Quantum speed limit of the double quantum dot in pure dephasing environment under measurement

doi:10.1088/1674-1056/ac4bd4

中国物理B ›› 2022, Vol. 31 ›› Issue (7): 70307-070307.doi: 10.1088/1674-1056/ac4bd4

Quantum speed limit of the double quantum dot in pure dephasing environment under measurement

Zhenyu Lin(林振宇)¹, Tian Liu(刘天)¹, Zongliang Li(李宗良)¹, Yanhui Zhang(张延惠)^1,†, and Kang Lan(蓝康)²

1 School of Physics and Electronics, Shandong Normal University, Jinan 250014, China;
2 School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, China

收稿日期:2021-10-22 修回日期:2022-01-12 接受日期:2022-01-17 出版日期:2022-06-09 发布日期:2022-06-09
通讯作者: Yanhui Zhang E-mail:yhzhang@sdnu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11974217).

Quantum speed limit of the double quantum dot in pure dephasing environment under measurement

Zhenyu Lin(林振宇)¹, Tian Liu(刘天)¹, Zongliang Li(李宗良)¹, Yanhui Zhang(张延惠)^1,†, and Kang Lan(蓝康)²

1 School of Physics and Electronics, Shandong Normal University, Jinan 250014, China;
2 School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, China

Received:2021-10-22 Revised:2022-01-12 Accepted:2022-01-17 Online:2022-06-09 Published:2022-06-09
Contact: Yanhui Zhang E-mail:yhzhang@sdnu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11974217).

摘要/Abstract

摘要： The quantum speed limit (QSL) of the double quantum dot (DQD) system has been theoretically investigated by adopting the detection of the quantum point contact (QPC) in the pure dephasing environment. The Mandelstam-Tamm (MT) type of the QSL bound which is based on the trace distance has been extended to the DQD system for calculating the shortest evolving time. The increase of decoherence rate can weaken the capacity for potential speedup (CPS) and delay the evolving process due to the frequently measurement localizing the electron in the DQD system. The system needs longer time to evolve to the target state as the enhancement of dephasing rate, because the strong interaction between pure dephasing environment and the DQD system could vary the oscillation of the electron. Increasing the dephasing rate can sharp the QSL bound, but the decoherence rate would weaken the former effect and vice versa. Moreover, the CPS would be raised by increasing the energy displacement, while the enhancement of the coupling strength between two quantum dots can diminish it. It is interesting that there has an inflection point, when the coupling strength is less than the value of the point, the increasing effect of the CPS from the energy displacement is dominant, otherwise the decreasing tendency of the CPS is determined by the coupling strength and suppress the action of the energy displacement if the coupling strength is greater than the point. Our results provide theoretical reference for studying the QSL time in a semiconductor device affected by numerous factors.

关键词: quantum speed limits, the DQD system, the pure dephasing environment, quantum measurement

Abstract: The quantum speed limit (QSL) of the double quantum dot (DQD) system has been theoretically investigated by adopting the detection of the quantum point contact (QPC) in the pure dephasing environment. The Mandelstam-Tamm (MT) type of the QSL bound which is based on the trace distance has been extended to the DQD system for calculating the shortest evolving time. The increase of decoherence rate can weaken the capacity for potential speedup (CPS) and delay the evolving process due to the frequently measurement localizing the electron in the DQD system. The system needs longer time to evolve to the target state as the enhancement of dephasing rate, because the strong interaction between pure dephasing environment and the DQD system could vary the oscillation of the electron. Increasing the dephasing rate can sharp the QSL bound, but the decoherence rate would weaken the former effect and vice versa. Moreover, the CPS would be raised by increasing the energy displacement, while the enhancement of the coupling strength between two quantum dots can diminish it. It is interesting that there has an inflection point, when the coupling strength is less than the value of the point, the increasing effect of the CPS from the energy displacement is dominant, otherwise the decreasing tendency of the CPS is determined by the coupling strength and suppress the action of the energy displacement if the coupling strength is greater than the point. Our results provide theoretical reference for studying the QSL time in a semiconductor device affected by numerous factors.

Key words: quantum speed limits, the DQD system, the pure dephasing environment, quantum measurement

中图分类号: (Decoherence; open systems; quantum statistical methods)

03.65.Yz

73.63.Kv (Quantum dots) 03.65.Ta (Foundations of quantum mechanics; measurement theory)

Zhenyu Lin(林振宇), Tian Liu(刘天), Zongliang Li(李宗良), Yanhui Zhang(张延惠), and Kang Lan(蓝康). Quantum speed limit of the double quantum dot in pure dephasing environment under measurement[J]. 中国物理B, 2022, 31(7): 70307-070307.

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Quantum speed limit of the double quantum dot in pure dephasing environment under measurement

Quantum speed limit of the double quantum dot in pure dephasing environment under measurement

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