Spectroscopy of Collective Excitations in Interacting Low-Dimensional Many-Body Systems Using Quench Dynamics

We study the problem of rapid change of the interaction parameter (quench) in a many-body low-dimensional system. It is shown that, measuring the correlation functions after the quench, the information about a spectrum of collective excitations in a system can be obtained. This observation is supported by analysis of several integrable models and we argue that it is valid for nonintegrable models as well. Our conclusions are supplemented by performing exact numerical simulations on finite systems. We propose that measuring the power spectrum in a dynamically split 1D Bose-Einsten condensate into two coupled condensates can be used as an experimental test of our predictions.

Figure 1

Power spectrum for a single QJJ consisting of two sites. At $t=0$ the tunneling amplitude is suddenly reduced from a very large value to $J=10$, the interaction strength $E_c=1$. The inset shows the energy levels of the QJJ with the arrows indicating a couple of possible oscillation frequencies.

Figure 2

Power spectrum for $K=1.6$ and $\Delta =0.4$ including single and two-breather contributions. Many other contributions are not visible on this scale. Arrows indicate $\delta$-peaks of type (i) (see the text below). The inset shows the power spectrum from the exact diagonalization on $6\times 2$ sites for the bosonic Hubbard model. Note the break in the vertical scale. Frequency units are defined by $M_s(\Delta ,K)$ for given $\Delta$ and $K$.