Abstract

Graphene has been theoretically shown to exhibit anomalous Rabi oscillations (AROs) far from resonance in addition to conventional Rabi oscillations close to resonance (classical light frequency matches particle-hole frequency). The ARO has been attributed to the pseudospin degree of freedom that is unique to graphene-like systems. In this work, we show the same phenomenon also occurs in the single-photon limit or even in a vacuum. This is to be expected for conventional Rabi oscillations; however, the prediction that AROs also occur in the single-photon situation means that this notion of ARO is robust and not an artifact of approximations. We also study collapse and revival of both conventional and AROs in response to a coherent radiation field and extract the collapse and revival times in both cases.

© 2014 Optical Society of America

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  1. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
    [CrossRef]
  2. A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselove, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009).
    [CrossRef]
  3. P. R. Wallace, “The band theory of graphite,” Phys. Rev. 71, 622–634 (1947).
    [CrossRef]
  4. I. I. Rabi, “Space quantization in gyrating magnetic field,” Phys. Rev. 51, 652–654 (1937).
    [CrossRef]
  5. L. Allen and J. H. Eberly, Optical Resonances and Two-Level Atoms (Wiley, 1975).
  6. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
  7. R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).
  8. C. Gerry and P. Knight, Introductory Quantum Optics, 3rd ed. (Cambridge University, 2005).
  9. F. W. Cummings, “Stimulated emission of radiation in a single mode,” Phys. Rev. 140, A1051–A1056 (1965).
    [CrossRef]
  10. E. T. Jaynes and F. W. Cummings, “Comparison of quantum and semiclassical radiation theories with application to the beam maser,” Proc. IEEE 51, 89–109 (1963).
    [CrossRef]
  11. J. H. Eberly, N. B. Narozhny, and J. J. Sanchez-Mondragon, “Periodic spontaneous collapse and revival in a simple quantum model,” Phys. Rev. Lett. 44, 1323–1326 (1980).
    [CrossRef]
  12. N. B. Narozhny, J. J. Sanchez-Mondragon, and J. H. Eberly, “Coherence versus incoherence: collapse and revival in a simple quantum model,” Phys. Rev. A 23, 236–247 (1981).
    [CrossRef]
  13. H. I. Yoo, J. J. Sanchez-Mondragon, and J. H. Eberly, “Non-linear dynamics of the fermion-boson model: interface between revivals and the transition to irregularity,” J. Phys. A 14, 1383–1397 (1981).
    [CrossRef]
  14. M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. M. Raimond, and S. Haroche, “Quantum Rabi oscillation: a direct test of field quantization in a cavity,” Phys. Rev. Lett. 76, 1800–1803 (1996).
    [CrossRef]
  15. P. Nussenzweig, F. Bernardot, M. Brune, J. Hare, J. M. Raimond, S. Haroche, and W. Gawlik, “Preparation of high-principle-quantum-number “circular” states of rubidium,” Phys. Rev. A 48, 3991–3994 (1993).
    [CrossRef]
  16. H. Haug and S. W. Koch, Quantum Theory of Optical and Electronic Properties of Semiconductors, 4th ed. (World Scientific, 2004).
  17. E. G. Mishchenko, “Dynamic conductivity of graphene beyond linear response,” Phys. Rev. Lett. 103, 246802 (2009).
    [CrossRef]
  18. K. L. Ishikawa, “Nonlinear optical response of graphene in time domain,” Phys. Rev. B 82, 201402(R) (2010).
    [CrossRef]
  19. B. Dora, K. Ziegler, P. Thalmeier, and M. Nakamura, “Rabi oscillations in Landau-quantized graphene,” Phys. Rev. Lett. 102, 036803 (2009).
    [CrossRef]
  20. Enamullah, V. Kumar, and G. S. Setlur, “Crossover of coherent Rabi oscillations in graphene,” Physica B 407, 4600–4609 (2012).
    [CrossRef]
  21. M. Breusing, S. Kuehn, T. Winzer, E. Malic, F. Milde, N. Severin, J. P. Rabe, C. Ropers, A. Knorr, and T. Elsaesser, “Ultrafast nonequillibrium carrier dynamics in a single graphene layer,” Phys. Rev. B 83, 153410 (2011).
    [CrossRef]
  22. S. Swain, “A concise expression for the all order Bloch-Siegert shift,” Phys. Lett. A 46, 435–436 (1974).
    [CrossRef]

2012 (1)

Enamullah, V. Kumar, and G. S. Setlur, “Crossover of coherent Rabi oscillations in graphene,” Physica B 407, 4600–4609 (2012).
[CrossRef]

2011 (1)

