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We present a computational technique to calculate time and momentum resolvednon-equilibrium spectral density of correlated systems using a tunnelingapproach akin scanning tunneling spectroscopy. The important difference is thatour probe is extended, basically a copy of the sample, allowing one to extractthe momentum information of the excitations. We illustrate the method bymeasuring the spectrum of a Mott-insulating extended Hubbard chain after asudden quench with the aid of time-dependent density matrix renormalizationgroup (tDMRG) calculations. We demonstrate that the system realizes anon-thermal state that is an admixture of spin and charge density wave states,with corresponding signatures that are recognizable as in-gap sub-bands. Inparticular, we identify a band of excitons and one of stable anti-bound statesat high energies that gains enhanced visibility after the pump. We do notappreciate noticeable relaxation within the time-scales considered, which isattributed to the lack of decay channels due to spin-charge separation. Theseideas can be readily applied to study transient dynamics and spectralsignatures of correlation-driven non-equilibrium processes.

Time and momentum-resolved tunneling spectroscopy of pump-driven non-thermal excitations in Mott insulators