Non-reciprocal energy transfer through the Casimir effect

A Casimir-based device that can utilize quantum vacuum fluctuations to realize some advanced functions will have potential applications in quantum information processing and quantum metrology. Here, a Casimir diode system that can regulate quantum vacuum-mediated energy transfer in one direction is demonstrated.
Non-reciprocal energy transfer through the Casimir effect

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Quantum mechanics predicts random fluctuations of electromagnetic fields in vacuum which leads to the well-known universal Casimir force between macroscopic bodies. The Casimir force dominates the interaction between two surfaces when the separation is in the range of tens and hundreds of nanometers. The Casimir pressure is comparable to the atmosphere when the separation between two plates is 10 nm. This inevitable attractive force may lead to undesirable effects in micro and nanodevices, including stiction and adhesions. Thus many efforts have been put in to reduce the Casimir effect on devices. On the other hand, we ask ourselves whether we can utilize the Casimir force itself for device function instead of reducing its undesired effect.

In 2019, Fong et al. showed the first realization of heat transfer by Casimir interaction, and the work reveals an unprecedented heat transfer mechanism in vacuum. However, the transfer is symmetric under such conditions. To fully realize the regulation of energy transfer by quantum vacuum fluctuations, we need to break the symmetry in analogy to the electrical diode.

In this work, we proposed and realized the first Casimir diode system experimentally. We built the dual-cantilever vacuum Casimir system from scratch in our lab. The schematic of the setup is shown in Figure.1. (a). Two modified micro-mechanical cantilevers can be modulated individually by the piezo chips and detected independently by the fiber interferometers. This novel dual-cantilever system not only allows us to study the targeted Casimir force between various materials but also gives us the chance to study the dynamics and energy transfer by quantum fluctuations. To realize the strong coupling and energy transfer between two cantilevers, we apply the parametric modulation scheme to the system. Compared to the conventional phonon transfer between two oscillators with identical frequencies, we can couple two oscillators with arbitrary frequencies, as shown in Figure.1. (b) and (c). For example, we have two cantilevers with a frequency difference of around 700 Hz in our experiment. When we modulate the separation between two surfaces with a frequency equivalent to the frequency difference between two cantilevers, we can couple two cantilevers parametrically by Casimir interaction. The Casimir coupling essentially originates from time-dependent boundary changes for quantum vacuum fluctuations between the two surfaces.

To realize the non-reciprocity, we utilized the unique topological structure near the exceptional point. The coupled dual-cantilever system can be treated as a two-level non-Hermitian system, and it possesses a spectral singularity (exceptional point) in the parameter space under some conditions. At the exceptional point, two eigenvalues are degenerate for both real and imaginary parts. In our experiment, we can control the modulation amplitude and modulation frequency independently to effectively modify the system eigenvalues. We applied additional loss to one of the cantilevers to possess an accessible exceptional point, as shown in Figure. 1. (d) and (e). We design a dynamical control loop near the exceptional point to break the symmetry. In the experiment, we drive one cantilever resonantly and send the pulse sequence (time-dependent dynamical control) just after the excitation. We observe non-reciprocal energy transfer between two cantilevers after 80-ms pulse sequence control on the system, as shown in Figure. 1. (f) and (g). The transfer direction depends on the control loop.

Overall, we have realized the first Casimir diode system that can rectify the energy transfer along the desired direction. The device provides more perspectives and opportunities for utilizing quantum vacuum fluctuations. Moreover, the Casimir diode system can potentially be used to create macroscopic quantum entangled states for quantum sensing and quantum information transducing. Compared to the conventional optomechanical coupling systems, which require a large number of real photons, the Casimir coupling by virtual photons can have better coherence and better performance in the quantum regime.

If you would like to know more about this work, please read the complete study in Nature Nanotechnology, “Non-reciprocal energy transfer through the Casimir effect.”

Figure 1. Non-reciprocal energy transfer with virtual photons. (a). Illustrations of a dual-cantilever Casimir system with fiber interferometer detection systems. (b). Schematic of parametric coupling between two cantilevers. (c). Transduction ratio between two cantilevers when parametric modulation is applied. (d) and (e). We engineer the system to possess an exceptional point (EP) in the parameter space (real and imaginary parts). (f) and (g). By dynamical control near the exceptional point, non-reciprocal energy transfer with high contrast is realized.

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