International Journal of Theoretical Physics

, Volume 57, Issue 11, pp 3443–3456 | Cite as

Higher-Order Nonclassical Properties of a Shifted Symmetric Cat State and a One-Dimensional Continuous Superposition of Coherent States

  • Nasir Alam
  • Kathakali Mandal
  • Anirban PathakEmail author


Role of quantum interference in the origin of higher-order nonclassical characteristics of radiation field has been probed vis-à-vis a discrete and a continuous superposition of coherent states. Specifically, the possibilities of observing higher-order nonclassical properties (e.g., higher-order antibunching (HOA), higher-order sub-Poissonian photon statistics (HOSPS), higher-order squeezing (HOS) of Hong-Mandel type and Hillery type) have been investigated using a shifted symmetric cat state that reduces to Yurke-Stoler, even and odd coherent states at various limits. This shifted symmetric cat state which can be viewed as a discrete superposition of coherent states is found to show HOA and HOSPS. Similarly, higher-order nonclassical properties of a one-dimensional continuous superposition of coherent states is also studied here. The investigation has revealed the existence of HOS and HOSPS in the one-dimensional continuous superposition of coherent states studied here. Effect of non-Gaussianity inducing operations (e.g., photon addition and addition followed by subtraction) on these superposition states have also been investigated. Finally, some comparisons have been made between the higher-order nonclassical properties of discrete and continuous superposition of coherent states.


Higher-order squeezing Higher-order antibunching Higher-order sub-Poissonian photon statistics Cat state Photon addition 



A.P. and N.A. thank the Department of Science and Technology (DST), India, for support provided through the DST project No. EMR/2015/000393. A.P. also thanks K. Thapliyal for some useful technical discussions. K.M. thanks Amit Verma for his help and interest in this work.


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Authors and Affiliations

  1. 1.Jaypee Institute of Information TechnologyNoidaIndia
  2. 2.Jaypee Institute of Information TechnologyNoidaIndia

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