# Efficient Biexciton Preparation in a Quantum Dot—Metal Nanoparticle System Using On-Off Pulses

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## Abstract

**:**

## 1. Introduction

## 2. Coupled SQD-MNP System

## 3. Biexciton State Preparation Using on-off Pulses

## 4. Numerical Results for the Coupled SQD-MNP System

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

SQD | Semiconductor Quantum Dot |

MNP | Metal Nanoparticle |

## References

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**Figure 1.**(

**a**) Coupled semiconductor quantum dot (SQD)-metal nanoparticle (MNP) nanosystem. (

**b**) Energy levels for the biexciton system.

**Figure 2.**Left-column top to bottom: (

**a**) Logarithm of the squared error between the two sides of transcendental Equation (27) as a function of the duration ${t}_{2}$ of the intermediate (off) pulse. The negative resonance indicated with red star corresponds to the solution. (

**c**) Corresponding on-off pulse-sequence. (

**e**) Time evolution of biexciton population ${\sigma}_{22}\left(t\right)$ (blue solid line) obtained by simulating the full Equation (6) with input the above pulse-sequence. For comparison, the red dashed line shows ${\sigma}_{22}\left(t\right)$ if relaxation is ignored from the system equations. These results are obtained for interparticle distance $R=14$ nm and biexciton energy shift ${E}_{B}=5$ meV. In the right-column (

**b**,

**d**,

**f**) we display similar plots for the case with the same $R=14$ nm but larger ${E}_{B}=8$ meV.

**Figure 3.**Left-column top to bottom: (

**a**) Logarithmic squared error (28), (

**c**) pulse-sequence, and (

**e**) time evolution of ${\sigma}_{22}\left(t\right)$, for $R=13$ nm and ${E}_{B}=2.5$ meV. In the right-column (

**b**,

**d**,

**f**) we display similar plots for the case with a larger interparticle distance $R=30$ nm but the same biexciton energy shift ${E}_{B}=2.5$ meV.

**Figure 4.**Left-column top to bottom: (

**a**) Logarithmic squared error (28), (

**c**) pulse-sequence, and (

**e**) time evolution of ${\sigma}_{22}\left(t\right)$, for $R=15$ nm and ${E}_{B}=1$ meV. In the right-column (

**b**,

**d**,

**f**) we display similar plots for the case with a larger interparticle distance $R=30$ nm but the same biexciton energy shift ${E}_{B}=1$ meV.

**Figure 5.**(

**a**) Pulse-sequence duration as a function of biexciton energy shift ${E}_{B}$, for four values of the interparticle distance, $R=13$ nm (blue solid line), $R=14$ nm (red dashed line), $R=15$ nm (black dashed-dotted line), $R=30$ nm (green dotted line). (

**b**) Pulse-sequence duration as a function of interparticle distance R, for four values of the biexciton energy shift, ${E}_{B}=1$ meV (blue solid line), ${E}_{B}=2.5$ meV (red dashed line), ${E}_{B}=5$ meV (black dashed-dotted line), ${E}_{B}=6$ meV (green dotted line).

**Figure 6.**(

**a**) Final value of the population ${\sigma}_{22}\left(T\right)$ from the numerical solution of Equation (6) using the pulse-sequence obtained for each pair of values $({E}_{B},R)$ in the range shown. (

**b**) ${\sigma}_{22}\left(T\right)$ for the pulse timings obtained with the fixed reference value ${R}_{0}=15$ nm and variable ${E}_{B}$, when applied to system Equation (6) with variable R in the range ${R}_{0}\pm 1$ nm and the corresponding ${E}_{B}$. (

**c**) ${\sigma}_{22}\left(T\right)$ for the pulse timings obtained with the fixed reference value ${E}_{B}^{0}=4$ meV and variable R, when applied to Equation (6) with variable ${E}_{B}$ in the range ${E}_{B}^{0}\pm 0.5$ meV and the corresponding R. (

**d**) ${\sigma}_{22}\left(T\right)$ for the pulse-sequence obtained with fixed ${R}_{0}=15$ nm and ${E}_{B}^{0}=4$ meV, when applied to Equation (6) with variable R in the range ${R}_{0}\pm 1$ nm and ${E}_{B}$ in the range ${E}_{B}^{0}\pm 0.5$ meV.

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**MDPI and ACS Style**

Smponias, A.; Stefanatos, D.; Paspalakis, E.
Efficient Biexciton Preparation in a Quantum Dot—Metal Nanoparticle System Using On-Off Pulses. *Nanomaterials* **2021**, *11*, 1859.
https://doi.org/10.3390/nano11071859

**AMA Style**

Smponias A, Stefanatos D, Paspalakis E.
Efficient Biexciton Preparation in a Quantum Dot—Metal Nanoparticle System Using On-Off Pulses. *Nanomaterials*. 2021; 11(7):1859.
https://doi.org/10.3390/nano11071859

**Chicago/Turabian Style**

Smponias, Athanasios, Dionisis Stefanatos, and Emmanuel Paspalakis.
2021. "Efficient Biexciton Preparation in a Quantum Dot—Metal Nanoparticle System Using On-Off Pulses" *Nanomaterials* 11, no. 7: 1859.
https://doi.org/10.3390/nano11071859