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.
Experimental realization of various quantum states of interest has become possible in the recent past due to the rapid developments in the field of quantum state engineering. Nonclassical properties of such states have led to various exciting applications, specifically in the area of quantum information processing. The present article aims to study lower-and higher-order nonclassical features of such an engineered quantum state (a generalized binomial state based on Abel's formula). Present study has revealed that the state studied here is highly nonclassical. Specifically, higher-order nonclassical properties of this state are reported using a set of witnesses, like higher-order antibunching, higher-order sub-Poissonian photon statistics, higher-order squeezing (both Hong Mandel type and Hillery type). A set of other witnesses for lower-and higher-order nonclassicality (e.g., Vogel's criterion and Agarwal's A parameter) have also been explored. Further, an analytic expression for the Wigner function of the generalized binomial state is reported and the same is used to witness nonclassicality and to quantify the amount of nonclassicality present in the system by computing the nonclassical volume (volume of the negative part of the Wigner function). Optical tomogram of the generalized binomial state is also computed for various conditions as Wigner function cannot be measured directly in an experiment in general, but the same can be obtained from the optical tomogram with the help of Radon transform. arXiv:1811.10557v1 [quant-ph] 26 Nov 2018 state (BS) [36] and can be defined aswhere B M n (p) is the probability amplitude of the binomial state which corresponds to the occurrence of n photons with equal probability p obtained in M independent ways [36]. Mathematically, the binomial state is equivalent to a molecular system having same photon emitting probability p from the different energy levels of the excited states of the molecule which undergoes the M level vibrational relaxation [37]. Binomial state being an intermediate state, reduces to various existing states at different limits. For example, it reduces to a (a) vacuum state |0 (if p→0,It is interesting to note that coherent states are closest to classical states and the number states are the most nonclassical states. Thus, fundamentally different states of electromagnetic field can be obtained as limiting cases of BS. Naturally, properties of BS has been studied since long [38].The interest on the BS is not restricted to the state of the form Eq.(1), it has been extended to various variants of BS, too. Specifically, in Refs. [39,40] negative binomial state was proposed, and subsequently its properties were studied in Refs. [10]. Similarly, reciprocal binomial state was introduced in Ref. [12] and studied in [9,10]. Further, a couple of generalized binomial states (GBS) 1 have been proposed [37] and their nonclassical properties have also been investigated [9,10]. More interestingly, possible applications of GBS have been explored in the field of quantum co...
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