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Trapped Ytterbium-173 Fermi gas across an orbital Feshbach resonance

M. Iskin

Published Aug 9, 2016• 0 citations
OpenAlex

Abstract

Starting with the two-band description of an orbital Feshbach resonance, we study superfluid properties of a trapped $^{173}$Yb Fermi gas under the assumptions of a local-density approximation for the trapping potential and a mean-field approximation for the intra-band Cooper pairings. In particular, we investigate the competition and interplay between the pair-breaking effect that is caused by the inter-band detuning energy, and the pair-breaking and thermal-broadening effects that are simultaneously caused by the temperature. We predict several experimental signatures that are directly caused by this interplay including a superfluid-normal phase separation within the trap, and could play decisive roles in probing two-band superfluidity in these systems.

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Trapped Yb173 Fermi gas across an orbital Feshbach resonance

M. Iskin

Starting with the two-band description of an orbital Feshbach resonance, we study superfluid properties of a trapped $^{173}\mathrm{Yb}$ Fermi gas under the assumptions of a local-density approximation for the trapping potential and a mean-field approximation for the intraband Cooper pairings. In particular, we investigate the competition and interplay between the pair-breaking effect that is caused by the interband detuning energy, and the pair-breaking and thermal-broadening effects that are simultaneously caused by the temperature. We predict several experimental signatures that are directly caused by this interplay including a spatial separation of superfluid and normal phases within the trap, and could play decisive roles in probing two-band superfluidity in these systems.

arXiv:1608.02773•Physical Review A•Jan 18, 2017•16 citations

Orbital Feshbach resonance of Fermi gases in an optical lattice

Haiyang Zhang, Fazal Badshah, Abdul Basit +1 more

In this paper, we study the orbital Feshbach resonance of ultracold two-electron 173 Yb Fermi gas in a one-dimensional optical lattice. We consider a two-band model under the assumptions of a local-density approximation for the optical lattice potential and a mean-field approximation for the intraband Cooper pairings. We get three crucially important properties for the system, the superfluid-Landau–Fermi-liquid (LFL) crossover corresponding to the tunneling energy, the particle condensation in the momentum space, and the superfluid-LFL phase transition corresponding to the temperature. We explain how to realize and manipulate these properties.

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We first show that the many-body Hamiltonian governing the physical properties of an alkaline-earth $^{173}\mathrm{Yb}$ Fermi gas across the recently realized orbital Feshbach resonance is exactly analogous to that of two-band $s$-wave superconductors with contact interactions; i.e., even though the free-particle bands have a tunable energy offset in between and are coupled by a Josephson-type attractive interband pair scattering, the intraband interactions have exactly the same strength. We then introduce two intraband order parameters within the BCS mean-field approximation and investigate the competition between their in-phase and out-of-phase (i.e., the so-called $\ensuremath{\pi}$-phase) solutions in the entire BCS-BEC evolution at zero temperature.

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Superfluid transition temperature in a trapped gas of Fermi atoms with a Feshbach resonance

Yutaro OHASHI, Adam Griffin

We investigate strong-coupling effects on the superfluid phase transition in a gas of Fermi atoms with a Feshbach resonance. The Feshbach resonance describes a composite quasiboson that can give rise to an additional pairing interaction between the Fermi atoms. This attractive interaction becomes stronger as the threshold energy $2\ensuremath{\nu}$ of the Feshbach resonance two-particle bound state is lowered. In a recent paper, we showed that in the uniform Fermi gas, this tunable pairing interaction naturally leads to a crossover from a BCS state to a Bose-Einstein condensate (BEC) of the Nozi\`eres and Schmitt-Rink kind, in which the BCS-type superfluid phase transition continuously changes into the BEC type as the threshold energy is decreased. In this paper, we extend our previous work by including the effect of a harmonic trap potential, treated within the local-density approximation. We also give results for both weak and strong coupling to the Feshbach resonance. We show that the BCS-BEC crossover phenomenon strongly modifies the shape of the atomic density profile at the superfluid phase-transition temperature ${T}_{\mathrm{c}},$ reflecting the change of the dominant particles going from Fermi atoms to composite bosons. In the BEC regime, these composite bosons are shown to first appear well above ${T}_{\mathrm{c}}.$ We also discuss the ``phase diagram'' above ${T}_{\mathrm{c}}$ as a function of the tunable threshold energy $2\ensuremath{\nu}.$ We introduce a characteristic temperature ${T}^{*}(2\ensuremath{\nu})$ describing the effective crossover in the normal phase from a Fermi gas of atoms to a gas of stable molecules.

