Noncommutative photon-added squeezed vacuum states. (English) Zbl 1439.81055
Summary: Noncommutative optical squeezed vacuum states are constructed as eigenstates of an appropriate two-photon annihilation operator corresponding to the Biedenharn-Macfarlane \(q\)-oscillator. We consider in details the role of noncommutativity parameter \(q\) on the nonclassical behaviors including quadrature squeezing and sub-Poissonian statistics. Also, we construct the noncommutative photon-added squeezed vacuum states and consider their Hillery-type higher-order squeezing and single-mode noise band.
Keywords:
Biedenharn-Macfarlane \(q\)-oscillator; squeezed vacuum states; photon-added squeezed states; weak and strong squeezing effects; higher-order squeezing; sub-Poissonian statistics; electric single-mode field operatorReferences:
| [1] | Glauber, R. J., Phys. Rev.130, 2529 (1963). |
| [2] | Glauber, R. J., Phys. Rev.131, 2766 (1963). · Zbl 1371.81166 |
| [3] | Sudarshan, E. C. G., Phys. Rev. Lett.10, 277 (1963). · Zbl 0113.21305 |
| [4] | Gazeau, J.-P., Coherent States in Quantum Physics (Wiley-VCH, 2009). |
| [5] | Dodonov, V. V., Malkin, I. A. and Man’ko, V. I., Physica72, 597 (1974). |
| [6] | Hillery, M., Phys. Rev. A36, 3796 (1987). |
| [7] | Gerry, C. C., J. Mod. Opt.40, 1053 (1993). · Zbl 0941.81552 |
| [8] | Buzek, V. and Knight, P. L., Progress in Optics, Vol. 34, ed. Wolf, E. (Elsevier, 1995), pp. 1-158. |
| [9] | de Matos Filho, R. L. and Vogel, W., Phys. Rev. A54, 4560 (1996). |
| [10] | Man’ko, V. I., Marmo, G., Porzio, A., Solimeno, S. and Zaccaria, F., Phys. Rev. A62, 053407 (2000). |
| [11] | Agarwal, G. S. and Tara, K., Phys. Rev. A43, 492 (1991). |
| [12] | Quesne, C., Phys. Lett. A288, 241 (2001). · Zbl 0972.81710 |
| [13] | Roman-Ancheyta, R., Gonzalez Gutierrez, C. and Recamier, J., J. Opt. Soc. Am. B31, 38 (2014). |
| [14] | Dehghani, A., Mojaveri, B. and Faseghandis, S. A., Mod. Phys. Lett. A34, 1950104 (2019). · Zbl 1412.81151 |
| [15] | Mehta, C. L., Roy, A. K. and Saxena, G. M., Phys. Rev. A46, 1565 (1992). |
| [16] | Xu, X.-X., Hu, L.-Y. and Fan, H.-Y., Mod. Phys. Lett. A24, 2623 (2009). |
| [17] | Carranza, R. and Gerry, C. C., J. Opt. Soc. Am. B29, 2581 (2012). |
| [18] | Walls, D. F., Nature (London)306, 141 (1983). |
| [19] | Loudon, R. and Knight, P. L., J. Mod. Opt.34, 709 (1987). · Zbl 0941.81613 |
| [20] | Buzek, V., J. Mod. Opt.37, 303 (1990). · Zbl 0941.81550 |
| [21] | Bagchi, B. and Bhaumik, D., Mod. Phys. Lett. A13, 623 (1998). |
| [22] | Shaterzadeh-Yazdi, Z., Turner, P. S. and Sanders, B. C., J. Phys. A: Math. Theor.41, 055309 (2008). · Zbl 1134.81382 |
| [23] | Buzek, V. and Knight, P. L., Opt. Commun.81, 331 (1991). |
| [24] | Buzek, V., Vidiella-Barranco, A. and Knight, P. L., Phys. Rev. A45, 6570 (1992). |
| [25] | Dodonov, V. V., J. Opt. B: Quantum Semiclass. Opt.4, R1 (2002). |
| [26] | Hong, C. K. and Mandel, L., Phys. Rev. Lett.54, 323 (1985). |
| [27] | Mandel, L., Opt. Lett.4, 205 (1979). |
| [28] | Dung, H. T., Shumovsky, A. S. and Bogolubov, N. N. Jr., Opt. Commun.90, 322 (1992). |
