Zero-point energy of ultracold atoms

TL;DR

This paper investigates the divergent zero-point energy in ultracold atomic gases, presents regularization methods, and discusses their impact on the equations of state, with implications for understanding quantum fluctuations in ultracold systems.

Contribution

It introduces three regularization approaches for zero-point energy divergences and analyzes their effects on the equations of state in ultracold atomic gases, including fermionic superfluids.

Findings

Zero-point energy divergences can be regularized using dimensional, momentum-cutoff, and convergence-factor methods.

Regularized zero-point fluctuations lead to finite corrections in the equation of state for interacting Bose gases.

The results agree with experimental data, confirming the role of quantum fluctuations in ultracold atom thermodynamics.

Abstract

We analyze the divergent zero-point energy of a dilute and ultracold gas of atoms in D spatial dimensions. For bosonic atoms we explicitly show how to regularize this divergent contribution, which appears in the Gaussian fluctuations of the functional integration, by using three different regularization approaches: dimensional regularization, momentum-cutoff regularization and convergence-factor regularization. In the case of the ideal Bose gas the divergent zero-point fluctuations are completely removed, while in the case of the interacting Bose gas these zero-point fluctuations give rise to a finite correction to the equation of state. The final convergent equation of state is independent of the regularization procedure but depends on the dimensionality of the system and the two-dimensional case is highly nontrivial. We also discuss very recent theoretical results on the divergent zero-point energy of the D-dimensional superfluid Fermi gas in the BCS-BEC crossover. In this case the zero-point energy is due to both fermionic single-particle excitations and bosonic collective excitations, and its regularization gives remarkable analytical results in the BEC regime of composite bosons. We compare the beyond-mean-field equations of state of both bosons and fermions with relevant experimental data on dilute and ultracold atoms quantitatively confirming the contribution of zero-point-energy quantum fluctuations to the thermodynamics of ultracold atoms at very low temperatures.