Abstract
We have investigated the dynamic of cooled and trapped polariton state using Landau–Zener–Stückelberg interferometry theory (LZSIT). The effects of exciton–cavity coupling and the laser cooling over the qubit dynamics are analyzed in multi-crossing scenarios, supporting some of our basic results (Kenfack et al. in Comput Condens Matter 11:47–54, 2017; Ekengoue et al. in Comput Condens Matter 14:106–113, 2018). We have performed detailed calculations of the energy eigenvalues, non-adiabatic and adiabatic transition probabilities in the framework of weak- and strong-coupling regime under the laser light. As a main result, we pointed out the braking down of the Pauli exclusion principle providing the applicability of LZSIT for the analysis of polariton’s dynamic through a model which satisfies Fermi–Dirac statistics. Moreover, we found the generation of arbitrary waveforms of interferometric signals including sinusoidal, for weak coupling and strong laser amplitude. Thus, the dynamics of the polariton induces the destruction and the construction of interferences patterns in strong coupling between cavity laser and qubit. Extremely accurate interferometric signals generation by means of geometric phase effect has been demonstrated in this work with the goal of realizing robust control of the quantum coherent states of the polaritonic system. This geometric phase enhancement, which is essentially originated from the dynamic behavior of cooled and trapped polariton, is a significant consequence of the fastest population transfer and quantized energy of the system. Therefore, the geometric phase plays a crucial role in the study of the alter crossings behavior through cooled and trapped polariton, especially in the population transfer and energy of the system.
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References
M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965)
A. Altland, V. Gurarie, Phys. Rev. Lett. 100(063602), 1–4 (2008)
A. Amo, J. Bloch, Comptes Rendus Phys. 17, 934–945 (2016)
C. Anton, T.C.H. Liew, D. Sarkar, M.D. Martin, Z. Hatzopoulos, P.S. Eldridge, P.G. Savvidis, L. Viña, Phys. Rev. B 89, 235312 (2014)
Y. Avishai, Phys. Rev. A 90(032116), 1–15 (2014)
L.I. Baihong, L.I. Yongfang, Landau–Zener tunneling in the process of sum frequency generation. In International Symposium on Photonics and Optoelectronics 92330T, ed. by Z. Zhou (Proc. of SPIE 9233, 2014), pp. 1–6
W.L. Barnes, A. Dereux, T.W. Ebbesen, Nature 424, 824–830 (2003)
R. Beals, R. Wong, Special Functions (Cambridge Press, Cambridge, 2010)
M.V. Berry, Proc. R. Soc. Lond. 392(1802), 45–57 (1984)
M.V. Berry, Prod. R. Soc. Lond A. 430, 405–411 (1990)
M. Born, K. Huang, Dynamical Theory of Crystal Lattices, (Oxford University Press, New York, 1954), reprinted in 1985; Huang, K. (1951). Proc. R. Soc. London Ser. A 208, 352
D. Bouwmeester, G.P. Karman, C.A. Schrama, J.P. Woerdman, Phys. Rev. A 53(2), 985–989 (1996)
I. Buluta, S. Ashhab, F. Nori, Rep. Prog. Phys. 74(104401), 1–16 (2011)
T. Chung, S.-Y. Lee, E.Y. Song, H.G. Chun, B. Lee, Sensors 11, 10907–10929 (2011)
J.I. Cirac, P. Zoller, Phys. Rev. Lett. 74, 4091 (1995)
A. Cuevas, B. Silva et al., Sci. Adv. 4(eaa06814), 1–8 (2018)
J.E. Danga, S.C. Kenfack, L.C. Fai, J. Phys. A Math. Theor. 49, 1–16 (2016)
S.S. Demirchyan, I.Y. Chestnov, A.P. Alodjants, M.M. Glazov, A.V. Kavokin, Phys. Rev. Lett. 112(196403), 1–5 (2014)
D.P. DiVincenzo, Fortschr. Phys. 48, 771–783 (2000)
S. Dodin, A. Garmon, L. Simine, D. Segal (2014). arXiv:1401.3770v1 [cond-mat.mes-hall]: 1–10
A.V. Dodonov, B. Militello, A. Napoli, A. Messina, Phys. Rev. A 93(052505), 1–9 (2016)
L. Du, Y. Hu, Z.-W. Zhou, G.-C. Guo, X. Zhou, New J. Phys. 12(063015), 1–11 (2009)
T.H. Duong, T.T. Dinh, T.H. Vo, T.T.V. Tran, A.V. Nguyen, J. Phys. Conf. Ser. 865(012007), 1–8 (2017)
C.M. Ekengoue, S.C. Kenfack, A.J. Fotue, M.F.C. Fobasso, G.N. Bawe Jr., L.C. Fai, Comput. Condens. Matter 14, 106–113 (2018)
A. Erdélyi, W. Magnus, F. Oberhettinger, F.G. Tricomi, Higher Transcendental Functions (The Bateman Manuscript Project Vol. 2) (McGraw-Hill, New York, 1953).
