Electron Shuttling Model

Available identifiers

MaRDI QIDQ6534342

quantum dynamical model of an electron to be shuttled in a Si/SiGe quantum bus

The clavier gate electrodes on the top surface generate a moving array of QD potentials.

Top view on the Si-QuBus with the four different clavier gate sets highlighted in color.

Description

Quantum dynamical modeling of an electron to be shuttled, governed by the electric potential generated by the clavier (and other) gates in a Silicon QuBus device. Spin and valley states as well as the respective interactions are neglected. Moreover, the current model is limited to the coherent wave packet evolution and disregards the effects of noise and dissipation.

List of mathematical expressions with quantities

Schrödinger Equation (Time Dependent)	$\mathrm{i}\hslash \frac{\partial }{\partial t}|\psi (t)⟩=\hat{H}|\psi (t)⟩$
$H$ symbol represents Quantum Hamiltonian Operator
$\hslash$ symbol represents Planck Constant
$\psi (t)$ symbol represents Quantum State Vector (Dynamic)
$t$ symbol represents Time
$\mathrm{i}$ symbol represents Imaginary Unit
Schrödinger Equation (Time Independent)	$\hat{H}|{\psi }_n⟩=E_n|{\psi }_n⟩$
$E_n$ symbol represents Quantum Eigen Energy
$H$ symbol represents Quantum Hamiltonian Operator
${\psi }_n$ symbol represents Quantum State Vector (Stationary)
$n$ symbol represents Quantum Number
Quantum Lindblad Equation	$\frac{\mathrm{d}}{\mathrm{d}t}\rho =-\frac{\mathrm{i}}{\hslash }[H,\rho ]+\sum _{k=1}^{N^2-1}{\gamma }_k(L_k\rho L_k^{†}-\frac{1}{2}[L_k^{†}{L}_k,\rho {]}_{+})$
$H$ symbol represents Quantum Hamiltonian Operator
$L$ symbol represents Quantum Jump Operator
$\gamma >0$ symbol represents Quantum Damping Rate
$\hslash$ symbol represents Planck Constant
$\rho$ symbol represents Quantum Density Operator
$t$ symbol represents Time
$\mathrm{i}$ symbol represents Imaginary Unit
Laplace Equation for the Electric Potential	$-\mathrm{\nabla }\left({ϵ}_s\mathrm{\nabla }\varphi \right)=0$
${ϵ}_s$ symbol represents Permittivity (Dielectric)
$\varphi$ symbol represents Electric Potential
Quantum Hamiltonian (Electric Charge)	$H=H_0+q\varphi$
$H_0$ symbol represents Quantum Hamiltonian Operator
$\varphi$ symbol represents Electric Potential
$q$ symbol represents Electric Charge
${\varphi }$ symbol represents Electric Potential
Dirichlet Boundary Condition for Electric Potential	$\varphi (r,t){|}_{{\mathrm{\Gamma }}_k}={\psi }_0+U_k(t)$
$U_k$ symbol represents Applied External Voltage
${\mathrm{\Gamma }}_k$ symbol represents Electrode Interfaces
$\varphi$ symbol represents Electric Potential
$t$ symbol represents Time
Neumann Boundary Condition for Electric Potential	${n\cdot \mathrm{\nabla }\varphi (r,t)|}_{{\mathrm{\Gamma }}_N}=0$
${\mathrm{\Gamma }}_N$ symbol represents Electrode Interfaces
$\varphi$ symbol represents Electric Potential
$t$ symbol represents Time
$n$ symbol represents Unit Normal Vector
Periodic Boundary Condition for Electric Potential	$\varphi (r,t)=\varphi (r+L,t)$
$L$ symbol represents Length of Unit Cell
$\varphi$ symbol represents Electric Potential
$t$ symbol represents Time

List of computational tasks

1. Semiconductor Charge Neutrality

2. Quantum Stationary States

3. Quantum Time Evolution

4. Optimal Control