  Induced interactions and bound states of charge carriers immersed in a
quantum medium are crucial for the investigation of quantum transport.
Ultracold atom-ion systems can provide a convenient platform for studying this
problem. Here, we investigate the static properties of one and two ionic
impurities in a bosonic bath using quantum Monte Carlo methods. We identify
three bipolaronic regimes depending on the strength of the atom-ion potential
and the number of its two-body bound states: a perturbative regime resembling
the situation of a pair of neutral impurities, a non-perturbative regime that
loses the quasi-particle character of the former, and a many-body bound state
regime that can arise only in the presence of a bound state in the two-body
potential. We further reveal strong bath-induced interactions between the two
ionic polarons. Our findings show that numerical simulations are indispensable
for describing highly correlated impurity models.
