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The photon-added spin coherent state as a new kind of coherent state has been defined by iterated actions of the proper raising operator on the ordinary spin coherent state. In this paper, the quantum statistical properties of photon-added spin coherent states such as photon number distribution, second-order correlation function and Wigner function are studied. It is found that the Wigner function shows the negativity in some regions and the second-order correlation function is less than unity. Therefore, the photon-added spin coherent state is a nonclassical state.
One of the most widely used and interesting quantum states in the field of quantum optics is the coherent state. The standard coherent states are related to the Heisenberg–Weyl group.[1] The generalized coherent states related to any arbitrary Lie group have been introduced and investigated by Perelomov.[2] Along these generalizations, the spin states analogous to the standard coherent states have been introduced by Radcliffe.[3] These states are related to the SU(2) group and have been receiving attention widely.[4–11] On the other hand, photon-added coherent states have been introduced by Agarwal and Tara and generated experimentally by Zavatta et al.[12,13] These states have received considerable attention and some generalizations on them take place.[14–16] Recently, analogous to photon added coherent states, the photon added spin coherent states have been introduced by Berrada.[17] Since nonclassical states attracted a great deal of interest in quantum computation and quantum information technology,[18–22] in the present paper, the nonclassical properties and statistical properties of these states are investigated.
The paper is organized as follows. In section
The standard spin coherent states have been introduced by acting spin raising operators
Analogous to ordinary photon-added coherent states, the photon-added spin coherent states have been introduced by Berrada by iterated actions (k times) of
In this section, some of the statistical properties of photon-added spin coherent states are investigated. For this purpose, the photon number distribution, the second-order correlation function, and the Wigner function of photon-added spin coherent states are discussed.
The photon number distribution of a photon-added spin coherent state is given by
Photon number distributions of the photon-added spin coherent states have been plotted for several values of j and k in Fig.
Quantum statistics of a state can be characterized by the second-order correlation function which is obtained by[23]
If
The Wigner function is one of the main tools to investigate the behavior of a quantum state and its nonclassicality.[24] Partial negativity of the Wigner function indicates the nonclassical feature of the quantum state. The Wigner function of a single-mode system in the coherent state representation β can be expressed as[25]
Figure
In summary, we study the statistical properties of the photon-added spin coherent states through the photon number distribution, second-order correlation function, and Wigner function. It is found that the photon added number k and spin number j affect these properties. In addition, the results show that the Wigner function is negative in some regions and the second-order correlation function represents antibunching behavior and so, the photon-added coherent state can be considered as a nonclassical state.
In general, the photon-added coherent state is an intermediate state between a (classical) coherent state and a (full quantum) Fock state. Here, adding photon (quanta) to the spin coherent states is a proper way to construct the photon-added spin coherent states and these states show more nonclassicality. This opportunity helps us to manipulate a nonclassical state with more control on its nonclassicality.
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