  Dissipation can usually induce detrimental decoherence in a quantum system.
However, engineered dissipation can be used to prepare and stabilize coherent
quantum many-body states. Here, we show that by engineering dissipators
containing photon pair operators, one can stabilize an exotic dark state, which
is a condensate of photon pairs with a phase-nematic order. In this system, the
usual superfluid order parameter, i.e. single-photon correlation, is absent,
while the photon pair correlation exhibits long-range order. Although the dark
state is not unique due to multiple parity sectors, we devise an additional
type of dissipators to stabilize the dark state in a particular parity sector
via a diffusive annihilation process which obeys Glauber dynamics in an Ising
model. Furthermore, we propose an implementation of these photon-pair
dissipators in circuit-QED architecture.
