Detecting quantum states with a positive Wigner function beyond mixtures of Gaussian states

We propose a criterion giving a sufficient condition for quantum states of a harmonic oscillator not to be expressible as a convex mixture of Gaussian states. This nontrivial property is inherent to, e.g., a single-photon state and the criterion thus allows one to reveal a signature of the state even in quantum states with a positive Wigner function. The criterion relies on directly measurable photon number probabilities and enables detection of this manifestation of a single-photon state in quantum states produced by solid-state single-photon sources in a weak coupling regime.     

Wigner function of the thermo number states

Based on thermo field dynamics (TFD) and using the thermo Wigner operator in the thermo entangled state representation we derive the Wigner function of number states at finite temperature (named thermo number states). The figure of Wigner function shows that its shape gets smoothed as the temperature rises, implying that the quantum noise becomes larger.     

The Wigner function in the relativistic quantum mechanics

A detailed study is presented of the relativistic Wigner function for a quantum spinless particle evolving in time according to the Salpeter equation.     

从离散Wigner函数的角度探讨量子相干性度量

量子相干性是量子信息处理的基本要素,在量子计算中扮演着重要的角色.为了便于讨论量子相干性在量子计算中的作用,本文从离散Wigner函数角度对量子相干性进行了探讨.首先对奇素数维量子系统的离散Wigner函数进行了分析,分离出表征相干性的部分,提出了一种可能的基于离散Wigner函数的量子相干性度量方法,并对其进行了量子相干性度量规范的分析;同时也比较了该度量与l_1范数相干性度量之间的关系.重要的是,这种度量方法能够明确给出量子相干性程度与衡量量子态量子计算加速能力的负性和之间不等式关系,由此可以解析地解释量子相干性仅是量子计算加速的必要条件.     

Quantum phase distribution and the number—phase Wigner function of the generalized squeezed vacuum states associated with solvable quantum systems

The quantum phase properties of the generalized squeezed vacuum states associated with solvable quantum systems are studied by using the Pegg-Barnett formalism.Then,two nonclassical features,i.e.,squeezing in the number and phase operators,as well as the number-phase Wigner function of the generalized squeezed states are investigated.Due to some actual physical situations,the present approach is applied to two classes of generalized squeezed states:solvable quantum systems with discrete spectra and nonlinear squeezed states with particular nonlinear functions.Finally,the time evolution of the nonclassical properties of the considered systems has been numerically investigated.     

Numerical representation of quantum states in the positive-P and Wigner representations

Numerical stochastic integration is a powerful tool for the investigation of quantum dynamics in interacting many-body systems. As with all numerical integration of differential equations, the initial conditions of the system being investigated must be specified. With application to quantum optics in mind, we show how various commonly considered quantum states can be numerically simulated by the use of widely available Gaussian and uniform random number generators. We note that the same methods can also be applied to computational studies of Bose–Einstein condensates, and give some examples of how this can be done.     

A quasi-classical formulation of the Wigner function approach to quantum ballistic transport

The time evolution of Wigner's function is shown to be a linear superposition of classical distributions unfolded by a family of classical hamiltonians.     

量子态的非相干光时域测量

提出了利用非相干光实现对量子态的时域高分辨率测量的新方法.以测量Autler-Townes效应为例,通过对信号解析表达式的详细讨论,阐述了利用这种方法测量量子态的物理过程,揭示出被测量的演化规律及测量过程对量子态的影响.研究结果表明利用这种方法既可以有效地、高分辨地测量很小的量子态能级间距和很大的原子能级间距,同时又可以测量相干量子态的横向弛豫速率.通过对时域和频域测量方法的比较表明利用非相干光对量子态的时域测量可以全面揭示量子态演化信息. 关键词： 非相干光 量子态测量 Autler-Townes 效应     

On constructing the wave function of a quantum particle from its Wigner phase-space distribution function

For a Schrödinger wave function, the part of the phase that depends only on time disappears in the construction of the corresponding Wigner phase-space (quasi)distribution function. Despite this, it can be recovered from the Wigner function using the quantum Hamilton–Jacobi equation. This is demonstrated for three simple cases.     

Wigner distribution function expression for the tunnelling time in quantum resonant structures

A definition of the tunnelling time in terms of the Wigner distribution function is proposed, which is shown to be identical to the expression for the tunnelling time derived in the group velocity approach.     

Wigner function study of a double quantum barrier resonant tunnelling diode

Resonant tunnelling structures are receiving attention as a testbed for theoretical approaches to quantum transport. We present a Wigner function study of a double quantum barrier resonant tunnelling device formed by layers of AlGaAs in GaAs. Our study deals with the influence of the boundary conditions on the initial distribution as well as on the time-evolution of the system. We use a Gaussian wave packet to study the numerical effects of the boundaries. We attempt to solve the system in both the time-evolution and steady-state cases, including self-consistency in the potential.     

Wigner function and Bell’s inequalities for even and odd coherent states

The Wigner function and the symplectic tomogram of an entangled quantum state, which is a superposition of the photon’s coherent states (even and odd coherent states), is studied. Photon statistics and violation of Bell’s inequality for the photon state are discussed.