M. Breusing, S. Kuehn, T. Winzer, E. Malic, F. Milde, N. Severin, J. P. Rabe, C. Ropers, A. Knorr, and T. Elsaesser, “Ultrafast nonequillibrium carrier dynamics in a single graphene layer,” Phys. Rev. B 83, 153410 (2011).
[CrossRef]

2010 (1)

K. L. Ishikawa, “Nonlinear optical response of graphene in time domain,” Phys. Rev. B 82, 201402(R) (2010).
[CrossRef]

2009 (3)

B. Dora, K. Ziegler, P. Thalmeier, and M. Nakamura, “Rabi oscillations in Landau-quantized graphene,” Phys. Rev. Lett. 102, 036803 (2009).
[CrossRef]

E. G. Mishchenko, “Dynamic conductivity of graphene beyond linear response,” Phys. Rev. Lett. 103, 246802 (2009).
[CrossRef]

A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselove, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009).
[CrossRef]

2004 (1)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef]

1996 (1)

M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. M. Raimond, and S. Haroche, “Quantum Rabi oscillation: a direct test of field quantization in a cavity,” Phys. Rev. Lett. 76, 1800–1803 (1996).
[CrossRef]

1993 (1)

P. Nussenzweig, F. Bernardot, M. Brune, J. Hare, J. M. Raimond, S. Haroche, and W. Gawlik, “Preparation of high-principle-quantum-number “circular” states of rubidium,” Phys. Rev. A 48, 3991–3994 (1993).
[CrossRef]

1981 (2)

N. B. Narozhny, J. J. Sanchez-Mondragon, and J. H. Eberly, “Coherence versus incoherence: collapse and revival in a simple quantum model,” Phys. Rev. A 23, 236–247 (1981).
[CrossRef]

H. I. Yoo, J. J. Sanchez-Mondragon, and J. H. Eberly, “Non-linear dynamics of the fermion-boson model: interface between revivals and the transition to irregularity,” J. Phys. A 14, 1383–1397 (1981).
[CrossRef]

1980 (1)

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

1974 (1)

S. Swain, “A concise expression for the all order Bloch-Siegert shift,” Phys. Lett. A 46, 435–436 (1974).
[CrossRef]

1965 (1)

F. W. Cummings, “Stimulated emission of radiation in a single mode,” Phys. Rev. 140, A1051–A1056 (1965).
[CrossRef]

1963 (1)

E. T. Jaynes and F. W. Cummings, “Comparison of quantum and semiclassical radiation theories with application to the beam maser,” Proc. IEEE 51, 89–109 (1963).
[CrossRef]

1947 (1)

P. R. Wallace, “The band theory of graphite,” Phys. Rev. 71, 622–634 (1947).
[CrossRef]

1937 (1)

I. I. Rabi, “Space quantization in gyrating magnetic field,” Phys. Rev. 51, 652–654 (1937).
[CrossRef]

Allen, L.

L. Allen and J. H. Eberly, Optical Resonances and Two-Level Atoms (Wiley, 1975).

Bernardot, F.

P. Nussenzweig, F. Bernardot, M. Brune, J. Hare, J. M. Raimond, S. Haroche, and W. Gawlik, “Preparation of high-principle-quantum-number “circular” states of rubidium,” Phys. Rev. A 48, 3991–3994 (1993).
[CrossRef]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).

Breusing, M.

M. Breusing, S. Kuehn, T. Winzer, E. Malic, F. Milde, N. Severin, J. P. Rabe, C. Ropers, A. Knorr, and T. Elsaesser, “Ultrafast nonequillibrium carrier dynamics in a single graphene layer,” Phys. Rev. B 83, 153410 (2011).
[CrossRef]

Brune, M.

M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. M. Raimond, and S. Haroche, “Quantum Rabi oscillation: a direct test of field quantization in a cavity,” Phys. Rev. Lett. 76, 1800–1803 (1996).
[CrossRef]

P. Nussenzweig, F. Bernardot, M. Brune, J. Hare, J. M. Raimond, S. Haroche, and W. Gawlik, “Preparation of high-principle-quantum-number “circular” states of rubidium,” Phys. Rev. A 48, 3991–3994 (1993).
[CrossRef]

Cummings, F. W.

F. W. Cummings, “Stimulated emission of radiation in a single mode,” Phys. Rev. 140, A1051–A1056 (1965).
[CrossRef]

E. T. Jaynes and F. W. Cummings, “Comparison of quantum and semiclassical radiation theories with application to the beam maser,” Proc. IEEE 51, 89–109 (1963).
[CrossRef]

Dora, B.

