Non-equilibrium phase transitions exist in damped-driven open quantum systems, when the continuous tuning of an external parameter leads to a transition between two robust steady states. In second-order transitions this change is abrupt at a critical point, whereas in first-order transitions the two phases can co-exist in a critical hysteresis domain. Here we report the observation of a first-order dissipative quantum phase transition in a driven circuit quantum electrodynamics (QED) system. It takes place when the photon blockade of the driven cavity-atom system is broken by increasing the drive power. The observed experimental signature is a bimodal phase space distribution with varying weights controlled by the drive strength. Our measurements show an improved stabilization of the classical attractors up to the milli-second range when the size of the quantum system is increased from one to three artificial atoms. The formation of such robust pointer states could be used for new quantum measurement schemes or to investigate multi-photon quantum many-body phases.The prototype of a nonlinear quantum system is the one described by the Jaynes-Cummings (JC) model of a two-level system coupled to a harmonic oscillator [1]. This model corresponds to very high accuracy to cavity QED systems [2], where atomic dipole transitions are coupled to quasi-resonant radiation modes of a resonator, or to circuit QED systems [3], where artificial atoms made of superconducting Josephson junctions are coupled to on-chip microwave resonators. The confinement of the photon into a small resonator volume results in a very strong coupling to the atom. Although the radiation mode spectrum is the well-known harmonic ladder, the coupling changes this to the significantly anharmonic JC spectrum, which allows for designing nonlinear processes within the low-intensity quantum domain and by means of only a single atom as a non-linear medium in the resonator.For monochromatic external driving with moderate power, the well-resolved resonances within the anharmonic JC spectrum [4][5][6][7] realize effectively a set of independent two-level systems each of which can be selectively addressed. When tuning the cavity driving to resonance with the lowest-lying excited state, at most a single photon can be in the resonator. This effect was named photon-blockade [8] in analogy with Coulomb blockade for electrons in a quantum well, and was experimentally demonstrated by observing photon anti-bunching in the transmitted radiation [9][10][11]. Photon blockade is, in fact, more than the single-photon effect. The next manifold containing two energy quanta, can be used as a two-photon gateway [12], and the concept can be further generalized to higher-order multi-photon transitions. The discrete quantum system with its anharmonic spectrum cannot be excited away from the well-resolved resonances. It is then fully reflective and stays in a dim state close to the ground state. When increasing the power of the drive, the effective two-level system under-goes power ...

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