Determination of effective mechanical properties of a double-layer beam by means of a nano-electromechanical transducer

We investigate the mechanical properties of a doubly-clamped, double-layer nanobeam embedded into an electromechanical system. The nanobeam consists of a highly pre-stressed silicon nitride and a superconducting niobium layer. By measuring the mechanical displacement spectral density both in the linear and the nonlinear Duffing regime, we determine the pre-stress and the effective Young's modulus of the nanobeam. An analytical double-layer model quantitatively corroborates the measured values. This suggests that this model can be used to design mechanical multilayer systems for electro- and optomechanical devices, including materials controllable by external parameters such as piezoelectric, magnetrostrictive, or in more general multiferroic materials.Comment: 4 pages, 4 figures, 1 supplemental materia

Circuit Electromechanics with a Non-Metallized Nanobeam

We have realized a nano-electromechanical hybrid system consisting of a silicon nitride beam dielectrically coupled to a superconducting microwave resonator. We characterize the sample by making use of the Duffing nonlinearity of the strongly driven beam. In particular, we calibrate the amplitude spectrum of the mechanical motion and determine the electromechanical vacuum coupling. A high quality factor of 480,000 at a resonance frequency of 14 MHz is achieved at 0.5 K. The experimentally determined electromechanical vacuum coupling of 11.5 mHz is quantitatively compared with finite element based model calculations.Comment: Typos and one reference have been correcte

A universal platform for magnetostriction measurements in thin films

We present a universal nanomechanical sensing platform for the investigation of magnetostriction in thin films. It is based on a doubly-clamped silicon nitride nanobeam resonator covered with a thin magnetostrictive film. Changing the magnetization direction within the film plane by an applied magnetic field generates a magnetostrictive stress and thus changes the resonance frequency of the nanobeam. A measurement of the resulting resonance frequency shift, e.g. by optical interferometry, allows to quantitatively determine the magnetostriction constants of the thin film. We use this method to determine the magnetostriction constants of a 10nm thick polycrystalline cobalt film, showing very good agreement with literature values. The presented technique can be useful in particular for the precise measurement of magnetostriction in a variety of (conducting and insulating) thin films, which can be deposited by e.g. electron beam deposition, thermal evaporation or sputtering

Tunable coupling of transmission-line microwave resonators mediated by an rf SQUID

10 pags., 5 figs.We realize tunable coupling between two superconducting transmission line resonators. The coupling is mediated by a non-hysteretic rf SQUID acting as a flux-tunable mutual inductance between the resonators. We present a spectroscopic characterization of the device. In particular, we observe couplings g/2π ranging between –320 MHz and 37 MHz. In the case of g 0, the microwave power cross transmission between the two resonators is reduced by almost four orders of magnitude as compared to the case where the coupling is switched on.The authors acknowledge support from the German Research Foundation through SFB 631 and FE 1564/1-1; the EU projects CCQED, PROMISCE and SCALEQIT; the doctorate program ExQM of the Elite Network of Bavaria; the Spanish MINECO projects FIS2012-33022, FIS2012-36673-C03-02, and FIS2015-69983-P; the CAM Research Network QUITEMAD+; the Basque Government IT472-10 and UPV/EHU UFI 11/55

Quantum state engineering with circuit electromechanical three-body interactions

We propose a hybrid system with quantum mechanical three-body interactions between photons, phonons, and qubit excitations. These interactions take place in a circuit quantum electrodynamical architecture with a superconducting microwave resonator coupled to a transmon qubit whose shunt capacitance is free to mechanically oscillate. We show that this system design features a three-mode polariton--mechanical mode and a nonlinear transmon--mechanical mode interaction in the strong coupling regime. Together with the strong resonator--transmon interaction, these properties provide intriguing opportunities for manipulations of this hybrid quantum system. We show, in particular, the feasibility of cooling the mechanical motion down to its ground state and preparing various nonclassical states including mechanical Fock and cat states and hybrid tripartite entangled states.Comment: 5+5 pages, 4+3 figures. To appear in Physical Review Letter

Quantum State Engineering with Circuit Electromechanical Three-Body Interactions

We propose a hybrid system with quantum mechanical three-body interactions between photons, phonons, and qubit excitations. These interactions take place in a circuit quantum electrodynamical architecture with a superconducting microwave resonator coupled to a transmon qubit whose shunt capacitance is free to mechanically oscillate. We show that this system design features a three-mode polariton--mechanical mode and a nonlinear transmon--mechanical mode interaction in the strong coupling regime. Together with the strong resonator--transmon interaction, these properties provide intriguing opportunities for manipulations of this hybrid quantum system. We show, in particular, the feasibility of cooling the mechanical motion down to its ground state and preparing various nonclassical states including mechanical Fock and cat states and hybrid tripartite entangled states.Comment: 5+5 pages, 4+3 figures. To appear in Physical Review Letter