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arXiv:2006.05593 · Physical Review Research

Critical theory for the breakdown of photon blockade

Jonathan B. Curtis, Igor Boettcher, Jeremy T. Young, Mohammad F. Maghrebi, H. J. Carmichael, Alexey Vyacheslavovich Gorshkov, Michael Foss‐Feig

Published Apr 21, 2021• 24 citations

Abstract

Photon blockade is the result of the interplay between the quantized nature of light and strong optical nonlinearities, whereby strong photon-photon repulsion prevents a quantum optical system from absorbing multiple photons.We theoretically study a single atom coupled to the light field, described by the resonantly driven Jaynes-Cummings model, in which case the photon blockade breaks down in a second-order phase transition at a critical drive strength.We show that this transition is associated to the spontaneous breaking of an antiunitary PT symmetry.Within a semiclassical approximation, we calculate the expectation values of observables in the steady state.We then move beyond the semiclassical approximation and approach the critical point from the disordered (blockaded) phase by reducing the Lindblad quantum master equation to a classical rate equation that we solve.The width of the steady-state distribution in Fock space is found to diverge as we approach the critical point with a simple power law, allowing us to calculate the critical scaling of steady-state observables without invoking mean-field theory.We propose a simple physical toy model for biased diffusion in the space of occupation numbers, which captures the universal properties of the steady state.We list several experimental platforms where this phenomenon may be observed.

DOI: 10.1103/physrevresearch.3.023062

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Photon blockade is the result of the interplay between the quantized nature of light and strong optical nonlinearities, whereby strong photon-photon repulsion prevents a quantum optical system from absorbing multiple photons.We theoretically study a single atom coupled to the light field, described by the resonantly driven Jaynes-Cummings model, in which case the photon blockade breaks down in a second-order phase transition at a critical drive strength.We show that this transition is associated to the spontaneous breaking of an antiunitary PT symmetry.Within a semiclassical approximation, we calculate the expectation values of observables in the steady state.We then move beyond the semiclassical approximation and approach the critical point from the disordered (blockaded) phase by reducing the Lindblad quantum master equation to a classical rate equation that we solve.The width of the steady-state distribution in Fock space is found to diverge as we approach the critical point with a simple power law, allowing us to calculate the critical scaling of steady-state observables without invoking mean-field theory.We propose a simple physical toy model for biased diffusion in the space of occupation numbers, which captures the universal properties of the steady state.We list several experimental platforms where this phenomenon may be observed.

Nonequilibrium 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 coexist in a critical hysteresis domain.Here, we report the observation of a first-order dissipative quantum phase transition in a driven circuit quantum electrodynamics 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 millisecond 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 multiphoton phases of finite-size, nonlinear, open quantum systems.

We follow the passage from complex amplitude bistability to phase bistability in the driven dissipative Jaynes-Cummings oscillator. Quasi -distribution functions in the steady state are employed, for varying qubit-cavity detuning and drive parameters, in order to track a first-order dissipative quantum phase transition up to the critical point marking a second-order transition and spontaneous symmetry breaking. We demonstrate the photon blockade breakdown in the dispersive regime, and find that the coexistence of cavity states in the regime of quantum bistability is accompanied by pronounced qubit-cavity entanglement. Focusing on the effect of quantum-activated switching for both coupled degrees of freedom, we move from a region of minimal entanglement in the dispersive regime, where we derive analytical perturbative results, to the threshold behaviour of spontaneous dressed-state polarization at resonance.

When the photonic mode in the Jaynes-Cummings model is driven by an external classical field, the system can undergo the photon-blockade breakdown phase transition at a critical point. Such a phase transition has been detailedly investigated, but the critical properties of the eigenstates remain largely unexplored so far. We here study the geometric criticality associated with these eigenstates. The amplitude and phase of the drive serve as the control parameter of the governing Hamiltonian. We find the quantum metric and Berry curvature tensors for each eigenstate display divergent behaviors in the critical region. More importantly, the divergence associated with bright eigenstates is much more pronounced than that for the unique dark state. Our theoretical results can be experimentally confirmed in circuit quantum electrodynamics systems, where the driven Jaynes-Cummings model has been realized.

The photon-blockade breakdown bistability can be intuitively explained invoking the energy spectrum of the interacting qubit-mode system. Yet, the neoclassical solution of the driven-dissipative Jaynes-Cummings model has been shown to capture several key aspects of the phenomenon. In this paper, we set out to compare a fully quantum solution with the neo- and semiclassical solutions. Although the neoclassical theory is founded on the assumption of a pure partial state for the qubit, it is not simply the γ →0 limit of the semiclassical theory, the semi- versus neoclassical duality being a case of non-commutativity of limits. Furthermore, we show that the neoclassical predictions still hold in the case of a small qubit decay. Tracing the bistable behavior for different detunings, we show that it is robust over a significant range of Δ values. We demonstrate that the aptitude of the neoclassical description is founded on the high quantum purity of the bright state of the photon-blockade breakdown bistability, which sharply differentiates this phenomenology from conventional optical bistability. It is thereby demonstrated that driven-dissipative dynamics can produce closely separable pure steady states in an interacting bipartite.