arXiv:cond-mat/0210185•Physical Review A•Mar 14, 2003•108 citations
Starting with the two-band description of an orbital Feshbach resonance, we study superfluid properties of a trapped 173^{173}173Yb Fermi gas under the assumptions of a local-density approximation for the trapping potential and a mean-field approximation for the intra-band Cooper pairings. In particular, we investigate the competition and interplay between the pair-breaking effect that is caused by the inter-band detuning energy, and the pair-breaking and thermal-broadening effects that are simultaneously caused by the temperature. We predict several experimental signatures that are directly caused by this interplay including a superfluid-normal phase separation within the trap, and could play decisive roles in probing two-band superfluidity in these systems.
Starting with the two-band description of an orbital Feshbach resonance, we study superfluid properties of a trapped 173Yb^{173}\mathrm{Yb}173Yb Fermi gas under the assumptions of a local-density approximation for the trapping potential and a mean-field approximation for the intraband Cooper pairings. In particular, we investigate the competition and interplay between the pair-breaking effect that is caused by the interband detuning energy, and the pair-breaking and thermal-broadening effects that are simultaneously caused by the temperature. We predict several experimental signatures that are directly caused by this interplay including a spatial separation of superfluid and normal phases within the trap, and could play decisive roles in probing two-band superfluidity in these systems.
In this paper, we study the orbital Feshbach resonance of ultracold two-electron 173 Yb Fermi gas in a one-dimensional optical lattice. We consider a two-band model under the assumptions of a local-density approximation for the optical lattice potential and a mean-field approximation for the intraband Cooper pairings. We get three crucially important properties for the system, the superfluid-Landau–Fermi-liquid (LFL) crossover corresponding to the tunneling energy, the particle condensation in the momentum space, and the superfluid-LFL phase transition corresponding to the temperature. We explain how to realize and manipulate these properties.
We theoretically investigate the superfluid properties of a two-band gas of 173Yb^{173}\mathrm{Yb}173Yb Fermi atoms with an orbital Feshbach resonance (OFR). To describe the BCS-BEC crossover region, we include superfluid fluctuations caused by interband and intraband pairing interactions associated with OFR by extending the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink to the two-band case below the superfluid phase transition temperature; however, the effects of an experimentally inaccessible deep bound state are removed to model a real 173Yb^{173}\mathrm{Yb}173Yb Fermi gas near OFR. We show that the condensate fraction in the upper closed channel gradually becomes smaller than that in the lower open channel as one moves from the strong- to the weak-coupling regime, because the OFR-pairing mechanism tunes the interaction strengths by adjusting the energy difference between the two bands. However, even when the closed-channel band is much higher in energy than the open-channel band in the weak-coupling regime, the magnitude of the superfluid order parameter in the closed channel is found to be still comparable to that in the open channel. As the reason for this, we point out a pair-tunneling effect by the OFR-induced interband interaction. In addition to these superfluid quantities, we also examine collective modes, such as the Goldstone mode, the Schmid (Higgs) mode, and Leggett mode, to clarify how they appear in the spectral weights of pair-correlation functions in each band. Since the realization of a multiband superfluid Fermi gas is a crucial issue in cold Fermi gas physics, our results would contribute to the basic understanding of this type of Fermi superfluid in the BCS-BEC crossover region.
We first show that the many-body Hamiltonian governing the physical properties of an alkaline-earth 173Yb^{173}\mathrm{Yb}173Yb Fermi gas across the recently realized orbital Feshbach resonance is exactly analogous to that of two-band sss-wave superconductors with contact interactions; i.e., even though the free-particle bands have a tunable energy offset in between and are coupled by a Josephson-type attractive interband pair scattering, the intraband interactions have exactly the same strength. We then introduce two intraband order parameters within the BCS mean-field approximation and investigate the competition between their in-phase and out-of-phase (i.e., the so-called $\ensuremath{\pi}$-phase) solutions in the entire BCS-BEC evolution at zero temperature.
We study static superfluid properties of alkali-earth-like Fermi atomic systems in the presence of orbital Feshbach resonance. Using a two-band description of the ground state and excited state and a mean-field approximation of the intraband atomic pairing, we investigate the phase transitions and crossover between BCS and Bose-Einstein-condensate (BEC) superfluidity. At zero temperature, we find exact BCS analytical solutions for the mean-field gap equations and number equations. Using these exact solutions, we calculate various static properties, such as superfluid order parameters, chemical potentials, density variations, density profiles, correlation and coherence lengths, ground-state energy, and Tan's contact density across the entire BCS-BEC crossover region. We anticipate that our closed-form analytical results can be used as a benchmark for future experimental and theoretical investigations and will have an impact on the current understanding of two-band superconductors such as MgB2{\mathrm{MgB}}_{2}MgB2​.
We investigate strong-coupling effects on the superfluid phase transition in a gas of Fermi atoms with a Feshbach resonance. The Feshbach resonance describes a composite quasiboson that can give rise to an additional pairing interaction between the Fermi atoms. This attractive interaction becomes stronger as the threshold energy $2\ensuremath{\nu}$ of the Feshbach resonance two-particle bound state is lowered. In a recent paper, we showed that in the uniform Fermi gas, this tunable pairing interaction naturally leads to a crossover from a BCS state to a Bose-Einstein condensate (BEC) of the Nozi\`eres and Schmitt-Rink kind, in which the BCS-type superfluid phase transition continuously changes into the BEC type as the threshold energy is decreased. In this paper, we extend our previous work by including the effect of a harmonic trap potential, treated within the local-density approximation. We also give results for both weak and strong coupling to the Feshbach resonance. We show that the BCS-BEC crossover phenomenon strongly modifies the shape of the atomic density profile at the superfluid phase-transition temperature Tc,{T}_{\mathrm{c}},Tc​, reflecting the change of the dominant particles going from Fermi atoms to composite bosons. In the BEC regime, these composite bosons are shown to first appear well above Tc.{T}_{\mathrm{c}}.Tc​. We also discuss the ``phase diagram'' above Tc{T}_{\mathrm{c}}Tc​ as a function of the tunable threshold energy $2\ensuremath{\nu}.$ We introduce a characteristic temperature ${T}^{*}(2\ensuremath{\nu})$ describing the effective crossover in the normal phase from a Fermi gas of atoms to a gas of stable molecules.