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

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 $Q_M$ 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.     

Generalized Photon Added and Subtracted f-Deformed Displaced Fock States

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.     

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

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.     

Higher-Order Nonclassical Properties of a Shifted Symmetric Cat State and a One-Dimensional Continuous Superposition of Coherent States

Role of quantum interference in the origin of higher-order nonclassical characteristics of radiation field has been probed vis-à-vis a discrete and a continuous superposition of coherent states. Specifically, the possibilities of observing higher-order nonclassical properties (e.g., higher-order antibunching (HOA), higher-order sub-Poissonian photon statistics (HOSPS), higher-order squeezing (HOS) of Hong-Mandel type and Hillery type) have been investigated using a shifted symmetric cat state that reduces to Yurke-Stoler, even and odd coherent states at various limits. This shifted symmetric cat state which can be viewed as a discrete superposition of coherent states is found to show HOA and HOSPS. Similarly, higher-order nonclassical properties of a one-dimensional continuous superposition of coherent states is also studied here. The investigation has revealed the existence of HOS and HOSPS in the one-dimensional continuous superposition of coherent states studied here. Effect of non-Gaussianity inducing operations (e.g., photon addition and addition followed by subtraction) on these superposition states have also been investigated. Finally, some comparisons have been made between the higher-order nonclassical properties of discrete and continuous superposition of coherent states.     

The Wigner function and phase properties of superposition of two coherent states with the vacuum state

This paper discusses some statistical properties of the superposition of two coherent states with a vacuum state, such as sub-Poissonian photon statistics and negativity of the Wigner function. Phase probability distribution and phase variance are calculated. Special cases of the constructed superposition states are presented. The results show that depending on the vacuum state coefficient γ and the coherent state coefficient α, it can generate a variety of nonclassical states.     

Enhancement of Non-Gaussianity and Nonclassicality of Photon-Added Displaced Fock State: A Quantitative Approach

Non-Gaussian and nonclassical states and processes are already found to be important resources for performing various tasks related to quantum gravity and quantum information processing. Considering these facts, a quantitative analysis of the nonclassical and non-Gaussian features is performed here for photon added displaced Fock state, as a test case, using a set of measures, namely entanglement potential, Wigner–Yanese skew information, Wigner logarithmic negativity, and relative entropy of non-Gaussianity. It is observed that Fock parameter always increases the amount of nonclassicality and non-Gaussianity, while photon addition is effective only for small values of the displacement parameter. Further, the nonclassical and non-Gaussian effects decrease initially with an increase in the displacement parameter before increasing for the large displacement to saturate to the corresponding Fock state (equivalently displaced Fock state) value. Finally, dynamics of the Wigner function under the effect of photon loss channel is used to show that only highly efficient detectors are able to detect Wigner negativity.     

Qudit-type entanglement of continuous variables via weak cross-Kerr non linearity

We propose a protocol for creating arbitrary qudit state (including entangled states) with arbitrary dimensionality in continuous variable system using weak cross-Kerr nonlinearity, linear beamsplitters, detectors not resolving photon numbers, and sources of coherent states. The equation for unique determination of the used coherent states amplitudes is found. The protocol is applicable for creating entangled states at distances of 100 km using cross-Kerr nonlinearity χ ≥ χ _min ≃ 0.01 and optical fiber quantum channel.     

叠加激发双模压缩真空态的量子统计特性(英文)

从激发双模压缩真空态a^+mb^+m|ξ>出发构造了叠加态|Ψ>,研究了|Ψ>的量子统计特性.结果表明:在一定的条件下,随着相位差的变化,叠加态|Ψ>的平均光子数出现类似于Rabi振荡的崩塌与复原现象,而且与单个激发双模压缩真空态a^+mb^+m|ξ>相比,在叠加态|Ψ>中光场的相位压缩和亚泊松光子统计特性都得到了加强.     

Model basis states for photons and "empty waves"

From the perspective of physical realism (PR), a photon is a localized entity that carries energy and momentum, and which is surrounded by a wave packet (anempty wave) that is devoid of observable energy or momentum. In creating quantized PR basis states for a photon wave packet, three requirements must be met:(1) The basis states must each carry the frequency of the wave;(2) They must closely resemble the photon, so that e.g. they scatter in the same manner from an optical mirror;(3) They must have infinitesimal energy, linear momentum, and angular momentum. An essentially zero-energy "empty wave" quantum-a "zeron"-is defined which meets these requirements. It is created as an asymmetric single-particle (or single-antiparticle) excitation of the vacuum state, with the "particle" (or "antiparticle") and its associated "hole" (or "antihole") forming a rotational bound state. The photon is reproduced as a symmetric particle-antiparticle excitation of the vacuum state, with the "particle" and "antiparticle" also forming a rotational bound state. The relativistic transformation problem is discussed. A key point in this development is the deduction of the correct equation of motion for a "hole" state in an external electrostatic field.     

Quantum statistical properties of photon-added spin coherent states

The photon-added spin coherent state as a new kind of coherent state has been defined by iterated actions of the proper raising operator on the ordinary spin coherent state. In this paper, the quantum statistical properties of photon-added spin coherent states such as photon number distribution, second-order correlation function and Wigner function are studied. It is found that the Wigner function shows the negativity in some regions and the second-order correlation function is less than unity. Therefore, the photon-added spin coherent state is a nonclassical state.     

