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稳定的Casimir平衡点来源于Casimir能函数曲线在空间构成陷阱处的最小值. 本文提出了一种基于双液体的可调控Casimir平衡点. 在金属衬底上, 由于有机溶液和水之间的不相溶性, 形成分层液体体系. 密度低的溶液在上层, 而密度高的溶液在底层. 研究发现, 沉浸在甲苯或苯溶液中的金属悬浮薄片存在稳定的Casimir平衡点. 此外, 倒置的溴苯@水系统中也存在Casimir平衡点. 这些Casimir平衡点距离液体分层界面的高度可通过水层的厚度实现灵活调控. 最后, 还分析讨论了系统温度和水的离子浓度对Casimir平衡点的影响. 本文开辟了一种调控Casimir平衡点的新途径, 并对微纳尺度颗粒的“量子囚禁”具有重要意义.
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关键词:
- Casimir平衡点 /
- 分层现象 /
- 悬浮 /
- 量子囚禁
The Casimir effect, a macroscopic manifestation of quantum phenomena, arises from zero-point energy and thermal fluctuations. When two objects are brought into close proximity, the Casimir effect manifests as a repulsive force, while at greater separations, it transforms into an attractive force. There exists a specific distance at which the Casimir force vanishes, which is referred to as the stable Casimir equilibrium. Stable Casimir equilibrium arises from the curve minimum value of the Casimir energy, which can create spatial trapping. The manipulation of stable Casimir equilibrium provides promising applications in fields such as tunable optical resonators and self-assembly. This work presents a scheme for achieving tunable Casimir equilibrium in a dual-liquid system. The system comprises a multilayered stratified structure with a gold substrate. Above the gold substrate, a stratified liquid system is formed due to the immiscibility between organic solutions and water. The lower-density solution is at the top, while the higher-density solution is at the bottom . Our results suggest that a stable Casimir equilibrium for a suspended gold nanoplate can be realized, when the suspended gold nanoplate is immersed in organic solution of toluene or benzene. Moreover, the height of the suspended gold nanoplate, determined by the stable Casimir equilibrium, can be precisely tuned by changing the thickness of the water layer. The effects of finite temperature and ionic concentration on the Casimir equilibria are also analyzed in this work. The results suggest that the separation height of Casimir equilibrium decreases with the increase of temperature. Interestingly, when the Debye shielding length is comparable to or smaller than the separation length, the ion concentration in water significantly affects the Casimir pressure allowing for extensive modulations of Casimir equilibrium. This work opens up a new avenue for adjusting Casimir equilibrium and has important applications in “quantum trapping” of micro-nano particles.
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Keywords:
- Casimir equilibria /
- stratification /
- suspensions /
- quantum trapping
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图 1 (a) 两不相溶液体中的Casimir悬浮示意图. 金纳米薄片距离液体分层界面为d. 溶液1的密度小于溶液2的密度; 而溶液2作为隔离层, 紧邻金属衬底且具有可调控厚度L. (b) 金、水、溴苯、苯和甲苯的介电常数随虚频率变化曲线
Fig. 1. (a) Schematic diagram of Casimir suspension in two immiscible liquids. The distance between the gold nanoplate and the stratified liquid interface is d. The density of solution 1 is less than that of solution 2, while solution 2 acts as an isolation layer, close to the metal substrate and has a controllable thickness L. (b) Dielectric constants of gold, water, bromobenzene, benzene, and toluene change with the imaginary frequency.
图 2 悬浮金纳米薄片受到的Casimir压强 (a) 苯@水; (b) 甲苯@水; (c) 溴苯@水; (d)倒置的溴苯@水. 压力的正号表示排斥力, 负号表示吸引力. 金纳米薄片的厚度L0 = 40 nm, 系统温度T = 300 K
Fig. 2. Casimir pressure acts on suspended metal nanoplates: (a) Benzene@water; (b) toluene@water; (c) bromobenzene@water; (d) tnverted bromobenzene@water. The positive sign of the pressure indicates repulsion, while the negative sign indicates attraction. Thickness of gold nanoplate L0 = 40 nm, and the temperature of system T = 300 K.
图 3 液体隔离层在有限厚度下, 双液体系统中金纳米薄片受到的Casimir压强 (a) 苯@水; (b) 甲苯@水; (c) 溴苯@水; (d) 倒置的溴苯@水
Fig. 3. Casimir pressure acts on gold nanoplates in dual-liquid systems, where the layer thickness of liquid isolation is finite: (a) Benzene@water; (b) toluene@water; (c) bromobenzene@water; (d) inverted bromobenzene@water.
图 4 不同温度下的Casimir压强 (a) 苯@水; (b) 甲苯@水; (c) 溴苯@水; (d)倒置的溴苯@水. 液体隔离层L的厚度设定为100 nm
Fig. 4. Casimir pressure at different temperatures: (a) Benzene@water; (b) toluene@water; (c) bromobenzene@water; (d) inverted bromobenzene@water. The thickness of the liquid isolation layer L is set to 100 nm.
图 5 不同德拜屏蔽长度下, Casimir压强随距离d的变化曲线 (a) 苯@水; (b) 倒置的溴苯@水. 液体隔离层L的厚度设定为100 nm, 系统温度T = 300 K
Fig. 5. Casimir pressure changes with separation d under different Debye screening lengths: (a) Benzene@water; (b) inverted bromobenzene@water. Thickness of the liquid isolation layer L is set to 100 nm, and the system temperature T = 300 K.
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