Two-photon quantum Rabi model with superconducting circuits

Abstract

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 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 twophoton interactions introduce a qubit-state-dependent Kerr term. Finally, we analyze the spectral collapse of the multi-qubit 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.

Observing the Spectral Collapse of Two-Photon Interaction Models

“…Notice that in the literature the TPI term is often written asσ (i) x â † a † +ââ , whereas we take here the interaction Hamiltonian to be in the full-quadratic form. The latter form of the interaction arises when the qubit is coupled to the square of the electric (or magnetic) field of the cavity mode and it is therefore a natural generalization of the standard dipolar coupling [19]. The system spectrum is shown in Figure 1a,b for N = 1 and N = 3, as a function of the coupling strength g 2 .…”

“…In particular, it was shown that in the context of circuit QED it is possible to engineer an intrinsically nondipolar coupling between a flux qubit and a microwave resonator. In this way, dipolar and two-photon interaction terms can be selectively activated [19] and, in the case of galvanic coupling, the interaction strength can be pushed into the USC regime [20]. In the following, we will briefly introduce the spectral properties of TPI models and we will show how they affect the optical response of the system.…”

“…Panel (a) shows[20] the spectrum for N = 1; different line styles denote the parity of the number of photons (positive for continuous red lines, negative for dotted black lines), which is a symmetry ofĤ 2ph . Panel (b) shows[19] the spectrum for N = 3, the solid red line corresponds to the two-photon DickeĤ 2ph , while the yellow dashed line corresponds to the model obtained including inter-spincouplings J N −1 i=1 σ i x σ i+1x of strength J = 0.2ωc. (c,d) Fluorescence spectrum[20] in arbitrary units of the output signal under coherent drive, for different values of the coupling strength.…”

Resolution of gauge ambiguities in ultrastrong-coupling cavity quantum electrodynamics

“…In these interaction regimes, several properties of coupled light-matter systems change drastically, opening the way to a wealth of new intriguing physical effects (see, e.g. [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]) which may offer opportunities for the development of quantum technologies [36][37][38][39][40][41][42][43][44].…”

Multiphoton Jaynes-Cummings Model: Arbitrary Rotations in Fock Space and Quantum Filters

“…When the interaction energy is a small perturbation on the free energies, the quantum Rabi model can be reduced to the well-known Jaynes-Cummings (JC) model [18] through the rotating-wave approximation, which describes the usual coherent exchange of a quantum of energy between a two-level atom and a single-mode bosonic field.The JC model can be extended to nonlinear versions (nondipolar light-matter interaction) [19], in particular the multiphoton JC model [20,21] that considers multiphoton exchange. Such a nonlinear Hamiltonian appears, at least for two-photon interaction, in trapped-ion domain [22,23], optical [24] and microwave [25] cavities, or even in superconducting circuits [26][27][28][29][30]. In Refs.…”