Quantum electromechanics with levitated nanoparticles

Preparing and observing quantum states of nanoscale particles is a challenging task with great relevance for quantum technologies and tests of fundamental physics. In contrast to atomic systems with discrete transitions, nanoparticles exhibit a practically continuous absorption spectrum and thus their quantum dynamics cannot be easily manipulated. Here, we demonstrate that charged nanoscale dielectrics can be artificially endowed with a discrete level structure by coherently interfacing their rotational and translational motion with a superconducting qubit. We propose a pulsed scheme for the generation and read-out of motional quantum superpositions and entanglement between several levitated nanoparticles, providing an all-electric platform for networked hybrid quantum devices.

Dynamic and Multimode Electromechanics

These notes discuss electromechanical devices in the quantum regime, a topic closely related to cavity optomechanics. Both cavity optomechanics and quantum electromechanics have their roots in gravitational-wave detection. As such, most of their applications are associated with ultrasensitive sensing. In contrast, these notes deal with an emerging application of quantum electromechanics: signal processing. Such applications are a natural consequence of shrinking the mechanical elements from the metre-scale resonators used in gravitational wave detectors to the micron scale, where quantum effects are more evident. Indeed, MEMS are a crucial technology for classical information processing and modern wireless communication. The advent of quantum information processing, particularly with superconducting circuits, means that there is now a need for analogue signal processing functions operating at microwave frequencies and in the quantum regime. Electromechanical devices have now entered this regime as they can store, amplify, squeeze, entangle, temporally shape, and frequency convert microwave signals.

The Electron and the Muon as Eigensolutions of the Quantum Electromechanics under the Green-Function δ (x2 + l2)

Replacing the Green function of Maxwell's electrodynamics δ(x2) by δ(x2 + l2) we obtain a Hamiltonian with a finite number of degrees of freedom for the classical motion of a pointcharge in its own electromagnetic field. After quantization we obtain a mass spectrum if we assume that a nonelectrodynamic bare mass M exists. The spectral terms are S1/2 , P1/2; P3/2 , D3/2; D5/2 etc. (k = +1, -1; +2, -2; +3 ...). It is possible to fit the length l in the Green function and the mass M so that the mass ratio of the lowest terms becomes m (P1/2)/m(S1/2) = mμ/me . We then get: l =4,896 · 10-91 ħ/mp c, M = 15,32mp . Hence the deviation from Maxwell's electrodynamic is extremely small, but not zero, and heavy leptons should exist near m = | M | . Some further leptonic states exist with masses similar to that of the muon. All states, those of the electron and the muon excepted, are γ-instable (life time 10-17 sec. resp. 10-26 sec.).