G. Falci, R. Fazio, G. Palma, J. Siewert, V. Vedral, Nature (London) 407, 355–358 (2000)
P. Forn-Diaz, J. Lisenfeld, D. Marcos, J.J. Garcia-Ripoll, E. Solano, C.J.P.M. Harmans, J.E. Mooij, Phys. Rev. Lett. 105(237001), 1–6 (2010)
Fujii, K. (2014). arXiv:13O1.3585v3n
K. Fujii, T. Suzuki, Int. J. Geom. Methods Mod. Phys. 8, 8 (2011)
H.F. Ghaemi, T. Thio, D.E. Grupp, T.W. Ebbesen, H.J. Lezec, Phys. Rev. B 58, 6779–6782 (1998)
I.S. Gradshteyn, I.M. Ryzhik, Table of Integrals, Series, Products (Academic Press, New York, 1994)
M. Greiner, O. Mandel, T. Esslinger, T.W. Hansch, I. Bloch, Nature 415, 39 (2002)
M. Grifoni, P. Hänggi, Phys. Rep. 304, 229–354 (1998)
C. Hicke, L.F. Santos, M.I. Dykman (2005). arXiv:quant-ph/0511264v1, pp. 1–7
J. Homola, S.S. Yee, G. Gauglitz, Sens. Actuat. B Chem. 54, 3–15 (1999)
Z. Hradil, A. Quattropani, V. Savona, P, Schwendimann. Journal of Statistical Physics 76, 299–305 (1994)
A. Izmalkov, M. Grajcar, E. Il’ichev, Th Wagner, H.-G. Meyer, A. Yu, Phys. Rev. Lett. 93, 037003 (2004)
A. Izmalkov, A. Izmalkov, S.H.W. van der Ploeg, S.N. Shevchenko, M. Grajcar, E. Il’ichev, U. Hubner, A.N. Omelyanchouk, H.G. Meyer, Phys. Rev. Lett. 101, 017003 (2008)
D. Jaksch, H.J. Briegel, J.I. Cirac, C.W. Gardiner, P. Zoller, Phys. Rev. Lett. 82, 1975 (1999)
D. Jaksch, C. Bruder, J.I. Cirac, C.W. Gardiner, P. Zoller, Phys. Rev. Lett. 81, 3108 (1998)
A. Joye, G. Mileti, C.-E. Pfister, Phys. Rev. A 44, 4280–4295 (1991)
T. Jun Park, Bull. Korean Chem. Soc. 11(26), 1735–1737 (2005)
Y. Kami, E.E. Nikitin, J. Chem. Phys. 100(2027), 2027–2033 (1994)
B.E. Kane, Nature 393, 133–137 (1998)
J. Keeling, V. Gurarie, Phys. Rev. Lett. 101(033001), 1–4 (2008)
S.C. Kenfack, C.M. Ekengoue, A.J. Fotue, F.C. Fobasso, G.N. Bawe, L.C. Fai, Comput. Condens. Matter 11, 47–54 (2017)
T.D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, J.L.O. Brien, Nature 464, 45–53 (2010)
P.G. Lagoudakis, N.G. Berloff, New J. Phys. 19(125008), 1–9 (2017)
R.B. Laughlin, Phys. Rev. Lett. 50, 1395–1398 (1983)
P.J. Leek, J.M. Fink, A. Blais, R. Bianchetti, M. Göppl, J.M. Gambetta, D.I. Schuster, L. Frunzio, R.J. Schoelkopf, A. Wallraff, Science 318, 1889–1892 (2007)
