Two-channel Bose-Hubbard model of atoms at a Feshbach resonance

Schneider, Philipp‐Immanuel; Sáenz, Alejandro

doi:10.1103/physreva.87.052712

Cited by 5 publications

(9 citation statements)

References 42 publications

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“…where U > 0 is the magnitude of the on-site attraction. In cold atom systems, the interaction can derive from an attractive Feshbach resonance [63,66]. We study the effect of this attractive interaction at the mean-field level using a BCS-like approximation.…”

Section: Non-interacting Model and Hofstadter Bandsmentioning

confidence: 99%

“…The key difference between the solid state case and the current set-up is that in the former system the change of sign of the superconducting gap is proposed to be realized by proximity effect with an unconventional superconductor (such as d-wave or s ± wave, which change sign in momentum space), while in our work the change of sign of the superconducting gap is due to a soliton in the s-wave superfluid. The other significant difference between the two proposals is that, while the proximity effect of unconventional d or s ± wave superconductivity on QSHI in solid state systems has not yet been demonstrated experimentally (and is probably going to be hard) the main ingredients of the same physics within our proposal, namely, the two-component Hofstadter model (thus a QSHI, [52][53][54][55][56][57][58][59]), on-site attractive interactions and non-zero SC pair potential [60][61][62][63][64][65][66], and creation of dark solitons [67][68][69][70], have all been individually realized in the cold atom systems.…”

Section: Non-interacting Model and Hofstadter Bandsmentioning

confidence: 99%

“…These systems are accurately modeled by a two-component Hofstadter model in a TR invariant scheme where the atoms experience opposite uniform magnetic fields for each of the two components [52][53][54][55][56][57][58][59]. Furthermore, swave superfluidity can be induced with an attractive Hubbard interaction arising from a Feshbach resonance between the fermions [60][61][62][63][64][65][66]. Specifically, we study a 2D TR invari-ant Hofstadter model, H 0 , with an attractive Hubbard interaction, H I : H = H 0 + H I .…”

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confidence: 99%

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Majorana Corner Modes with Solitons in an Attractive Hubbard-Hofstadter Model of Cold Atom Optical Lattices

et al. 2019

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Higher order topological superconductors hosting Majorana-Kramers pairs (MKPs) as corner modes have recently been proposed in a two-dimensional (2D) quantum spin Hall insulator (QSHI) proximity-coupled to unconventional cuprate or iron-based superconductors. Here, we show such MKPs can be realized using a conventional s-wave superfluid with a soliton in cold atom systems governed by the Hubbard-Hofstadter model. The MKPs emerge in the presence of interaction at the corners defined by the intersections of line solitons and the one-dimensional edges of the system. Our scheme is based on the recently realized cold atom Hubbard-Hofstadter lattice and will pave the way for observing possible higher order topological superfluidity with conventional s-wave superfluids/superconductors.

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Section: Non-interacting Model and Hofstadter Bandsmentioning

confidence: 99%

Section: Non-interacting Model and Hofstadter Bandsmentioning

confidence: 99%

mentioning

confidence: 99%

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Majorana Corner Modes with Solitons in an Attractive Hubbard-Hofstadter Model of Cold Atom Optical Lattices

et al. 2019

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“…It is important to choose an appropriate model interaction potential to represent the potential V int (|r 1 − r 2 |). Usually, for a standard Hubbard model for ultracold atoms, V int (r) is replaced by the zero-range delta-type pseudopotential which is found to be applicable when the s-wave scattering length a s is much smaller than the length scale of the trap under harmonic approximation [28]. Furthermore, this delta-potential approximation breaks down when the effective range of interaction is finite or large as in the case of magnetic Feshbach resonances [29], particularly when the width of the resonance is very narrow [28,30].…”

Section: Building Up the Models: Calculation Of Interaction Parametersmentioning

confidence: 99%

Fermionic versus bosonic two-site Hubbard models with a pair of interacting cold atoms

Mal¹,

Adhikary²,

Deb³

2019

J. Phys. B: At. Mol. Opt. Phys.

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In a recent work, Murmann et. al. [Phys. Rev. Lett. 114, 080402 (2015)] have experimentally prepared and manipulated a double-well optical potential containing a pair of Fermi atoms as a possible building block of Hubbard model. Here, we carry out a detailed theoretical study on the properties of both fermionic and bosonic two-site Hubbard models with a pair of interacting atoms in a trap with a double-well structure along z-axis and a 2D harmonic confinement along the transverse directions. We consider fermions as of two-component type and bosons as of spinless as well as of two spin components. We first discuss building up the Hubbard models using the model finite-range interaction potentials of Jost and Kohn. In general, a finite range of interaction leads to on-site, inter-site, exchange and partial-exchange terms. We show that, given the same input parameters for both bosonic and fermionic two-site Hubbard models, many of the statistical properties such as the single-and double-occupancy of a site, and the probabilities for the single-particle and pair tunneling are similar in both fermionic and bosonic cases. But, quantum entanglement and quantum fluctuations are found to be markedly different for the two cases. We discuss atom-atom entanglement in two spatial modes corresponding to the two sites of the double-well. Our results show that the entanglement of a pair of spin-half fermions is always greater than that of spinless bosons; and when the fermions are maximally entangled the fluctuation in the two-mode phase difference is largely squeezed. In contrast, spinless bosons never exhibit phase squeezing, but shows squeezing in two-mode population imbalance depending on the system parameters.

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“…Although the real Feshbach resonance is usually characterized by a two-channel model theory, the freedom of the choice of the interaction potential between ultracold atoms enables us to extract the key information from this simple single-channel model. This toy model is effectively equivalent to the two-channel model, and is already sufficient to realistically mimic the narrow Feshbach resonance [22]. We may easily solve the scattering problem within this interatomic potential, in presence and absence of the barrier, respectively.…”

Section: About the Energy-dependent Interactionmentioning

confidence: 99%

Virial expansion of a harmonically trapped Fermi gas across a narrow Feshbach resonance

2014

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We theoretically investigate the high-temperature thermodynamics of a harmonically trapped Fermi gas across a narrow Feshbach resonance by using the second-order quantum virial expansion, and point out some new features compared to the broad resonance. The interatomic interaction is modeled by the pseudopotential with an additional parameter, i.e., the effective range, to characterize the narrow-resonance width. Deep inside the width of a narrow Feshbach resonance, we find the second virial coefficient evolves with the effective range from the well-known universal value 1/4 in the broad-resonance limit to one another value 1/2 in the narrow-resonance limit. This means the Fermi gas interacts more strongly at the narrow resonance. In addition, far beyond the resonance width, we find the harmonically trapped Fermi gas still manifests an appreciable interaction effect across a narrow Feshbach resonance, which is contrary to our knowledge of the broad Feshbach resonance. All our results can be directly tested in current narrow Feshbach resonance experiments, which are generally carried out in a harmonic trap.

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Two-channel Bose-Hubbard model of atoms at a Feshbach resonance

Cited by 5 publications

References 42 publications

Majorana Corner Modes with Solitons in an Attractive Hubbard-Hofstadter Model of Cold Atom Optical Lattices

Majorana Corner Modes with Solitons in an Attractive Hubbard-Hofstadter Model of Cold Atom Optical Lattices

Fermionic versus bosonic two-site Hubbard models with a pair of interacting cold atoms

Virial expansion of a harmonically trapped Fermi gas across a narrow Feshbach resonance

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