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arXiv:1208.5123 · Journal of Physics B Atomic Molecular and Optical Physics

Nonclassical properties of states engineered by superpositions of quantum operations on classical states

Arpita Chatterjee, Himadri Shekhar Dhar, Rupamanjari Ghosh

Published Sep 10, 2012• 20 citations
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Abstract

We consider an experimentally realizable scheme for manipulating quantum states using a general superposition of products of field annihilation ( ) and creation ( ) operators of the type ( ), with s 2 + t 2 = 1. Such an operation, when applied on states with classical features, is shown to introduce strong nonclassicality. We quantify the generated degree of nonclassicality by the negative volume of Wigner distribution in the phase space and investigate two other observable nonclassical features, sub-Poissonian statistics and squeezing. We find that the operation introduces negativity in the Wigner distribution of an input coherent state and changes the Gaussianity of an input thermal state. This provides the possibility of engineering quantum states with specific nonclassical features.

DOI
10.1088/0953-4075/45/20/205501

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We consider an experimentally realizable scheme for manipulating quantum states using a general superposition of products of field annihilation ( ) and creation ( ) operators of the type ( ), with s 2 + t 2 = 1. Such an operation, when applied on states with classical features, is shown to introduce strong nonclassicality. We quantify the generated degree of nonclassicality by the negative volume of Wigner distribution in the phase space and investigate two other observable nonclassical features, sub-Poissonian statistics and squeezing. We find that the operation introduces negativity in the Wigner distribution of an input coherent state and changes the Gaussianity of an input thermal state. This provides the possibility of engineering quantum states with specific nonclassical features.
Abstract The nonclassicality is the prerequisite for quantum states to be applied into quantum information, especially for quantum metrology. Here we theoretically investigate the non-classical properties of the non-Gaussian state generated by repeatedly operating a number-conserving generalized superposition of products (GSP), i.e., ( s 1 aa † + t 1 a † a ) m with s 1 2 + t 1 2 = 1 , on the squeezed thermal state (STS), in terms of second-order correlation function, Mandel’s Q parameter, quadrature squeezing and Wigner function (WF). It is shown that, compared to the cases of the STS, the GSP-STS with the high-order GSP operations ( m > 1) at the small-squeezing levels can be beneficial to the existence of the photon-antibunching effect, the sub-Poissonian distribution and the partial negativity of the WF, apart from the quadrature squeezing. In addition, for the case of m = 1, we also compare with the non-classical properties of several different non-Gaussian resources, involving the photon-subtracted-then-added (PSTA) STS, the GSP-STS and the photon-added-then-subtracted (PATS) STS. It is found that the PSTA-STS with respect to the sub-Poissonian distribution and the partial negativity of the WF has a better performance than others. Significantly, the generated GSP-STS has an obvious advantage of showing the photon-antibunching effects, compared to the PSTA-STS and the PATS-STS, which means that our scheme may have an excellent guidance for the practical implementations in quantum information.
Abstract Two new photon‐modulated states are introduced by operating a more general coherent superposition on two classical states (coherent and thermal) and their nonclassicality caused by the operation is investigated via examining the squeezing, sub‐Poissonian statistics, nonclassical depth, and negativity of Wigner distribution. Their density‐operator and Wigner‐distribution evolutions in the thermal channel are also explored. It is found that the high‐order operation has better performance in creating nonclassicality for certain ratios r and more robustness against decoherence of the two photon‐modulated states for thermal noise. For convenience, a new three‐variable special polynomial and its generating function are introduced via the normal ordering of operators.
Detecting nonclassical properties that do not allow classical interpretation of photoelectric counting events is one of the crucial themes in quantum optics. Observation of individual nonclassical effects for a single-mode field, however, has been so far practically confined to sub-Poissonian statistics and quadrature squeezing. We show that a photon-added classical (coherent or thermal) state exhibits generalized nonclassical features in all orders of creation and annihilation operators, thereby becoming a promising candidate for studying higher-order nonclassical effects. Our analysis demonstrates the robustness of these effects against nonideal experimental conditions.
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.
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.