# Quantum Photovoltaic Cells Driven by Photon Pulses

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## Abstract

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## 1. Introduction

## 2. Quantum Thermodynamics of Open Quantum Systems

## 3. A Two-Level System Driven by Photon Pulses

## 4. Quantum Photocell Driven by Photon Pulses

## 5. Summary

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**A two-level system with energy levels ${E}_{0}$ and ${E}_{1}$ in contact with a cold thermal bath at ${T}_{c}$ is driven by Gaussian photon pulses serving as an energy source in our work.

**Figure 2.**(

**a**) The density matrix elements of the two-level system and the sequence of Gaussian photon pulses $g(t)$ are plotted over time. (

**b**) The rate of energy change $\frac{dE(t)}{dt}$, the power $P(t)$, and the heat current $J(t)$ are calculated as functions of time. (

**c**) The energy $E(t)$, the work $W(t)$, the heat transfer $Q(t)$, and the system entropy $S(t)$ are plotted as functions of time. (

**d**) The rate of system entropy change $\frac{dS}{dt}$ and the entropy production $\sigma (t)$ are plotted over time. The parameters are taken as $\langle n\rangle =1$, $\gamma ={10}^{-2}{\omega}_{0}$, $\Omega ={\omega}_{0}/4\pi $, and $\hslash {\omega}_{0}=1\phantom{\rule{0.277778em}{0ex}}\mathrm{eV}$.

**Figure 3.**(

**a**) The density matrix elements of the two-level system and the sequence of Gaussian photon pulses $g(t)$ are plotted over time. (

**b**) The rate of energy change $\frac{dE(t)}{dt}$, the power $P(t)$, and the heat current $J(t)$ are plotted as functions of time. (

**c**) The energy $E(t)$, the work $W(t)$, the heat transfer $Q(t)$, and the system entropy $S(t)$ are calculated as functions of time. (

**d**) The rate of system entropy change $\frac{dS}{dt}$ and the entropy production $\sigma (t)$ are shown over time. The parameters are $\langle n\rangle =10$, $\gamma ={10}^{-2}{\omega}_{0}$, $\Omega ={\omega}_{0}/4\pi $, and $\hslash {\omega}_{0}=1\phantom{\rule{0.277778em}{0ex}}\mathrm{eV}$.

**Figure 4.**When a Gaussian photon pulse is overlapped with the subsequent Gaussian photon pulse and the interval between them is regular, (

**a**) the density matrix elements of the two-level system, (

**b**) the rate of energy change $\frac{dE(t)}{dt}$, the power $P(t)$, the heat current $J(t)$, (

**c**) energy $E(t)$, work $W(t)$, heat $Q(t)$ system entropy $S(t)$, (

**d**) the rate of system entropy change $\frac{dS}{dt}$ and the entropy production $\sigma (t)$ are plotted as a function of time. The parameters are taken as $\langle n\rangle =1$, $\gamma ={10}^{-2}{\omega}_{0}$, $\Omega ={\omega}_{0}/4\pi $, and $\hslash {\omega}_{0}=1\phantom{\rule{0.277778em}{0ex}}\mathrm{eV}$.

**Figure 5.**When an irregularly spaced sequence of photon pulses is applied, (

**a**) the density matrix elements of the two-level system and the sequence of Gaussian photon pulses $g(t)$, (

**b**) the rate of energy change $\frac{dE(t)}{dt}$, the power $P(t)$, and the heat current $J(t)$, (

**c**) the energy $E(t)$, work $W(t)$, and heat $Q(t)$, and the system entropy $S(t)$, (

**d**) the rate of system entropy change $\frac{dS}{dt}$ and the entropy production $\sigma (t)$ are plotted as functions of time. Parameters: $\langle n\rangle =1$, $\gamma ={10}^{-2}{\omega}_{0}$, $\Omega ={\omega}_{0}/4\pi $, and $\hslash {\omega}_{0}=1\phantom{\rule{0.277778em}{0ex}}\mathrm{eV}$.

