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

Chianca, Vito; Olsen, M. K.

doi:10.1103/physreva.84.043636

Cited by 28 publications

(48 citation statements)

References 27 publications

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“…We follow the approach to the Bose-Hubbard model [28,29] taken by Milburn et al [30], also generalizing this to three [31,32] and four wells [33]. All our systems are in a linear configuration with only the first well initially occupied.…”

Section: Physical Model and Hamiltoniansmentioning

confidence: 99%

Spreading of entanglement and steering along small Bose-Hubbard chains

Olsen

2015

Phys. Rev. A

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We investigate how entanglement spreads along small Bose-Hubbard chains, with only the first well initially occupied by a mesoscopic number of atoms, as the number of sites increases. For two-and three-well chains in the noninteracting case, we are able to obtain analytical solutions and show that the presence of entanglement depends on having a sub-Poissonian state of the atoms in the first well. In these cases, the correlations we calculate are completely periodic. Restoring the collisional interactions or moving to a four-well chain necessitates a numerical treatment, for which we use the fully quantum positive-P representation. We examine two different correlations and find that adding collisional interactions destroys the periodicity of the correlations and causes them to degrade with time. This happens well before there is a noticeable effect on the periodicity of the solutions for the number of atoms in each well.

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Section: Physical Model and Hamiltoniansmentioning

confidence: 99%

Spreading of entanglement and steering along small Bose-Hubbard chains

Olsen

2015

Phys. Rev. A

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“…As expected, we see that the average populations of wells 1 and 3 are identical. We also see that the oscillations are highly regular over the time investigated, with no sign of the damping of oscillations seen in other BoseHubbard systems [24,26]. While this will happen for higher collisional nonlinearities, these also degrade the entanglement.…”

Section: Resultsmentioning

confidence: 65%

“…In this article we will follow the approach taken by Milburn et al [24], generalizng this to three wells [25,26], and using the fully quantum positive-P phase space representation [27]. We consider this to be the most suitable approach here because the equations are exact, it allows for an easy representation of mesoscopic numbers of atoms, it can be used to calculate quantum correlations, and it can simulate different quantum initial states [28].…”

Section: Physical Model Hamiltonian and Equations Of Motionmentioning

confidence: 99%

Ultracold atomic mode splitter for the entanglement of separated atomic samples

Chianca

Olsen

2015

Phys. Rev. A

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We propose and analyze the use of a three-well Bose-Hubbard model for the creation of two spatially separated entangled atomic samples. Our three wells are in a linear configuration, with all atoms initially in the middle well, which gives some spatial separation of the two end wells. The evolution from the initial quantum state allows for the development of entanglement between the atomic modes in the two end wells. We show how the detected entanglement and the well occupations are time dependent. We propose a method for preserving the entanglement by turning off the different interactions when it reaches its first maximum. We analyze the system with both Fock and coherent initial states, showing that the violations of the chosen inequality exist only for initial Fock states and that the collisional nonlinearity degrades them. This system is a preliminary step towards producing entangled atomic samples that can be spatially separated using recently developed methods of potential manipulation and thus help close the locality loophole in tests of quantum mechanics.

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“…Due to the quartic nature of the interaction term, the evolution equation for the Wigner distribution will require truncation of thirdorder derivative terms. The impact of such truncation error is well understood in this context, with known signatures such as the inability of TWA to replicate revivals in population oscillations between modes [36]. We point out that we consider only the two-mode model in this instance so that truncation error can be monitored rigorously (via comparison to solution of the Schrödinger equation in a truncated Fock basis).…”

Section: Application To Bose-hubbard Modelmentioning

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

Cited by 28 publications

References 27 publications

Spreading of entanglement and steering along small Bose-Hubbard chains

Spreading of entanglement and steering along small Bose-Hubbard chains

Ultracold atomic mode splitter for the entanglement of separated atomic samples

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

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