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在环境噪声影响下, 考虑了一对分别被限制在双势阱中通过引力相互作用耦合的有质量粒子系统的量子态动力学行为. 采用几何量子失协的方法, 研究了稳定经典场与衰减场噪声对该有质量粒子系统量子态关联动力学的影响; 用量子速率极限时间来描述量子态演化加速的潜力, 结果发现: 改变系统与环境各项参数可以调控量子速率极限时间, 实现有质量粒子系统量子态动力学演化的加速. 增强两粒子间的引力耦合强度能加速量子态演化; 衰减场的衰减率在一定程度上也能调节系统量子速率极限时间, 从而达到加速量子态演化的目的. 引力耦合强度会影响两粒子系统量子失协振荡的频率. 值得注意的是, 在衰减场噪声影响下, 有质量粒子系统量子失协与量子速率极限时间相对应地表现出随时间的振荡行为, 量子失协的增加对应着量子速率极限时间的减小, 即系统量子失协的增加有利于量子态演化的加速.The exploration of the quantum nature of gravity has always been the focus of academic research. In this work, we consider a double “gravitational cat state” quantum system consisting of a pair of massive particles coupled with gravitational interaction confined in their respective double potential wells. Specifically, we model the double “gravitational cat state” system as a two-qubit system by assuming that the system is initially in the two-qubit Bell state, and investigate the effects of stable classical field and decayed field noise on the quantum speed limit time (QSLT) and trace distance discord (TDD) dynamics of the double “gravitational cat state”. The results show that the QSLT can be controlled by changing the parameters of the system and the environment, and the quantum state dynamic evolution of the system with massive particles can be accelerated. The quantum state evolution can be accelerated by increasing the gravitational coupling intensity between the two massive particles. The decay rate of the decaying field can also regulate the QSLT of the system to a certain extent, so as to accelerate the quantum state evolution, as shown in the attached figure (a). Under the influence of decaying field noise, it is worth noting that the intensity of gravitational coupling affects the frequency of quantum discord oscillations in this two-particle system. The QSLT shows an oscillating trend with time: rapidly increasing to a certain value in a short period of time, then beginning to decline, and then oscillating until it reaches a stable value. That is to say, the evolution of quantum states goes through an oscillatory cycle of first deceleration and then acceleration until the evolution rate becomes stable after a certain period of time. At the same time, there are similar oscillations in the dynamics of quantum discord. Moreover, by comparing these two, it is found that the QSLT decreases in the process of increasing the quantum discord in the system. When the discord oscillation has regularity, the QSLT tends to a certain value, and the quantum discord of the double “gravitational cat state” system has a certain relationship with the QSLT as shown in the attached figure (b). In other words, the quantum discord will affect the rate of quantum state evolution to some extent, and the increase of quantum discord between systems will be more conducive to the evolution of quantum states.
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Keywords:
- open system dynamics /
- quantum speed limits time /
- quantum discord /
- gravitational cat state
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图 1 双“引力猫态”的物理模型, 两个双势阱位于不同的轴上, 两平行轴之间的距离为$ d{=}\sqrt {{{d'}^2} - {L^2}} $
Fig. 1. Physical model of the double “gravitational cat state”, where two double wells are located on different axes and the distance between the two parallel axes is $ d{=}\sqrt {{{d'}^2} - {L^2}} $.
图 2 稳定经典场噪声影响下双“引力猫态” QSLT与实际演化时间的比值$ {{{\tau _{{\mathrm{QSL}}}}} {/ } {{\tau _{\mathrm{D}}}}} $随引力耦合强度$ \gamma $和经典场噪声参数$ \delta $的变化. 这里双“引力猫态”与场之间的耦合$ \lambda = 1 $, 实际演化时间$ {\tau _{\mathrm{D}}} = 1 $
Fig. 2. Ratio $ {{{\tau _{{\mathrm{QSL}}}}} {/ } {{\tau _{\mathrm{D}}}}} $ of the quantum speed limit time to the actual evolution time for the double “gravitational cat state” under the influence of stable classical field noise as a function of the gravitational coupling $ \gamma $ and the parameters of the classical field noise $ \delta $. Here the coupling between the double “gravitational cat state” and the field is $ \lambda = 1 $ and the evolutional time is $ {\tau _{\mathrm{D}}} = 1 $.
