Path integral formulation of the tunneling dynamics of a superfluid Fermi gas in an optical potential

To describe the tunneling dynamics of a stack of two-dimensional fermionic superfluids in an optical potential, we derive an effective action functional from a path integral treatment. This effective action leads, in the saddle point approximation, to equations of motion for the density and the phase of the superfluid Fermi gas in each layer. In the strong coupling limit (where bosonic molecules are formed) these equations reduce to a discrete nonlinear Schrodinger equation, where the molecular tunneling amplitude is reduced for large binding energies. In the weak coupling (BCS) regime, we study the evolution of the stacked superfluids and derive an approximate analytical expression for the Josephson oscillation frequency in an external harmonic potential. Both in the weak and intermediate coupling regimes the detection of the Josephson oscillations described by our path integral treatment constitutes experimental evidence for the fermionic superfluid regime.Comment: 13 pages + 2 figure

Ground state and optical conductivity of interacting polarons in a quantum dot

The ground-state energy, the addition energies and the optical absorption spectra are derived for interacting polarons in parabolic quantum dots in three and two dimensions. A path integral formalism for identical particles is used in order to take into account the fermion statistics. The approach is applied to both closed-shell and open-shell systems of interacting polarons. Using a generalization of the Jensen-Feynman variational principle, the ground-state energy of a confined N-polaron system is analyzed as a function of N and of the electron-phonon coupling constant. As distinct from the few-electron systems without the electron-phonon interaction, three types of spin polarization are possible for the ground state of the few-polaron systems: (i) a spin-polarized state, (ii) a state where the spin is determined by Hund's rule, (iii) a state with the minimal possible spin. A transition from a state fulfilling Hund's rule, to a spin-polarized state occurs when decreasing the electron density. In the strong-coupling limit, the system of interacting polarons turns into a state with the minimal possible spin. These transitions should be experimentally observable in the optical absorption spectra of quantum dots.Comment: 33 pages, 9 figures, E-mail addresses: [email protected], [email protected], [email protected], [email protected], accepted for Phys. Rev.

The vortex state in the BEC to BCS crossover: a path-integral description

We derive a path-integral description of the vortex state of a fermionic superfluid in the crossover region between the molecular condensate (BEC) regime and the Cooper pairing (BCS) regime. This path-integral formalism, supplemented by a suitable choice for the saddle point value of the pairing field in the presence of a vortex, offers a unified description that encompasses both the BEC and BCS limits. The vortex core size is studied as a function of the tunable interaction strength between the fermionic atoms. We find that in the BEC regime, the core size is determined by the molecular healing length, whereas in the BCS regime, the core size is proportional only to the Fermi wave length. The observation of such quantized vortices in dilute Fermi gases would provide an unambiguous proof of the realization of superfluidity in these gases.Comment: 10 pages, 2 figure

Optical Absorption Spectra of Bipolarons

The absorption of large bipolarons is investigated using the path-integral method. The response of a bipolaron to an external electromagnetic field is derived in the framework of the memory-function approach. The bipolaron optical absorption spectrum consists of a series of relatively narrow peaks. The peculiarities of the bipolaron optical absorption as a function of the frequency of the electromagnetic field may be attributed to the transitions involving relaxed excited states and scattering states of a bipolaron.Comment: 14 pages, 3 figures, E-mail addresses: [email protected], [email protected]; to be published in Phys. Rev.

Quantum theory of intersubband polarons

We present a microscopic quantum theory of intersubband polarons, quasiparticles originated from the coupling between intersubband transitions and longitudinal optical phonons. To this aim we develop a second quantized theory taking into account both the Fr\"ohlich interaction between phonons and intersubband transitions and the Coulomb interaction between the intersubband transitions themselves. Our results show that the coupling between the phonons and the intersubband transitions is extremely intense, thanks both to the collective nature of the intersubband excitations and to the natural tight confinement of optical phonons. Not only the coupling is strong enough to spectroscopically resolve the resonant splitting between the modes (strong coupling regime), but it can become comparable to the bare frequency of the excitations (ultrastrong coupling regime). We thus predict the possibility to exploit intersubband polarons both for applied optoelectronic research, where a precise control of the phonon resonances is needed, and also to observe fundamental quantum vacuum physics, typical of the ultrastrong coupling regime

Nucleation of superconductivity in mesoscopic star-shaped superconductors

We study the phase transition of a star-shaped superconductor, which covers smoothly the range from zero to two dimensions with respect to the superconducting coherence length. Detailed measurements and numerical calculations show that the nucleation of superconductivity in this device is very inhomogeneous, resulting in rich structure in the superconducting transition as a function of temperature and magnetic field. The superconducting order parameter is strongly enhanced and mostly robust in regions close to multiple boundaries.Comment: 4 pages, 5 figures, E-mail addresses: [email protected] (V. Chandrasekhar), [email protected] (J. T. Devreese