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Register a new userThe Wigner Function of Ground State and One-Dimensional Numerics
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In this paper, the ground state Wigner function of a many-body system is explored theoretically and numerically. First, an eigenvalue problem for Wigner function is derived based on the energy operator of the system. The validity of finding the ground state through solving this eigenvalue problem is obtained by building a correspondence between its solution and the solution of stationary Schrodinger equation. Then, a numerical method is designed for solving proposed eigenvalue problem in one dimensional case, which can be briefly described by i) a simplified model is derived based on a quantum hydrodynamic model [Z. Cai et al, J. Math. Chem., 2013] to reduce the dimension of the problem, ii) an imaginary time propagation method is designed for solving the model, and numerical techniques such as solution reconstruction are proposed for the feasibility of the method. Results of several numerical experiments verify our method, in which the potential application of the method for large scale system is demonstrated by examples with density functional theory.
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We present an experimental realisation of the direct scheme for measuring the Wigner function of a single quantized light mode. In this method, the Wigner function is determined as the expectation value of the photon number parity operator for the phase space displaced quantum state.
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Quantum engineering now allows to design and construct multi-qubit states in a range of physical systems. These states are typically quite complex in nature, with disparate, but relevant properties that include both single and multi-qubit coherences and even entanglement. All these properties can be assessed by reconstructing the density matrix of those states - but the large parameter space can mean physical insight of the nature of those states and their coherence can be hard to achieve. Here we explore how the Wigner function of a multipartite system and its visualization provides rich information on the nature of the state, not only at illustrative level but also at the quantitative level. We test our tools in a photonic architecture making use of the multiple degrees of freedom of two photons.
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