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Annalen der Physik

Quantum Phase Properties: Quantum Phase Properties of Photon Added and Subtracted Displaced Fock States (Ann. Phys. 11/2019)

Priya Malpani, Kishore Thapliyal, Nasir Alam, Anirban Pathak, Hari Narayanan V., Subhashish Banerjee

Published Nov 1, 2019• 0 citations
Publisher

Abstract

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.

DOI
10.1002/andp.201970043

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Abstract Quantum phase properties of photon added and subtracted displaced Fock states (and their limiting cases) 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.

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Annalen der Physik•Oct 4, 2020•10 citations
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.
Abstract Quantum phase properties of photon added and subtracted displaced Fock states (and their limiting cases) 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.
The main focus of this thesis is to study the nonclassical and phase properties of a family of engineered quantum states, most of which show various nonclassical features. The beauty of these states is that these states can be used to establish quantum supremacy. Earlier, a considerable amount of works has been reported on various types of quantum states and their nonclassical properties. Here, complementing the earlier works, the effect of non-Gaussianity inducing operators on the nonclassical and phase properties of displaced Fock states have been studied. This thesis includes 6 chapters. In Chapter 1, motivation behind performing the present work is stated explicitly, also the basic concepts of quantum optics are discussed with a specific attention on the witnesses and measures of nonclassicality. In Chapter 2, nonclassical properties of photon added and subtracted displaced Fock states have been studied using various witnesses of lower- and higher-order nonclassicality which are introduced in Chapter 1. In Chapter 3, we have continued our investigation on photon added and subtracted displaced Fock states (and their limiting cases). In this chapter, quantum phase properties 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. In Chapter 4, we have continued our investigation on the impact of non-Gaussianity inducing operators on the nonclassical and phase properties of the displaced Fock states. In Chapter 5, we have performed a comparison between to process that are used in quantum state engineering to induce nonclassical features. Finally, this thesis is concluded in Chapter 6, where we have summarized the findings of this thesis and have also described scope of the future works.
We have witnessed proliferate growth in theoretical and experimental efforts to understand and control physical systems in a quantum level. In a quantum optics laboratory, Gaussian states, whose phase properties are described by Gaussian probability-like functions, were generated but there was some limitation to use them for various tasks of quantum information processing. There have been suggestions and realisations to engineer the quantum state by subtracting or adding single photons from/to a Gaussian field. It is also possible to test fundamental quantum theories using these techniques. We discuss various issues in subtraction and addition of single photons.
Abstract In this paper, by making use of the nonlinear coherent states approach, the generalized photon added and subtracted f ‐deformed displaced Fock states are introduced. In other words, a natural link between photon added and subtracted displaced Fock states and nonlinear coherent states associated with nonlinear oscillator algebra is obtained. It is found that various kinds of nonclassical states can be generated by adopting appropriately controlling parameters in both linear and nonlinear regimes. Moreover, examining some of the most nonclassical properties such as Mandel's Q parameter, different types of squeezing, namely, quadrature, amplitude–squared and phase entropic squeezing, and Vogel's characteristic function, the nonclassicality features of the considered quantum states of interest are studied. Furthermore, to obtain the degree of quantum coherence, the relative entropy of coherence is investigated. Indeed, the nonclassicality aspects of the states obtained have been numerically studied to understand the roles of deformation functions, photons added and subtracted, and photon number occupied in the Fock state on physical properties. It is demonstrated that the depth and the domain of the nonclassicality features of the system can properly be controlled by selecting the suitable parameters.