B. Dora, K. Ziegler, P. Thalmeier, and M. Nakamura, “Rabi oscillations in Landau-quantized graphene,” Phys. Rev. Lett. 102, 036803 (2009).
[CrossRef]

Dreyer, J.

M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. M. Raimond, and S. Haroche, “Quantum Rabi oscillation: a direct test of field quantization in a cavity,” Phys. Rev. Lett. 76, 1800–1803 (1996).
[CrossRef]

Dubonos, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef]

Eberly, J. H.

N. B. Narozhny, J. J. Sanchez-Mondragon, and J. H. Eberly, “Coherence versus incoherence: collapse and revival in a simple quantum model,” Phys. Rev. A 23, 236–247 (1981).
[CrossRef]

H. I. Yoo, J. J. Sanchez-Mondragon, and J. H. Eberly, “Non-linear dynamics of the fermion-boson model: interface between revivals and the transition to irregularity,” J. Phys. A 14, 1383–1397 (1981).
[CrossRef]

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

L. Allen and J. H. Eberly, Optical Resonances and Two-Level Atoms (Wiley, 1975).

Elsaesser, T.

M. Breusing, S. Kuehn, T. Winzer, E. Malic, F. Milde, N. Severin, J. P. Rabe, C. Ropers, A. Knorr, and T. Elsaesser, “Ultrafast nonequillibrium carrier dynamics in a single graphene layer,” Phys. Rev. B 83, 153410 (2011).
[CrossRef]

Enamullah,

Enamullah, V. Kumar, and G. S. Setlur, “Crossover of coherent Rabi oscillations in graphene,” Physica B 407, 4600–4609 (2012).
[CrossRef]

Firsov, A. A.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef]

Gawlik, W.

P. Nussenzweig, F. Bernardot, M. Brune, J. Hare, J. M. Raimond, S. Haroche, and W. Gawlik, “Preparation of high-principle-quantum-number “circular” states of rubidium,” Phys. Rev. A 48, 3991–3994 (1993).
[CrossRef]

Geim, A. K.

A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselove, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009).
[CrossRef]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef]

Gerry, C.

C. Gerry and P. Knight, Introductory Quantum Optics, 3rd ed. (Cambridge University, 2005).

Grigorieva, I. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef]

Guinea, F.

A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselove, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009).
[CrossRef]

Hagley, E.

M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. M. Raimond, and S. Haroche, “Quantum Rabi oscillation: a direct test of field quantization in a cavity,” Phys. Rev. Lett. 76, 1800–1803 (1996).
[CrossRef]

Hare, J.

P. Nussenzweig, F. Bernardot, M. Brune, J. Hare, J. M. Raimond, S. Haroche, and W. Gawlik, “Preparation of high-principle-quantum-number “circular” states of rubidium,” Phys. Rev. A 48, 3991–3994 (1993).
[CrossRef]

Haroche, S.

M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. M. Raimond, and S. Haroche, “Quantum Rabi oscillation: a direct test of field quantization in a cavity,” Phys. Rev. Lett. 76, 1800–1803 (1996).
[CrossRef]

P. Nussenzweig, F. Bernardot, M. Brune, J. Hare, J. M. Raimond, S. Haroche, and W. Gawlik, “Preparation of high-principle-quantum-number “circular” states of rubidium,” Phys. Rev. A 48, 3991–3994 (1993).
[CrossRef]

Haug, H.

H. Haug and S. W. Koch, Quantum Theory of Optical and Electronic Properties of Semiconductors, 4th ed. (World Scientific, 2004).

Ishikawa, K. L.

K. L. Ishikawa, “Nonlinear optical response of graphene in time domain,” Phys. Rev. B 82, 201402(R) (2010).
[CrossRef]

Jaynes, E. T.

E. T. Jaynes and F. W. Cummings, “Comparison of quantum and semiclassical radiation theories with application to the beam maser,” Proc. IEEE 51, 89–109 (1963).
[CrossRef]

Jiang, D.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef]

Knight, P.

C. Gerry and P. Knight, Introductory Quantum Optics, 3rd ed. (Cambridge University, 2005).

Knorr, A.

M. Breusing, S. Kuehn, T. Winzer, E. Malic, F. Milde, N. Severin, J. P. Rabe, C. Ropers, A. Knorr, and T. Elsaesser, “Ultrafast nonequillibrium carrier dynamics in a single graphene layer,” Phys. Rev. B 83, 153410 (2011).
[CrossRef]

Koch, S. W.

H. Haug and S. W. Koch, Quantum Theory of Optical and Electronic Properties of Semiconductors, 4th ed. (World Scientific, 2004).

Kuehn, S.

