Coupling-energy driven pumping through quantum dots: the role of coherences

Abstract

We study the impact of off-resonant tunneling and coherences on the electron pumping through quantum dots. Thereby, we focus on two electron-pump setups where lowest-order tunneling processes are suppressed and the pump is exclusively driven by modulations of the coupling energy. The first setup is driven by switching on and off the couplings between the quantum dot and the leads, while the second setup employs measurements of the dot occupation. We derive exact solutions for arbitrarily strong tunnel couplings in the absence of Coulomb interaction, identify parameter regimes with optimal pumping currents or optimal energy efficiency, and discuss similarities between both pumping mechanisms.

Figures (20)

• Figure 1: Sketch of an open quantum system subject to repeated interventions erasing the system--environment coherences and thereby the coupling energy. In between, coherences may rebuild and the energy of system plus environment may increase on the cost of the coupling energy.
• Figure 2: Schematic visualization of the fermionic reaction--coordinate mapping RC: A quantum dot (QD) coupled to two Lorentzian shaped baths is equivalent to the situation where the QD is coupled to two reaction--coordinates (RC) that are coupled to two new baths with wideband spectral--coupling densities.
• Figure 3: Schematic visualization of the functionality (step 1 and step 2 form one pumping cycle) of pumping scheme 1: The pump consists of a quantum dot (QD) that has a time--independent onsite potential $\varepsilon$ and is located between two baths at zero temperature. The difference of the chemical potentials $\mu_1$ and $\mu_2$ of the baths is given by $V$. Here, the pumping results only from the coupling and decoupling processes with the baths. In order to study non--Markovian effects, we consider structured baths with Lorentzian shaped spectral densities $\Gamma_1(\omega)$, $\Gamma_2(\omega)$zedlerWeakcouplingApproximationsNonMarkovian2009a.
• Figure 4: The coupling function $g_\nu (t)$ for $\nu=1,2$ as a function of time $t$ with the duration $t_1$ of step 1 and the duration $t_2$ of step 2. The functions fulfill the relation $g_1(t)=1-g_2(t)$.
• Figure 5: Average number of electrons $N_\text{pump}\approx\left<n_{\text{stat},1}\right>$ pumped during one cycle as a function of the width $\Delta_1$ (logarithmic scale) and the peak position $\omega_1$ (logarithmic scale) of the spectral coupling--density of the first bath in the slow--pumping regime, $t_1,t_2 \rightarrow \infty$. The QD--orbital energy $\varepsilon=V+0^+$ is directly above the chemical potential of the second bath. The coupling with the first bath is $\Gamma_1=100\,V$ whereas the coupling with the second bath is chosen sufficiently weak (formally $\Gamma_2\searrow 0$) such that the QD is completely emptied after step 2. Pumping is suppressed for $\omega_1 > \frac{\Delta_1 \Gamma_1}{2 \varepsilon}$ (region I) and is largest in region II.