Document Type : Research

Authors

1 Department of Physics, Vali-e-Asr University of Rafsanjan,

2 Department of Physics, Faculty of Science, Vali-e-Asr University of Rafsanjan

3 Department of Photonics, Graduate University of Advanced Technology, Kerman

Abstract

In this paper, a new class of nonclassical states of radiation is presented. For this purpose, after clarifying the application of displaced number states align with expressing the significance of noiseless signal amplification, amplified displaced number states are introduced. Then, examining some of the most important criteria, such as Mandel’s parameter, second-order correlation function, Vogel’s characteristic function, and Wigner distribution function, the nonclassicality of the introduced quantum states is studied. In each case, the roles of gain factor and number of photons of the number states in the above-mentioned physical quantities are discussed. The numerical results show remarkable values of sub-Poissonian statistics of the field and photon antibunching. Afterward, as the necessary and sufficient condition for the nonclassicality of a quantum state, the behavior of the Vogel’s characteristic function is analyzed. We will see that the Vogel function for quantum states of interests goes beyond the value of characteristic function of the ground state, which results in the nonclassicality of the introduced states. Moreover, the negativity of the Wigner–Weyl distribution function, as another appearance of the nonclassicality of the considered states, is also observed. Consequently, the mentioned evidence implies that the amplified displaced number states can be regarded as successful candidates for nonclassical light.

