Figure 1

Time evolution of the number correlation functions $R_{1,1}(t,0)$ (top panel) and $R_{1,2}(t,0)$ (bottom panel) of the bosonic bath (3), initially prepared in an equally weighted superposition of the bosonic eigenstates. $N=7$, $L=9$. The ratio between interatomic interaction strength and tunneling coupling is fixed at $W_B/J_B=3/7$, what ensures that we are in the parameter range of Wigner-Dyson spectral statistics, at $\overline{n}\simeq 1$ [8]. Time is measured in units of the site-to-site tunneling period ${\tau }_B=h/J_B$. The dashed lines show the bosonic correlation functions which result from substituting the Bose-Hubbard Hamiltonian (3) by a random matrix of the Gaussian orthogonal ensemble.Reuse & Permissions

Figure 2

Normalized mean velocity of the Fermi atoms, in units of $v_0=J_{F}d/\hslash$ for $Fd=0.57\times J_F$, $J_B=J_F$ for fermion-boson interaction strengths $W_{FB}=0.101\times J_F$, $0.143\times J_F$, $0.202\times J_F$ (from top to bottom), and $N=7$, $L=9$. The typical time scale of the interaction induced decay of the fermionic Bloch oscillations fits the time scale ${\gamma }^{-1}$ predicted by Eq. (8) (dash-dotted vertical lines) very well. The same observation holds for fixed $W_{FB}$ and variable $Fd$ (not shown here).Reuse & Permissions

Figure 3

Mean velocity $v(t)$ of the fermionic component (top panel, solid line), in units of $v_0=J_{F}d/\hslash$, and average energy $E_B(t)$ of the bosonic component (bottom panel, solid line), in units of $J_F$, for a low temperature ($k_{B}T\simeq 2.86\times J_B$) initial state of the bosonic bath. $Fd=0.143\times J_F$, $W_{FB}=0.143\times J_F$, $W_B/J_B=3/7$, $J_B=J_F$, $N=7$, $L=9$. The dashed lines indicate the corresponding solutions for a thermalized initial state of the bath, $k_{B}T\simeq 150\times J_B$. For a nonequilibrium initial condition of the bath the finite drift velocity $\overline{v}(t)$ manifests as a clear, nonvanishing offset of the fermionic mean velocity with respect to the Markovian result indicated by the dashed line (top panel). The dash-dotted line in the bottom plot is obtained by integration of Eq. (11).Reuse & Permissions

Figure 4

Fermionic drift velocity $\overline{v}$ (stars), in units of $v_0=J_{F}d/\hslash$, vs static forcing $Fd$, in units of $J_F$, compared to the prediction of Eq. (12) (continuous line), for the same parameters. The Bloch frequency ${\omega }_B=Fd/\hslash$ increases with $F$, while the effective decay rate $\gamma \simeq 0.037J_F/\hslash$, derived from (8) for $N=7$, $L=9$, $W_{FB}=0.143\times J_F$, $W_B/J_B=3/7$, $J_B=J_F$, is constant. Note the clear transition from Ohmic ($\overline{v}\sim Fd$) to negative differential conductance ($\overline{v}\sim 1/Fd$), at a finite value of $Fd$.Reuse & Permissions