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arXiv:physics/0501137

Destroying the superfluid state of fermionic atoms by the magnetic field in Feshbach resonance experiments

G. M. Genkin

Published Jan 26, 2005• 0 citations
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Abstract

We show that the superfluid state (SF) of fermionic atoms exist only for the magnetic fields lesser than the critical magnetic field. This critical magnetic field is determined by the equality of the Zeeman energy splitting for atoms with different spin projections to the energy gap of fermionic atoms without a magnetic field. For magnetic fields usually using in Feshbach resonance experiments a SF state is lost because these fields are much more than the critical field. We show that the transition temperature $ T_c $ of the SF state decreases as the magnetic field increases.

DOI
10.48550/arxiv.physics/0501137

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We show that the superfluid state (SF) of fermionic atoms exist only for the magnetic fields lesser than the critical magnetic field. This critical magnetic field is determined by the equality of the Zeeman energy splitting for atoms with different spin projections to the energy gap of fermionic atoms without a magnetic field. For magnetic fields usually using in Feshbach resonance experiments a SF state is lost because these fields are much more than the critical field. We show that the transition temperature TcT_cTc​ of the SF state decreases as the magnetic field increases.
We derived the energy gap of a breached pairing superfluidity phase of fermionic atoms in an external magnetic field in Feshbach resonance experiments which is determined by the magnetic - field detuning from the Feshbach resonance. We show that a BCS superfluid state exists only for the magnetic - field detuning smaller than one critical, and this critical magnetic - field detuning is determined by the equality of the Zeeman energy splitting for the magnetic - field detuning to the energy gap $ Δ_0 $.
Abstract We discuss the possible signatures of superfluidity induced by the Feshbach resonance in the ultracold gas of fermion atoms. Optically or magnetically trapped atoms such as 6Li or 40K are used in two hyperfine states where part of them is converted into the diatomic molecules. These fermion and boson entities get coupled in a presence of the external magnetic field. Eventually, at critical Tc, they simultaneously undergo transition to the superfluid state. Approaching this transition from above there appear various signatures manifesting a gradually emerging order parameter, but yet the long range coherence is not established due to the strong quantum fluctuations. Fermion atoms are characterized by the gapped excitation spectrum (pseudogap) up to temperature Tp (larger than Tc) while boson molecules exhibit collective features such as first sound showing up above a certain critical momentum q.crit (T) Upon lowering temperature to Tc this critical value shifts to zero and hence there appears the Goldstone mode signaling the symmetry broken superfluid state. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
After the experimental realization of Bose-Einstein condensation in dilute gases of alkali atoms, experimentalists started to trap the fermionic isotopes. The degenerate state for fermions was reported in 1999. The main objective of these experiments is to obtain superfluidity of fermionic gases. When there are attractive interactions between the fermions, the Fermi sea becomes unstable with respect to the formation of atomic Cooper pairs and the system becomes a superfluid. It turns out that the existing experimental cooling techniques allow minimum temperatures for fermions of the order of the Fermi temperature. Using Feshbach resonances induced by magnetic fields enhances the effective interactions between the atoms leading to superfluid transition temperatures of the order of the Fermi energy. This is a completely new regime of fermionic superfluidity far from the BCS superconductors, He and even high- superconductors. The achievement of superfluidity on gases
We consider atomic Fermi gases where Feshbach resonances can be used to study the whole BCS-Bose-Einstein condensate crossover. We show how a probing field transferring atoms out of the superfluid can be used to detect the onset of the superfluid transition in the high-T(c) and BCS regimes. The number of transferred atoms, as a function of the energy given by the probing field, peaks at the gap energy. The shape of the peak is asymmetric due to the single particle excitation gap. Since the excitation gap also includes a pseudogap contribution, the asymmetry alone is not a signature of superfluidity. The incoherent nature of the noncondensed pairs leads to broadening of the peak. The broadening decays below the critical temperature, causing a drastic increase in the asymmetry. This provides a signature of the transition.
We determine the critical Zeeman energy splitting of a homogeneous Fermi superfluid at unitary in terms of the Fermi energy ${\ensuremath{\epsilon}}_{\text{F}}$ according to recent experimental results in Laboratoire Kastler Brossel (LKB)-Lhomond. Based on the universal equations of state for the superfluid and normal phases, we show that there exist two critical fields Hc1{H}_{c1}Hc1​ and Hc2{H}_{c2}Hc2​, between which a superfluid-normal mixed phase is energetically favored. Universal formulas for the critical fields and the critical population imbalance Pc{P}_{c}Pc​ are derived. We have found a universal relation between the critical fields and the critical imbalances: ${H}_{c1}=\ensuremath{\gamma}\ensuremath{\xi}{\ensuremath{\epsilon}}_{\text{F}}$ and ${H}_{c2}=(1+\ensuremath{\gamma}{P}_{c}){}^{2/3}{H}_{c1}$, where $\ensuremath{\xi}$ is the universal constant and $\ensuremath{\gamma}$ is the critical value of the chemical potential imbalance in the grand canonical ensemble. Since $\ensuremath{\xi}$, $\ensuremath{\gamma}$, and Pc{P}_{c}Pc​ have been measured in the experiments, we can determine the critical Zeeman fields without the detailed information of the equation of state for the polarized normal phase. Using the experimental data from LKB-Lhomond, we have found ${H}_{c1}\ensuremath{\simeq}0.37{\ensuremath{\epsilon}}_{\text{F}}$ and ${H}_{c2}\ensuremath{\simeq}0.44{\ensuremath{\epsilon}}_{\text{F}}$. Our result of the polarization PPP as a function of the Zeeman field $H/{\ensuremath{\epsilon}}_{\text{F}}$ is in good agreement with the data extracted from the experiments. We also give an estimation of the critical magnetic field for dilute neutron matter at which the matter gets spin polarized, assuming the properties of the dilute neutron matter are close to those of the unitary Fermi gas.