Bare-Excitation Ground State of a Spinless-Fermion–Boson Model and $W$-State Engineering in an Array of Superconducting Qubits and Resonators

This Letter unravels an interesting property of a one-dimensional lattice model that describes a single itinerant spinless fermion (excitation) coupled to zero-dimensional (dispersionless) bosons through two different nonlocal coupling mechanisms. Namely, below a critical value of the effective excitation-boson coupling strength, the exact ground state of this model is the zero-quasimomentum Bloch state of a bare (i.e., completely undressed) excitation. It is demonstrated here how this last property of the lattice model under consideration can be exploited for a fast, deterministic preparation of multipartite $W$ states in a readily realizable system of inductively coupled superconducting qubits and microwave resonators.

Figure 1

(a) Schematic of the qubit-resonator system, whose $n$th repeating unit (indicated by the dashed rectangle) comprises SC qubit $Q_n$, resonator $R_n$, and coupler circuit $B_n$. The fluxes from the resonator modes $n$ and $n+1$ thread the upper loops of the coupler circuit $B_n$, effectively giving rise to an indirect inductive qubit-resonator coupling. (b) Pictorial illustration of the effective lattice model of the system, with the excitation hopping amplitude $t_0({\varphi }_{\mathrm{dc}})$ and each lattice site hosting dispersionless bosons with the frequency $\delta \omega ={\omega }_c-{\omega }_0$.

Figure 2

Ground-state energy of the system with $\delta \omega /2\pi =300\mathrm{MHz}$ as a function of the effective coupling strength ${\lambda }_{e\text{−}b}$. For ${\lambda }_{e\text{−}b}<{\lambda }_{e\text{−}b}^c\approx 0.72$ (i.e., ${\varphi }_{\mathrm{dc}}<0.972\pi$) the ground state of the system corresponds to a bare excitation, while for ${\lambda }_{e\text{−}b}\ge {\lambda }_{e\text{−}b}^c$ it corresponds to a heavily dressed (polaronic) one.