We study the phase diagram of two-flavor dense QCD at finite isospin and baryon chemical potentials in the framework of the Nambu–Jona-Lasinio model. We focus on the case with arbitrary isospin chemical potential ${\mu }_{\mathrm{I}}$ and small baryon chemical potential ${\mu }_{\mathrm{B}}\le {\mu }_{\mathrm{B}}^{\chi }$ where ${\mu }_{\mathrm{B}}^{\chi }$ is the critical chemical potential for the first-order chiral phase transition to happen at ${\mu }_{\mathrm{I}}=0$. The ${\mu }_{\mathrm{I}}-{\mu }_{\mathrm{B}}$ phase diagram shows a rich phase structure since the system undergoes a crossover from a Bose-Einstein condensate of charged pions to a BCS superfluid with condensed quark-antiquark Cooper pairs when ${\mu }_{\mathrm{I}}$ increases at ${\mu }_{\mathrm{B}}=0$, and a nonzero baryon chemical potential serves as a mismatch between the pairing species. We observe a gapless pion condensation phase near the quadruple point $({\mu }_{\mathrm{I}},{\mu }_{\mathrm{B}})=(m_{\pi },M_{\mathrm{N}}-1.5m_{\pi })$ where $m_{\pi }$, $M_{\mathrm{N}}$ are the vacuum masses of pions and nucleons, respectively. The first-order chiral phase transition becomes a smooth crossover when ${\mu }_{\mathrm{I}}>0.82m_{\pi }$. At very large isospin chemical potential, ${\mu }_{\mathrm{I}}>6.36m_{\pi }$, an inhomogeneous Larkin-Ovchinnikov-Fulde-Ferrell superfluid phase, appears in a window of ${\mu }_{\mathrm{B}}$, which should in principle exist for arbitrary large ${\mu }_{\mathrm{I}}$. Between the gapless and the Larkin-Ovchinnikov-Fulde-Ferrell phases, the pion superfluid phase and the normal quark matter phase are connected by a first-order phase transition. In the normal phase above the superfluid domain, we find that charged pions are still bound states even though ${\mu }_{\mathrm{I}}$ becomes very large, which is quite different from that at finite temperature. Our phase diagram is in good agreement with that found in imbalanced cold atom systems.

• Received 20 June 2010

DOI:https://doi.org/10.1103/PhysRevD.82.056006