Visibility and stability of superstripes in a spin-orbit-coupled Bose-Einstein condensate

We consider a spin-$1/2$ Bose-Einstein condensate with equal Rashba and Dresselhaus spin-orbit coupling. After reviewing some relevant features of the quantum phases of the system, we present a short study on how their properties are changed by the presence of non-zero magnetic detunings and spin-asymmetric interactions. At small values of the Raman coupling and of the magnetic field the so-called stripe phase occurs, which displays both superfluidity and periodic density modulations, in analogy with supersolids. We finally review a recent proposal (Phys. Rev. A 90, 041604) to improve the visibility of the fringes, based on the space separation of the two spin components into a 2D bi-layer configuration and on the application of a $\pi/2$ Bragg pulse, and we show that this new configuration also yields a sizable increase of the stability of the stripe phase against magnetic fluctuations.