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      Variational Truncated Wigner Approximation

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          Abstract

          In this paper we reconsider the notion of an optimal effective Hamiltonian for the semiclassical propagation of the Wigner distribution in phase space. An explicit expression for the optimal effective Hamiltonian is obtained in the short time limit by minimizing the Hilbert-Schmidt distance between the semiclassical approximation and the real state of the system. The method is illustrated for the quartic oscillator.

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          Bemerkung �ber die angen�herte G�ltigkeit der klassischen Mechanik innerhalb der Quantenmechanik

          P. Ehrenfest (1927)
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            Reconstruction of non-classical cavity field states with snapshots of their decoherence

            Samuel Deléglise, Serge Haroche, Jean-Michel Raimond … (2008)
            The state of a microscopic system encodes its complete quantum description, from which the probabilities of all measurement outcomes are inferred. Being a statistical concept, the state cannot be obtained from a single system realization. It can be reconstructed from an ensemble of copies, by performing measurements on different realizations. Reconstructing the state of a set of trapped particles shielded from their environment is an important step for the investigation of the quantum to classical boundary. While trapped atom state reconstructions have been achieved, it is challenging to perform similar experiments with trapped photons which require cavities storing light for very long times. Here, we report the complete reconstruction and pictorial representation of a variety of radiation states trapped in a cavity in which several photons survive long enough to be repeatedly measured. Information is extracted from the field by atoms crossing the cavity one by one. We exhibit a gallery of pictures featuring coherent states, Fock states with a definite photon number and Schrodinger cat states which are superpositions of coherent states with different phases. These states are equivalently represented by their density matrices in the photon-number basis or by their Wigner functions, which are distributions of the field complex amplitude. Quasi-classical coherent states have a Gaussian-shaped Wigner function while Fock and Schrodinger cat Wigner functions show oscillations and negativities revealing quantum interferences. Cavity damping induces decoherence which quickly washes out the Wigner functions oscillations. We observe this process and realize movies of decoherence by reconstructing snapshots of Schrodinger cat states at successive times.
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              Dynamical quantum noise in Bose-Einstein condensates

              R. Graham, D. F. Walls, M. J. Collett … (1998)
              We introduce the study of dynamical quantum noise in Bose-Einstein condensates through numerical simulation of stochastic partial differential equations obtained using phase space representations. We derive evolution equations for a single trapped condensate in both the positive-\(P\) and Wigner representations, and perform simulations to compare the predictions of the two methods. The positive-\(P\) approach is found to be highly susceptible to the stability problems that have been observed in other strongly nonlinear, weakly damped systems. Using the Wigner representation, we examine the evolution of several quantities of interest using from a variety of choices of initial state for the condensate, and compare results to those for single-mode models.
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                Author and article information

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                Publication date Created: 2013-12-09
                Publication date Updated: 2013-12-30
                Article
                DOI: 10.1103/PhysRevE.89.042107
                ArXiV ID: 1312.2354
                SO-VID: 119f383b-65a0-4ff6-abe3-aec4b61827e2
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                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Categories quant-ph

                ScienceOpen disciplines: Quantum physics & Field theory
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                ScienceOpen disciplines: Quantum physics & Field theory

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