M. Breusing, S. Kuehn, T. Winzer, E. Malic, F. Milde, N. Severin, J. P. Rabe, C. Ropers, A. Knorr, and T. Elsaesser, “Ultrafast nonequillibrium carrier dynamics in a single graphene layer,” Phys. Rev. B 83, 153410 (2011).
[CrossRef]

Kumar, V.

Enamullah, V. Kumar, and G. S. Setlur, “Crossover of coherent Rabi oscillations in graphene,” Physica B 407, 4600–4609 (2012).
[CrossRef]

Maali, A.

M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. M. Raimond, and S. Haroche, “Quantum Rabi oscillation: a direct test of field quantization in a cavity,” Phys. Rev. Lett. 76, 1800–1803 (1996).
[CrossRef]

Malic, E.

M. Breusing, S. Kuehn, T. Winzer, E. Malic, F. Milde, N. Severin, J. P. Rabe, C. Ropers, A. Knorr, and T. Elsaesser, “Ultrafast nonequillibrium carrier dynamics in a single graphene layer,” Phys. Rev. B 83, 153410 (2011).
[CrossRef]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

Milde, F.

M. Breusing, S. Kuehn, T. Winzer, E. Malic, F. Milde, N. Severin, J. P. Rabe, C. Ropers, A. Knorr, and T. Elsaesser, “Ultrafast nonequillibrium carrier dynamics in a single graphene layer,” Phys. Rev. B 83, 153410 (2011).
[CrossRef]

Mishchenko, E. G.

E. G. Mishchenko, “Dynamic conductivity of graphene beyond linear response,” Phys. Rev. Lett. 103, 246802 (2009).
[CrossRef]

Morozov, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef]

Nakamura, M.

B. Dora, K. Ziegler, P. Thalmeier, and M. Nakamura, “Rabi oscillations in Landau-quantized graphene,” Phys. Rev. Lett. 102, 036803 (2009).
[CrossRef]

Narozhny, N. B.

N. B. Narozhny, J. J. Sanchez-Mondragon, and J. H. Eberly, “Coherence versus incoherence: collapse and revival in a simple quantum model,” Phys. Rev. A 23, 236–247 (1981).
[CrossRef]

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

Neto, A. H. C.

A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselove, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009).
[CrossRef]

Novoselov, K. S.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef]

Novoselove, K. S.

A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselove, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009).
[CrossRef]

Nussenzweig, P.

P. Nussenzweig, F. Bernardot, M. Brune, J. Hare, J. M. Raimond, S. Haroche, and W. Gawlik, “Preparation of high-principle-quantum-number “circular” states of rubidium,” Phys. Rev. A 48, 3991–3994 (1993).
[CrossRef]

Peres, N. M. R.

A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselove, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009).
[CrossRef]

Rabe, J. P.

M. Breusing, S. Kuehn, T. Winzer, E. Malic, F. Milde, N. Severin, J. P. Rabe, C. Ropers, A. Knorr, and T. Elsaesser, “Ultrafast nonequillibrium carrier dynamics in a single graphene layer,” Phys. Rev. B 83, 153410 (2011).
[CrossRef]

Rabi, I. I.

I. I. Rabi, “Space quantization in gyrating magnetic field,” Phys. Rev. 51, 652–654 (1937).
[CrossRef]

Raimond, J. M.

M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. M. Raimond, and S. Haroche, “Quantum Rabi oscillation: a direct test of field quantization in a cavity,” Phys. Rev. Lett. 76, 1800–1803 (1996).
[CrossRef]

P. Nussenzweig, F. Bernardot, M. Brune, J. Hare, J. M. Raimond, S. Haroche, and W. Gawlik, “Preparation of high-principle-quantum-number “circular” states of rubidium,” Phys. Rev. A 48, 3991–3994 (1993).
[CrossRef]

Ropers, C.

M. Breusing, S. Kuehn, T. Winzer, E. Malic, F. Milde, N. Severin, J. P. Rabe, C. Ropers, A. Knorr, and T. Elsaesser, “Ultrafast nonequillibrium carrier dynamics in a single graphene layer,” Phys. Rev. B 83, 153410 (2011).
[CrossRef]

Sanchez-Mondragon, J. J.

H. I. Yoo, J. J. Sanchez-Mondragon, and J. H. Eberly, “Non-linear dynamics of the fermion-boson model: interface between revivals and the transition to irregularity,” J. Phys. A 14, 1383–1397 (1981).
[CrossRef]

N. B. Narozhny, J. J. Sanchez-Mondragon, and J. H. Eberly, “Coherence versus incoherence: collapse and revival in a simple quantum model,” Phys. Rev. A 23, 236–247 (1981).
[CrossRef]

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

Schmidt-Kaler, F.

