Exploring the thermodynamics of spin-1 Bose gases with synthetic magnetization

We study the thermodynamic properties of a spin-1 Bose gas across the Bose-Einstein condensation transition. We present the theoretical description of the thermodynamics of a trapped ideal spin-1 Bose gas and we describe the phases that can be obtained in this system as a function of the temperature and of the populations in the different spin components. We propose a simple way to realize a 'synthetic magnetization' that can be used to probe the entire phase diagram while keeping the real magnetization of the system fixed. We experimentally demonstrate the use of such method to explore different phases in a sample with zero total magnetization. Our work opens up new perspectives to study isothermal quenching dynamics through different magnetic phases in spinor condensates.