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Register a new userUltracold spin-balanced fermionic quantum liquids with renormalized $P$-wave interactions
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Added by
Jose Manuel Alarc\\'on
Publication date
2021
fields
Physics
and research's language is
English
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We consider spin-$1/2$ fermionic atoms whose dynamics are governed by low-energy $P$-wave interactions. These are renormalized within the ladder resummation scheme, and directly expressed as functions of the effective range parameters. Then, we show that, in a large scattering parameter regime, the zero-temperature equation of state exhibits a minimum, indicating the existence of a liquid phase. We also characterize the properties, such as the energy per particle, the compressibility or speed of sound of the liquid at equilibrium. The liquid exists near, but not strictly on, the unitary limit, which suggests the feasibility of realizing ultracold quantum liquids of fermions using $P$-wave Feshbach resonances.
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We consider the non-equilibrium orbital dynamics of spin-polarized ultracold fermions in the first excited band of an optical lattice. A specific lattice depth and filling configuration is designed to allow the $p_x$ and $p_y$ excited orbital degrees of freedom to act as a pseudo-spin. Starting from the full Hamiltonian for p-wave interactions in a periodic potential, we derive an extended Hubbard-type model that describes the anisotropic lattice dynamics of the excited orbitals at low energy. We then show how dispersion engineering can provide a viable route to realizing collective behavior driven by p-wave interactions. In particular, Bragg dressing and lattice depth can reduce single-particle dispersion rates, such that a collective many-body gap is opened with only moderate Feshbach enhancement of p-wave interactions. Physical insight into the emergent gap-protected collective dynamics is gained by projecting the Hamiltonian into the Dicke manifold, yielding a one-axis twisting model for the orbital pseudo-spin that can be probed using conventional Ramsey-style interferometry. Experimentally realistic protocols to prepare and measure the many-body dynamics are discussed, including the effects of band relaxation, particle loss, spin-orbit coupling, and doping.
We propose a new method of detecting the onset of superfluidity in a two-component ultracold fermionic gas of atoms governed by an attractive short-range interaction. By studying the two-body correlation functions we find that a measurement of the momentum distribution of the density and spin response functions allows one to access separately the normal and anomalous densities. The change in sign at low momentum transfer of the density response function signals the transition between a BEC and a BCS regimes, characterized by small and large pairs, respectively. This change in sign of the density response function represents an unambiguous signature of the BEC to BCS crossover. Also, we predict spin rotational symmetry-breaking in this system.
We show that, near a Feshbach resonance, a strong p-wave resonance is present at low energy in atom-dimer scattering for $^6$Li-$^{40}$K fermionic mixtures. This resonance is due to a virtual bound state, in the atom-dimer system, which is present at this low energy. When the mass ratio between the two fermionic elements is increased, this virtual bound state goes to a known real bound state which appears when the mass ratio reaches 8.17. This resonance should affect a number of physical properties. These include the equation of state of unbalanced mixtures at very low temperature but also the equation of state of balanced mixtures at moderate or high temperature. The frequency and the damping of collective modes should also provide a convenient way to evidence this resonance. Finally it should be possible to modify the effective mass of one the fermionic species by making use of an optical lattice. This would allow to study the strong dependence of the resonance as a function of the mass ratio of the two fermionic elements.
We show that recently suggested subwavelength lattices offer remarkable prospects for the observation of novel superfluids of fermionic polar molecules. It becomes realistic to obtain a topological $p$-wave superfluid of microwave-dressed polar molecules in 2D lattices at temperatures of the order of tens of nanokelvins, which is promising for topologically protected quantum information processing. Another foreseen novel phase is an interlayer $p$-wave superfluid of polar molecules in a bilayer geometry.
The highly controllable ultracold atoms in a one-dimensional (1D) trap provide a new platform for the ultimate simulation of quantum magnetism. In this regard, the Neel-antiferromagnetism and the itinerant ferromagnetism are of central importance and great interest. Here we show that these magnetic orders can be achieved in the strongly interacting spin-1/2 trapped Fermi gases with additional p-wave interactions. In this strong coupling limit, the 1D trapped Fermi gas exhibit an effective Heisenberg spin XXZ chain in the anisotropic p-wave scattering channels. For a particular p-wave attraction or repulsion within the same species of fermionic atoms, the system displays ferromagnetic domains with full spin segregation or the anti-ferromagnetic spin configuration in the ground state. Such engineered magnetisms are likely to be probed in a quasi-1D trapped Fermi gas of $^{40}$ K atoms with very close s-wave and p-wave Feshbach resonances.
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