Introduction

This time we will improve the quantum well. Specifically, by adding a potential barrier to the center of the quantum well, we will make it play a more role as a quantum bit.

5 Quantum well improvement

5.1 Addition of barriers

In order to treat the quantum well as a bit, the quantum well is improved here. Specifically, a potential wall is created at the center of the quantum well. If the height of this potential is $ V_b [eV] $ and the width is $ W $, the potential is expressed as follows.

V(x)=\left\{\begin{array}{ll}
V_b & (|x|\leq \frac{W}{2})\\
0 &　(\frac{W}{2} < |x| \leq \frac{L}{2})\\
+\infty & (|x| > \frac{L}{2})
\end{array}
\right.
\quad (5.1)

5.2 Plot of quantum wells with barriers

Let's plot the state when the size $ V_b $ of the barrier between the ground state and the first excited state is increased by 3 [eV] little by little.

5.2.1 In the ground state

5.2.2 In the first excited state

From the above results, it was found that it can be divided into two for about $ 30 [eV] $.

5.3 Applying an electric field to a quantum well with barriers

Using the above result, an electric field is applied to the quantum well with a barrier. If there is a barrier, the electric field applied to the quantum well will have an effect even if it is much smaller than before. Last time it was increased in 1.0e9 units, but this time it can be seen to change just by increasing it in 1.0e6 units. Let's check this.

5.3.1 In the ground state

It can be confirmed that the electric field is about 10e7 and almost all distribution is on the left.

5.3.2 In the first excited state

It can be confirmed that the electric field is about 10e7 and almost all distribution is on the right.

reference

EMAN Physics

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[PYTHON] Read "Quantum computer made in 14 days". Day 5 Quantum well improvement / addition of barriers