M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. M. Raimond, and S. Haroche, “Quantum Rabi oscillation: a direct test of field quantization in a cavity,” Phys. Rev. Lett. 76, 1800–1803 (1996).
[CrossRef]

Setlur, G. S.

Enamullah, V. Kumar, and G. S. Setlur, “Crossover of coherent Rabi oscillations in graphene,” Physica B 407, 4600–4609 (2012).
[CrossRef]

Severin, N.

M. Breusing, S. Kuehn, T. Winzer, E. Malic, F. Milde, N. Severin, J. P. Rabe, C. Ropers, A. Knorr, and T. Elsaesser, “Ultrafast nonequillibrium carrier dynamics in a single graphene layer,” Phys. Rev. B 83, 153410 (2011).
[CrossRef]

Swain, S.

S. Swain, “A concise expression for the all order Bloch-Siegert shift,” Phys. Lett. A 46, 435–436 (1974).
[CrossRef]

Thalmeier, P.

B. Dora, K. Ziegler, P. Thalmeier, and M. Nakamura, “Rabi oscillations in Landau-quantized graphene,” Phys. Rev. Lett. 102, 036803 (2009).
[CrossRef]

Wallace, P. R.

P. R. Wallace, “The band theory of graphite,” Phys. Rev. 71, 622–634 (1947).
[CrossRef]

Winzer, T.

M. Breusing, S. Kuehn, T. Winzer, E. Malic, F. Milde, N. Severin, J. P. Rabe, C. Ropers, A. Knorr, and T. Elsaesser, “Ultrafast nonequillibrium carrier dynamics in a single graphene layer,” Phys. Rev. B 83, 153410 (2011).
[CrossRef]

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

Yoo, H. I.

H. I. Yoo, J. J. Sanchez-Mondragon, and J. H. Eberly, “Non-linear dynamics of the fermion-boson model: interface between revivals and the transition to irregularity,” J. Phys. A 14, 1383–1397 (1981).
[CrossRef]

Zhang, Y.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef]

Ziegler, K.

B. Dora, K. Ziegler, P. Thalmeier, and M. Nakamura, “Rabi oscillations in Landau-quantized graphene,” Phys. Rev. Lett. 102, 036803 (2009).
[CrossRef]

J. Phys. A (1)

H. I. Yoo, J. J. Sanchez-Mondragon, and J. H. Eberly, “Non-linear dynamics of the fermion-boson model: interface between revivals and the transition to irregularity,” J. Phys. A 14, 1383–1397 (1981).
[CrossRef]

Phys. Lett. A (1)

S. Swain, “A concise expression for the all order Bloch-Siegert shift,” Phys. Lett. A 46, 435–436 (1974).
[CrossRef]

Phys. Rev. (3)

P. R. Wallace, “The band theory of graphite,” Phys. Rev. 71, 622–634 (1947).
[CrossRef]

I. I. Rabi, “Space quantization in gyrating magnetic field,” Phys. Rev. 51, 652–654 (1937).
[CrossRef]

F. W. Cummings, “Stimulated emission of radiation in a single mode,” Phys. Rev. 140, A1051–A1056 (1965).
[CrossRef]

Phys. Rev. A (2)

N. B. Narozhny, J. J. Sanchez-Mondragon, and J. H. Eberly, “Coherence versus incoherence: collapse and revival in a simple quantum model,” Phys. Rev. A 23, 236–247 (1981).
[CrossRef]

P. Nussenzweig, F. Bernardot, M. Brune, J. Hare, J. M. Raimond, S. Haroche, and W. Gawlik, “Preparation of high-principle-quantum-number “circular” states of rubidium,” Phys. Rev. A 48, 3991–3994 (1993).
[CrossRef]

Phys. Rev. B (2)

K. L. Ishikawa, “Nonlinear optical response of graphene in time domain,” Phys. Rev. B 82, 201402(R) (2010).
[CrossRef]

M. Breusing, S. Kuehn, T. Winzer, E. Malic, F. Milde, N. Severin, J. P. Rabe, C. Ropers, A. Knorr, and T. Elsaesser, “Ultrafast nonequillibrium carrier dynamics in a single graphene layer,” Phys. Rev. B 83, 153410 (2011).
[CrossRef]

Phys. Rev. Lett. (4)

E. G. Mishchenko, “Dynamic conductivity of graphene beyond linear response,” Phys. Rev. Lett. 103, 246802 (2009).
[CrossRef]

