Abstract
We have studied the effect of a beam splitter on the excited coherent states, which are an intermediate state between the fock state and the coherent state. These states are obtained due to successive elementary one-photon excitations of a coherent state. We have used linear entropy to measure the entanglement generated through a beam splitter when a single-mode excited coherent state is injected at each input port of the beam splitter. We have used our very generalized results to study the possible generation of entanglement for few more specific cases also. Furthermore, we have also studied the nonclassical photon statistics of the output field through the Mandel’s Q parameter and have found the correlation between the photon statistics and the entanglement of the output state.
Similar content being viewed by others
References
Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935)
Schrodinger, E.: The present status of quantum mechanics. Naturwissenschaften 23, 807 (1935)
Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)
Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865 (2009)
Bennett, C.H., Brassard, G., Crepeau, C., Jozsa, R., Peres, A., Wootters, W.K.: Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels. Phys. Rev. Lett. 70, 1895 (1992)
Bennett, C.H., Brassard, G.: Quantum cryptography: public key distribution and coin tossing. In: Proceedings of IEEE international conference on computers systems and signal processing, vol 175, p. 8 (1984)
Bell, J.S.: On the Einstein–Podolsky–Rosen paradox. Physics 1, 195 (1964)
Glauber, R.J.: Coherent and incoherent states of the radiation field. Phys. Rev. 131, 2766 (1963)
Sudharshan, E.C.G.: Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams. Phys. Rev. Lett. 10, 277 (1963)
Titulaer, U.M., Glauber, R.J.: Correlation functions for coherent fields. Phys. Rev. 140, B676 (1965)
Mandel, L.: Non-classical states of the electromagnetic field. Phys. Scr. T12, 34 (1986)
Wang, X.: Theorem for the beam-splitter entangler. Phys. Rev. A 66, 024303 (2002)
Zou, X.T., Mandel, L.: Photon-antibunching and sub-Poissonian photon statistics. Phy. Rev A. 41, 475 (1990)
Tan, S.M., Walls, D.F., Collett, M.J.: Nonlocality of a single photon. Phys. Rev. Lett. 66, 252 (1991)
Toth, G., Simon, C., Cirac, J.I.: Entanglement detection based on interference and particle counting. Phys. Rev. A 68, 062310 (2003)
Zheng, S.B., Guo, G.C.: Efficient scheme for two-atom entanglement and quantum information processing in cavity QED. Phys. Rev. Lett. 85, 2392 (2000)
Gershenfeld, N., Chuang, I.L.: Bulk spin-resonance quantum computation. Science 275, 235 (1995)
Sanders, B.C.: Entangled coherent states. Phys. Rev. A 45, 6811 (1992)
Paris, M.G.A.: Entanglement and visibility at the output of a Mach–Zehnder interferometer. Phys. Rev. A 59, 1615 (1999)
Kim, M.S., Son, W., Buzek, V., Knight, P.L.: Entanglement by a beam splitter: nonclassicality as a prerequisite for entanglement. Phy. Rev A 65, 032323 (2002)
Wootters, W.K.: Entanglement of formation and concurrence. Quantum Inf. Comput. 1, 27 (2001)
Bennett, C.H., Bernstein, H.J., Popescu, S., Schumacher, B.: Concentrating partial entanglement by local operations. Phys. Rev. A 53, 2046 (1996)
Vidal, G., Werner, R.F.: Computable measure of entanglement. Phys. Rev. A 65, 032314 (2002)
Berrada, K., El Baz, M., Saif, F., Hassouni, Y., Mnia, S.: Entanglement generation from deformed spin coherent states using a beam splitter. J. Phys. A Math. Theor. 42, 285306 (2009)
Gerry, C.C., Benmoussa, A.: Beam splitting and entanglement: generalized coherent states, group contraction, and the classical limit. Phys. Rev. A 71, 062319 (2005)
Milivojevic, M.: Maximal thermal entanglement using three-spin interactions. Quantum Inf. Process. 18, 48 (2019)
Park, D.: Thermal entanglement and thermal discord in two-qubit Heisenberg XYZ chain with Dzyaloshinskii–Moriya interactions. Quantum Inf. Process. 18, 172 (2019)
