Transition to Fulde-Ferrel-Larkin-Ovchinnikov phases near the tricritical point : an analytical study

We explore analytically the nature of the transition to the Fulde-Ferrel-Larkin-Ovchinnikov superfluid phases in the vicinity of the tricritical point, where these phases begin to appear. We make use of an expansion of the free energy up to an overall sixth order, both in order parameter amplitude and in wavevector. We first explore the minimization of this free energy within a subspace, made of arbitrary superpositions of plane waves with wavevectors of different orientations but same modulus. We show that the standard second order FFLO phase transition is unstable and that a first order transition occurs at higher temperature. Within this subspace we prove that it is favorable to have a real order parameter and that, among these states, those with the smallest number of plane waves are prefered. This leads to an order parameter with a $\cos({\bf q}_{0}. {\bf r})$ dependence, in agreement with preceding work. Finally we show that the order parameter at the transition is only very slightly modified by higher harmonics contributions when the constraint of working within the above subspace is released.Comment: 11 pages, revte

Cavity squeezing by a quantum conductor

Hybrid architectures integrating mesoscopic electronic conductors with resonant microwave cavities have a great potential for investigating unexplored regimes of electron-photon coupling. In this context, producing nonclassical squeezed light is a key step towards quantum communication with scalable solid-state devices. Here we show that parametric driving of the electronic conductor induces a squeezed steady state in the cavity. We find that squeezing properties of the cavity are essentially determined by the electronic noise correlators of the quantum conductor. In the case of a tunnel junction, we predict that squeezing is optimized by applying a time-periodic series of quantized $\delta-$peaks in the bias voltage. For an asymmetric quantum dot, we show that a sharp Leviton pulse is able to achieve perfect cavity squeezing.Comment: 13 pages, 4 figures, includes Supplementary inf

On global location-domination in graphs

A dominating set $S$ of a graph $G$ is called locating-dominating, LD-set for short, if every vertex $v$ not in $S$ is uniquely determined by the set of neighbors of $v$ belonging to $S$. Locating-dominating sets of minimum cardinality are called $LD$-codes and the cardinality of an LD-code is the location-domination number $\lambda(G)$. An LD-set $S$ of a graph $G$ is global if it is an LD-set of both $G$ and its complement $\overline{G}$. The global location-domination number $\lambda_g(G)$ is the minimum cardinality of a global LD-set of $G$. In this work, we give some relations between locating-dominating sets and the location-domination number in a graph and its complement.Comment: 15 pages: 2 tables; 8 figures; 20 reference