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This paper advances quantum simulation techniques by applying a variational reduced density matrix method to one-dimensional ultracold bosonic systems, offering an accurate alternative to mean-field approaches like the Gross-Pitaevskii equation. The study effectively bridges the gap between few-body analytic solutions and many-body limits across varying interaction strengths, providing precise calculations for ground-state energies and correlation functions in trapped quantum gases.
Reduced density matrix approach to one-dimensional ultracold bosonic systems
arXiv:2503.15811v3 Announce Type: replace-cross Abstract: The variational determination of the two-boson reduced density matrix is described for a one-dimensional system of $N$ (where $N$ ranges from $2$ to $10^4$) harmonically trapped bosons interacting via contact interaction. The ground-state energies are calculated, and compared to existing methods in the field, including the analytic case (for $N=2)$ and mean-field approaches such as the one-dimensional Gross-Pitaevskii equation and its variations. Structural properties including the density and correlation functions are also derived, including the behaviour of the correlation function when boson coordinates coincide, collectively demonstrating the capacity of the reduced density matrix method to accurately calculate ground-state properties of bosonic systems comprising few to many bosons, including the cross-over region between these extremes, across a large range of interaction strengths.
Abstract:The variational determination of the two-boson reduced density matrix is described for a one-dimensional system of $N$ (where $N$ ranges from $2$ to $10^4$) harmonically trapped bosons interacting via contact interaction. The ground-state energies are calculated, and compared to existing methods in the field, including the analytic case (for $N=2)$ and mean-field approaches such as the one-dimensional Gross-Pitaevskii equation and its variations. Structural properties including the density and correlation functions are also derived, including the behaviour of the correlation function when boson coordinates coincide, collectively demonstrating the capacity of the reduced density matrix method to accurately calculate ground-state properties of bosonic systems comprising few to many bosons, including the cross-over region between these extremes, across a large range of interaction strengths.
Quantum Gases (cond-mat.quant-gas); Quantum Physics (quant-ph)
arXiv:2503.15811 [cond-mat.quant-gas]
(or arXiv:2503.15811v3 [cond-mat.quant-gas] for this version)
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