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arXiv:cond-mat/0408469

High Temperature Universal Properties of Atomic Gases Near Feshbach Resonance with Non-Zero Orbital Angular Momentum

Tin-Lun Ho, Neldeltcho Zahariev

Published Aug 21, 2004• 0 citations
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Abstract

We show that the high temperature behavior of atomic gases near Feshbach Resonance with non-zero orbital angular momentum $(\ell >0)$ belong to a universality class different from that of s-wave resonances. The universal interaction energy is $2(2\ell +1)$ times larger than that of the s-wave when approaching the resonance from the atomic side, but is essentially zero on the molecular side; contrary to s-wave resonances where interaction energies on both sides are the same except for a sign change. The measurement of these universality properties should be feasible in current experiments.

DOI
10.48550/arxiv.cond-mat/0408469

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We show that the high temperature behavior of atomic gases near Feshbach Resonance with non-zero orbital angular momentum (ℓ>0)(\ell >0)(ℓ>0) belong to a universality class different from that of s-wave resonances. The universal interaction energy is 2(2ℓ+1)2(2\ell +1)2(2ℓ+1) times larger than that of the s-wave when approaching the resonance from the atomic side, but is essentially zero on the molecular side; contrary to s-wave resonances where interaction energies on both sides are the same except for a sign change. The measurement of these universality properties should be feasible in current experiments.
It is well-known that cold atoms near sss-wave Feshbach resonances have universal properties that are insensitive to the short-range details of the interaction. What is less known is that atoms near higher partial-wave Feshbach resonances also have remarkable universal properties. We illustrate this with a single atom interacting resonantly with two fixed static centers. At a Feshbach resonance point with orbital angular momentum $L\ensuremath{\ge}1$, we find 2L+12L+12L+1 shallow bound states whose energies behave like 1/R2L+11/{R}^{2L+1}1/R2L+1 when the distance RRR between the two centers is large. We then compute corrections to the binding energies due to other parameters in the effective range expansions. For completeness we also compute the binding energies near sss-wave Feshbach resonances, taking into account the corrections. Afterwards we turn to the bound states at large but finite scattering volumes. For ppp-wave and higher partial-wave resonances we derive a simple formula for the energies in terms of a parameter called ``proximity parameter.'' These results are applicable to a free atom interacting resonantly with two atoms that are localized to two lattice sites of an optical lattice, and to one light atom interacting with two heavy ones in free space. Modifications of the low energy physics due to the long range van der Waals potential are also discussed.
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We consider a two-component Fermi gas interacting via a Feshbach molecular state. It is shown that only for broad resonances where the Feshbach state is strongly coupled to the free particle continuum can the gas be expected to enter a universal state in the unitarity limit on the atomic side of the resonance where there are no molecules present. The universal state is distinct from the molecular gas state on the other side of the resonance. We furthermore calculate the energy of the gas for this universal state and our results are related to current experiments on 6Li^{6}\mathrm{Li}6Li and 40K^{40}\mathrm{K}40K.
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We analyze the evolution of superfluidity for nonzero orbital angular momentum channels from the Bardeen-Cooper-Schrieffer (BCS) to the Bose-Einstein condensation (BEC) limit in three dimensions. First, we analyze the low-energy scattering properties of finite range interactions for all possible angular momentum channels. Second, we discuss ground-state (T=0)(T=0)(T=0) superfluid properties including the order parameter, chemical potential, quasiparticle excitation spectrum, momentum distribution, atomic compressibility, ground-state energy, and low-energy collective excitations. We show that a quantum phase transition occurs for nonzero angular momentum pairing, unlike the sss-wave case where the BCS to BEC evolution is just a crossover. Third, we present a Gaussian fluctuation theory near the critical temperature (T=Tc)(T={T}_{\mathrm{c}})(T=Tc​), and we analyze the number of bound, scattering, and unbound fermions as well as the chemical potential. Finally, we derive the time-dependent Ginzburg-Landau functional near Tc{T}_{\mathrm{c}}Tc​, and compare the Ginzburg-Landau coherence length with the zero-temperature average Cooper pair size.