Long-range spin transport in asymmetric quadruple quantum dots configurations

TL;DR

The paper studies long-range coherent transport in a linear quadruple quantum dot array with reduced symmetry. It employs a Lindblad master-equation framework together with an effective co-tunneling description to identify resonance conditions that minimize occupation of central dots and enable transfer between the outer dots. Using Schrieffer-Wolff-type reasoning, it derives simple effective Hamiltonians for single-particle and multi-electron regimes, showing robust long-range transfer under resonances such as $\tilde{\varepsilon}_1=\tilde{\varepsilon}_4$ and $E_{1110}=E_{0111}$, with dephasing and spin-blockade providing characteristic signatures. The results provide design principles and expected experimental observables for long-range quantum state transfer in QQD arrays, motivating future implementations in quantum information architectures.

Abstract

We theoretically investigate long-range coherent charge transport in linear quadruple quantum dot (QQD) arrays under reduced symmetry configurations. Employing a master equation approach, we identify precise resonant conditions that enable minimal occupation of intermediate dots, thereby facilitating long-range transfer between distant sites. Our results highlight the critical role of parameter asymmetry and coherent tunneling mechanisms in achieving efficient quantum state transfer.

Figures (12)

• Figure 1: (a) Linear quadruple quantum dot array, coupled to leads with rates $\Gamma_{L,R}$, defined by chemical potentials $\mu_{L,R}$. Electrons can flow from the source (left lead) to the drain (right lead) through the quantum dot array. Interdot tunneling rates are denoted by $\tau_i$. Each dot is characterized by its on-site energy $\varepsilon_i$. When states $(2, 0, 0, 1)$ and $(1, 0, 0, 2)$ are degenerate, and the middle dots are out of resonance, long-range transport occurs between the first and last dots, denoted with a gray dashed line. (b) Schematic representation of gates defining the QQD, together with the source and drain leads. The plunger states $V_L$ and $V_R$ are applied to the first and fourth dots, respectively.
• Figure 2: Dynamics (solid lines) for a single particle in a quadruple quantum dot. The effective model, given by Eq. (\ref{['eq:effective_model']}), is shown as dashed lines. The system parameters are $\tau_i = \tau$, $\varepsilon_1 = \varepsilon_4=0$, and $\varepsilon_2 = \varepsilon_3 = 10\tau$.
• Figure 3: Comparison of current for a highly symmetric configuration (a) and an asymmetric configuration (b), as shown on the top of each panel. White dashed lines denote the analytical resonance condition from Eq. (\ref{['eq:resonance_condition_one_particle_detuning']}). Panels (c, d) show the average charge (left axis) and current (right axis) along the white horizontal arrows in the top panels, with $\varepsilon_3=5\;\mu\text{eV}$. Green dot-dashed lines represent average charge in the outer dots, red dashed lines for the inner dots, and the blue solid lines indicate the current. Vertical dashed lines mark the position of the resonance. The width of the arrows in the top panels indicates the strength of the tunneling rates. The parameters for the symmetric case (a, c) are $\tau_i=\left[2, 2, 2\right]\;\mu\text{eV}$ and $\varepsilon_1=\varepsilon_4=0$, while for the asymmetric case (b, d) are $\tau_i=\left[2, 1, 3\right]\;\mu\text{eV}$, $\varepsilon_1=0$, and $\varepsilon_4=0.4\;\mu\text{eV}$.
• Figure 4: Current through the quadruple quantum dot array in the single-particle regime. White lines denote the region of positive charge current, as described in the main text. Black lines indicate various resonance conditions. Dashed lines correspond to long-range transfers between first and third, and second and fourth dots. With a dot-dashed line we denote a long-range transition between the first and last dots. Lines fade out in regions of high current to emphasize the current features. The parameters are $\tau_i=\left[3,5,2\right]\;\mu\text{eV}$, $T_2=10\;\mathrm{ns}$, $\mu_{L(R)} = \pm37.5\;\mu\text{eV}$, $\varepsilon_{20}=7\;\mu\text{eV}$, and $\varepsilon_{30}=-5\;\mu\text{eV}$.
• Figure 5: Dynamics (solid lines) for three particles in a quadruple quantum dot array. The effective model from Eq. (\ref{['eq:effective_model_2001']}) shown with dashed lines. System parameters are given by $\tau_i = \tau=3 \;\mu\text{eV}$, $\varepsilon_i=\left[-1836.2, -700, -655, -1714\right] \;\mu\text{eV}$, $U_i = \left[1720, 1500, 1220, 1600\right] \;\mu\text{eV}$, $V_i=\left[450, 200, 100\right] \;\mu\text{eV}$.