B. Dora, K. Ziegler, P. Thalmeier, and M. Nakamura, “Rabi oscillations in Landau-quantized graphene,” Phys. Rev. Lett. 102, 036803 (2009).
[CrossRef]

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

M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. M. Raimond, and S. Haroche, “Quantum Rabi oscillation: a direct test of field quantization in a cavity,” Phys. Rev. Lett. 76, 1800–1803 (1996).
[CrossRef]

Physica B (1)

Enamullah, V. Kumar, and G. S. Setlur, “Crossover of coherent Rabi oscillations in graphene,” Physica B 407, 4600–4609 (2012).
[CrossRef]

Proc. IEEE (1)

E. T. Jaynes and F. W. Cummings, “Comparison of quantum and semiclassical radiation theories with application to the beam maser,” Proc. IEEE 51, 89–109 (1963).
[CrossRef]

Rev. Mod. Phys. (1)

A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselove, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009).
[CrossRef]

Science (1)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef]

Other (5)

L. Allen and J. H. Eberly, Optical Resonances and Two-Level Atoms (Wiley, 1975).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).

C. Gerry and P. Knight, Introductory Quantum Optics, 3rd ed. (Cambridge University, 2005).

H. Haug and S. W. Koch, Quantum Theory of Optical and Electronic Properties of Semiconductors, 4th ed. (World Scientific, 2004).

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Figures (3)

Fig. 1.
Fig. 1.

Collapse and revival phenomenon. The real part of the polarization is plotted versus time (t|λ|2/ω). To plot, we have taken n¯=10.

Fig. 2.
Fig. 2.

Collapse times versus the average number of photons n¯.

Fig. 3.
Fig. 3.

Revival times versus the average number of photons n¯.

Equations (71)

