We present a circuit-QED scheme which makes it possible to reach the ultrastrong-coupling regime of a nondipolar interaction between a single qubit and a quantum resonator. We show that the system Hamiltonian is well approximated by a two-photon quantum Rabi model and propose a simple scattering experiment to probe its fundamental properties. In particular, we identify a driving scheme that reveals the change in selection rules characterizing the breakdown of the rotating-wave approximation and the transition from strong to ultrastrong two-photon interactions. Finally, we show that a frequency crowding in a narrow spectral region is observable in the output fluorescence spectrum as the coupling strength approaches the collapse point, paving the way to the direct observation of the onset of the spectral collapse in a solid-state device.
We present a circuit-QED scheme which makes it possible to reach the ultrastrong-coupling regime of a nondipolar interaction between a single qubit and a quantum resonator. We show that the system Hamiltonian is well approximated by a two-photon quantum Rabi model and propose a simple scattering experiment to probe its fundamental properties. In particular, we identify a driving scheme that reveals the change in selection rules characterizing the breakdown of the rotating-wave approximation and the transition from strong to ultrastrong two-photon interactions. Finally, we show that a frequency crowding in a narrow spectral region is observable in the output fluorescence spectrum as the coupling strength approaches the collapse point, paving the way to the direct observation of the onset of the spectral collapse in a solid-state device.
Until very recently, two-photon interaction processes have been considered only as arising from second- or higher-order effects in driven systems, and so limited to extremely small coupling strengths. However, a variety of novel physical phenomena emerges in the strong and ultrastrong coupling regimes. Strikingly, for a critical value of the coupling strength the discrete spectrum collapses into a continuous band. In this extended abstract, we discuss recent proposals to implement genuine two-photon interactions in an undriven solid-state system, in the framework of circuit QED. In particular, we review counterintuitive spectral features of two-photon interaction models and we show how the onset of the spectral collapse can be observed in feasible scattering experiments.
Understanding the interaction between light and matter is very relevant for fundamental studies of quantum electrodynamics and for the development of quantum technologies. The quantum Rabi model captures the physics of a single atom interacting with a single photon at all regimes of coupling strength. We report the spectroscopic observation of a resonant transition that breaks a selection rule in the quantum Rabi model, implemented using an LC resonator and an artificial atom, a superconducting qubit. The eigenstates of the system consist of a superposition of bare qubit-resonator states with a relative sign. When the qubit-resonator coupling strength is negligible compared to their own frequencies, the matrix element between excited eigenstates of different sign is very small in presence of a resonator drive, establishing a sign-preserving selection rule. Here, our qubit-resonator system operates in the ultrastrong coupling regime, where the coupling strength is 10% of the resonator frequency, allowing sign-changing transitions to be activated and, therefore, detected. This work shows that sign-changing transitions are an unambiguous, distinctive signature of systems operating in the ultrastrong coupling regime of the quantum Rabi model. These results pave the way to further studies of sign-preserving selection rules in multiqubit and multiphoton models.
We use a recently derived gauge-invariant formulation of the problem of a two-level system coupled to an optical cavity to explore the transition between the weak and the ultrastrong coupling regimes of light-matter interaction. We explore this transition using the intensity correlations ${g}^{(2)}(\ensuremath{\tau})$ of the emitted light, and we find strong, unbounded bunching of the emission from systems governed by the Rabi Hamiltonian. Surprisingly, this effect is observed not only in the ultrastrong coupling regime, but also for weakly coupled systems, where the Jaynes-Cummings Hamiltonian would predict the opposite, antibunched emission. This suggests that the higher-order correlations are a particularly sensitive probe of the divergence between the Jaynes-Cummings and Rabi Hamiltonians, and they can serve as an indicator of the breakdown of the rotating wave approximation. Our findings indicate also that the boundary between the weakly, strongly, and ultra-strongly-coupled dynamics is much richer than currently accepted.
We propose a superconducting circuit to implement a two-photon quantum Rabi model in a solid-state device, where a qubit and a resonator are coupled by a two-photon interaction. We analyze the input-output relations for this circuit in the strong-coupling regime and find that fundamental quantum-optical phenomena are qualitatively modified. For instance, two-photon interactions are shown to yield a single- or two-photon blockade when a pumping field is either applied to the cavity mode or to the qubit, respectively. In addition, we derive an effective Hamiltonian for perturbative ultrastrong two-photon couplings in the dispersive regime, where two-photon interactions introduce a qubit-state-dependent Kerr term. Finally, we analyze the spectral collapse of the multiqubit two-photon quantum Rabi model and find a scaling of the critical coupling with the number of qubits. Using realistic parameters with the circuit proposed, three qubits are sufficient to reach the collapse point.
We revisit the derivation of Rabi- and Dicke-type models, which are commonly used for the study of quantum light-matter interactions in cavity and circuit QED. We demonstrate that the validity of the two-level approximation, which is an essential step in this derivation, depends explicitly on the choice of gauge once the system enters the ultrastrong-coupling regime. In particular, while in the electric dipole gauge the two-level approximation can be performed as long as the Rabi frequency remains much smaller than the energies of all higher-lying levels, it can dramatically fail in the Coulomb gauge, even for systems with an extremely anharmonic spectrum. We extensively investigate this phenomenon both in the single-dipole (Rabi) and multidipole (Dicke) case, and consider the specific examples of dipoles confined by double-well and square-well potentials, and of circuit QED systems with flux qubits coupled to an LC resonator.
Cavity and circuit QED study light-matter interaction at its most fundamental level. Yet, this interaction is most often neglected when considering the coupling of this system with an environment. In this paper, we show how this simplification, which leads to the standard quantum optics master equation, is at the root of unphysical effects. Including qubit relaxation and dephasing, and cavity relaxation, we derive a master equation that takes into account the qubit-resonator coupling. Special attention is given to the ultrastrong coupling regime, where the failure of the quantum optical master equation is manifest. In this situation, our model predicts an asymmetry in the vacuum Rabi splitting that could be used to probe dephasing noise at unexplored frequencies. We also show how fluctuations in the qubit frequency can cause sideband transitions, squeezing, and Casimir-like photon generation.