Tuning the tricritical point with spin-orbit coupling in polarized fermionic condensates

We investigate a two-component atomic Fermi gas with population imbalance in the presence of Rashba-type spin-orbit coupling (SOC). As a competition between SOC and population imbalance, the finite-temperature phase diagram reveals a large variety of new features, including the expanding of the superfluid state regime and the shrinking of both the phase separation and the normal regimes. For sufficiently strong SOC, the phase separation region disappears, giving way to the superfluid state. We find that the tricritical point moves toward a regime of low temperature, high magnetic field, and high polarization as the SOC increases.     

Self-avoiding tethered membranes at the tricritical point

The scaling properties of self-avoiding tethered membranes at the tricritical point (Θ-point) are studied by perturbative renormalization group methods. To treat the 3-body repulsive interaction (known to be relevant for polymers), new analytical and numerical tools are developed and applied to 1-loop calculations. These techniques are a prerequisite to higher-order calculations for self-avoiding membranes. The crossover between the 3-body interaction and the modified 2-body interaction, attractive at long range, is studied through a new double ε-expansion. It is shown that the latter interaction is relevant for 2-dimensional membranes at the Θ-point.     

The Landau theory and the tricritical point

We show from the Landau theory of the tricritical point that the transition line has not necessarily a continuous slope and that it is possible to find behavior analogous to those of the tricritical points of first and second kind, analyzed by Reatto.     

Nonequilibrium tricritical point in a system with long-range interactions

Systems with long-range interactions display a short-time relaxation towards quasistationary states whose lifetime increases with system size. With reference to the Hamiltonian mean field model, we here show that a maximum entropy principle, based on Lynden-Bell's pioneering idea of "violent relaxation," predicts the presence of out-of-equilibrium phase transitions separating the relaxation towards homogeneous (zero magnetization) or inhomogeneous (nonzero magnetization) quasistationary states. When varying the initial condition within a family of "water bags" with different initial magnetization and energy, first- and second-order phase transition lines are found that merge at an out-of-equilibrium tricritical point. Metastability is theoretically predicted and numerically checked around the first-order phase transition line.     

Deformation of a trapped Fermi gas with unequal spin populations

The real-space densities of a polarized strongly interacting two-component Fermi gas of 6Li atoms reveal two low-temperature regimes, both with a fully paired core. At the lowest temperatures, the unpolarized core deforms with increasing polarization. Sharp boundaries between the core and the excess unpaired atoms are consistent with a phase separation driven by a first-order phase transition. In contrast, at higher temperatures the core does not deform but remains unpolarized up to a critical polarization. The boundaries are not sharp in this case, indicating a partially polarized shell between the core and the unpaired atoms. The temperature dependence is consistent with a tricritical point in the phase diagram.     

Competing order parameters and a tricritical point with a difference

We propose a mean-field, phenomenological Ginzburg–Landau free energy functional with two competing order parameters for a two-component, spin-polarized Fermi gas. This free energy supports a tricritical point which is different from the conventional one and this change offers a correct understanding of the experimental phase diagram of imbalanced Fermi systems (Shin et al. (2008) [17]). The specific heat also happens to be different than in standard theory.     

Squeezing entangled state of two particles with unequal masses

For two unequal-mass particles, we construct the entangled state representation and then derive the corresponding squeezing operator. This squeezing operator has a natural realization in the entangled state representation, which exhibits the intrinsic relation between squeezing and quantum entanglement. This squeezing operator involves both two-mode squeezing and the direct product of two single-mode squeezings. The maximum squeezing occurs when the two particles possess equal mass. When two particles' mass difference becomes large, the component of the two single-mode squeezings becomes dominant.     

On the tricritical point induced by random transverse fields

In contradiction to a paper of Pirc it is shown that for a classical n-vector model with annealed random transverse fields only the second-order phase transition is possible and no tricritical points appear. The free energy functional for such systems is evaluated within the Landau theory.     

On the tricritical point in MnSi under high pressures

The magnetic susceptibility of a MnSi single crystal is measured in the region of the ferromagnetic phase transition under pressures up to 0.8 GPa in compressed helium. It is found that the tricritical point on the phase-transition curve corresponds to a much lower pressure and a considerably higher temperature (P _tr ≈ 0.355 GPa and T _tr ≈ 25.2 K) than was reported earlier (P _tr ≈ 1.2 GPa and T _tr ≈ 12 K). New results impose certain limitations on theoretical analysis of tricritical phenomena in MnSi.     

Attractive Fermi gases with unequal spin populations in highly elongated traps

We investigate two-component attractive Fermi gases with imbalanced spin populations in trapped one-dimensional configurations. The ground state properties are determined with the local density approximation, starting from the exact Bethe-ansatz equations for the homogeneous case. We predict that the atoms are distributed according to a two-shell structure: a partially polarized phase in the center of the trap and either a fully paired or a fully polarized phase in the wings. The partially polarized core is expected to be a superfluid of the Fulde-Ferrell-Larkin-Ovchinnikov type. The size of the cloud as well as the critical spin polarization needed to suppress the fully paired shell are calculated as a function of the coupling strength.     

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 preferred. This leads to an order parameter with a cos( ^. ) 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. Received 20 February 2002 / Received in final form 4 June 2002 Published online 13 August 2002     

Sound propagation near the tricritical point of FeCl2

The magnetically induced phase transitions, near the tricritical point of FeCl₂ were studied by acoustic velocity measurements. Longitudinal waves propagating along the (100) trigonal axis exhibit a critical shift in the velocity along the second order λ-line and anomalous change at the first order phase transitions. The phase diagram in the plane of temperature and applied magnetic field is constructed near the tricritical point.     

Lifshitz tricritical point and its relation to the FFLO superconducting state

We study the phase diagram of spatially inhomogeneous Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) superconducting state using the Ginzburg–Landau (GL) free energy, derived from the microscopic Hamiltonian of the system, and notice that it has a very clear Lifshitz tricritical point. We find the specific heat jumps abruptly near the first-order line in the emergent phase diagram which is very similar to the recent experimental observation in layered organic superconductor. Comparison with experimental data allows us to obtain quantitative relations between the parameters of phenomenological free energy. The region of the phase diagram where the specific heat jumps can be probed by doing a dynamical analysis of the free energy.