arXiv:2304.05054 · Journal of the Optical Society of America B

Lower- versus higher-order nonclassicalities for a coherent superposed quantum state

Deepak Deepak, Arpita Chatterjee

Published Sep 17, 2021• 2 citations

Abstract

A coherent state is defined conventionally in different ways such as a displaced vacuum state, an eigenket of an annihilation operator, or as an infinite dimensional Poissonian superposition of Fock states. In this work, we describe a superposition ( t a + r a † ) of field annihilation and creation operators acting on a continuous variable coherent state | α ⟩ and specify it by | ψ ⟩ . We analyze the lower- as well as higher-order nonclassical properties of | ψ ⟩ . The comparison is performed by using a set of nonclassicality witnesses (e.g., higher-order photon statistics, higher-order antibunching, higher-order sub-Poissonian statistics, higher-order squeezing, Agarwal–Tara parameter, Klyshko’s condition, and a relatively new concept, matrix of phase-space distribution). It is found that the higher-order criteria are much more efficient to detect the presence of nonclassicality as compared to lower-order conditions except squeezing, where the lower-order one is more competent than its higher-order counterpart.

DOI: 10.1364/josab.424140

Related papers

Lower‐ and Higher‐Order Nonclassical Properties of Photon Added and Subtracted Displaced Fock States

Priya Malpani, Nasir Alam, Kishore Thapliyal +3 more

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.

arXiv:1808.01458Annalen der PhysikJan 10, 201935 citations

A comparison between higher-order nonclassicalities of superposition engineered coherent and thermal states

Deepak Deepak, Arpita Chatterjee

We consider an experimentally obtainable superposition (SUP) operator, defined by using a generalized superposition of products of field annihilation (a) and creation (a†) operators of the type A = saa† + ta†a with s2 + t2 = 1. We apply this SUP operator on coherent and thermal quantum states, and the states thus produced are referred to as SUP-operated coherent state (SOCS) and SUP-operated thermal state (SOTS), respectively. In the present work, we report a comparative study between the higher-order nonclassical properties of SOCS and SOTS. The comparison is performed by using a set of nonclassicality witnesses (e.g., higher-order anti-bunching, higher-order sub-Poissonian photon statistics, higher-order squeezing, Agarwal–Tara parameter, Klyshko’s condition). The existence of higher-order nonclassicalities in SOCS and SOTS have been investigated for the first time. In view of possible experimental verification of the proposed scheme, we present exact calculations to reveal the effect of non-unit quantum efficiency of quantum detector on higher-order nonclassicalities.

arXiv:2204.06712Canadian Journal of PhysicsAug 2, 20214 citations

Non-classicalities exhibited by the superposition of Schrödinger’s cat state with the vacuum of the optical field

Karunesh Kumar Mishra, Dhiraj Yadav, Gaurav K. Shukla +1 more

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.

Physica ScriptaJan 26, 202112 citations

Higher-order nonclassical effects generated by multiple-photon annihilation-then-creation and creation-then-annihilation coherent states

袁洪春, 徐学翔, 肖进 +2 more

We explore two observable nonclassical properties of quantum states generated by repeatedly operating annihilationthen-creation(AC) and creation-then-annihilation(CA) on the coherent state, respectively, such as higher-order subPoissonian statistics and higher-order squeezing-enhanced effect. The corresponding analytical expressions are derived in detail depending on m. By numerically comparing those quantum properties, it is found that these states above have very different nonclassical properties and nonclassicality is exhibited more strongly after AC operation than after CA operation.

中国物理B：英文版Jan 1, 20160 citations

Four-photon nonlinear coherent states

O. Abbasi, Akbar Jafari

We have introduced the notion of ‘four-photon nonlinear coherent states’ (FPNCSs) as right eigenstates of the fourth power of the generalized annihilation operator A4. It has been shown that there are four possible sets of such states which all can be expressed as the deformed Schrödinger cat type states derived from the superposition of four nonlinear coherent states (NCSs) which are π/2 out of phase. The nonclassical properties of the FPNCSs would be studied for two well-known quantum systems, a Kerr-like medium and a trapped laser-driven ion far from the Lamb-Dicke regime. We have found that the depth or the domain of the nonclassical features of FPNCSs in terms of sub-Poissonian photon statistics, higher order squeezing as well as amplitude-squared squeezing are higher than the corresponding standard states. Specifically, the proposed states in this paper exhibit sub-Poissonian statistics over an extensive range of real amplitudes which is in contrast with the lower level of sub-Poissonian characteristics of four-photon standard coherent states. Also the depth or domain of the nonclassical features of the FPNCSs can be modified by changing the magnitude of the nonlinearity parameters. Analysis of the quasi-probability distributions like Glauber–Sudarshan P-function, Husimi Q-function and Wigner distribution function verifies the nonclassical nature of the presented states. Studying the cavity field evolution in the interaction of a single two-level atom with an even NCS in the framework of f-deformed Jaynes-Cummings model shows that such a system can potentially be considered as a possible source for generating the proposed states.

Journal of Modern OpticsJul 14, 20163 citations

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

Priya Malpani, Nasir Alam, Kishore Thapliyal +3 more

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.

arXiv:1907.03257Annalen der PhysikNov 20, 201910 citations