Keywords

[1]  Lee, N., Benichi, H., Takeno, Y., Takeda, S., Webb, J., Huntington, E., & Furusawa, A. Teleportation of nonclassical wave packets of light. Science, 332(6027), 2011. 330-333.
[2]   Sergienko, A. V. (Ed.). Quantum Communications and Cryptography. CRC Press. 2018)
[3]   Prabhakar, S., Shields, T., Dada, A. C., Ebrahim, M., Taylor, G. G., Morozov, D., ... & Clerici, M. Two-photon quantum interference and entanglement at 2.1 μm. Science Advances, 6(13), 2020. eaay5195.
[4]   Mehta, K., Achanta, V. G., & Dasgupta, S. Generation of non-classical states of photons from a metal–dielectric interface: a novel architecture for quantum information processing. Nanoscale, 12(1), 2020. 256-261.
[5]   Zou, X., Pahlke, K., & Mathis, W. Generation of two-mode nonclassical states and a quantum-phase-gate operation in trapped-ion cavity QED. Physical Review A, 65(6), 2002. 064303.
[6]   Deleglise, S., Dotsenko, I., Sayrin, C., Bernu, J., Brune, M., Raimond, J. M., & Haroche, S. Reconstruction of non-classical cavity field states with snapshots of their decoherence. Nature, 455(7212), 2008. 510-514.
[7]   Faghihi, M. J., & Tavassoly, M. K. Number-phase entropic squeezing and nonclassical properties of a three-level atom interacting with a two-mode field: intensity-dependent coupling, deformed Kerr medium, and detuning effects. Journal of the Optical Society of America B, 30(11), 2013. 2810-2818.
[8]   Baghshahi, H. R., & Faghihi, M. J. f-deformed cavity mode coupled to a Λ-type atom in the presence of dissipation and Kerr nonlinearity. Journal of the Optical Society of America B, 39(11), 2022. 2925-2933.
[9]   Alam, N., Verma, A., & Pathak, A. Higher-order nonclassicalities of finite dimensional coherent states: A comparative study. Physics Letters A, 382(28), 2018. 1842-1851.
[10]   de Matos Filho, R. L., & Vogel, W. Nonlinear coherent states. Physical Review A, 54(5), 1996. 4560.
[11]   Man'ko, V. I., Marmo, G., Sudarshan, E. C. G., & Zaccaria, F. f-Oscillators and nonlinear coherent states. Physica Scripta, 55(5), 1997. 528.
[12]   Roknizadeh, R., & Tavassoly, M. K. The construction of some important classes of generalized coherent states: the nonlinear coherent states method. Journal of Physics A: Mathematical and General, 37(33), 2004. 8111.
[13]   Torkzadeh-Tabrizi, S., Faghihi, M. J., & Honarasa, G. Phase space nonclassicality and sub-Poissonianity of deformed photon-added nonlinear cat states: algebraic and group theoretical approach. Optics Letters, 48(3), 2023. 688-691.
[14]   Alsing, P., Guo, D. S., & Carmichael, H. J. Dynamic Stark effect for the Jaynes-Cummings system. Physical Review A, 45(7), 1992. 5135.
[15]   Wunsche, A. Displaced Fock states and their connection to quasiprobabilities. Quantum Optics: Journal of the European Optical Society Part B, 3(6), 1991. 359.
[16]   Zheng-Feng, H. Fluctuation of phase in the displaced number states. Journal of Modern Optics, 39(6), 1992. 1381-1397.
[17]   Dodonov, V. V., & De Souza, L. A. Decoherence of superpositions of displaced number states. Journal of Optics B: Quantum and Semiclassical Optics, 7(12), 2005. S490.
[18]   de Oliveira, F. A. M., Kim, M. S., Knight, P. L., & Buek, V. Properties of displaced number states. Physical Review A, 41(5), 1990. 2645.
[19]   Podoshvedov, S. A. Displaced photon states as resource for dense coding. Physical Review A, 79(1), 2009. 012319.
[20]   Podoshvedov, S. A. Quantum teleportation through an entangled state composed of displaced vacuum and single-photon states. Journal of Experimental and Theoretical Physics, 106, 2008. 435-441.
[21]   Maldonado-Villamizar, F. H., Alderete, C. H., & Rodríguez-Lara, B. M. Squeezed displaced entangled states in the quantum Rabi model. Physical Review A, 100(1), 2019. 013811.
[22]   Lvovsky, A. I., & Babichev, S. A. Synthesis and tomographic characterization of the displaced Fock state of light. Physical Review A, 66(1), 2002. 011801.
[23]   de Oliveira, G. C., de Almeida, A. R., de Queirós, I. P., Moraes, A. M., & Dantas, C. M. Alternative proposal for the generation of the displaced number state. Physica A: Statistical Mechanics and its Applications, 351(2-4), 2005. 251-259.
[24]   Scarani, V., Iblisdir, S., Gisin, N., & Acin, A. Quantum cloning. Reviews of Modern Physics, 77(4), 2005. 1225.