D. Leibfried, B. DeMarco, V. Meyer, D. Lucas, M. Barrett, J. Britton, W.M. Itano, B. Jelenkovi, Nature 422, 412 (2003)
J. Liu, L.-B. Fu, B.-Y. Ou, S.-G. Chen, Q. Niu, (2001). arXiv:quant-ph/0105140v1 29: 1–17
Y. Luo, M. Chamanzar, A. Apuzzo, R. Salas-Montiel, K.N. Nguyen et al., Nano Lett. 15, 849–856 (2015)
R.K. Malla, E.G. Mishchenko, M.E. Raikh, (2017). arXiv:1705.05968v1 [cond-mat.mes-hall]: 1–8
C.F.J. Matthews, K. Poulios, J.D.A. Meinecke, A. Politi, A. Peruzzo, N. Ismail, K. Wörhoff, M.G. Thompson, J.L. O’Brien, Sci. Rep. 1539(3), 1–6 (2013)
C. Monroe, D.M. Meekhof, B.E. King, W.M. Itano, D.J. Wineland, Phys. Rev. Lett. 75, 4714 (1995)
M. Müller, S. Bounouar, K.D. Jons, M. Glassl, P. Michler, Nat. Photon 8, 224–228 (2014)
A. Nahata, R.A. Linke, T. Ishi, K. Ohashi, Opt. Lett. 28, 423–425 (2003)
K. Nakamura, Quantum Chaos, Cambridge Nonlinear Science Series 3 (Cambridge University Press, Cambridge, 1993)
K. Nakamura, S.A. Rice, Phys. Rev. A 49, 2217–2219 (1994)
P.D. Nation, J.R. Johansson, M.P. Blencowe, F. Nori, Rev. Mod. Phys. 84(1), 1–14 (2012)
F. Niemczyk, H. Deppe, E.P. Huebl, F. Menzel, M.J. Hocke, J.J. Schwarz, D. Garcia- Ripoll, T. Zueco, E. Hümmer, A. Solano et al., Nat. Phys. 6, 772–776 (2010)
A.P. Nizovtsev, S.Y. Kilin, F. Jelezko, T. Gaebal, I. Popa, A. Gruber, J. Wrachtrup, Optics and Spectrosc. 99, 233–244 (2005)
L. Novotny, R.X. Bian, X.S. Xie, Phys. Rev. Lett. 79, 645–648 (1997)
W.D. Oliver, Y. Yu, J.C. Lee, K.K. Berggren, L.S. Levitov, T.P. Orlando, Science 310, 1653–1657 (2005)
V.N. Ostrovsky, M.V. Volkov, J.P. Hansen, S. Selstø, Phys. Rev. B 75(014441), 1–7 (2007)
G. Pavlovic (2010). [cond-mat.other]. Université Blaise Pascal - Clermont-Ferrand II. HAL Id: tel-00632151, https://tel.archives-ouvertes.fr/tel-00632151
H. Ribeiro, J.R. Petta, G. Burkard, Phys. Rev. B 82(115445), 1–8 (2010)
K. Saito, M. Wubs, S. Kohler, P. Hänggi, Y. Kayanuma (2006). arXiv:condmat/0603188v3 [cond-mat.mes-hall], pp. 1–7
S. Shevchenko, S. Ashhab, F. Nori, Phys. Rep. 492, 1–30 (2010)
A.V. Shytov, Phys. Rev. A 70(052708), 1–3 (2004)
M. Sillanpää, T. Lehtinen, A. Paila, Y. Makhlin, P. Hakonen, Phys. Rev. Lett. 96(187002), 1–4 (2006)
M. Sillanpää, T. Lehtinen, A. Paila, Y. Makhlin, L. Roschier, P. Hakonen, Phys. Rev. Lett. 95(206806), 1–4 (2005)
