Quantum physics was invented to account for two fundamental features of measurement resultstheir discreetness and randomness. Emblematic of these features is Bohr's idea of quantum jumps between two discrete energy levels of an atom 1 . Experimentally, quantum jumps were first observed in an atomic ion driven by a weak deterministic force while under strong continuous energy measurement 2-4 . The times at which the discontinuous jump transitions occur are reputed to be fundamentally unpredictable. Can there be, despite the indeterminism of quantum physics, a possibility to know if a quantum jump is about to occur or not? Here, we answer this question affirmatively by experimentally demonstrating that the jump from the ground to an excited state of a superconducting artificial three-level atom can be tracked as it follows a predictable "flight," by monitoring the population of an auxiliary energy level coupled to the ground state. The experimental results demonstrate that the jump evolution when completed is continuous, coherent, and deterministic. Furthermore, exploiting these features and using real-time monitoring and feedback, we catch and reverse a quantum jump mid-flight, thus deterministically preventing its completion. Our results, which agree with theoretical predictions essentially without adjustable parameters, support the modern quantum trajectory theory 5-9 and provide new ground for the exploration of real-time intervention techniques in the control of quantum systems, such as early detection of error syndromes.Bohr conceived of quantum jumps 1 in 1913, and while Einstein elevated their hypothesis to the level of a quantitative rule with his AB coefficient theory 10,11 , Schrödinger strongly objected to their existence 12 . The nature and existence of quantum jumps remained a subject of controversy for seven decades until they were directly observed in a single system 2-4 . Since then, quantum jumps have been observed in a variety of atomic [13][14][15][16] and solid-state 17-21 systems. Recently, quantum jumps have been recognized as an essential phenomenon in quantum feedback control 22,23 , and in particular, for detecting and correcting decoherence-induced errors in quantum information systems 24,25 .

The mean-field steady states of a generalized model of N two-state systems interacting with one mode of the radiation field in the presence of external driving and dissipation are surveyed as a function of three control parameters: one governs the interaction strength relative to the resonance frequency, thus accessing the Dicke quantum phase transition, a second the relative strength of counter-rotating to rotating-wave interactions, and a third the amplitude of an external field driving the cavity mode. We unify the dissipative extension of the Dicke quantum phase transition with the recently reported breakdown of photon blockade [H. J. Carmichael, Phys. Rev. X 5, 031028 (2015)]; key to the unification is a previously unreported phase of the Dicke model and a renormalized critical drive strength in the breakdown of photon blockade. For the simplest case of one two-state system, we complement mean-field results with a full quantum treatment: we derive quasi-energies to recover the renormalized critical drive strength, extend the multi-photon resonances of photon blockade to a counter-rotating interaction, and explore quantum fluctuations through quantum trajectory simulations.PACS numbers: PACS numbers go here arXiv:1806.05761v1 [quant-ph]

A system evolving under the driven Jaynes-Cummings (JC) model will undergo a phase transition at a critical driving field amplitude. This transition is foreshadowed by a collapse of the quasienergy level spectra of the system and remains present as the model is extended to include a counter-rotating interaction. We study this critical response and obtain the eigenvalues and eigenstates of the extended model by presenting a correspondence between the JC model and a charged Dirac particle subject to an external electromagnetic field. Under this correspondence, the field and two-level system that compose the JC model map to the external and internal degrees of freedom describing the Dirac particle, respectively. The phases of the system below (above) the critical drive are then characterized by discrete (continuous) solutions, with the manipulations required to obtain these solutions appearing naturally as Lorentz transformations.