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HG=cA(σ⃗AB·ϵ⃗)cB+cB(σ⃗BA·ϵ⃗)cA+λ*cAcBbeiωt+λbcBcAeiωt.
HPSL=ϵ(cc+dd)+λcdbeiωt+λ*bdceiωt.
σ+=cd;σ=dc,
it0,1,n|Φ(t)G=(σ⃗BA·ϵ⃗)1,0,n|Φ(t)G+n+1λeiωt1,0,n+1|Φ(t)G,
it1,0,n+1|Φ(t)G=(σ⃗AB·ϵ⃗)0,1,n+1|Φ(t)G+n+1λ*eiωt0,1,n|Φ(t)G.
it0,0,n|Φ(t)PSL=nλ*eiωt1,1,n1|Φ(t)PSL,
it1,1,n1|Φ(t)PSL=2ϵ1,1,n1|Φ(t)PSL+nλeiωt0,0,n|Φ(t)PSL.
j⃗G(t)=σ⃗BAnΦ(t)|0,1,n1,0,n|Φ(t)+σ⃗ABnΦ(t)|1,0,n0,1,n|Φ(t),
j⃗PSL(t)=p⃗vcnΦ(t)|1,1,n0,0,n|Φ(t)p⃗vcnΦ(t)|0,0,n1,1,n|Φ(t).
pG(t)=Φ(t)|cAcB|Φ(t)=nΦ(t)|1,0,n0,1,n|Φ(t).
pPSL(t)=Φ(t)|dc|Φ(t)=nΦ(t)|0,0,n1,1,n|Φ(t).
0,0,n|Φ(t)PSL=0,0,n|Φ(t)PSL,reiωt.
z=4n|λ|2+(2ϵ+ω)2.
0,0,n|Φ(t)PSL,r=ie12t(2iϵ+iω+iz)2z(2iϵ(1+eitz)+iω+iz+eitz(iω+iz)),1,1,n1|Φ(t)PSL=e12t(2iϵ+iω+iz)(1+eitz)λzn.
=+eiϵt+,reiϵteiΔt.
it0,1,n|Φ(t)G,++ϵ0,1,n|Φ(t)G,+=n+1λ1,0,n+1|Φ(t)G,,r+(σ⃗BA·ϵ⃗)1,0,n|Φ(t)G,+,
it1,0,n+1|Φ(t)G,++ϵ1,0,n+1|Φ(t)G,+=(σ⃗AB·ϵ⃗)0,1,n+1|Φ(t)G,+,
it0,1,n|Φ(t)G,,rΔ0,1,n|Φ(t)G,,rϵ0,1,n|Φ(t)G,,r=(σ⃗BA·ϵ⃗)1,0,n|Φ(t)G,,r,
it1,0,n+1|Φ(t)G,,rΔ1,0,n+1|Φ(t)G,,rϵ1,0,n+1|Φ(t)G,,r=(σ⃗AB·ϵ⃗)0,1,n+1|Φ(t)G,,r+n+1λ*0,1,n|Φ(t)G,+.
jG,s(t)1,0,0|Φ(t)G,,r*0,1,0|Φ(t)G,,r+1,0,0|Φ(t)G,+*0,1,0|Φ(t)G,++1,0,1|Φ(t)G,+*0,1,1|Φ(t)G,++1,0,1|Φ(t)G,,r*0,1,1|Φ(t)G,,r,
it0,1,0|Φ(t)G,++ϵ0,1,0|Φ(t)G,+=(σ⃗BA·ϵ⃗)1,0,0|Φ(t)G,++λ1,0,1|Φ(t)G,,r,
it1,0,1|Φ(t)G,,rΔ1,0,1|Φ(t)G,,rϵ1,0,1|Φ(t)G,,r=(σ⃗AB·ϵ⃗)0,1,1|Φ(t)G,,r+λ*0,1,0|Φ(t)G,+,
it0,1,1|Φ(t)G,,rΔ0,1,1|Φ(t)G,,rϵ0,1,1|Φ(t)G,,r=(σ⃗BA·ϵ⃗)1,0,1|Φ(t)G,,r,
it1,0,0|Φ(t)G,++ϵ1,0,0|Φ(t)G,+=(σ⃗AB·ϵ⃗)0,1,0|Φ(t)G,+.
=s++eiωt+eiωt.
0,1,n|Φ(t)G,+=n+1λω1,0,n+1|Φ(t)G,s;1,0,n+1|Φ(t)G,+=(σ⃗AB·ϵ⃗)ω0,1,n+1|Φ(t)G,+0,1,n|Φ(t)G,=(σ⃗BA·ϵ⃗)ω1,0,n|Φ(t)G,;1,0,n+1|Φ(t)G,=n+1λ*ω0,1,n|Φ(t)G,s.
it0,1,n|Φ(t)G,s=(σ⃗BA·ϵ⃗)1,0,n|Φ(t)G,s(n+1)|λ|2ω0,1,n|Φ(t)G,s
it1,0,n|Φ(t)G,s=(σ⃗AB·ϵ⃗)0,1,n|Φ(t)G,s+n|λ|2ω1,0,n|Φ(t)G,s.
|λ|4n(1+n)|λ|2ωΩ+ω2(ϵΩ)(ϵ+Ω)=0.
Ω±(n)=|λ|2±|λ|4(1+2n)2+4ϵ2ω22ω.
ΩARWA(n)=2|λ|4(n+12)2+ϵ2ω2ω.
0,1,n|Φ(t)G=dω2πeiωtf01(n,ω);1,0,n|Φ(t)G=dω2πeiωtf10(n,ω).
ωf01(n,ω)=(σ⃗BA·ϵ⃗)f10(n,ω)+n+1λf10(n+1,ωω)
ωf10(n+1,ω)=(σ⃗AB·ϵ⃗)f01(n+1,ω)+n+1λ*f01(n,ω+ω).
C1(ω,n)f01(n,ω)=a1(ω,n)f01(n1,ω+ω)+b1(ω,n)f01(n+1,ωω)
C1(ω,n)=(ωϵ2ω(n+1)|λ|2ωω),a1(ω,n)=(σ⃗BA·ϵ⃗)nλ*ω;b1(ω,n)=n+1λ(σ⃗AB·ϵ⃗)(ωω).
