This work 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 excitation. It is demonstrated here how this last property of the 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.
We propose a scheme for investigating the nonequilibrium aspects of small-polaron physics using an array of superconducting qubits and microwave resonators. This system, which can berealized with transmon or gatemon qubits, serves as an analog simulator for a lattice model describing a nonlocal coupling of a quantum particle (excitation) to dispersionless phonons. We study its dynamics following an excitation-phonon (qubit-resonator) interaction quench using a numerically exact approach based on a Chebyshev-moment expansion of the time-evolution operator of the system. We thereby glean heretofore unavailable insights into the process of the small-polaron formation resulting from strongly momentum-dependent excitation-phonon interactions, most prominently about its inherent dynamical timescale. To further characterize this complex process, we evaluate the excitation-phonon entanglement entropy and show that initially prepared bare-excitation Bloch states here dynamically evolve into small-polaron states that are close to being maximally entangled. Finally, by computing the dynamical variances of the phonon position and momentum quadratures, we demonstrate a pronounced non-Gaussian character of the latter states, with a strong antisqueezing in both quadratures.
We propose an analog superconducting quantum simulator for a one-dimensional model featuring momentum-dependent (nonlocal) electron-phonon couplings of Su-Schrieffer-Heeger and „breathing-mode“types. Because its corresponding vertex function depends on both the electron- and phonon quasimomenta, this model does not belong to the realm of validity of the Gerlach-L\“{o}wen theorem that rules out any nonanalyticities in single-particle properties. The superconducting circuit behind the proposed simulator entails an array of transmon qubits and microwave resonators. By applying microwave driving fields to the qubits, a small-polaron Bloch state with an arbitrary quasimomentum can be prepared in this system within times several orders of magnitude shorter than the typical qubit decoherence times. We demonstrate that in this system — by varying the circuit parameters — one can readily reach the critical coupling strength required for observing the sharp transition from a nondegenerate (single-particle) ground state corresponding to zero quasimomentum (Kgs=0) to a twofold-degenerate small-polaron ground state at nonzero quasimomenta Kgs and −Kgs. Through exact numerical diagonalization of our effective Hamiltonian, we show how this nonanalyticity is reflected in the relevant single-particle properties (ground-state energy, quasiparticle residue, average number of phonons). The proposed setup provides an ideal testbed for studying quantum dynamics of polaron formation in systems with strongly momentum-dependent electron-phonon interactions.
We propose an analog quantum simulator for the Holstein molecular-crystal model based on a dispersive superconducting circuit QED system composed of transmon qubits and microwave resonators.By varying the circuit parameters, one can readily access both the adiabatic and the anti-adiabatic regimes of this model, and realize the coupling strengths required for small-polaron formation. We present a pumping scheme for preparing small-polaron states of arbitrary quasimomentum within time scales much shorter than the qubit decoherence time. The ground state of the system is characterized by anomalous amplitude fluctuation and measurement-based momentum squeezing in the resonator modes.