Multiple-Photon-Added and -Subtracted Two-Mode Binomial States:Nonclassicality and Entanglement *

We theoretically analyze the nonclassicality and entanglement of two new non-Gaussian entangled states generated by applying multiple-photon addition and subtraction to a two-mode binomial state. The nonclassical properties are investigated in terms of the partial negativity of the Wigner functions, whose results show that their nonclassicality can be enhanced via one-mode even-number photon operations and two-mode symmetrical operations for the initial two-mode binomial state. We also find that there exists some enhancement in the entanglement properties in certain parameter ranges via one-mode photon-addition and two-mode symmetrical operations.     

Separability and Entanglement of the Qudit X-State with j = 3/2

We study the qudit state with spin j = 3/2 and the density matrix of the form corresponding to the X state of two qubits and consider the entanglement and separability properties. We use the qubit portrait of qudit states to obtain the entropic inequalities for the entangled state of a single qudit. We present the tomographic-probability representation of the qudit X-state and obtain the Shannon and q entropic characteristics in explicit forms.     

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

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.     

多光子偏振态与单光子高维空间态之间的相互变换及其应用

基于一种特殊的控制非门,实现多光子偏振态与单光子空间高维态之间的相互变换,使得对多光子偏振态的操作可以通过对单光子的操作来完成,由此可以实现任意多光子正定算符值测量和多光子任意幺正操作.这种实现方式是以一定概率完成的,但其效率要优于此前的方案,在目前的实验条件下是可行的. 关键词： 单光子空间态 特殊控制非门 线性光学多端口干涉仪     

Photon Excitations Excitated the Sqeezing Properties of the Excited Entangled Coherent States

In our previous paper, we have introduced a new kind of continuous-variable-type entangled states, called double-mode excited entangled coherent states. In this paper, we study sum squeezing properties of such excited entangled coherent states. We focus on discussing the influence of photon excitations on sum squeezing properties. It is found that the photon excitations seriously affected sqeezing properties of the excited entangled coherent states. With increasing the number of the photon excitations m, the higher-order terms move away from its initial state |ψ ₀〉 and the degrees of sum squeezing are increasing. In this sense, it implies that the photon excitations excitated the sum sqeezing properties of the double-mode excited entangled coherent states.     

Superposition of two coherent states π out of phase with average photon number as relative phase

This paper discusses nonclassical features of the superposition of two coherent states π out of phase with each other and parameterized solely by amplitude α, that is, when the relative phase has a relationship with average photon number ∣α∣². In particular, it discusses oscillatory and sub-Poissonian photon statistics, degree of quadrature squeezing, and quasiprobability distribution functions. We examine that some nonclassical properties of these states are different from those of the even and odd coherent states.     

Excited Two-Mode Generalized Squeezed Vacuum State as a Squeezed Two-Variable Hermite Polynomial Excitation State

A new class of excited two-mode generalized squeezed vacuum states denoted by |r,s,m,n〉 are presented, which are obtained by repeatedly applying creation operators a ^† and b ^† on the two-mode generalized squeezed vacuum state. We find that it is just regarded as a generalized squeezed two-variable Hermite polynomial excitation on the vacuum state and its normalization constant is just a Jacobi polynomial. Their statistical properties are investigated such as squeezing properties, photon number distribution and the violations of Cauchy-Schwartz inequality. Especially, the Wigner function for |r,s,m,n〉 depending on the excitation photon numbers is discussed graphically.     

虚光场对玻色-爱因斯坦凝聚体与二项式光场相互作用系统中光场压缩性质的影响

在二项式光场和二能级原子玻色-爱因斯坦凝聚体相互作用系统中, 应用全量子理论, 分别在旋波近似和非旋波近似下, 研究了光场的压缩特性以及原子本征频率、原子-光场的耦合系数、光场参数以及虚光场对系统光场压缩特性的影响. 研究表明, 光场的两个正交分量均被周期性压缩, 光场压缩持续时间与原子的本征频率有关, 压缩深度与二项式光场概率分布参数和虚光场有关, 光场与原子的耦合系数决定了光场涨落的崩塌-回复频率. 关键词： 量子光学 玻色-爱因斯坦凝聚 虚光场 光场压缩     

Calculation of Photon Path Distribution Based on Photon Behavior Analysis in a Scattering Medium

We calculated the photon path distribution (PPD) in a scattering medium based on a theoretical analysis, which utilizes the relationship between the photon intensity and photon pathlength. This PPD is defined by local photon pathlengths for photons having total pathlengths of l between the light input points and detection points. The PPD of photons that consist of the impulse response at time t (= l/c) was calculated for a 2-D model. Precise analysis of photon migration in the scattering medium is essential in order to carry out image reconstruction of diffuse optical tomography (DOT). We show the PPD at time t (the total pathlength l = ct) and demonstrate its effectiveness. Our method for describing photon migration is intuitive and allows finding weight functions in DOT.