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中国物理B：英文版

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, 熊超, 朱锡芳

Published Jan 1, 2016• 0 citations
OpenAlex

Abstract

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.

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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.
We study the nonclassical properties of arbitrary number photon creation-then-annihilation operation(CA) and annihilation-then-creation operation(AC) to the coherent states,and give the analytical expression.Because of the noncoummutativity of between annihilation operator and the creation operator,the states generated by AC operation and CA operation have different nonclassical properties.We firstly derive the analytical expressions of normalization factor for these states,and then study the statistics characteristics by some nonclassical properties,such as the Mandel Q parameters,the photon number distribution and the Wigner function.It is shown that these states have a very distinct nonclassical properties,and the nonclassical state generated by AC operation can present more clear nonclassicality than those generated by the CA operation.
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.
We investigate the nonclassical properties of arbitrary number photon annihilation-then-creation operation (AC) and creation-then-annihilation operation (CA) to the thermal state (TS), whose normalization factors are related to the polylogarithm function. Then we compare their quantum characters, such as photon number distribution, average photon number, Mandel Q -parameter, purity and the Wigner function. Because of the noncommutativity between the annihilation operator and the creation operator, the ACTS and the CATS have different nonclassical properties. It is found that nonclassical properties are exhibited more strongly after AC than after CA. In addition we also examine their non-Gaussianity. The result shows that the ACTS can present a slightly bigger non-Gaussianity than the CATS.
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.