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Optomechanics with Quantum Vacuum Fluctuations

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This thesis presents the first realization of non-reciprocal energy transfer between two cantilevers by quantum vacuum fluctuations. According to quantum mechanics, vacuum is not empty but full of fluctuations due to zero-point energy. Such quantum vacuum fluctuations can lead to an attractive force between two neutral plates in vacuum – the so-called Casimir effect – which has attracted great attention as macroscopic evidence of quantum electromagnetic fluctuations, and can dominate the interaction between neutral surfaces at small separations. The first experimental demonstration of diode-like energy transport in vacuum reported in this thesis is a breakthrough in Casimir-based devices. It represents an efficient and robust way of regulating phonon transport along one preferable direction in vacuum. In addition, the three-body Casimir effects investigated in this thesis were used to realize a transistor-like three-terminal device with quantum vacuum fluctuations. These two breakthroughs pave the way for exploring and developing advanced Casimir-based devices with potential applications in quantum information science. This thesis also includes a study of the non-contact Casimir friction, which will enrich the understanding of quantum vacuum fluctuations.

Table of Contents

Frontmatter
Chapter 1. Introduction
Abstract
Quantum mechanics predicts an infinite number of random fluctuations in vacuum because of the zero-point energy of the electromagnetic fields. Quantum vacuum fluctuations lead to the Casimir force between two neutral macroscopic objects, the Casimir torque between two anisotropic bodies, and the quantum vacuum friction between two moving bodies. In this thesis, we focus on using optomechanical systems (the multi-cantilever system and the levitated optomechanical system) to study Casimir force, Casimir torque, and quantum vacuum friction.
Zhujing Xu
Chapter 2. Measurement and Calculation of Casimir Force
Abstract
Measurement of Casimir force has been progressively improved since the first observation of Casimir force in 1958. In this chapter, we will first introduce our home-built dual-cantilever vacuum system and the detection scheme. We will present the measurement methods and results of Casimir force between two mechanical cantilevers in vacuum. At a separation of x, the Casimir force between an ideally conductive sphere with radius R and an ideally conductive plate is \(F^0_C (x) = -\frac {\pi ^3\hbar c}{360}\frac {R}{x^3}\). However, we need to consider the finite conductivity, finite temperature, and material dispersion in the calculation. Our measurements agree well with the calculation based on Lifshitz theory. We will also discuss the thermal contributions and the effect of gold thin film thickness on the Casimir force. Parts of the contents in this chapter have been published in Xu et al. (Nat Nanotechnol 17(2):148–152, 2022).
Zhujing Xu
Chapter 3. Experimental Realization of a Casimir Diode: Non-reciprocal Energy Transfer by Casimir Force
Abstract
The Casimir effect is essential for micro- and nanotechnologies because it is inevitably huge at a small separation. The Casimir interaction has been used to realize various advanced function. However, a non-reciprocal Casimir device is still unexplored. In this chapter, we will introduce our recent realization of non-reciprocal energy transfer between two micro-mechanical oscillators by Casimir effect. We will first show how we realize a strong coupling and energy transfer by the parametric coupling scheme. This will be followed by a measurement of the exceptional point in the parameter space by a careful design. We will then present the results of non-reciprocal energy transfer by dynamically driving the system near the exceptional point. In the last section of this chapter, we will show detailed derivations of the effective system Hamiltonian and the exceptional point. Parts of the contents in this chapter have been published in Xu et al. (Nat Nanotechnol 17(2):148–152, 2022).
Zhujing Xu
Chapter 4. Experimental Realization of a Casimir Transistor: Switching and Amplifying Energy Transfer in a Three-Body Casimir System
Abstract
