Critical Quantum Metrology in the Non-Linear Quantum Rabi Model.

The quantum Rabi model (QRM) with linear coupling between light mode and qubit exhibits the analog of a second-order phase transition for vanishing mode frequency which allows for criticality-enhanced quantum metrology in a few-body system. We show that the QRM including a nonlinear coupling term exhibits much higher measurement precisions due to its first-order-like phase transition at finite frequency, avoiding the detrimental slowing-down effect close to the critical point of the linear QRM. When a bias term is added to the Hamiltonian, the system can be used as a fluxmeter or magnetometer if implemented in circuit QED platforms.

Universal Scaling and Critical Exponents of the Anisotropic Quantum Rabi Model.

We investigate the quantum phase transition of the anisotropic quantum Rabi model, in which the rotating and counterrotating terms are allowed to have different coupling strengths. The model interpolates between two known limits with distinct universal properties. Through a combination of analytic and numerical approaches, we extract the phase diagram, scaling functions, and critical exponents, which determine the universality class at finite anisotropy (identical to the isotropic limit). We also reveal other interesting features, including a superradiance-induced freezing of the effective mass and discontinuous scaling functions in the Jaynes-Cummings limit. Our findings are extended to the few-body quantum phase transitions with N>1 spins, where we expose the same effective parameters, scaling properties, and phase diagram. Thus, a stronger form of universality is established, valid from N=1 up to the thermodynamic limit.

Is the nature of itinerant ferromagnetism playing a role in the competition between spin polarization and singlet pair correlations?

We consider the competition between spin singlet pairing and itinerant ferromagnetism whose magnetization is yielded by a relative shift of the bands with opposite spin polarization or by asymmetric spin-dependent bandwidths. Within the framework of the exact solution of an extended version of the reduced BCS model, the structure of the coexisting state is shown to have general features that are not related to the character of the ferromagnetism. The role of different types of ferromagnet is then investigated for the proximity effect in a system made of a bilayer junction with a spin singlet superconductor interfaced with a ferromagnet in the clean limit. We show that the qualitative behaviour of the proximity effect does not depend on the nature of the ferromagnetism. Differences emerge at the borderline with the half-metallic regime. For the spin-dependent bandwidth type of ferromagnetism the pairing amplitude exhibits an oscillating behaviour until the density of the minority spin carrier becomes almost zero. The crossover from an oscillating to an exponentially damped profile occurs away from the half-metallic limit when a spin exchange type ferromagnet is considered.

Exact solution for a trapped Fermi gas with population imbalance and BCS pairing.

The problem of a two-component Fermi gas in a harmonic trap, with an imbalanced population and a pairing interaction of zero total momentum, is mapped onto the exactly solvable reduced BCS model. For a one-dimensional trap, the complete ground state diagram is determined with various topological features in ground state energy spectra. In addition to the conventional two-shell density profile of a paired core and polarized outer wings, a three-shell structure as well as a double-peak superfluid distribution are unveiled.