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

We present a computational technique to calculate time- and momentum-resolved nonequilibrium spectral density of correlated systems using a tunneling approach akin to scanning tunneling spectroscopy. The important difference is that our probe is extended, basically a copy of the sample, allowing one to extract the momentum information of the excitations. We illustrate the method by measuring the spectrum of a Mott-insulating extended Hubbard chain after a sudden quench with the aid of time-dependent density-matrix renormalization-group calculations. We demonstrate that the system realizes a nonthermal state that is an admixture of spin and charge density wave states, with corresponding signatures that are recognizable as in-gap subbands. In particular, we identify a band of excitons and one of stable antibound states at high energies that gains enhanced visibility after the pump. We do not appreciate noticeable relaxation within the time scales considered, which is attributed to the lack of decay channels due to spin-charge separation. These ideas can be readily applied to study transient dynamics and spectral signatures of correlation-driven nonequilibrium processes.

Figure 1

(a) Proposed tunneling setup: a sample chain is connected to a probe chain via a tunneling barrier. The probe chain is set at a target gate voltage $V_g$. (b) Particles tunnel for a short period of time to the probe chain, where their momentum distribution $n\left(k\right)$ is measured.

Figure 2

Spectral function for a tight-binding chain obtained from the momentum distribution function $n_d\left(k\right)$ of a parallel probing chain after being in contact with the physical system for a time $t_{\text{probe}}$. Each momentum $k$ is obtained exactly by solving the two-level problem described above. Panels (a)–(c) correspond to $t_{\text{probe}}=3,7,9$ in units of $1/J$. Curves (d)–(f) show a cut in frequency along the $k=\pi$ line for the same times as in (a)–(c).

Figure 3

Momentum-resolved spectrum of the 1D extended Hubbard model at half filling at (a) zero temperature, where negative (positive) frequencies correspond to occupied (empty) states, and (b) $T=2.5J$, obtained with the tDMRG method for a chain of length $L=40$, and interaction $U=20,V=5$.

Figure 4

Momentum-resolved tunneling spectrum of the 1D extended Hubbard model at half filling after a sudden quench in the interactions from $U_0=2,V_0=0$ to $U=20,V=5$, obtained with the tDMRG method for a chain of length $L=32$ a time (a) $t_{\mathrm{wait}}=0$ and (b) $t_{\mathrm{wait}}=5$ after the quench, and a probe time $t_{\mathrm{probe}}=7.9$

Figure 5

(a) Integrated spectral weight as a function of $V_g$ for $t_{\mathrm{wait}}=0$ and different probe times, demonstrating the resolution improvement. (b) Same as (a) but for $t_{\mathrm{wait}}=0$ and 5, at the final $t_{\mathrm{probe}}=7.9$.

Figure 6

(a) Same as Fig. 4 obtained with exact diagonalization for a chain with $L=4$ and four probe sites. Horizontal color bars represent different transition frequencies, as explained in the text. (b) Histogram showing the contribution of different eigenstates to the resulting distribution after the quench. (c) Local density of double occupied sites for each eigenstate.