Hybrid Sampling Method for BEC Fluctuations*

We demonstrate the advantages of a new hybrid sampling method for solving the problem of ensemble BEC fluctuations for the cases of bosons in a harmonic trap (both isotropic and elliptical) and an infinite well both for 1D and 3D geometries.

We combine the field's workhorse - the classical fields approximation (CF) - with our new method - Fock state sampling (FSS) - and we obtain an extremely robust method without the problems of CF, i.e. without the "cutoff problem" (UV divergency). The method maintains its general applicability to many different systems and allows us to study a wide range of properties, not only BEC fluctuations.

FSS was first demonstrated in [1] where we compare experimental data (first experimental measurement of BEC fluctuations) with our theoretical predictions. Since then, FSS was applied for many different systems and geometries [2], providing us with access to both canonical and microcanonical ensembles for the study of BEC statistics. Our new hybrid sampling method retains this ability to study different ensembles and geometries.

References

[1] M. B. Christensen, T. Vibel, A. J. Hilliard, M. B. Kruk, K. Pawłowski, D. Hryniuk, K. Rzążewski, M. A. Kristensen, J. J. Arlt; “Observation of Microcanonical Atom Number Fluctuations in a Bose-Einstein Condensate”; Phys. Rev. Lett. 126, 153601, 2021

[2] M. B. Kruk, D. Hryniuk, M. Kristensen, T. Vibel, K. Pawłowski, J. Arlt, K. Rzążewski, “Microcanonical and Canonical Fluctuations in atomic Bose-Einstein Condensates -- Fock state sampling approach”, SciPost Phys. 14, 036 (2023)