Magnetic tuning of the relativistic BCS-BEC crossover

Abstract

The effect of an applied magnetic field in the crossover from Bose-Einstein condensate (BEC) to Bardeen-Cooper-Schrieffer (BCS) pairing regimes is investigated. We use a model of relativistic fermions and bosons inspired by those previously used in the context of cold fermionic atoms and in the magnetic-color-flavor-locking phase of color superconductivity. It turns out that as with cold atom systems, an applied magnetic field can also tune the BCS-BEC crossover in the relativistic case. We find that no matter what the initial state is at B = 0, for large enough magnetic fields the system always settles into a pure BCS regime. In contrast to the atomic case, the magnetic field tuning of the crossover in the relativistic system is not connected to a Feshbach resonance, but to the relative numbers of Landau levels with either BEC or BCS type of dispersion relations that are occupied at each magnetic field strength.

Equation of state in a strongly interacting relativistic system

“…On the other hand, the increase of the coupling constant strength at low density can modify the properties of the ground state as indicated by the significant decrease of the Cooper-pair coherence length, which can reach values of the order of the interquark spacing [10]. As already found in other physical contexts [11], this fact strongly suggests the possibility of a crossover from a color-superconducting BCS dynamics to a Bose-Einstein condensate (BEC) one [12][13][14][15], where although the symmetry breaking order parameter (the diquark condensate) is the same, the quasiparticle spectra in the two regions are completely different. As we will show by numerical calculations, in the BCS region, where the diquark coupling is relatively weak, the energy spectrum of the excitations has a fermionic nature, while in the strong-coupling region, formed by the BEC molecules, the energy spectrum of the quasiparticles is bosonic.…”

“…By increasing the magnetic field strength, increases [32], and the system is led to crossover from the BEC region to the BCS one [14]. At very strong magnetic fields, when all the particles are localized in the lowest Landau level, only BCS diquarks are allowed [14]. On the other hand, the pure magnetic contribution to the pressure is negative [33].…”

(Inverse) magnetic catalysis in non-relativistic Bose-Einstein condensation

“…Our system corresponds to the BEC limit of the BCS/BEC crossover, which has been studied extensively in the absence of magnetic field for nonrelativistic fermions [19,20] and relativistic ones [21][22][23][24]. We found that the critical temperature for the BEC was dramatically affected by the magnetic field exhibiting magnetic catalysis or inverse magnetic catalysis depending on the coupling strength.…”

Anisotropy in the equation of state of strongly magnetized quark matter within the Nambu–Jona-Lasinio model

“…For field strengths comparable to the magnetic masses of charged gluons, the formation of a gluon-vortex state can take place [15,16] and, as explained in [10], the vortex formation corresponds to a phase transition from a magnetic-CFL to a Paramagnetic-CFL phase. There are many other effects produced by a strong magnetic fields in combination with superconductivity [17][18][19][20][21][22], such as the BEC-BCS crossover [1,[23][24][25][26] and the modification of chiral inhomogeneous phases [27][28][29][30].…”