  Charge qubits can be created and manipulated in solid-state
double-quantum-dot (DQD) platforms. Typically, these systems are strongly
affected by quantum noise stemming from coupling to substrate phonons. This is
usually assumed to lead to decoherence towards steady states that are diagonal
in the energy eigenbasis. In this article we show, to the contrary, that due to
the presence of phonons the equilibrium steady state of the DQD charge qubit
spontaneously exhibits coherence in the energy eigenbasis with high purity. The
magnitude and phase of the coherence can be controlled by tuning the
Hamiltonian parameters of the qubit. The coherence is also robust to presence
of fermionic leads. In addition, we show that this steady-state coherence can
be used to drive an auxiliary cavity mode coupled to the DQD.