图 3 经典噪声场存在衰减时, 双“引力猫态” QSLT与实际演化时间的比值$ {{{\tau _{{\mathrm{QSL}}}}} {/ } {{\tau _{\mathrm{D}}}}} $随引力耦合强度$ \gamma $和场衰减率$ \chi $的变化. 这里$ \delta = 1 $, 双“引力猫态”与场之间的耦合$ \lambda = 1 $, 实际演化时间$ {\tau _{\mathrm{D}}} = 1 $
Fig. 3. Ratio $ {{{\tau _{{\mathrm{QSL}}}}} {/ } {{\tau _{\mathrm{D}}}}} $ of the quantum speed limit time to the actual evolution time under the influence of classical decaying field for the double “gravitational cat state” as a function of the gravitational coupling $ \gamma $ and the decay rates $ \chi $. Here the coupling between the double “gravitational cat state” and the field is $ \lambda = 1 $, for $ \delta = 1 $, and the evolutional time is $ {\tau _{\mathrm{D}}} = 1 $.
图 4 噪声场存在衰减时, 双“引力猫态”QSLT与实际演化时间的比值$ {{{\tau _{{\mathrm{QSL}}}}} {/ } {{\tau _{\mathrm{D}}}}} $随场衰减率$ \chi $和随机数$ \delta $的变化. 这里双“引力猫态”与场之间的耦合$ \lambda = 1 $, $ \gamma = 0.1 $, 实际演化时间$ {\tau _{\mathrm{D}}} = 1 $
Fig. 4. Ratio $ {{{\tau _{{\mathrm{QSL}}}}} {/ } {{\tau _{\mathrm{D}}}}} $ of the quantum speed limit time to the actual evolution time under the influence of classical decaying field for the double “gravitational cat state” as a function of the parameters of the random field noise $ \delta $and the decay rates $ \chi $. Here the coupling between the double “gravitational cat state” and the field is $ \lambda = 1 $, for $ \gamma = 0.1 $; and the evolutional time is $ {\tau _{\mathrm{D}}} = 1 $.
图 5 稳定经典场噪声影响下双 “引力猫态” TDD在不同的稳定经典场参数$ \delta $下随时间$ t $的变化 (a)引力耦合强度较弱时$ \gamma = 0.1 $; (b)引力耦合强度较强时$ \gamma = 10 $
Fig. 5. Trace distance discord under the influence of stable classical field noise for the double “gravitational cat state” as a function of the parameters of the classical field noise $ \delta $and evolution time $ t $: (a) The coupling between the double “gravitational cat state” is weak, for $ \gamma = 0.1 $; (b) the coupling between the double “gravitational cat state” is strong, for $ \gamma = 10 $.
图 6 在强耦合和弱耦合时, 双 “引力猫态”TDD随时间的变化, 此时$ \delta = 1 $ (a)经典场噪声影响下; (b)噪声场存在衰减, $ \chi = 1 $
Fig. 6. Trace distance discord under different coupling strength for the double “gravitational cat state” as a function of the evolution time $ t $, and $ \delta = 1 $: (a) Classical field noise; (b) general local decaying field, $ \chi = 1 $.
图 7 噪声场存在衰减时, 双“引力猫态” TDD和QSLT与实际演化时间的比值$ {{{\tau _{{\mathrm{QSL}}}}} {/ } {{\tau _{\mathrm{D}}}}} $作为初始时间的函数. 驱动时间$ {\tau _{\mathrm{D}}} = 1 $, $ \gamma = 1 $ (a) $ \chi = 1 $; (b) $ \chi = 2 $
Fig. 7. Trace distance discord and the ratio $ {{{\tau _{{\mathrm{QSL}}}}} {/ } {{\tau _{\mathrm{D}}}}} $ of the quantum speed limit time to the actual evolution time under the influence of classical decaying field for the double “gravitational cat state” as a function of the initial evolution time $ t $, for $ {\tau _{\mathrm{D}}} = 1 $, $ \gamma = 1 $: (a) $ \chi = 1 $; (b) $ \chi = 2 $.
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