Transmon-Based Simulator Of Nonlocal Electron-Phonon Coupling: A Platform For Observing Sharp Small-Polaron Transitions

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 coupling vertex function depends on both the electron and phonon quasimomenta, this model does not belong to the realm of validity of the Gerlach-Lowen 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-by varying the externally tunable 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 (K-gs = 0) to a twofold-degenerate small-polaron ground state at nonzero quasimomenta K-gs and - K-gs. 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). We also show that the proposed setup provides an ideal testbed for studying the nonequilibrium dynamics of small-polaron formation in the presence of strongly momentum-dependent electron-phonon interactions.