Dynamically Generated Double Occupancy as a Probe of Cold Atom Systems

The experimental investigation of quantum phases in optical lattice systems provides major challenges. Recently, dynamical generation of double occupancy via modulation of the hopping amplitude $t$ has been used to characterize the strongly correlated phase of fermionic atoms. Here, we want to validate this experimental technique with a theoretical study of the driven Hubbard model using analytic methods. We find that conclusive evidence for a Mott phase can be inferred from such a measurement, provided that sufficiently low temperatures $k_{B}T\ll t$ can be reached.

Figure 1

Regimes where the dynamically generated double-occupancy probe is analyzed: High temperatures (I) are discussed in the atomic limit. The regime at zero temperature and low densities (II) involves the solution of a two-particle problem; the situation at half filling and $T=0$ (III) is done within a slave-spin mean-field analysis.

Figure 2

Characteristic DGDO signal for the different regimes (I)–(III) of Fig. 1. (a) For the high temperature region (I), we find an increase in $\delta {\mathcal{D}}_{\mathrm{tot}}$ for increasing $U/T$ and a saturation value $\delta {\mathcal{D}}_{\mathrm{tot}}\to {\rho }^2$ at $U\gg T$. (b) For the low-density phase at $T=0$, we find the same behavior with a saturating response at $u=U/U_c\gg 1$ where $\delta {\mathcal{D}}_{\mathrm{tot}}\to {\rho }^2[1-\sin (4\pi \rho )/4\pi \rho ]$. The response of the system at half filling and $T=0$ (III) changes its behavior significantly at $u=1$. (c) Spectral DGDO signal $\delta \mathcal{D}(\omega )$ with peaks at $\hslash \omega =\Delta$ and around $\hslash \omega \approx \max (U_c,U)$ identifying transitions between the Gutzwiller and upper Hubbard, and those between the lower and higher Hubbard bands, respectively. (d) Total weights $\delta {\mathcal{D}}_{\mathrm{tot}}^{⟨,⟩}$ accumulated in the two peaks in (c). Shown in grey is the fluctuation region $|u-1|<u^{\mathrm{fl}}$ where our mean-field analysis is not valid.

Figure 3

The single-particle spectral density (per spin $\sigma$) $A_{\sigma }(\omega )$ calculated within the slave-spin theory for different interaction strengths $u$. In the metallic phase, panels (a) and (b), the DGDO probe can induce transitions to the upper Hubbard band from either the coherent Gutzwiller band at $\hslash \omega =0$ or the lower Hubbard band, see (b). In the insulating state, only the latter possibility remains, see (d).