Other Results QUANTUM DOTS AND OPTICAL CAVITIES PHOTONS, COUPLED - - PowerPoint PPT Presentation

Other Results

PHOTONS, COUPLED QUANTUM DOTS AND QUBITS

QUANTUM DOTS AND OPTICAL CAVITIES

TWO EXCITONS IN QD WITH COHERENT FIELD

From the following article: Wiring up quantum systems

• R. J. Schoelkopf & S. M. Girvin

Nature 451, 664-669(7 February 2008) doi:10.1038/451664a

EXITONIC MODEL

   

   

B B B A A A c B B B qd A A A qd

a a i a a i a a H

          

                    , 2 , 2

 

c B qd A qd

L L L H i dt d        ,

 

A A A A A A A A qd

g L

1 1 1

2 2          

 

B B B B B B B B qd

g L

1 1 1

2 2          

 

a a a a a a g L

c c   

      2

MASTER EQUATION

RABI OSCLLIATIONS

• Time (T.I): 0.013ns

CORRELATION

SQUARE OF THE DENSITY TRACE OPERATOR

• T.I: (0.001415ns -0. 12ns ), peaks: 0.0046, 0.0066

y 0.0197ns

TWO EXCITONS AND SPIN OF QDs IN EMPTY FIELD

• RABI OSCILLATIONS BY EXCITONS
• T.I: 0.0286ns

DENSITY MATRIX

Table: Matrix Density of the QDs and photon in the cavity.

EVOLUTION OF d(t)

DENSITY MATRIX DIAGONALIZATION

• Eigenvectors:

c B A 1 



   



   

t c t b t c t b

c B A c B A c B A

2 1 1 1

2

     

EVOLUTION OF THE ENTANGLEMENT STATES FOR EXCITONS

T.I: 0.0286ns

EVOLUTION OF THE ENTANGLEMENT STATES WITH SPIN

• T.I: 0.0715ns

TOTAL ENTROPY

Exciton Spin

 

       

 

   

 

 

, ,

ln 2 ln 2 / ln 2

A B c

S a t a t b t c t b t c t              

DIAGONALIZATION OF RESTRICTED DENSITY OPERATOR IN A AND B

• Eigenvectors:

B A 0 1 



 

B A B A

1 1 2 1

2

  

EVOLUTION OF THE ENTANGLEMENT STATES OF REDUCED EXCITONS

SQUARE TRACE OF DENSITY OPERATOR BY EXCITONS

CORRELATION OF EXCITONS

ENVIRONMENTS NO DISSIPATIVE

• Equations to solve:
• Solutions:

MATRIX DENSITY

• EIGENVECTOR:

   



   

t c t b t c t b

c B A c B A c B A

2 1 1 1

2

     

DECOHERENCE IN EXCITONS

DIAGONALIZATION OF REDUCED DENSITY OPERATOR IN A AND B

• Eigenvectors:

B A 0 1 



 

B A B A

1 1 2 1

2

  

TRACE OF SQUARE OF DENSITY OPERATOR

RABI FREQUENCES

• EXCITONES=√2*λ= √2* 315GHz
• ESPIN= √2*λeff= √2* 24.18GHz

ONE EXCTION OR SPIN

• Excitons interaction in the quantum dot with a

coherent field, the interlaced state is not defined, but the range of entanglement was predominant during the system dynamics.

CONCLUSIONS

• In the interaction of quantum dot excitons

with empty field in times proportional to a half-integer number of π on Rabi frequency were obtained maximally entangled states as Bell states, useful in computer science and information quantum.

• In the interaction of quantum dot spins with

empty field, the dynamics were similar to that

• f excitons with empty field, but in this model,

the frequency of Rabbi and coherence times are greater because model conditions.

• Spin model, is predominant over the exciton

due to the coherence time exceeds the time for a certain computation operation (0.04ns).

They analyze the dynamics of a single quantum dot (with exciton or spin) interacting with the different fields in the cavity, we obtained results that analyze the behavior of quantum gates with two-level systems

RECTANGULAR DOUBLE BARRIER POTENTIAL

PÖSCHL-TELLER DOUBLE BARRIER POTENTIAL RASHBA AND DRESSELHAUS EFFECTS

B

S



 

k k Cos k Sen  

010

 

100

 

001

z

k k

 V

 

2 , L R

z z V z V Cosh a

 

          

001

L

a 

w

a

w R

a a 

B  B  B  B 

   2Z(l /R) 0.5 eV 6 mK  0.02 T1.3109 s R  8 m

 .

0.05

0.10

0.15 0.20 0.25

2

4 6 8 10 Energy [meV] B [T] E2 – E1 E3 – E1 E1 – E1

T 2 . 5

0 

B 

• rbital

Zeeman     

Anticrossing due to Rashba coupling