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Strong vibrational coupling in room temperature plasmonic resonators
Junzhong Wang1, Kuai Yu2, Yang Yang1
1College of Electronic Science and Technology, Shenzhen University, Shenzhen, 518060, China.
Abstract:
Strong vibrational coupling has been realized in a variety of mechanical systems. However, there have been no experimental observations of strong coupling of the acoustic modes of plasmonic nanostructures, due to rapid energy dissipation in these systems. Here we realized strong vibrational coupling in ultra-high frequency plasmonic nanoresonators by increasing the vibrational quality factors by an order of magnitude. We achieved the highest frequency quality factor products of f × Q = 1.0 × 1013 Hz for the fundamental mechanical modes, which exceeds the value of 0.6 × 1013 Hz required for ground state cooling. Avoided crossing was observed between vibrational modes of two plasmonic nanoresonators with a coupling rate of g = 7.5 ± 1.2 GHz, an order of magnitude larger than the dissipation rates. The intermodal strong coupling was consistent with theoretical calculations using a coupled oscillator model. Our results enabled a platform for future observation and control of the quantum behavior of phonon modes in metallic nanoparticles.
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Titration Calculations: Strong Acid - Strong Base
A titration is carried out for 25.00 mL of 0.100 M HCl (strong acid) with 0.100 M of a strong base NaOH. The pH at different volumes of added base solution can be calculated as follows:
(a) Titrant volume = 0 mL. The solution pH is due to the acid ionization of HCl. Because this is a strong acid, the ionization is complete and the hydronium ion molarity is 0.100 M. The pH of the solution is then:
Strong Acid and Base Solutions
Titration of a Strong Acid with a Strong Base
Vibrating Concrete
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Titration Calculations: Weak Acid - Strong Base
For the titration of 25.00 mL of 0.100 M CH3CO2H with 0.100 M NaOH, the reaction can be represented as:

