, R. Morandotti, and Y. Silberberg, “Quantum and classical correlations in waveguide lattices,” Phys. Rev. Lett.102, 253904 (2009).
[CrossRef] [PubMed]

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]

Cárdenas, A. Z.

B. M. Rodríguez-Lara, A. Z. Cárdenas, F. Soto-Eguibar, and H. M. Moya-Cessa, “A photonic crystal realization of a phase driven two-level atom,” Opt. Commun.292, 87–91 (2013).
[CrossRef]

Casanova, J.

J. Casanova, G. Romero, I. Lizuain, J. J. García-Ripoll, and E. Solano, “Deep strong coupling regime of the Jaynes-Cummings model,” Phys. Rev. Lett.105, 263603 (2010).
[CrossRef]

Cerf, N. J.

N. J. Cerf, C. Adami, and P. G. Kwiat, “Optical simulation of quantum logic,” Phys. Rev. A57, R1477–R1480 (1998).
[CrossRef]

Chan, J. W.

Christodoulides, D.

A. Perez-Leija, R. Keil, A. Kay, H. Moya-Cessa, S. Nolte, L.-C. Kwek, B.M. Rodríguez-Lara, A. Szameit, and D. Christodoulides, “Coherent quantum transport in photonic lattices,” Phys. Rev. A87, 012309 (2013).
[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. A85, 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] [PubMed]

A. Perez-Leija, H. Moya-Cessa, A. Szameit, and D. N. Christodoulides, “Glauber-Fock photonic lattices,” Opt. Lett.35, 2409–2411 (2010).
[CrossRef] [PubMed]

Y. Lahini, Y. Bromberg, D. N. Christodoulides, and Y. Silberberg, “Quantum correlations in two-particle Anderson localization,” Phys. Rev. Lett.105, 163905 (2010).
[CrossRef]

Coppa, A.

G. Della Valle, M. Ornigotti, T. T. Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, “Adiabatic light transfer via dressed states in optical waveguide arrays,” Appl. Phys. Lett.92, 011106 (2008).
[CrossRef]

Cordero, S.

S. Cordero and J. Récamier, “Selective transition and complete revivals of a single two-level atom in the Jaynes-Cummings Hamiltonian with an additional Kerr medium,” J. Phys. B: At. Mol. Opt. Phys.44, 135502 (2011).
[CrossRef]

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G. Della Valle, M. Ornigotti, T. T. Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, “Adiabatic light transfer via dressed states in optical waveguide arrays,” Appl. Phys. Lett.92, 011106 (2008).
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A. Crespi, S. Longhi, and R. Osellame, “Photonic realization of the quantum Rabi model,” Phys. Rev. Lett.108, 163601 (2012).
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H. B. Perets, Y. Lahini, F. Pozzi, M. Sorel, R. Morandotti, and Y. Silberberg, “Realization of quantum walks with negligible decoherence in waveguide lattices,” Phys. Rev. Lett.100, 170506 (2008).
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A. Perez-Leija, R. Keil, A. Kay, H. Moya-Cessa, S. Nolte, L.-C. Kwek, B.M. Rodríguez-Lara, A. Szameit, and D. Christodoulides, “Coherent quantum transport in photonic lattices,” Phys. Rev. A87, 012309 (2013).
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[CrossRef]

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B. M. Rodríguez-Lara, A. Z. Cárdenas, F. Soto-Eguibar, and H. M. Moya-Cessa, “A photonic crystal realization of a phase driven two-level atom,” Opt. Commun.292, 87–91 (2013).
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[CrossRef]

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M. H. Naderi, M. Soltanolkotabi, and R. Roknizadeh, “A theoretical scheme for generation of nonlinear coherent states in a micromaser under intensity-dependent Jaynes-Cummings model,” Eur. Phys. J. D32, 397–408 (2005).
[CrossRef]

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J. Casanova, G. Romero, I. Lizuain, J. J. García-Ripoll, and E. Solano, “Deep strong coupling regime of the Jaynes-Cummings model,” Phys. Rev. Lett.105, 263603 (2010).
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J. H. Eberly, N. B. Narozhny, and J. J. Sanchez-Mondragon, “Periodic spontaneuous collapse and revival in a simple quantum model,” Phys. Rev. Lett.44, 1323–1326 (1980).
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H. B. Perets, Y. Lahini, F. Pozzi, M. Sorel, R. Morandotti, and Y. Silberberg, “Realization of quantum walks with negligible decoherence in waveguide lattices,” Phys. Rev. Lett.100, 170506 (2008).
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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. A85, 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] [PubMed]

F. Dreisow, M. Heinrich, R. Keil, A. Tunnermann, S. Nolte, S. Longhi, and A. Szameit, “Classical simulation of relativistic zitterbewegung in photonic lattices,” Phys. Rev. Lett.105, 143902 (2010).
[CrossRef]

A. Perez-Leija, H. Moya-Cessa, A. Szameit, and D. N. Christodoulides, “Glauber-Fock photonic lattices,” Opt. Lett.35, 2409–2411 (2010).
[CrossRef] [PubMed]

F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, A. Tunnermann, and S. Longhi, “Bloch-Zener oscillations in binary superlattices,” Phys. Rev. Lett.102, 076802 (2009).
[CrossRef] [PubMed]

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C. Thompson, G. Vemuri, and G. S. Agarwal, “Quantum physics inspired optical effects in tight-binding lattices: Phase-controlled photonic transport,” Phys. Rev. B84, 214302 (2011).
[CrossRef]

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H. Moya-Cessa and P. Tombesi, “Filtering number states of the vibrational motion of an ion,” Phys. Rev. A61, 025401 (2000).
[CrossRef]

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F. Dreisow, M. Heinrich, R. Keil, A. Tunnermann, S. Nolte, S. Longhi, and A. Szameit, “Classical simulation of relativistic zitterbewegung in photonic lattices,” Phys. Rev. Lett.105, 143902 (2010).
[CrossRef]

F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, A. Tunnermann, and S. Longhi, “Bloch-Zener oscillations in binary superlattices,” Phys. Rev. Lett.102, 076802 (2009).
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C. Thompson, G. Vemuri, and G. S. Agarwal, “Quantum physics inspired optical effects in tight-binding lattices: Phase-controlled photonic transport,” Phys. Rev. B84, 214302 (2011).
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H. Moya-Cessa, F. Soto-Eguibar, J. M. Vargas-Martínez, R. Juárez-Amaro, and A. Zúñiga Segundo, “Ion-laser interactions: The most complete solution,” Physics Reports513, 229–261 (2012).
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[CrossRef] [PubMed]

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[CrossRef]

A. Perez-Leija, R. Keil, A. Kay, H. Moya-Cessa, S. Nolte, L.-C. Kwek, B.M. Rodríguez-Lara, A. Szameit, and D. Christodoulides, “Coherent quantum transport in photonic lattices,” Phys. Rev. A87, 012309 (2013).
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[CrossRef]

H. Moya-Cessa and P. Tombesi, “Filtering number states of the vibrational motion of an ion,” Phys. Rev. A61, 025401 (2000).
[CrossRef]

Phys. Rev. B (2)

C. Thompson, G. Vemuri, and G. S. Agarwal, “Quantum physics inspired optical effects in tight-binding lattices: Phase-controlled photonic transport,” Phys. Rev. B84, 214302 (2011).
[CrossRef]

S. Longhi, “Klein tunneling in binary photonic superlattices,” Phys. Rev. B81, 075102 (2010).
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F. Dreisow, M. Heinrich, R. Keil, A. Tunnermann, S. Nolte, S. Longhi, and A. Szameit, “Classical simulation of relativistic zitterbewegung in photonic lattices,” Phys. Rev. Lett.105, 143902 (2010).
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F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, A. Tunnermann, and S. Longhi, “Bloch-Zener oscillations in binary superlattices,” Phys. Rev. Lett.102, 076802 (2009).
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H. Moya-Cessa, F. Soto-Eguibar, J. M. Vargas-Martínez, R. Juárez-Amaro, and A. Zúñiga Segundo, “Ion-laser interactions: The most complete solution,” Physics Reports513, 229–261 (2012).
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Figures (3)

Fig. 1
Fig. 1

The classical simulation of the time evolution for the separable initial state |ψ(0)〉 = |α+, g〉 with α = 5 under BS dynamics on resonance, ω0 = ωf, and coupling parameters g = 0.1ωf, g+ = 0. (a) Propagation of the initial field in the corresponding positive parity photonic lattice of the classical simulator. The time evolution of the (b) mean photon number, (c) mean atomic excitation energy, (d) mean von Neumann entropy, and (e) fidelity reconstructed from the classical simulation. The lattice is composed by three hundred coupled photonic waveguides.

Fig. 2
Fig. 2

The classical simulation of the time evolution for the entangled initial state |ψ(0)〉 = |α+, g〉 + |α, e〉 with α = 5 under BS dynamics on resonance, ω0 = ωf, and coupling parameters g = 0.1ωf, g+ = 0. (a) Propagation of the initial field in the corresponding positive parity photonic lattice of the classical simulator. The time evolution of the (b) mean photon number, (c) exponential of the mean atomic excitation energy, (d) mean von Neumann entropy, and (e) fidelity reconstructed from the classical simulation. The lattice is composed by three hundred coupled photonic waveguides.

Fig. 3
Fig. 3

The classical simulation of the time evolution for the separable initial state |ψ(0)〉 = |0, e〉 under BS plus counter rotating terms dynamics on resonance, ω0 = ωf, and coupling parameters g = g+ = 2ωf. (a) Propagation of the initial field in the corresponding negative parity photonic lattice of the classical simulator. The time evolution of the (b) mean photon number, (c) mean atomic excitation energy, (d) mean von Neumann entropy, and (e) fidelity reconstructed from the classical simulation. The lattice is composed by two thousand coupled photonic waveguides.

Equations (40)

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H ^ = ω f a ^ a ^ + ω 0 S ^ z + λ [ a ^ k a ^ l f ( a ^ a ^ ) S ^ + + f ( a ^ a ^ ) a ^ l a ^ k S ^ ] .
H ^ = h ( n ^ ) + ω 0 2 σ ^ z + g ( a ^ f ( n ^ ) n ^ σ ^ + + f ( n ^ ) n ^ a ^ σ ^ ) + g + ( a ^ f ( n ^ ) n ^ σ ^ + f ( n ^ ) n ^ a ^ σ ^ + ) ,
Π ^ = ( 1 ) n ^ σ ^ z ;
| + , j = ( B ^ ) j | 0 , g = { | 0 , g , | 1 , e , | 2 , g , } ,
| , j = ( B ^ ) j | 0 , e = { | 0 , e , | 1 , g , | 2 , e , } ,
H ^ = ( V ^ 0 0 1 ) ( h ( n ^ + 1 ) + ω 0 / 2 g f ( n ^ ) g f ( n ^ ) h ( n ^ + 1 ) ω 0 / 2 ) ( V ^ 0 0 1 ) ,
= ( V ^ 0 0 1 ) ( Γ ( n ^ ) + Ω ( n ^ ) Γ ( n ^ ) Ω ( n ^ ) 2 g f ( n ^ ) 2 g f ( n ^ ) ) ( λ + ( n ^ ) 0 0 λ ( n ^ ) ) × ( Γ ( n ^ ) + Ω ( n ^ ) Γ ( n ^ ) Ω ( n ^ ) 2 g f ( n ^ ) 2 g f ( n ^ ) ) 1 ( V ^ 0 0 1 ) ,
Γ ( n ^ ) = h ( n ^ 1 ) h ( n ^ ) + ω 0 ,
Ω ( n ^ ) = Γ 2 ( n ^ ) + 4 g 2 f 2 ( n ^ ) ,
λ ± ( n ^ ) = h ( n ^ 1 ) + h ( n ^ ) + Ω ( n ^ ) 2 .
U ^ ( t ) = = ( V ^ 0 0 1 ) ( Γ ( n ^ ) + Ω ( n ^ ) Γ ( n ^ ) Ω ( n ^ ) 2 g f ( n ^ ) 2 g f ( n ^ ) ) ( e i λ + ( n ^ ) t 0 0 e i λ ( n ^ ) t ) × ( Γ ( n ^ ) + Ω ( n ^ ) Γ ( n ^ ) Ω ( n ^ ) 2 g f ( n ^ ) 2 g f ( n ^ ) ) 1 ( V ^ 0 0 1 ) .
i t | ψ ( t ) = H ^ | ψ ( t ) ,
| ψ ( ± ) ( t ) = j = 0 j ( ± ) ( t ) | ± , j .
i t 0 ( ± ) = d ( ± ) ( 0 ) 0 ( ± ) + g ± f ( 1 ) 1 ( ± ) ,
i t 2 k + 1 ( ± ) = d ( ± ) ( 2 k + 1 ) 2 k + 1 ( ± ) + g ± f ( 2 k + 1 ) 2 k ( ± ) + g f ( 2 k + 2 ) 2 k + 2 ( ± ) , k 0 ,
i t 2 k ( ± ) = d ( ± ) ( 2 k ) 2 k ( ± ) + g f ( 2 k ) 2 k 1 ( ± ) + g ± f ( 2 k + 1 ) 2 k + 1 ( ± ) , k 1 ,
d ( ± ) ( j ) = h ( j ) ( 1 ) j ω 0 2 .
p 0 ( ± ) ( λ ) = 1 ,
p 1 ( ± ) ( λ ) = [ d ( ± ) ( 0 ) λ ] p 0 ( ± ) ( λ ) ,
p 2 k ( ± ) ( λ ) = [ d ( ± ) ( 2 k 1 ) λ ] p 2 k 1 ( ± ) g ± 2 f 2 k ( 2 k ) p 2 k 2 ,
p 2 k + 1 ( ± ) ( λ ) = [ d ( ± ) ( 2 k ) λ ] p 2 k 1 ( ) g 2 f 2 k ( 2 k ) p 2 k 1 , k 1.
n ^ ( t ) = ψ ( + ) ( t ) | n ^ | ψ ( + ) ( t ) + ψ ( ) ( t ) | n ^ | ψ ( ) ( t ) ,
j = 0 N 1 j [ | j ( + ) ( t ) | 2 + | j ( t ) | 2 ] ,
σ ^ z ( t ) = ψ ( + ) ( t ) | σ ^ z | ψ ( + ) ( t ) + ψ ( ) ( t ) | σ ^ z | ψ ( ) ( t ) ,
j = 0 ( N 1 ) / 2 [ | 2 j + 1 ( + ) ( t ) | 2 | 2 j ( + ) ( t ) | 2 ] + j = 0 ( N 1 ) / 2 [ | 2 j ( ) ( t ) | 2 | 2 j + 1 ( ) ( t ) | 2 ] ,
σ ^ x ( t ) = ψ ( t ) | σ ^ x | ψ ( t ) ,
j = 0 N 1 Re [ ( j ( + ) ( t ) ) * j ( ) ( t ) ] ,
= | ψ ( 0 ) | ψ ( t ) | ,
| j = 0 N 1 ( j ( + ) ( 0 ) ) * j ( + ) ( t ) + ( j ( ) ( 0 ) ) * j ( ) ( t ) | .
S ^ = Tr ρ ^ a ln ρ ^ a
ρ ^ a ( t ) = Tr f | ψ ( t ) ψ ( t ) | ,
j = 0 ( N 1 / 2 ) ( | 2 j + 1 ( + ) | 2 + | 2 j ( ) | 2 2 j + 1 ( + ) ( 2 j + 1 ( ) ) * + 2 j ( ) ( 2 j ( + ) ) * 2 j ( + ) ( 2 j ( ) ) * + 2 j + 1 ( ) ( 2 j + 1 ( + ) ) * | 2 j ( + ) | 2 + | 2 j ( + ) | 2 ) ,
| ψ F ( 0 ) = c e | n , e + c g | n , g ,
= { c g | + , n + c e | , n , n even , c e | + , n + c g | , n , n odd .
| ψ C ( 0 ) = | α , g ,
= e | α | / 2 n = 0 α n n ! | n , g ,
= e | α | / 2 n = 0 ( α 2 n 2 n ! | + , 2 n + α 2 n + 1 ( 2 n + 1 ) ! | , 2 n + 1 ) .
e | α | / 2 n = 0 α n n ! | + , n = | α + , g + | α , e ,
H ^ B S = ω f n ^ + ω 0 2 σ ^ z + g ( a ^ n ^ σ ^ + + n ^ a ^ σ ^ ) ,
H ^ = ω f n ^ + ω 0 2 σ ^ z + g ( a ^ n ^ σ ^ + + n ^ a ^ σ ^ ) + g + ( a ^ n ^ σ ^ + n ^ a ^ σ ^ + ) .

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