C2n(ω,n)f01(n,ω)=a2n(ω,n)f01(n2n,ω+2nω)+b2n(ω,n)f01(n+2n,ω2nω),C2n(ω,n)=C2n1(ω,n)a2n1(ω,n)b2n1(ω+2n1ω,n2n1)C2n1(ω+2n1ω,n2n1)b2n1(ω,n)a2n1(ω2n1ω,n+2n1)C2n1(ω2n1ω,n+2n1),a2n(ω,n)=a2n1(ω,n)a2n1(ω+2n1ω,n2n1)C2n1(ω+2n1ω,n2n1),b2n(ω,n)=b2n1(ω,n)b2n1(ω2n1ω,n+2n1)C2n1(ω2n1ω,n+2n1).
C2n(ω,n)=0,
C1(ω,n)(ω(n+1)|λ|2ω)=0.
C2(ω,n)f2(ω,ω,ϵ)=ωϵ2ω|λ|2(1+n)(ωω)(1+n)ϵ2|λ|2(ωω)2(ω|λ|2(2+n)(ω2ω)ϵ2(ωω)ω)nϵ2|λ|2ω2(|λ|2nω+ω+ωϵ2(ω+ω))=0.
Limϵf2(ϵ+x,2ϵ+Δ,ϵ)=2x|λ|2(n+1)2(xΔ)+O(1ϵ)=0.
Ω±(n)=ϵ+12(Δ±|λ|2(1+n)+Δ2).
ΩRWA(n)=|λ|2(1+n)+Δ2.
Limωf2(xω,ω,rω)=1ω(|λ|2(n+1)+r2|λ|2nx+x)+O(1ω2)=0.
Ω±(n)=12ω(|λ|2±|λ|4(1+2n)2+4r2).
ΩARWA(n)=2|λ|4(n+12)2+ϵ2ω2ω.
Limϵ(f4(ϵ+x,2ϵ+Δ,ϵ)f2(ϵ+x,2ϵ+Δ,ϵ))=|λ|4(n+1)(n+2)96(xΔ)2ϵ+O(1ϵ2).
Limω(f4(xω,ω,rω)f2(xω,ω,rω))=|λ|4(n1)nr42(|λ|2nx)2ω7.
Ω±(n)=|λ|2±2|λ|4(n+12)2+ϵ2ω22ω.
(1,0,n|Φ(t)G,s)*=e12w¯ww¯nn!1ΩARWA(n)[(Ω+(n)+(n+1)|λ|2ω)eiΩ+(n)t(Ω(n)+(n+1)|λ|2ω)eiΩ(n)t],
0,1,n+1|Φ(t)G,s=e12w¯wwn+1(n+1)!ϵ2ϵABΩARWA(n+1)(eiΩ+(n+1)teiΩ(n+1)t),
0,1,n|Φ(t)G,+=n+1λωe12w¯ww(n+1)(n+1)!1ΩARWA(n+1)[(Ω+(n+1)+(n+2)|λ|2ω)eiΩ+(n+1)t(Ω(n+1)+(n+2)|λ|2ω)eiΩ(n+1)t],
(1,0,n+1|Φ(t)G,)*=n+1λωe12w¯ww¯nn!ϵ2ϵBAΩARWA(n)(eiΩ+(n)teiΩ(n)t).
pG(t)=Φ(t)|cAcB|Φ(t)=n=0Φ(t)|1,0,n0,1,n|Φ(t).
pG,+(t)=n=0(1,0,n|Φ(t)G,s)*0,1,n|Φ(t)G,++n=0(1,0,n+1|Φ(t)G,)*0,1,n+1|Φ(t)G,s.
pG,+(t)n=0λωwen¯n¯nn!(2ϵ2+(12ΩARWA(n¯)2|λ|2ω)(12ΩARWA(n¯)+(n¯+3/2)|λ|2ω))ΩARWA2(n¯)eiΩARWA(n¯)tei(nn¯)ΩARWA(n¯)t.
j+(t)=12π|λ|24ivF2ωtn=0λωwen¯n¯nn!ei2|λ|2(n¯+12)ωtei(nn¯)2|λ|2ωt.
trev=2πmΩARWA(n¯),
I=n=0en¯n¯nn!eiΩARWA(n¯)tei(nn¯)ΩARWA(n¯)t
I=eiΩARWA(n¯)tein¯ΩARWA(n¯)ten¯en¯Exp[itΩARWA(n¯)].
Exp[itΩARWA(n¯)]1+itΩARWA(n¯)+12(itΩARWA(n¯))2+IeiΩARWA(n¯)ten¯12t2ΩARWA2(n¯).
en¯12tcol2ΩARWA2(n¯)=110
tcol=2Log(10)n¯ΩARWA2(n¯).
trevtcol=2πn¯2Log(10),
trev,ARWA=ωπ|λ|2;tcol,ARWA=12π2Log(10)n¯ωπ|λ|2;trev,RWA=4πn¯|λ|;tcol,RWA=12π2Log(10)4π|λ|.
H=ψAvσ⃗AB·(p⃗ecA⃗(t))ψB+ψBvσ⃗BA·(p⃗ecA⃗*(t))ψA.
p(t)=ψA(t)ψB(t);p*(t)=ψB(t)ψA(t);n(t)=ψA(t)ψA(t)ψB(t)ψB(t).
itn(t)=2vσ⃗AB·(p⃗ecA⃗(t))p(t)c.c.,itp(t)=vσ⃗BA·(p⃗ecA⃗*(t))n(t),itp*(t)=vσ⃗AB·(p⃗ecA⃗(t))n(t).
A(t)=Re(A0eiωt),
ωARWA=(4v2p2+(vecA0)4ω2sin2(2θ)Sin2δ)12.
ωRWA=A0evc(1cos(2θ)cos(2χp)cos(δ)sin(2θ)sin(2χp)),

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