Zero-point energy of ultracold atoms

Year: 2016

Authors: Salasnich L., Toigo F.

Autors Affiliation: Dipartimento di Fisica e Astronomia ‘‘Galileo Galilei’’ and CNISM, Università di Padova, via Marzolo 8, 35131 Padova, Italy; CNR-INO, via Nello Carrara, 1 – 50019 Sesto Fiorentino, Italy

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.


Volume: 640      Pages from: 1  to: 29

KeyWords: quantum field theory; bose-einstein condensation;
DOI: 10.1016/j.physrep.2016.06.003

Citations: 47
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