Polymer Bose--Einstein Condensates

TL;DR

This paper investigates how polymer quantization from loop quantum gravity affects Bose--Einstein condensates in a harmonic trap, revealing a shift in critical temperature and setting bounds on the polymer length scale.

Contribution

It introduces a semiclassical analysis of polymer Bose--Einstein condensates and quantifies the impact of polymer length on the condensation temperature.

Findings

Critical temperature shifts due to polymer effects.

Bound on polymer length scale up to ~10^{-16} m^2.

Potential experimental methods to detect polymer quantum effects.

Abstract

In this work we analyze a non--interacting one dimensional polymer Bose--Einstein condensate in an harmonic trap within the semiclassical approximation. We use an effective Hamiltonian coming from the polymer quantization that arises in loop quantum gravity. We calculate the number of particles in order to obtain the critical temperature. The Bose--Einstein functions are replaced by series, whose high order terms are related to powers of the polymer length. It is shown that the condensation temperature presents a shift respect to the standard case, for small values of the polymer scale. In typical experimental conditions, it is possible to establish a bound for $\lambda^{2}$ up to $ \lesssim 10 ^{-16}$m$^2$. To improve this bound we should decrease the frequency of the trap and also decrease the number of particles.