**Figure 6.**Schematic diagram of a donor-acceptor photocell. ${\gamma}_{01}$ is the spontaneous decay due to the coupling with the cold thermal bath. ${\gamma}_{21}$ and ${\gamma}_{03}$ are the transfer rate between the donor and the acceptor. $\Gamma $ stands for the external load or electrical resistance.

**Figure 7.**(

**a**) The diagonal matrix elements of the density operator of the photocell and the pulse profiles are plotted as a function of time. (

**b**) The changes in the energy of the donor and acceptor ${(dE/dt)}_{D}={E}_{D}^{\prime}$ and ${(dE/dt)}_{A}={E}_{A}^{\prime}$, the power delivered to the donor ${P}_{D}(t)$ by the photon pulses, the power output ${P}_{\mathrm{out}}$, and the heat currents of the donor and acceptor ${J}_{D}$ and ${J}_{A}$ are plotted as a function of time. (

**c**) The entropy of the quantum photocell, $S(t)$, the entropy of the donor, ${S}_{D}(t)$, and the entropy of the acceptor, ${S}_{A}(t)$, are calculated as a function of time. (

**d**) The current $I(t)$, the voltage $V(t)$, and the efficiency $\eta $ are plotted as a function of time. Parameters: $\langle n\rangle =10$, ${\gamma}_{12}={\gamma}_{03}={10}^{-2}{\omega}_{0}$, ${\gamma}_{01}={10}^{-2}{\omega}_{0}$, $\Gamma =0.1{\omega}_{0}$, $\Omega ={\omega}_{0}/4\pi $, and $\hslash {\omega}_{0}={E}_{1}-{E}_{0}=1.8\phantom{\rule{0.277778em}{0ex}}\mathrm{eV}$.

**Figure 8.**(

**a**) From discrete mode to (

**b**) the continuous mode operation by changing the interval of the pulses. Parameters: $\langle n\rangle =1$, ${\gamma}_{21}={\gamma}_{03}={10}^{-3}{\omega}_{0}$, ${\gamma}_{01}={10}^{-2}{\omega}_{0}$, and $\Omega ={\omega}_{0}/4\pi $.

Energy gap of the two-level system | ${E}_{1}-{E}_{0}=\hslash {\omega}_{0}=1.0$ eV |

Energy gap of the donor of the quantum photocell | ${E}_{1}-{E}_{0}=\hslash {\omega}_{0}=1.8$ eV |

Energy gap of the acceptor of the quantum photocell | ${E}_{2}-{E}_{3}=1.6$ eV |

Weisskopf-Winger constant | $\gamma /{\omega}_{0}={\gamma}_{01}/{\omega}_{0}={10}^{-3}\sim {10}^{-6}$ |

Phonon decay constant | ${\gamma}_{12}/{\omega}_{0}={\gamma}_{03}/{\omega}_{0}={10}^{-2}\sim {10}^{-3}$ |

Photon number of a pulse | $\langle n\rangle ={\left|\alpha \right|}^{2}=1\phantom{\rule{0.277778em}{0ex}}\mathrm{or}\phantom{\rule{0.277778em}{0ex}}10$ |

Temperature of the cold bath | ${T}_{c}$ = 300 K |

Width of a Gaussian pulse | $\Omega ={\omega}_{0}/4\pi $ |

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**MDPI and ACS Style**

Oh, S.; Park, J.J.; Nha, H.
Quantum Photovoltaic Cells Driven by Photon Pulses. *Entropy* **2020**, *22*, 693.
https://doi.org/10.3390/e22060693

**AMA Style**

Oh S, Park JJ, Nha H.
Quantum Photovoltaic Cells Driven by Photon Pulses. *Entropy*. 2020; 22(6):693.
https://doi.org/10.3390/e22060693

**Chicago/Turabian Style**

Oh, Sangchul, Jung Jun Park, and Hyunchul Nha.
2020. "Quantum Photovoltaic Cells Driven by Photon Pulses" *Entropy* 22, no. 6: 693.
https://doi.org/10.3390/e22060693