D.D. Solnyshkov, O. Bleu, G. Malpuech, Superlattices Microstruct. 83, 466–475 (2015)
Sun, G-Z., Wen, X., Mao, B., Chen, J., Yu, Y., Wu, P., Han, S. (2010). Nature Communication : 1–7
L. Tang, S.E. Kocabas, S. Latif, A.K. Okyay, D.-S. Ly-Gagnon et al., Nat Photonics 2, 226–229 (2008)
S.I. Tsintzos, N.T. Pelekanos, G. Konstantinidis, Z. Hatzopoulos, P.G. Savvidis, Nature 453(7193), 372–375 (2008)
J.A.H. Van Nieuwstadt, M. Sandtke, R.H. Harmsen, F.B. Segerink, J.C. Prangsma et al., Phys. Rev. Lett. 97(146102), 1–4 (2006)
X. Wang, Y. Deng, Q. Li, Y. Huang, Z. Gong, K.B. Tom, J. Yao (2016). Official journal of the CIOMP 2047–7538/16. Light: Science & Applications 5, e16179: 1–6
Wilczek, F. (1990). World Scientific, 5.
C.M. Wilson, T. Duty, F. Persson, M. Sandberg, G. Johansson, P. Delsing, Phys. Rev. Lett. 98(257003), 1–4 (2007)
Wolf, P., Borde, Ch. J., Clairon, A., Duchane, L., Londragn, A., Lemonde, P., Santarelli, G. et al. (2009). Doi : https://doi.org/10.1007/S1686-008-9118-5 (2009).
M. Wubs, K. Saito, S. Kohler, Y. Kayanuma, P. Hänggi, New J. Phys. 7(218), 1–14 (2005)
T. Xinsheng, D.-W. Zhang, Z. Zhang, Y. Yu, H. Siyuan, S.-L. Zhu, Phys. Rev. Letts. 112(027001), 1–5 (2014)
Y. Yan, B. Wu (2008). arXiv:0811.1388v1 [quant-ph]: 1–7
J. Yang, S. Pang, A.N. Jordan (2017). Phys. Rev. A 96, 020301(R): 1–5
H.P. Ye, H.F. Wang, S.P. Yeo, C.W. Qiu, Electromagn. Waves 136, 17–27 (2013)
M. Zamfirescu, A. Kavokin, B. Gil, G. Malpuech, M. Kaliteevski, Phys. Rev. B 65(161205), 1–16 (2002)
A.V. Zayatsa, I.I. Smolyaninov, A.A. Maradudinc, Phys. Rep. 408, 131–314 (2005)
C. Zener, Proc. R. Soc. London Ser. A 137, 696–702 (1932)
J. Zhang, L. Zhang, W. Xu, J. Phys. D Appl. Phys. 45(113001), 1–19 (2012)
X. Zhang, Z.W. Liu, Nat. Mater. 7, 435–441 (2008)
F. Zhou, F. Liu, L. Xiao, K. Cui, X. Feng, W. Zhang, Y. Huang, Nano-Micro Lett. 9, 1–8 (2017)
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Kenfack-Sadem, C., Ekengoue, C.M., Danga, J.E. et al. Laser control of polariton using Landau–Zener–Stückelberg interferometry theory. Eur. Phys. J. Plus 135, 815 (2020). https://doi.org/10.1140/epjp/s13360-020-00790-1
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DOI: https://doi.org/10.1140/epjp/s13360-020-00790-1