Zero-point energy of ultracold atoms

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• 作者：Luca Salasnich^a ; ^b ; ^{luca.salasnich@unipd.it" class="auth_mail" title="E-mail the corresponding author} ; Flavio Toigo^a
• 刊名：Physics Reports
• 出版年：2016
• 出版时间：14 June 2016
• 年：2016
• 卷：640
• 期：Complete
• 页码：1-29
• 全文大小：831 K

文摘

We analyze the divergent zero-point energy of a dilute and ultracold gas of atoms in D$D$ 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$D$-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.