[25]   Xiang, G. Y., Ralph, T. C., Lund, A. P., Walk, N., & Pryde, G. J. Heralded noiseless linear amplification and distillation of entanglement. Nature Photonics, 4(5), 2010. 316-319.
[26]   Fiurášek, J. Teleportation-based noiseless quantum amplification of coherent states of light. Optics Express, 30(2), 2022. 1466-1489.
[27]   Ralph, T. C., & Lund, A. P. Nondeterministic noiseless linear amplification of quantum systems. In AIP Conference Proceedings. Vol. 1110, No. 1, (2009, April). pp. 155-160. American Institute of Physics.
[28]   Zavatta, A., Fiurášek, J., & Bellini, M. A high-fidelity noiseless amplifier for quantum light states. Nature Photonics, 5(1), 2011. 52-56.
[29]   Yang, S., Zhang, S., Zou, X., Bi, S., & Lin, X. Improving noiseless linear amplification for optical quantum communication with quadrature squeezing. Physical Review A, 87(2), 2013. 024302.
[30]   Xiang, G. Y., Ralph, T. C., Lund, A. P., Walk, N., & Pryde, G. J. Heralded noiseless linear amplification and distillation of entanglement. Nature Photonics, 4(5), 2010. 316-319.
[31]   Ferreyrol, F., Barbieri, M., Blandino, R., Fossier, S., Tualle-Brouri, R., & Grangier, P. Implementation of a nondeterministic optical noiseless amplifier. Physical Review Letters, 104(12), 2010. 123603.
[32]   Mičuda, M., Straka, I., Miková, M., Dušek, M., Cerf, N. J., Fiurášek, J., & Ježek, M. Noiseless loss suppression in quantum optical communication. Physical Review Letters, 109(18), 2012. 180503.
[33]   Kocsis, S., Xiang, G. Y., Ralph, T. C., & Pryde, G. J. Heralded noiseless amplification of a photon polarization qubit. Nature Physics, 9(1), 2013. 23-28.
[34]   Fiurášek, J., & Cerf, N. J. Gaussian postselection and virtual noiseless amplification in continuous-variable quantum key distribution. Physical Review A, 86(6), 2012. 060302.
[35]   Blandino, R., Leverrier, A., Barbieri, M., Etesse, J., Grangier, P., & Tualle-Brouri, R. Improving the maximum transmission distance of continuous-variable quantum key distribution using a noiseless amplifier. Physical Review A, 86(1), 2012. 012327.
[36]   Brask, J. B., Brunner, N., Cavalcanti, D., & Leverrier, A. Bell tests for continuous-variable systems using hybrid measurements and heralded amplifiers. Physical Review A, 85(4), 2012. 042116.
[37]   Kim, Y. S., Lee, J. C., Kwon, O., & Kim, Y. H. Protecting entanglement from decoherence using weak measurement and quantum measurement reversal. Nature Physics, 8(2), 2012. 117-120.
[38]   Xiang, G. Y., Ralph, T. C., Lund, A. P., Walk, N., & Pryde, G. J. Heralded noiseless linear amplification and distillation of entanglement. Nature Photonics, 4(5), 2010. 316-319.
[39]   Ferreyrol, F., Barbieri, M., Blandino, R., Fossier, S., Tualle-Brouri, R., & Grangier, P. Implementation of a nondeterministic optical noiseless amplifier. Physical Review Letters, 104(12), 2010. 123603.
[40]   Mičuda, M., Straka, I., Miková, M., Dušek, M., Cerf, N. J., Fiurášek, J., & Ježek, M. Noiseless loss suppression in quantum optical communication. Physical Review Letters, 109(18), 2012. 180503.
[41]   Dias, J., & Ralph, T. C. Quantum repeaters using continuous-variable teleportation. Physical Review A, 95(2), 2017. 022312.
[42]   Adnane, H., Bina, M., Albarelli, F., Gharbi, A., & Paris, M. G. Quantum state engineering by nondeterministic noiseless linear amplification. Physical Review A, 99(6), 2019. 063823.
[43]   Farzan, M. E., Faghihi, M. J., & Honarasa, G. Nonclassical properties of f-deformed photon-added squeezed Kerr states. Physica A: Statistical Mechanics and its Applications, 565, 2021. 125569.
[44]   Feng, L. J., & Gong, S. Q. Two-photon blockade generated and enhanced by mechanical squeezing. Physical Review A, 103(4), 2021. 043509.
[45]   Vogel, W. Nonclassical states: An observable criterion. Physical Review Letters, 84(9), 2000. 1849.
[46]   Faghihi, M. J. Generalized Photon Added and Subtracted f‐Deformed Displaced Fock States. Annalen der Physik, 532(12), 2020. 2000215.
[47]   Scully, M. O., & Zubairy, M. S. Quantum Optics. Cambridge University Press. 1999.
[48]   Gerry, C. C., & Knight, P. L. Introductory Quantum Optics. Cambridge University Press. 2005.
[49]   Ghorbani, M., Faghihi, M. J., & Safari, H. Wigner function and entanglement dynamics of a two-atom two-mode nonlinear Jaynes–Cummings model. Journal of the Optical Society of America B, 34(9), 2017. 1884-1893.
[50]   Ficek, Z., & Wahiddin, M. R. Quantum Optics for Beginners. CRC Press. 2014.