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Lower bound of energy dissipation in optical excitation transfer via optical near-field interactions

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Abstract

We theoretically analyzed the lower bound of energy dissipation required for optical excitation transfer from smaller quantum dots to larger ones via optical near-field interactions. The coherent interaction between two quantum dots via optical near-fields results in unidirectional excitation transfer by an energy dissipation process occurring in the larger dot. We investigated the lower bound of this energy dissipation, or the intersublevel energy difference at the larger dot, when the excitation appearing in the larger dot originated from the excitation transfer via optical near-field interactions. We demonstrate that the energy dissipation could be as low as 25 μeV. Compared with the bit flip energy of an electrically wired device, this is about 104 times more energy efficient. The achievable integration density of nanophotonic devices is also analyzed based on the energy dissipation and the error ratio while assuming a Yukawa-type potential for the optical near-field interactions.

©2010 Optical Society of America

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Figures (4)

Fig. 1
Fig. 1 (a) Optical near-field interaction between a smaller quantum dot (QD S ) and a larger one (QD L ). The input light is given by external propagating light at an optical frequency ωext . (b) State transition diagram of the two-dot system.
Fig. 2
Fig. 2 Two representative quantum dot systems: (a) System A, where the inter-dot interaction is strong (100 ps), and (b) System B, where the interaction is negligible (10,000 ps). (c) Yukawa-type screened potential of an optical near-field interaction between two QDs as a function of the inter-dot distance.
Fig. 3
Fig. 3 Evolutions of the populations of the radiation from QD S (dashed curve) and QD L (solid curve) with 150 fs-duration input pulse radiating both System A and System B. The energy dissipation in QD L is arranged to be (i) 2.5 meV, (ii) 17 μeV, and (iii) 0.25 μeV.
Fig. 4
Fig. 4 (a) Steady-state population involving energy level E L 1 in System A (squares) and System B as a function of the energy dissipation. For System B, three different cases are shown, with U B -1 of 500, 1,000, and 10,000 ps respectively indicated by , , and marks. (b) Energy dissipation as a function of error ratio regarding optical excitation transfer and classical electrically wired device (more specifically a CMOS logic gate) based on Ref [2]. The energy dissipation of optical excitation transfer is about 104 times lower than that in classical electrically wired devices. (c) As the optical near-field interaction time of System B decreases, the lower bound of the error ratio increases, indicating that the performance could be degraded with increasing integration density. The error ratio is evaluated as the number of independent functional blocks within an area of 1 μm2.

Equations (8)

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H ^ i n t = d 3 r i , j = e , h ψ ^ i ( r ) e r · E ( r ) ψ ^ j ( r ) ,
E ( n x , n y , n z ) = E B + 2 π 2 2 M L 2 ( n x 2 + n y 2 + n z 2 ) ,
d ρ ( t ) d t = i [ H i n t + H e x t ( t ) , ρ ( t ) ] + γ S 2 ( 2 S ρ ( t ) S S S ρ ( t ) ρ ( t ) S S ) + Γ 2 ( 2 L 2 ρ ( t ) L 2 L 2 L 2 ρ ( t ) ρ ( t ) L 2 L 2 ) + γ L 2 ( 2 L 1 ρ ( t ) L 1 L 1 L 1 ρ ( t ) ρ ( t ) L 1 L 1 ) ,
H i n t = ( 0 0 0 0 0 0 0 0 0 0 0 U S L 1 e i ( Ω S Ω L 1 ) 0 0 0 0 0 0 0 U S L 2 e i ( Ω S Ω L 2 ) 0 0 0 0 0 U S L 1 e i ( Ω S Ω L 1 ) U S L 2 e i ( Ω S Ω L 2 ) 0 0 0 0 0 0 0 0 0 0 U S L 2 e i ( Ω S Ω L 2 ) U S L 1 e i ( Ω S Ω L 1 ) 0 0 0 0 0 U S L 2 e i ( Ω S Ω L 2 ) 0 0 0 0 0 0 0 U S L 1 e i ( Ω S Ω L 1 ) 0 0 0 0 0 0 0 0 0 0 0 ) ,
S = ( 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ) , L 2 = ( 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ) , L 1 = ( 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ) ,
H e x t ( t ) = g a t e ( t ) × [ ( exp ( i ( Ω S ω e x t ) S + exp ( i ( Ω S ω e x t ) S ) + ( exp ( i ( Ω L 1 ω e x t ) ) L 1 + exp ( i ( Ω L 1 ω e x t ) ) L 1 ) ] ,
U = A exp ( μ r ) r ,
E d = k B T ln ( 3 2 P E )
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