The Casimir interaction can be used to couple two mechanical resonators and improve the quality factor of a mechanical resonator. While the Casimir effect between two objects has been extensively studied, the Casimir force between three objects is still unexplored. It is interesting to study the three-body interactions by quantum vacuum fluctuations. In this chapter, we will demonstrate the first observation of Casimir effects between three separate objects. A transistor-like energy transfer is realized in this three-channel Casimir system, which can switch and amplify the Casimir mediated energy transfer. We will first introduce the three-cantilever system. This is followed by the the measurement of Casimir force in this three-body system. Later on, we will present the observation of level repulsion in the three-body system due to Casimir coupling. The coupling and level repulsion can be well explained by an effective Hamiltonian that will also be discussed. In the last part of this chapter, we will show how we realize the transistor-like energy transfer in this three-object Casimir system. Parts of the contents in this chapter have been published in Xu et al. (Nat Commun 13(1):6148, 2022).
Zhujing Xu
Chapter 5. Proposal on Detecting Rotational Quantum Vacuum Friction
Abstract
Quantum friction predicts that two neutral bodies with a relative motion will experience a friction force due to quantum vacuum fluctuations. However, quantum vacuum friction has never been observed experimentally due to its small amplitude. In this chapter, we propose to detect the rotational vacuum friction torque by a levitated nanorotor near a surface. We will first introduce our ultrasensitive torque sensor with an unprecedented torque sensitivity. After that, we will present the calculation of rotational quantum vacuum friction on a rotating silica sphere near a silica surface. Compared to the torque sensitivity, our system will be able to detect the rotational vacuum friction torque. Besides, we also investigate on the rotational vacuum friction torque for a barium strontium titanate (BST) system. The rotational vacuum friction torque can be enhanced by several orders at a rotating frequency around GHz because of the resonant photon tunneling. Parts of the contents in this chapter have been published in Ahn et al. (Nat Nanotechnol 15(2):89–93, 2020) and Xu et al. (Nanophotonics 10(1):537–543, 2021).
Zhujing Xu
Chapter 6. Proposal on Detecting Casimir Torque
Abstract
Many efforts were made to improve the precision in the Casimir force measurement and to harness the Casimir effect in various devices. Similar to the Casimir force that comes from the linear momentum of virtual photons, virtual photons also carry angular momentum, and this induces the Casimir torque between anisotropic materials. In spite of significant interests and theoretical proposals toward detecting Casimir torque, there is only one reported experimental observation of Casimir torque in 2018. The measurement was conducted between a liquid crystal and a solid birefringent crystal. To ensure the parallelism of two surfaces, the vacuum gap is replaced by an isotropic material. To our knowledge, Casimir torque between two objects with a vacuum gap has never been detected yet. In this chapter, we propose a scheme to detect the Casimir torque by our ultrasensitive optical levitation system. We will present the calculation of the Casimir torque between a levitated nanorod and a birefringent surface at a sub-wavelength distance. Compared to the torque sensitivity of the levitation system, we will demonstrate that it is promising to detect the Casimir torque across a vacuum gap in the near future, and our levitation setup is expected to provide a better accuracy for the Casimir torque measurement. Parts of the contents in this chapter have been published in Xu and Li (Phys Rev A 96:033843, 2017).
Zhujing Xu
Chapter 7. Conclusion and Outlook
Abstract
In the present thesis, we have introduced our home-built multi-cantilever vacuum system. We use the multi-cantilever systems to measure the Casimir effect and study the energy transfer by quantum vacuum fluctuations. In this chapter, we will introduce several topics that can possibly be studied by our Casimir vacuum system in the near future. We will first introduce our preliminary design of a Casimir microelectromechanical systems (MEMS) accelerometer by utilizing the strong nonlinearity of the Casimir force and parametric amplification scheme. The simulated signal under an external acceleration will be presented to demonstrate the sensitivity of the Casimir MEMS accelerometer. Next, we will investigate on switching the Casimir force between a vanadium oxide (VO\({ }_2\)) surface and a gold surface. VO\({ }_2\) has a metal–insulator transition temperature at 340 K that is accessible in the experiment. The transition from insulator to metal can generate an abrupt Casimir force increment at the transition temperature. The calculation of the Casimir effect between VO\({ }_2\) and gold will be presented. In the last part of this chapter, we will discuss a few possible schemes to engineer the repulsive Casimir force in vacuum that has never been observed yet.
Zhujing Xu
Backmatter
Metadata
Title
Optomechanics with Quantum Vacuum Fluctuations
Author
Zhujing Xu
Copyright Year
2024
Electronic ISBN
978-3-031-43052-7
Print ISBN
978-3-031-43051-0
DOI
https://doi.org/10.1007/978-3-031-43052-7

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