Pairing correlations in a trapped one-dimensional Fermi gas

Kudla, Stephen S.; Gautreau, Dominique; Sheehy, Daniel E.

doi:10.1103/physreva.91.043612

Cited by 5 publications

(7 citation statements)

References 26 publications

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“…2a. We find a local density and pairing amplitude that are spatially inhomogeneous due to the imposed trapping potential, with shapes that are consistent with earlier work based on mean-field theory and Bethe ansatz [59]. Furthermore, the one-body density and pairing matrices are mostly diagonal in index space.…”

Section: A Harmonic Trapsupporting

confidence: 88%

Hartree-Fock-Bogoliubov theory of trapped one-dimensional imbalanced Fermi systems

Patton,

Sheehy

2020

Preprint

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Ground state Hartree-Fock-Bogoliubov (HFB) theory is applied to imbalanced spin-1 /2 onedimensional Fermi systems that are spatially confined by either a harmonic or a hard-wall trapping potential. It has been hoped that such systems, which can be realized using ultracold atomic gases, would exhibit the long-sought-after Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid phase. The HFB formalism generalizes the standard Bogoliubov quasi-particle transformation, by allowing for Cooper pairing to exist between all possible single-particle states, and accounts for the effects of the inhomogeneous trapping potential as well as the mean-field Hartree potential. This provides an unbiased framework to describe inhomgenous densities and pairing correlations in the FFLO state of a confined 1D gas. In a harmonic trap, numerical minimization of the HFB ground state energy yields a spatially oscillating order parameter reminiscent of the FFLO state. However, we find that this state has almost no imprint in the local fermion densities (consistent with experiments that found no evidence of the FFLO phase). In contrast, for a hard-wall geometry, we find a strong signature of the spatial oscillations of the FFLO pairing amplitude reflected in the local in situ densities. In the hard wall case, the excess spins are strongly localized near regions where there is a node in the pairing amplitude, creating an unmistakeable crystalline modulation of the density.

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Section: A Harmonic Trapsupporting

confidence: 88%

Hartree-Fock-Bogoliubov theory of trapped one-dimensional imbalanced Fermi systems

Patton,

Sheehy

2020

Preprint

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“…In Ref. [51] the balanced case was studied using a similar variational wave function. It was found that including this additional variational parameter was necessary to allow the cloud size to decrease with increasing strength of attraction (which is what is expected on physical grounds and is observed experimentally).…”

Section: Variational Energymentioning

confidence: 99%

“…[51] it was shown that a simple variational BCStype wave function that involved pairing of harmonicoscillator states could account for pairing correlations in a balanced trapped 1D gas without the necessity of invoking the LDA. Here, we propose a similar wave function for the imbalanced case that incorporates FFLO pairing correlations in a natural way.…”

Section: Introductionmentioning

confidence: 99%

Trapped imbalanced fermionic superfluids in one dimension: A variational approach

et al. 2017

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We propose and analyze a variational wave function for a population-imbalanced one-dimensional Fermi gas that allows for Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type pairing correlations among the two fermion species, while also accounting for the harmonic confining potential. In the strongly interacting regime, we find large spatial oscillations of the order parameter, indicative of an FFLO state. The obtained density profiles versus imbalance are consistent with recent experimental results as well as with theoretical calculations based on combining Bethe ansatz with the local density approximation. Although we find no signature of the FFLO state in the densities of the two fermion species, we show that the oscillations of the order parameter appear in density-density correlations, both in-situ and after free expansion. Furthermore, above a critical polarization, the value of which depends on the interaction, we find the unpaired Fermi-gas state to be energetically more favorable.

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“…have been of much interest as they can be measured in experiment and are, within mean-field theory, directly proportional to the gap C kγ,pσ = δ k,−p δ γ,σ |∆| 2 /(4E 2 k,γ ) [12][13][14][15][16][17][18]. We compute the time-evolved density-density correlations C kγ,pσ (t) by inserting the exponentials e itH(J f ,J f ,U f ) inside all expectation values in Eq.…”

Section: Time Evolution Of the Density-density Correlation Functionmentioning

confidence: 99%

“…Greiner et al have demonstrated that measuring the shot noise in absorption images makes the densitydensity correlations experimentally accessible [13]. This has motivated several further studies of the density-density correlations [14][15][16] as well as proposals to use them in order to distinguish different phases of ultracold fermions [17][18][19][20]. An alternative approach to measuring the correlations in a Fermionic gas is to observe the time-evoulution after a quench of either the lattice depth or the interactions between atoms.…”

Section: Introductionmentioning

confidence: 99%

Sudden-quench dynamics of Bardeen-Cooper-Schrieffer states in deep optical lattices

2016

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We determine the exact dynamics of an initial Bardeen-Cooper-Schrieffer (BCS) state of ultra-cold atoms in a deep hexagonal optical lattice. The dynamical evolution is triggered by a quench of the lattice potential, such that the interaction strength U f is much larger than the hopping amplitude J f . The quench initiates collective oscillations with frequency |U f |/(2π) in the momentum occupation numbers and imprints an oscillating phase with the same frequency on the BCS order parameter ∆. The oscillation frequency of ∆ is not reproduced by treating the time evolution in mean-field theory. In our theory, the momentum noise (i.e. density-density) correlation functions oscillate at frequency |U f |/2π as well as at its second harmonic. For a very deep lattice, with zero tunneling energy, the oscillations of momentum occupation numbers are undamped. Non-zero tunneling after the quench leads to dephasing of the different momentum modes and a subsequent damping of the oscillations. The damping occurs even for a finite-temperature initial BCS state, but not for a non-interacting Fermi gas. Furthermore, damping is stronger for larger order parameter and may therefore be used as a signature of the BCS state. Finally, our theory shows that the noise correlation functions in a honeycomb lattice will develop strong anti-correlations near the Dirac point. 67.85.Lm

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Pairing correlations in a trapped one-dimensional Fermi gas

Cited by 5 publications

References 26 publications

Hartree-Fock-Bogoliubov theory of trapped one-dimensional imbalanced Fermi systems

Hartree-Fock-Bogoliubov theory of trapped one-dimensional imbalanced Fermi systems

Trapped imbalanced fermionic superfluids in one dimension: A variational approach

Sudden-quench dynamics of Bardeen-Cooper-Schrieffer states in deep optical lattices

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