Quasiparticle Dynamics in a Bose Insulator Probed by Interband Bragg Spectroscopy

We investigate experimentally and theoretically the dynamical properties of a Mott insulator in decoupled one-dimensional chains. Using a theoretical analysis of the Bragg excitation scheme, we show that the spectrum of interband transitions holds information on the single-particle Green’s function of the insulator. In particular, the existence of particle-hole coherence due to quantum fluctuations in the Mott state is clearly seen in the Bragg spectra and quantified. Finally, we propose a scheme to directly measure the full, momentum-resolved spectral function as obtained in the angle-resolved photoemission spectroscopy of solids.

Figure 1

An array of 1D gases created by a 2D optical lattice is driven into the MI state by a third (OL) in the $Ox$ direction. The energy band structure in the 1D lattice is depicted on the left with red solid lines. The lowest band corresponds to particles in the MI, and above it are the higher single-particle energy bands. Two laser beams (Bragg beams, green arrows) excite the initial MI by transferring a particle to a high-energy band and leaving a hole in the many-body state.

Figure 2

Interband Bragg spectra. (a) Energy absorption rate $D(\omega )$ over the energy range of the second and third Bloch band for a Bragg momentum transfer $q=0.96\pi /a$ and for a lattice depth $s_x=9$. The (blue and green) dots are the experimental data with error bars indicating statistical uncertainties after averaging over four to five experimental acquisitions; the black lines are the theoretical predictions for $D(\omega )$. (b) Integrated spectral weight $W$ in the third band. (c) and (d) Skewness (third moment) of $S(q,\omega )$ in the second (c) and third (d) band. The measured values are compared to the theoretical prediction including particle-hole coherence (thick lines) and to the contribution of the single-particle density of states alone (thin lines). The shaded area indicates the systematic uncertainty in determination of $s_x$ in the experiment.

Figure 3

Response functions. (a) Diagram describing the Bragg excitation in the linear response. The black squares describe the coupling of the Bragg beams to the density fluctuations. The full (dashed) lines denote the GF of a hole in the MI (of an upper band particle). The gray area $\Gamma$ stands for the final-state interactions between the upper band particle and the MI hole. (b) In a $T$-matrix approximation, the final state interaction gives rise to a ladder diagram, where the wiggly lines denote the interaction between the upper band particle and the hole. (c) In the absence of final state interactions, the bare bubble describes the experimental response.