Christophe Mora

Extension of Bogoliubov theory to quasicondensates

We present an extension of the well-known Bogoliubov theory to treat low-dimensional degenerate Bose gases in the limit of weak interactions and low density fluctuations. We use a density-phase representation and show that a precise definition of the phase operator requires a space discretization in cells of size l. We perform a systematic expansion of the Hamiltonian in terms of two small parameters, the relative density fluctuations inside a cell and the phase change over a cell. The resulting macroscopic observables can be computed in one, two, and three dimensions with no ultraviolet or infrared divergence. Furthermore, this approach exactly matches Bogoliubovs approach when there is a true condensate. We give the resulting expressions for the equation of state of the gas, the ground state energy, and the first order and second order correlation functions of the field. Explicit calculations are done for homogeneous systems.

Coupling a quantum dot, fermionic leads, and a microwave cavity on a chip.

We demonstrate a hybrid architecture consisting of a quantum dot circuit coupled to a single mode of the electromagnetic field. We use single wall carbon nanotube based circuits inserted in superconducting microwave cavities. By probing the nanotube dot using a dispersive readout in the Coulomb blockade and the Kondo regime, we determine an electron-photon coupling strength which should enable circuit QED experiments with more complex quantum dot circuits.

Ultra-cold polarized Fermi gases

Recent experiments with ultra-cold atoms have demonstrated the possibility of realizing fermionic superfluids with imbalanced spin populations experimentally. We discuss how these developments have shed new light on a half-century-old open problem in condensed matter physics, and raised new interrogations of their own.

Four-body Efimov effect for three fermions and a lighter particle.

We study three same-spin-state fermions of mass M interacting with a distinguishable particle of mass m in the unitary limit where the interaction has a zero range and an infinite s-wave scattering length. We predict an interval of mass ratio 13.384<M/m<13.607 where there exists a purely four-body Efimov effect, leading to the occurrence of weakly bound tetramers without Efimov trimers.

Universal resistances of the quantum resistance–capacitance circuit

The properties of electric conductors change markedly once quantum phenomena become relevant. So far, work on quantum coherent electron transport has largely focused on static properties, but new theoretical work now looks at such phenomena in the regime of fast alternating currents.

Ground state of a tightly bound composite dimer immersed in a Fermi sea

In this paper we present a theoretical investigation for the ground state of an impurity immersed in a Fermi sea. The molecular regime is considered where a two-body bound state between the impurity and one of the fermions is formed. Both interaction and exchange of the bound fermion take place between the dimer and the Fermi sea. We develop a formalism based on a two channel model allowing us to expand systematically the ground state energy of this immersed dimer with the scattering length

Mesoscopic admittance of a double quantum dot

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Ground State Energy of the Two-Dimensional Weakly Interacting Bose Gas: First Correction Beyond Bogoliubov Theory

. Working up to order

Current noise through a Kondo quantum dot in a SU(N) Fermi liquid state.

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Transition to Fulde-Ferrell-Larkin-Ovchinnikov phases in three dimensions : A quasiclassical investigation at low temperature with fourier expansion

, associated to the creation of two particle-hole pairs, reveals the first signature of the composite nature of the bosonic dimer. Finally, a complementary variational study provides an accurate estimate of the dimer energy even at large scattering length.