Results

1.Electric field dependence on gate voltage

Conclusions

Key concepts

Background and Motivation: Qubit for a quantum computerThe individual control of a long-lived qubit is essential to construct a scalable quantum computer. A qubit based on a single electron spin with

high fidelity localized in silicon quantum dot has been realized in previous work and the qubit can be controlled by Stark shifting the g-factor or

local magnetic field via nanomagnet. Here, we focus on the manipulation of a multi-qubit system on silicon quantum dots, investigating the

possibility to operate the two dots as a so called singlet-triplet and to investigate the speed of an operation.

Simulating manipulation of coupled electron spin in silicon

based quantum dots Author: Wister Huang

Supervisor: Prof.Andrew Dzurak, Dr.Menno Veldhorst, Henry Yang

Reserch theme: Fundamental and Enabling Research

Aims and Objective: Individual control of a qubit Simulate electric field dependence on gate voltage to get better calibration of the ESR frequency

Calculate the electric field |𝐸𝑧| on both dots with the relevant gates voltages tunability to figure out whether the device can operate the two

dots as a singlet -triplet.

Calculate the magnetic field gradient to determine the how fast we can operate the dots.

The electric field around dot1 (the area under the G4 gate) area increases as G4 gate increases,

and decreases as the Confinement Gate (C Gate) increases. This indicates that the electric field

around the dot can be tuned by the gate voltage, resulting in a Stark shift that can tune the electron

spin resonance and allowing us to change the ESR frequency in a wide range.

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2.7 2.8 2.9 3 3.1 3.2 3.3

|Ez|(

MV

/m)

Vc(V)

|Ez| vs G1 gate voltage

Dot2Ez Dot1Ez dEz

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10

20

30

40

50

60

70

-5 -4 -3 -2 -1 0

|Ez|(

MV

/m)

Vc(V)

|Ez| vs Confinement gate voltage

Dot2 Ez Dot1Ez dEz

2. A gate tunable dot

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250300350400450

The magnet gradient of the nanomagnet

-150 -100 -50 0 50 100 150 200

50

100

150

200

250

300Perpendicular magnetic field(mT)

Dot1

Dot2

3. Magnetic field gradient simulation

A maximum magnetic field difference of 40mT

between two dots is created by placing a

nanomagnet on the device, which will cause a

transition between singlet and triplet according

to the following formula.

The probability of the singlet state:

This results in a fast operation time:

𝑔∗𝜇𝐵∆𝐵𝜏𝑠ℏ

=π ⟹ 𝜏𝑠 =ℏπ

𝑔∗𝜇𝐵∆𝐵= 0.45𝑛𝑠

A large perpendicular electric field difference of 20MV/m is realized between the two dots area as is

shown in the figure above (where dot1 is the dot under G4 and dot2 is the dot under G2) , and this

difference can be tuned by varying gate G1. The two dots will have electron spin resonance

frequency difference as

∆𝑣 =𝑢𝐵∆𝑔

ℎ𝐵𝑑𝑐 =

𝑢𝐵ℎ

𝐵𝑑𝑐𝜂2𝑔 0 Δ|𝐸𝑧|2 = 172.33𝑀𝐻𝑧

The ESR linewidth can be narrowed down to Δ𝑣𝐸𝑆𝑅 = 2.4 ± 0.2 𝑘𝐻𝑧 which is far less than the electron

spin resonance frequency difference ∆𝑣 between the two dot, allowing us to manipulate the dot

individually and precisely.

Qubit (quantum bit): Whereas the classical bit is the basic component of a

conventional computer, the qubit could be a building block for a quantum computer. A

qubit is given by the superstition 𝛼 0 > +𝛽 1 >.

Singlet-Triplet qubit: Two electron combine to form one of the three states with total

spin one is called triplet, or a state of spin 0 call triplet.

ESR(Electron spin resonance): The energy level between a spin-up and spin-down

states are split in external magnetic field, when a electromagnetic wave with a

frequency corresponding to the energy difference between the two states is applied,

an electron can move between the two states.

Coherence manipulation procedure of a singlet-triplet qubit:

The electric fields determine the dot can be tuned in a wide range by varying top gate

and confinement gate voltage. Consequently the ESR frequency can be gate voltage

tuned.

Large electric field difference about 20MV/m can be realized between two dots, resulting

in a ESR frequency tunability orders of magnitude larger than the ESR linewidth,

indicating we can easily manipulate the dots individually.

Magnetic field differences up to 40mT is obtained in the simulation, which allows an

operation as fast as 450ps.

Future Work

Experimentally examine the tunability of the different gates .

Redesign the device in order to implement nanomagnet.

Investigate the reason why the electric field difference between two dots remain unchanged

when the confinement gate voltage changes.

𝑃 𝑠 = 0.5(1 + 𝑉𝑐𝑜𝑠(𝜏𝑠𝑔∗𝜇𝐵∆𝐵)/ℏ)

Designing model in TCAD Mesh the calculation area

TCAD-Devise designing interface

Plotting the result

ISE Techplot

t=0 t = τs

The layout of the device

Simulation Method

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x 105

Y(um)

|Ez| of the dot at Vc=-1.28V

X(um)

|Ez|

(V/c

m)

00.02

0.040.06

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-0.05

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0.050

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x 105

X(um)

|Ez| of the dot at Vc=-0.28V

Y(um)

|Ez|(

V/c

m)

00.02

0.040.06

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x 105

Y(um)

|Ez| of the dot at Vg4=2.44V

X(um)

|Ez|

(V/c

m)

00.02

0.040.06

0.08

-0.05

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0.050

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x 105

Y(um)

|Ez| of the dot at Vg4=1.94V

X(um)

|Ez|

(V/c

m)

Vary C gate voltage with G4 gate voltage constant

Vary G4 gate voltage with C gate voltage constant

X(nm)

Y(n

m)