| [29] | Wang, X. G., Sanders, B. C. and Pan, Sh., J. Phys. A: Math. Gen.33, 7451 (2000). · Zbl 0962.81026 |
| [30] | Wang, X. and Sanders, B. C., Phys. Rev. A65, 012303 (2001). |
| [31] | Sanders, B. C., J. Phys. A: Math. Theor.45, 244002 (2012). · Zbl 1248.81084 |
| [32] | Sanders, B. C., Forty-five years of entangled coherent states, in Proc. of the First Int. Workshop on ECS and Its Application to QIS; T.M.Q.C (2013), pp. 111-113. |
| [33] | Milburn, G. J. and Braunstein, S. L., Phys. Rev. A60, 937 (1999). |
| [34] | Ban, M., J. Opt. B: Quantum Semiclass. Opt.1, L9 (1999). |
| [35] | Sivakumar, S., J. Phys. A: Math. Gen.32, 3441 (1999). · Zbl 0962.81025 |
| [36] | Dodonov, V. V., Marchiolli, M. A., Korennoy, Y. A., Manko, V. I. and Moukhin, Y. A., Phys. Rev. A58, 4087 (1998). |
| [37] | Hu, L.-Y. and Fan, H.-Y., Phys. Scripta79, 035004 (2009). |
| [38] | Zhang, Z. and Fan, H., Phys. Lett. A165, 14 (1992). |
| [39] | Hu, L.-Y. and Zhang, Z.-M., J. Opt. Soc. Am. B30, 518 (2013). |
| [40] | Xin, Z.-Z., Duan, Y.-B., Zhang, H.-M., Hirayama, M. and Matumoto, K., J. Phys. B29, 4493 (1996). |
| [41] | Agarwal, G. S. and Tara, K., Phys. Rev. A46, 485 (1992). |
| [42] | Hu, L.-Y. and Zhang, Z.-M., J. Opt. Soc. Am. B29, 529 (2012). |
| [43] | Dodonov, V. V., Korennoy, Y. A., Manko, V. I. and Moukhin, Y. A., Quantum Semiclass. Opt.8, 413 (1996). |
| [44] | Arik, M. and Coon, D. D., J. Math. Phys.17, 524 (1976). · Zbl 0941.81549 |
| [45] | Biedenharn, L. C., J. Phys. A: Math. Gen.22, L873 (1989). · Zbl 0708.17015 |
| [46] | Macfarlane, A. J., J. Phys. A: Math. Gen.22, 4581 (1989). · Zbl 0722.17009 |
| [47] | Buzek, V., J. Mod. Opt.39, 949 (1992). · Zbl 0941.81633 |
| [48] | Yang, Y. and Yu, Z., Mod. Phys. Lett. A11, 199 (1996). · Zbl 1022.81594 |
| [49] | Bagchi, B. and Bhaumik, D., Mod. Phys. Lett. A13, 811 (1998). |
| [50] | Quesne, C., J. Phys. A: Math. Gen.35, 9213 (2002). · Zbl 1044.81064 |
| [51] | Quesne, C., Penson, K. A. and Tkachuk, V. M., Phys. Lett. A313, 29 (2003). · Zbl 1037.81051 |
| [52] | Liu, X.-M. and Quesne, C., Phys. Lett. A317, 210 (2003). · Zbl 1056.81038 |
| [53] | Fakhri, H. and Hashemi, A., Phys. Rev. A93, 013802 (2016). |
| [54] | Batouli, J., El Baz, M. and Maaouni, A., Mod. Phys. Lett. A31, 1650190 (2016). · Zbl 1351.81060 |
| [55] | Dey, S. and Hussin, V., Phys. Rev. A93, 053824 (2016). |
| [56] | Fakhri, H. and Sayyah-Fard, M., Ann. Phys.387, 14 (2017). · Zbl 1377.81070 |
| [57] | Fakhri, H. and Sayyah-Fard, M., Quantum Inf. Process.19, 19 (2020). · Zbl 1508.81070 |
| [58] | Fakhri, H. and Mousavi-Gharalari, S. E., Eur. Phys. J. Plus135, 253 (2020). |
| [59] | Klimyk, A. and Schmüdgen, K., Quantum Groups and Their Representations (Springer-Verlag, 1997). · Zbl 0891.17010 |
| [60] | Ismail, M. E. H., Classical and Quantum Orthogonal Polynomials in One Variable (Cambridge Univ. Press, 2005). · Zbl 1082.42016 |
| [61] | Milburn, G. and Walls, D. F., Opt. Commun.39, 401 (1981). |
| [62] | Loudon, R., The Quantum Theory of Light (Oxford Univ. Press, 2000). · Zbl 1009.81003 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
