Nonclassical properties of photon added and subtracted displaced Fock states are studied using various witnesses of lower-and higher-order nonclassicality. Compact analytic expressions are obtained for the nonclassicality witnesses. Using those expressions, it is established that these states and the states that can be obtained as their limiting cases (except coherent states) are highly nonclassical as they show the existence of lower-and higher-order antibunching and sub-Poissonian photon statistics, in addition to the nonclassical features revealed through the Mandel Q M parameter, zeros of Q function, Klyshko's criterion, and Agarwal-Tara criterion. Further, some comparison between the nonclassicality of photon added and subtracted displaced Fock states have been performed using witnesses of nonclassicality. This has established that between the two types of non-Gaussianity inducing operations (i.e., photon addition and subtraction) used here, photon addition influences the nonclassical properties more strongly. Further, optical designs for the generation of photon added and subtracted displaced Fock states from squeezed vacuum state have also been proposed.

In article 1900141, Priya Malpani, Anirban Pathak, and co‐workers studied different aspects of quantum phase properties of a set of engineered quantum states, which can be reduced from photon added/subtracted displaced Fock state, in view of their applications in quantum technology. This image represents the polar plot for quantum phase distribution of this set of engineered quantum states.

Various nonclassical and quantum phase properties of photon added then subtracted displaced Fock state have been examined systematically and rigorously. Higher-order moments of the relevant bosonic operators are computed to test the nonclassicality of the state of interest, which reduces to various quantum states (having applications in quantum optics, metrology and information processing) in different limits ranging from the coherent (classical) state to the Fock (most nonclassical) states. The nonclassical features are discussed using Klyshko's, Vogel's, and Agarwal-Tara's criteria as well as the criteria of lowerand higher-order antibunching, sub-Poissonian photon statistics and squeezing. In addition, phase distribution function and quantum phase fluctuation have been studied. These properties are examined for various combinations of number of photon addition and/or subtraction and Fock parameter. The examination has revealed that photon addition generally improves nonclassicality, and this advantage enhances for the large (small) values of displacement parameter using photon subtraction (Fock parameter). The higher-order sub-Poissonian photon statistics is only observed for the odd orders. In general, higher-order nonclassicality criteria are found to detect nonclassicality even in the cases when corresponding lower-order criteria failed to do so. Photon subtraction is observed to induce squeezing, but only large number of photon addition can be used to probe squeezing for large values of displacement parameter. Further, photon subtraction is found to alter the phase properties more than photon addition, while Fock parameter has an opposite effect of the photon addition/subtraction. Finally, nonclassicality and non-Gaussianity is also established using Q function.

Quantum phase properties of photon added and subtracted displaced Fock states (and a set of quantum states which can be obtained as the limiting cases of these states) are investigated from a number of perspectives, and it is shown that the quantum phase properties are dependent on the quantum state engineering operations performed. Specifically, the analytic expressions for quantum phase distributions and angular Q distribution as well as measures of quantum phase fluctuation and phase dispersion are obtained. The uniform phase distribution of the initial Fock states is observed to be transformed by the unitary operation (i.e., displacement operator) into non-Gaussian shape, except for the initial vacuum state. It is observed that the phase distribution is symmetric with respect to the phase of the displacement parameter and becomes progressively narrower as its amplitude increases. The non-unitary (photon addition/subtraction) operations make it even narrower in contrast to the Fock parameter, which leads to broadness. The photon subtraction is observed to be a more powerful quantum state engineering tool in comparison to the photon addition. Further, one of the quantum phase fluctuation parameters is found to reveal the existence of antibunching in both the engineered quantum states under consideration. Finally, the relevance of the engineered quantum states in the quantum phase estimation is also discussed, and photon added displaced Fock state is shown to be preferable for the task.

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