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

Olsen, M. K.; Bradley, Ashton S.

doi:10.1016/j.optcom.2009.06.033

Cited by 84 publications

(101 citation statements)

References 49 publications

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“…The truncated Wigner equations are solved numerically by taking averages over a large number of stochastic trajectories, with initial conditions sampled probabilistically [12,19].…”

Section: Physical Model Hamiltonian and Equations Of Motionmentioning

confidence: 99%

Quantum phase-space analysis of population equilibration in multiwell ultracold atomic systems

Chianca

Olsen

2011

Phys. Rev. A

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We examine the medium time quantum dynamics and population equilibration of two, three and four-well Bose-Hubbard models using stochastic integration in the truncated Wigner phase-space representation. We find that all three systems will enter at least a temporary state of equilibrium, with the details depending on both the classical initial conditions and the initial quantum statistics.We find that classical integrability is not necessarily a good guide as to whether equilibration will occur. We construct an effective single-particle reduced density matrix for each of the systems, using the expectation values of operator moments, and use this to calculate an effective entropy.Knowing the expected maximum values of this entropy for each system, we are able to quantify the different approaches to equilibrium.

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“…The truncated Wigner equations are solved numerically by taking averages over a large number of stochastic trajectories, with initial conditions sampled probabilistically [12,19].…”

Section: Physical Model Hamiltonian and Equations Of Motionmentioning

confidence: 99%

Quantum phase-space analysis of population equilibration in multiwell ultracold atomic systems

Chianca

Olsen

2011

Phys. Rev. A

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“…In Refs. [25,26] Olsen et al demonstrated explicitly that sampling of W |n (α) indeed produced all moments |α| m W of the exact Wigner distribution up to O(1/n 2 ) relative to the leading order, implying that the contribution of all but the final oscillation in W |n (α) can be considered approximately negligible. In light of this, one could also regardW |n (α), Eq.…”

Section: Formal Derivationmentioning

confidence: 99%

Approximate particle number distribution from direct stochastic sampling of the Wigner function

2016

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We consider the Wigner quasi-probability distribution function of a single mode of an electromagnetic or matter-wave field to address the question of whether a direct stochastic sampling and binning of the absolute square of the complex field amplitude can yield a distribution functionPn that closely approximates the true particle number probability distribution Pn of the underlying quantum state. By providing an operational definition of the binned distributionPn in terms of the Wigner function, we explicitly calculate the overlap betweeñ Pn and Pn and hence quantify the statistical distance between the two distributions. We find that there is indeed a close quantitative correspondence betweenPn and Pn for a wide range of quantum states that have smooth and broad Wigner function relative to the scale of oscillations of the Wigner function for the relevant Fock state. However, we also find counterexamples, including states with high mode occupation, for whichPn does not closely approximate Pn.

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“…The latter can, for instance, represent coherent, thermal, squeezed or Fock states [43] and its time evolution is governed by classical trajectories evolving according to Eqs. (11).…”

Section: B the Initial Statementioning

confidence: 99%

Elastic and inelastic transmission in guided atom lasers: A truncated Wigner approach

Dujardin

Argüelles²,

Schlagheck

2015

Phys. Rev. A

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We study the transport properties of an ultracold gas of Bose-Einstein condensate that is coupled from a magnetic trap into a one-dimensional waveguide. Our theoretical approach to tackle this problem is based on the truncated Wigner method for which we assume the system to consist of two semi-infinite non-interacting leads and a finite interacting scattering region with two constrictions modelling an atomic quantum dot. The transmission is computed in the steady-state regime and we find a good agreement between truncated Wigner and Matrix-Product State calculations. We also identify clear signatures of inelastic resonant scattering by analyzing the distribution of energy in the transmitted atomic matter wave beam.

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

Cited by 84 publications

References 49 publications

Quantum phase-space analysis of population equilibration in multiwell ultracold atomic systems

Quantum phase-space analysis of population equilibration in multiwell ultracold atomic systems

Approximate particle number distribution from direct stochastic sampling of the Wigner function

Elastic and inelastic transmission in guided atom lasers: A truncated Wigner approach

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