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arXiv:1907.03257 · Annalen der Physik

Manipulating Nonclassicality via Quantum State Engineering Processes: Vacuum Filtration and Single Photon Addition

Priya Malpani, Nasir Alam, Kishore Thapliyal, Anirban Pathak, Venkatakrishnan Narayanan, Subhashish Banerjee

Published Nov 20, 2019• 10 citations
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Abstract

Abstract The effect of two quantum state engineering processes that can be used to burn a hole at vacuum in the photon number distribution of quantum states of radiation field is compared using various witnesses of lower‐ and higher‐order nonclassicality as well as a measure of nonclassicality. Specifically, the modification in nonclassical properties due to vacuum state filtration and a single photon addition on an even coherent state, binomial state, and Kerr state are investigated using the criteria of lower‐ and higher‐order antibunching, squeezing, and sub‐Poissonian photon statistics. Further, the amount of nonclassicality present in these engineered quantum states having enormous applications in continuous variable quantum communication is quantified and analyzed by using an linear entropy‐based entanglement potential. It is observed that all the quantum states studied here are highly nonclassical, and the hole‐burning processes can introduce/enhance nonclassical features. However, it is not true in general. A hole at vacuum implies a maximally nonclassical state (as far as Lee's nonclassical depth is concerned), but a particular process of hole burning at vacuum does not ensure the existence of any particular nonclassical feature. Specifically, lower‐ and higher‐order squeezing are not observed for photon‐added and vacuum filtered even coherent states.

DOI
10.1002/andp.201900337

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Abstract The effect of two quantum state engineering processes that can be used to burn a hole at vacuum in the photon number distribution of quantum states of radiation field is compared using various witnesses of lower‐ and higher‐order nonclassicality as well as a measure of nonclassicality. Specifically, the modification in nonclassical properties due to vacuum state filtration and a single photon addition on an even coherent state, binomial state, and Kerr state are investigated using the criteria of lower‐ and higher‐order antibunching, squeezing, and sub‐Poissonian photon statistics. Further, the amount of nonclassicality present in these engineered quantum states having enormous applications in continuous variable quantum communication is quantified and analyzed by using an linear entropy‐based entanglement potential. It is observed that all the quantum states studied here are highly nonclassical, and the hole‐burning processes can introduce/enhance nonclassical features. However, it is not true in general. A hole at vacuum implies a maximally nonclassical state (as far as Lee's nonclassical depth is concerned), but a particular process of hole burning at vacuum does not ensure the existence of any particular nonclassical feature. Specifically, lower‐ and higher‐order squeezing are not observed for photon‐added and vacuum filtered even coherent states.
In quantum optics, nonclassical properties of various quantum states of radiation field are frequently studied. Some of those states are finite dimensional and referred to as qudits. These states are important because of their potential applications in quantum information processing. Further, nonclassical states are those which do not have any classical counterpart. Consequently, to establish quantum supremacy, we always require nonclassical state. Recently, Sivakumar and Meher have studied the nonclassical properties of the number state filtered coherent state, and shown that the number state filtering introduces nonclassical features into coherent state which is otherwise classical. This observation motivated us to investigate the role of hole burning (state filtering) on a state which is already nonclassical. Specifically, we have selected a Binomial state which is known to be nonclassical as our test bed and burnt a hole at vacuum (equivalently filtered the vacuum state). To check the nonclassical properties of vacuum filtered binomial state, we have used Vogel’s criterion, criterion of higher- and lower-order antibunching, criterion of higher-order sub-Poissonian photon statistics, Linear entropy etc. The investigation results show that vacuum filtered binomial state studied here is highly nonclassical, and the hole burning process enhances the nonclassical depth.
In quantum optics, nonclassical properties of various quantum states of radiation field are frequently studied. Some of those states are finite dimensional and referred to as qudits. These states are important because of their potential applications in quantum information processing. Further, nonclassical states are those which do not have any classical counterpart. Consequently, to establish quantum supremacy, we always require nonclassical state. Recently, Sivakumar and Meher have studied the nonclassical properties of the number state filtered coherent state, and shown that the number state filtering introduces nonclassical features into coherent state which is otherwise classical. This observation motivated us to investigate the role of hole burning (state filtering) on a state which is already nonclassical. Specifically, we have selected a Binomial state which is known to be nonclassical as our test bed and burnt a hole at vacuum (equivalently filtered the vacuum state). To check the nonclassical properties of vacuum filtered binomial state, we have used Vogel's criterion, criterion of higher- and lower-order antibunching, criterion of higher-order sub-Poissonian photon statistics, Linear entropy etc. The investigation results show that vacuum filtered binomial state studied here is highly nonclassical, and the hole burning process enhances the nonclassical depth.
In the recent years, effect of photon addition and subtraction to a quantum state of light is explored for coherent state, thermal state, Schrödinger cat state, Gaussian state and many more. It is reported that the phenomena of photon addition or subtraction significantly affect nonclassical properties of the states of light. Here we wish to study the effect of photon addition and subtraction to the binomial start of radiation on the nonclassical properties of the state. We observed that the depth of nonclassicality increases with photon addition and decreases with photon subtraction in antibunching and squeezing phenomenon. We also report significant changes in photon number distribution and variable with depending parameters.
Abstract 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 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.
Number state filtering in coherent states leads to sub-Poissonian photon statistics. These states are more suitable for phase estimation when compared with the coherent states. Nonclassicality of these states is quantified in terms of the negativity of the Wigner function and the entanglement potential. Filtering of the vacuum from a coherent state is almost like the photon-addition. However, filtering makes the state more resilient against dissipation than photon-addition. Vacuum state filtered coherent states perform better than the photon-added coherent states for a two-way quantum key distribution protocol. A scheme to generate these states in multi-photon atom-field interaction is presented.
Abstract Superposition of two coherent states, the Schrodinger’s cat state, can exhibit different nonclassical properties having foundational applications in quantum information processing. We consider the ‘superposition of Schrodinger’s cat state with the vacuum state (SCVS)’ of the optical field. We discuss different witness of nonclassicality properties such as lower- and higher-order squeezing (viz., squeezing, Hong & Mandel’s fourth-order squeezing, amplitude-squared squeezing) and sub-Poissonian photon statistics. Further, we discuss the negativity of the Wigner function of SCVS indicating the nonclassicality of the state under investigation. We find that the vacuum state contribution in SCVS exhibits different nonclassicalities under some conditions stronger where the nonclassicalities exhibited by the state without vacuum state contribution are weaker.