Zurek, W.H.: Decoherence, einselection, and the quantum origins of the classical. Rev. Mod. Phys. 75, 715 (2003)
Yu, T., Eberly, J.H.: Sudden death of entanglement. Science 323, 598 (2009)
Almeida, M.P., de Melo, F., HorMeyll, M., Salles, A., Walborn, S.P., Souto Ribeiro, P.H., Davidovich, L.: Environment-induced sudden death of entanglement. Science 316, 579 (2007)
Schroedinger, E.: Der stetigeÜ bergang von der Mikro- zur Makromechanik. Naturwissenschaften 14, 664 (1926)
Jurco, B.: On coherent states for the simplest quantum groups. Lett. Math. Phys. 21, 51 (1991)
Dodonov, V.V.: ’Nonclassical’ states in quantum optics: a ’squeezed’ review of the first 75 years. J. Opt. B: Quantum Semiclass. Opt. 4, R1 (2002)
Kimble, H.J.: Photon antibunching in resonance fluorescence. Phys. Rev. Lett. 39, 691 (1977)
Teich, M.C., Saleh, B.E.A.: Observation of sub-Poisson Franck–Hertz light at 253.7 nm. J.Opt. Soc. Am. B 2, 275 (1985)
Hong, C.K., Mandel, L.: Higher-order squeezing of a quantum field. Phys. Rev. Lett. 54, 323 (1985)
Ling-An, Wu, Kimble, H.J., Hall, J.L., Huifa, Wu: Generation of squeezed states by parametric down conversion. Phys. Rev. Lett 57, 2520 (1986)
van Enk, S.J., Hirota, O.: Entangled coherent states: teleportation and decoherence. Phys. Rev. A 64, 022313 (2001)
Jeong, H., Kim, M.S.: Efficient quantum computation using coherent states. Phys. Rev. A 65, 042305 (2002)
Agarwal, G.S., Tara, K.: Nonclassical properties of states generated by the excitations on a coherent state. Phys. Rev. A 43, 497 (1991)
Zavatta, A., Viciani, S., Bellini, M.: Quantum-to-classical transition with single-photon-added coherent states of light. Science 306, 660 (2004)
Zavatta, A., Viciani, S., Bellini, M.: Single-photon excitation of a coherent state: catching the elementary step of stimulated light emission. Phys. Rev. A 72, 023820 (2005)
Yang, C., Li, F.-L.: Nonclassicality of photon-subtracted and photon-added- then-subtracted Gaussian states. J. Opt. Soc. Am. B 26(4), 830 (2009)
Parigi, V., Zavatta, A., Bellini, M.: Manipulating thermal light states by the controlled additon and subtraction of single photons. Laser Phys. Lett. 5(3), 246 (2008)
Pinheiro, P.V.P., Ramos, R.V.: Quantum communication with photon-added coherent states. Quantum Inf. Process. 12, 537 (2013)
Singh, G., Choudhary, A.: Excitation of coherent states: wave function development and analysis. arXiv:1412.0841 [quant-ph] (2014)
Scully, M.O., Zubairy, M.: Quantum Optics, vol. 630. Cambridge University Press, Cambridge (1997)
Markham, D., Vedral, V.: Classicality of spin-coherent states via entanglement and distinguishability. Phys. Rev. A 67, 042113 (2003)
Nielsen, M.A.: Conditions for a class of entanglement transformations. Phys. Rev. Lett. 83, 439 (1999)
Wang, D., Li, M., Zhu, F., Yin, Z.Q., Chen, W., Han, Z.F., Guo, G.C., Wang, Q.: Quantum key distribution with the single-photon-added coherent source. Phys. Rev. A 90, 062315 (2014)
Zhang, J.-S., Xu, J.-B.: Entanglement and nonlocality of photon-added entangled coherent states and quantum probabilistic teleportation. Phys. Scr. 79, 025008 (2009)
Banaszek, K., Wódkiewicz, K.: Nonlocality of the Einstein–Podolsky–Rosen state in the Wigner representation. Phys. Rev. A 58, 4345 (1998)
DellAnno, F., DeSiena, S., Illuminati, F.: Realistic continuous-variable quantum teleportation with non-Gaussian resources. Phys. Rev. A 81, 012333 (2010)
Raymond Ooi, C.H., Berrada, K.: Beam splitter entangler for nonlinear bosonic fields. Laser Phys. 22, 1449–1454 (2012)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Soorat, R., Nitharshini, S., Anil Kumar, M. et al. Nonclassical photon statistics and bipartite entanglement generation of excited coherent states. Quantum Inf Process 19, 297 (2020). https://doi.org/10.1007/s11128-020-02756-9
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11128-020-02756-9