In dealing with Bose-Einstein statistics, assuming that the ground state energy is zero, it is concluded that the chemical potential of Bose gas system must be negative. How can we explain the zero energy ground state and its meaning?
The ground state energy of any stable system, that's not coupled to gravity, can be set equal to zero, as a direct calculation of the partition function of the free scalar field-that describes a free Bose gas-shows. This doesn't have anything to do with the chemical potential (that controls the density, not the energy). The reason is that the ground state energy of any stable system is bounded from below and global time translation invariance (that's where the absence of coupling to gravity is used) implies that only energy differences are observable. Therefore the value of the ground state energy isn't observable and can be set to zero.
Chemical potential of the photon gas is exactly zero. Think about the definition of the chemical potential.Whenever it is zero, it means that it costs zero energy to insert or to take away a particle from the sytem since interparticle forces are zero. And this is signature of superconductivity/superfluidity. Take a look at beautiful works by Fritz London http://www.amazon.com/Fritz-London-Scientific-Kostas-Gavroglu/dp/052102319X/ref=sr_1_1?ie=UTF8&qid=1463079677&sr=8-1&keywords=Fritz+london , especially his 2 volumes on Bose condensation and superconductivity.