Revealing higher-order light and matter energy exchanges using quantum trajectories in ultrastrong coupling

Abstract

The dynamics of open quantum systems is often modelled using master equations, which describe the expected outcome of an experiment (i.e., the average over many realizations of the same dynamics). Quantum trajectories, instead, model the outcome of ideal single experiments -- the ``clicks'' of a perfect detector due to, e.g., spontaneous emission. The correct description of quantum jumps, which are related to random events characterizing a sudden change in the wave function of an open quantum system, is pivotal to the definition of quantum trajectories. In this article, we extend the formalism of quantum trajectories to open quantum systems with ultrastrong coupling (USC) between light and matter by properly defining jump operators in this regime. In such systems, exotic higher-order quantum-state- and energy-transfer can take place without conserving the total number of excitations in the system. The emitted field of such USC systems bears signatures of these higher-order processes, and significantly differs from similar processes at lower coupling strengths. Notably, the emission statistics must be taken at a single quantum trajectory level, since the signatures of these processes are washed out by the ``averaging'' of a master equation. We analyze the impact of the chosen unravelling (i.e., how one collects the output field of the system) for the quantum trajectories and show that these effects of the higher-order USC processes can be revealed in experiments by constructing histograms of detected quantum jumps. We illustrate these ideas by analyzing the excitation of two atoms by a single photon~[Garziano et al., Phys. Rev. Lett.117, 043601 (2016)]. For example, quantum trajectories reveal that keeping track of the quantum jumps from the atoms allow to reconstruct both the oscillations between one photon and two atoms, as well as emerging Rabi oscillations between the two atoms.

22 pages, 8 figures

References in corpus (13)

• Quantum fluids of light
• Beyond the Jaynes-Cummings model: circuit QED in the ultrastrong coupling regime
• Deep Strong Coupling Regime of the Jaynes-Cummings model
• Input-output theory of cavities in the ultra-strong coupling regime: the case of a time-independent vacuum Rabi frequency
• Signatures of a dissipative phase transition in photon correlation measurements
• Scattering in the ultrastrong regime: nonlinear optics with one photon
• Cavity Quantum Electrodynamics at Arbitrary Light-Matter Coupling Strengths
• Stochastic pure state representation for open quantum systems
• Quantum coherence in ultrastrong optomechanics
• Implications of gauge freedom for nonrelativistic quantum electrodynamics
• Parity-dependent State Engineering and Tomography in the ultrastrong coupling regime
• Dissipation and detection of polaritons in ultrastrong coupling regime
• Dissipative state transfer and Maxwell's demon in single quantum trajectories: Excitation transfer between two noninteracting qubits via unbalanced dissipation rates

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• Spontaneous emission in Casimir-Rabi oscillations through a weak optomechanical coupling
• Phonon-photon conversion as mechanism for cooling and coherence transfer
• Bilateral photon emission from a vibrating mirror and multiphoton entanglement generation
• Release of virtual photon and phonon pairs from qubit-plasmon-phonon ultrastrong coupling system