Low Noise Opto-Electro-Mechanical Modulator for RF-to-Optical Transduction in Quantum Communications

Abstract

In this work, we present an Opto-Electro-Mechanical Modulator (OEMM) for RF-to-optical transduction realized via an ultra-coherent nanomembrane resonator capacitively coupled to an rf injection circuit made of a microfabricated read-out able to improve the electro-optomechanical interaction. This device configuration can be embedded in a Fabry-Perot cavity for electromagnetic cooling of the LC circuit in a dilution refrigerator exploiting the opto-electro-mechanical interaction. To this aim, an optically measured steady-state frequency shift of 380 Hz was seen with a polarization voltage of 30 V and a Q-factor of the assembled device above 106 at room temperature. The rf-sputtered titanium nitride layer can be made superconductive to develop efficient quantum transducers.

Keywords: electro-optics; hybrid systems; low noise N/MEMS resonators; optomechanics; quantum transduction.

Figure 1

Opto–Electro-Mechanical Modulator. (a) Schematic of the setup with a detailed view of the cross-section of the OEMM embedded in the high-finesse Fabry–Perot Cavity. The rf weak $\delta V$ signal is transferred to the cavity optical field after polarizing the coupling capacitor $C_m\left(x\right)$ with a DC voltage bias $V_{DC}$. (b,c) The two components of the OEMM device: the electrode connected to the LC circuit (b) and the floating electrode on the silicon nitride membrane (c). Materials are also specified, while the substrate is floating-zone crystalline silicon for both components.

Figure 2

Dissipation of the metalized membrane. (a) The Q-factor of the bilayer SiN/TiN membrane without edge losses $Q_{SiN/TiN}$ (red) and with edge loss of the SiN layer $Q_{SiN/TiN}^{Tot}$ (blue). Green stars are the experimental points of the measured Q-factor for the two first axisymmetric modes with index (0,1) and (0,2). (b) Optical image of the SiN stoichiometric nanomembrane (light blue) with the TiN layer (brown). The membrane is endowed with the on-chip shield for recoil losses (see Ref. [54]) (right). Detailed view of the TiN notch in the membrane electrode used for the mode identification and the component assembly.

Figure 3

Main steps of the microfabrication process flow-chart.

Figure 4

Detailed view of the interaction region in the OEMM assembled device (left). The OEMMs clamped to the OFHC copper block (center) and the diving PCB board used in the optical setup (right).

Figure 5

Experimental setup. Michelson interferometer with shot-noise limited homodyne detection.

Figure 6

Mechanical mode characterization. (a) Voltage spectral noise of the homodyne signal (blue) and the shot-noise contribution (red). Mechanical modes of the functionalized ${\mathrm{Si}}_3{\mathrm{N}}_4$ membrane correspondence to the peaks of the spectrum. The first mode has frequency $f_{(0,1)}=260.65$ kHz. The green dashed lines are the calculated frequencies from the FEM simulation. (b) Calculated mode shapes via FEM simulation, corresponding to the calculated mode frequencies present in the spectrum. Axisymmetric modes and modes with two-fold degeneracy are classified according to the number of nodal and circumference indexes. Frequency increases from the top to the bottom and from left to right.

Figure 7

Measurement of the mechanical Q-factor for different modes after the final assembling of the device. Red points correspond to measurements at $V_{DC}$ = 0 V, the blue point corresponds to the measurement at $V_{DC}$ = 30 V. Inset: voltage spectral noise (VSN) density of the homodyne signal during the ring-down measurement of the fundamental mode (0,1) at $V_{DC}$ = 0 V (dotted red line) and $V_{DC}$ = 30 V (dotted blue line) and corresponding fit (continuous lines), with best fit values ${\tau }_{0V}=4.668\pm 0.008$ s and ${\tau }_{30V}=2.476\pm 0.004$ s, respectively.

Figure 8

Measurement of the frequency shift of the (1,1) mode as a function of the DC voltage bias $V_{DC}$ (blue square). The red line is the fit of the data using Equation (15), with best value of the average distance between the electrodes and the membrane of $d=(5.12\pm 0.14)$$\mathsf{\mu }$m and using the following parameters: effective area $A_{eff}=0.075$ ${\mathrm{mm}}^2$; membrane mass $m_{eff}=420$ ng; measured unperturbed mode frequency $f_0=f_{11}=$ 399,587 Hz.