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Journal of Physics Condensed Matter

Emergent force and work fluctuations in a bilayer superfluid Bose–Fermi mixture in mixed dimensions

Mehmet Günay

Published Feb 14, 2022• 1 citation
Publisher

Abstract

Abstract We investigate a system of two-atomic species in mixed dimensions, in which one species is spread in a three-dimensional space and the other species is confined in two parallel layers. The presence of atoms in three-dimensions creates an induced potential for the ones confined in layers. Depending on the scattering (coherence) length and the layer separation, the formation of p-wave pairing within the same layer or s-wave pairing between different layers has been suggested. It was shown that these pairs cannot coexist when time-reversal symmetry is on, and there appears a transition from p-wave to s-wave as the ratio of the layer separation and the effective scattering length decreases. Here, we study the thermodynamical signatures of such transition and find that with the formation of the inter-layer pairing, an emergent force to be present at the critical point and show that it can be derived from the ground state energy. This result offers a tool for experimentally realizing such transitions, and can find notable potential in the field of quantum-thermodynamics.

DOI
10.1088/1361-648x/ac54e6

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Abstract We investigate a system of two-atomic species in mixed dimensions, in which one species is spread in a three-dimensional space and the other species is confined in two parallel layers. The presence of atoms in three-dimensions creates an induced potential for the ones confined in layers. Depending on the scattering (coherence) length and the layer separation, the formation of p-wave pairing within the same layer or s-wave pairing between different layers has been suggested. It was shown that these pairs cannot coexist when time-reversal symmetry is on, and there appears a transition from p-wave to s-wave as the ratio of the layer separation and the effective scattering length decreases. Here, we study the thermodynamical signatures of such transition and find that with the formation of the inter-layer pairing, an emergent force to be present at the critical point and show that it can be derived from the ground state energy. This result offers a tool for experimentally realizing such transitions, and can find notable potential in the field of quantum-thermodynamics.
We investigate a system of two-atomic species in mixed dimensions, in which one species is spread in a three-dimensional space and the other species is confined in two parallel layers. The presence of atoms in 3-dimensions creates an induced potential for the ones confined in layers. Depending on the effective scattering length and the layer separation, the formation of p-wave pairing within the same layer or s-wave pairing between different layers has been suggested. It is shown that these pairs cannot coexist when time-reversal symmetry (TRS) is on, and there appears a transition from p-wave to s-wave as the ratio of the layer separation and the effective scattering length decreases. With the formation of the inter-layer pairing, we find an emergent force to be present at the critical point and show that it can be derived from the thermodynamic potential. This result offers a tool for experimentally realizing such transitions, and can find notable potential in the field of quantum-thermodynamics.
A mixed dimensional system of fermions in two layers immersed in a Bose-Einstein condensate (BEC) is shown to be a promising setup to realize topological superfluids with time-reversal symmetry (TRS). The induced interaction between the fermions mediated by the BEC gives rise to a competition between ppp-wave pairing within each layer and sss-wave pairing between the layers. When the layers are far apart, intralayer pairing dominates and the system forms a topological superfluid either with or without TRS. With decreasing layer separation or increasing BEC coherence length, interlayer pairing sets in. We show that this leads either to a second-order transition breaking TRS where the edge modes gradually become gapped or to a first-order transition to a topologically trivial sss-wave superfluid. Our results provide a realistic road map for experimentally realizing a topological superfluid with TRS in a cold atomic system.
We investigate a two-species Fermi gas in which one species is confined in two parallel layers and interacts with the other species in the three-dimensional space by a tunable short-range interaction. Based on the controlled weak coupling analysis and the exact three-body calculation, we show that the system has a rich phase diagram in the plane of the effective scattering length and the layer separation. Resulting phases include an interlayer sss-wave pairing, an intralayer ppp-wave pairing, a dimer Bose-Einstein condensation, and a Fermi gas of stable Efimov-like trimers. Our system provides a widely applicable scheme to induce long-range interlayer correlations in ultracold atoms.
Similar to what has recently been achieved with Bose-Bose mixtures [G. Lamporesi, J. Catani, G. Barontini, Y. Nishida, M. Inguscio, and F. Minardi, Phys. Rev. Lett. 104, 153202 (2010)], mixed-dimensional Fermi-Fermi mixtures can be created by applying a species-selective one-dimensional optical lattice to a two-species Fermi gas ($\ensuremath{\sigma}\ensuremath{\equiv}{\ensuremath{\uparrow},\ensuremath{\downarrow}}$), in such a way that both species are confined to quasi--two-dimensional geometries determined by their hoppings along the lattice direction. We investigated the ground-state phase diagram of superfluidity for such mixtures in the BCS-BEC evolution, and found normal, gapped superfluid, gapless superfluid, and phase separated regions. In particular, we found a stable gapless superfluid phase where the unpaired $\ensuremath{\uparrow}$ and $\ensuremath{\downarrow}$ fermions coexist with the paired (or superfluid) ones in different momentum space regions. This phase is in some ways similar to the Sarma state found in mixtures with densities, but in our case, the gapless superfluid phase is unpolarized and most importantly it is stable against phase separation.
We consider a system of repulsively interacting Bose-Fermi mixtures of spin-polarized uniform atomic gases at zero temperature. We examine possible realization of ppp-wave superfluidity of fermions due to an effective attractive interaction via density fluctuations of Bose-Einstein condensate within mean-field approximation. We find the ground state of the system by direct energy comparison of the ppp-wave superfluid state in a single uniform mixed phase and normal Fermi gas state in a phase-separated phase, and suggest an occurrence of the ppp-wave superfluidity for a strong boson-fermion interaction regime. We study some signatures of the ppp-wave superfluid, such as anisotropic energy gap and quasiparticle energy in the axial state, that have not been observed in spin-unpolarized superfluid of atomic fermions. We also show that a Cooper pair is a tightly bound state, such as a diatomic molecule in the strong boson-fermion coupling regime, and suggest an observable indication of the ppp-wave superfluid in the real experiment.
Ultracold atom experiments offer the unique opportunity to study mixing of different types of superfluid states. Our interest is in superfluid mixtures comprising of particles with different statistics---Bose and Fermi. Such scenarios occur naturally, for example, in dense quantum chromodynamics (QCD) matter. Interestingly, cold atomic experiments are performed in traps with finite spatial extent, thus critically destabilizing the occurrence of various homogeneous phases. Critical to this analysis is the understanding that the trapped system can undergo phase separation, resulting in a unique situation where phase transition in either species (bosons or fermions) can overlap with the phase separation between possible phases. In the present work, we illustrate how this intriguing interplay manifests in an interacting two-species atomic mixture---one bosonic and another fermionic with two spin components---within a realistic trap configuration. We further show that such interplay of transitions can render the nature of the ground state to be highly sensitive to the experimental parameters and the dimensionality of the system.