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The funding for the article is corrected to: Open access funding provided by Universita degli Studi di Firenze within the CRUI-CARE Agreement. The original article has been corrected.

Abstract Phenomenological models aiming to join gravity and quantum mechanics often predict effects that are potentially measurable in refined low-energy experiments. For instance, modified commutation relations between position and momentum, that account for a minimal scale length, yield a dynamics that can be codified in additional Hamiltonian terms. When applied to the paradigmatic case of a mechanical oscillator, such terms, at the lowest order in the deformation parameter, introduce a weak intrinsic nonlinearity and, consequently, deviations from the classical trajectory. This point of view has stimulated several experimental proposals and realizations, leading to meaningful upper limits to the deformation parameter. All such experiments are based on classical mechanical oscillators, i.e., excited from a thermal state. We remark indeed that decoherence, that plays a major role in distinguishing the classical from the quantum behavior of (macroscopic) systems, is not usually included in phenomenological quantum gravity models. However, it would not be surprising if peculiar features that are predicted by considering the joined roles of gravity and quantum physics should manifest themselves just on purely quantum objects. On the basis of this consideration, we propose experiments aiming to observe possible quantum gravity effects on macroscopic mechanical oscillators that are preliminary prepared in a high purity state, and we report on the status of their realization. Graphical abstract

We present a complete theory for laser cooling of a macroscopic radio-frequency LC electrical circuit by means of an optoelectromechanical system, consisting of an optical cavity dispersively coupled to a nanomechanical oscillator, which is in turn capacitively coupled to the LC circuit of interest. We determine the optimal parameter regime where the LC resonator can be cooled down to its quantum ground state, which requires a large optomechanical cooperativity, and a larger electromechanical cooperativity. Moreover, comparable optomechanical and electromechanical coupling rates are preferable for reaching the quantum ground state., Comment: 11 pages, 4 figures

We study the non-linear dynamics of a multimode optomechanical system constituted of a driven high-finesse Fabry–Pérot cavity containing two vibrating dielectric membranes. The analytical study allows to derive a full and consistent description of the displacement detection by a probe beam in the non-linear regime, enabling the faithful detection of membrane displacements well above the usual sensing limit corresponding to the cavity linewidth. In the weak driving regime where the system is in a pre-synchronized situation, the unexcited oscillator has a small, synchronized component at the frequency of the excited one; both large and small amplitude resonator motions are transduced in a nontrivial way by the non-linear response of the optical probe beam. We find perfect agreement between the experimental results, the numerical simulations, and an analytical approach based on slowly-varying amplitude equations.

Strong interactions between Rydberg excitations in cold gases give rise to strong correlations within these samples. Here we present a series of techniques that allow to visualize such correlations either directly, by varying the degree of interaction between the excitations, or indirectly, through the analysis of the full counting statistics (FCS) of the excitation events. Combining the information obtained by both methods provides a more complete characterization of the system, and allows the study of the correlations emerging in the system as a consequence of the strongly interacting nature of Rydberg excitations.

We study theoretically and experimentally the behavior of an optomechanical system where two vibrating dielectric membranes are placed inside a driven Fabry-Pérot cavity. We prove that multi−element systems of mechanical resonators are suitable for enhancing optomechanical performances, and we report a ∼2.47 gain in the optomechanical coupling strength of the membrane relative motion with respect to the single membrane case. With this configuration it is possible to enable cavity optomechanics in the strong single-photon coupling regime.

An opto-electro-mechanical system formed by a nano-membrane capacitively coupled to an LC resonator and to an optical interferometer has recently been proposed and employed for the highly sensitive optical readout of radio-frequency signals [1]. We propose and experimentally demonstrate how the bandwidth of such a transducer can be increased by controlling the interference between two electromechanical interaction pathways of a two-mode mechanical system. We have realized a device based on a SiN nanomembrane coated with a 30 nm-thick Nb film which is coupled to an LC resonator and optically readout by an interferometer [2]. Operating this proof-of-principle device at room temperature, we achieve a sensitivity of 300 nV/√Hz over a bandwidth of 15 kHz in the presence of radio-frequency noise, and an optimal shot-noise-limited sensitivity of 10 nV/√Hz over a bandwidth of 5 kHz. The performance of the device can be improved by controlling the frequency mismatch of the two mechanical modes and the electrode distance and, for the same given sensitivity, a mechanical multimode transducer can achieve a bandwidth significantly larger than that for a single-mode one by creating constructive interference between the two opto-electro-mechanical interaction pathways [3]. The nature of the interference can be controlled by choosing proper electrode configurations with respect to the membrane vibrational modes involved. We show that such an interference allows to create nonreciprocal transmission between optical and radio-frequency signals. One can for example isolate the optical output from radiofrequency noise or viceversa depending upon the electrode configuration.

We study the optomechanical behaviour of a driven Fabry-P\'erot cavity containing two vibrating dielectric membranes. We characterize the cavity-mode frequency shift as a function of the two-membrane positions, and report a $\sim 2.47$ gain in the optomechanical coupling strength of the membrane relative motion with respect to the single membrane case. This is achieved when the two membranes are properly positioned to form an inner cavity which is resonant with the driving field. We also show that this two-membrane system has the capability to tune the single-photon optomechanical coupling on demand, and represents a promising platform for implementing cavity optomechanics with distinct oscillators. Such a configuration has the potential to enable cavity optomechanics in the strong single-photon coupling regime, and to study synchronization in optically linked mechanical resonators.

Le projet « balance du watt » propose de relier la definition du kilogramme a la constante de Planck. La pesee de la masse impliquee necessite une determination de l'acceleration de la pesanteur g avec une exactitude meilleure que 10^−8. Les travaux resumes dans cet article visent a realiser cette determination a l'aide d'un gravimetre atomique et d'un site gravimetrique dedie.

In view of the integration of membrane resonators with more complex MEMS structures, we developed a general fabrication procedure for circular shape SiNx membranes using Deep Reactive Ion Etching (DRIE). Large area and high-stress SiNx membranes were fabricated and used as optomechanical resonators in a Michelson interferometer, where Q values up to 1.3 x 10(6) were measured at cryogenic temperatures, and in a Fabry-Perot cavity, where an optical finesse up to 50000 has been observed. (C) 2016 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

We investigate a general scheme for generating, either dynamically or in the steady state, continuous variable entanglement between two mechanical resonators with different frequencies. We employ an optomechanical system in which a single optical cavity mode driven by a suitably chosen two-tone field is coupled to the two resonators. Significantly large mechanical entanglement can be achieved, which is extremely robust with respect to temperature., To appear in New J. Phys. Small extensions in response to the points raised by the referee and Refs added

From a two-level model for nonlinear Landau-Zener tunnelling between two energy bands of a Bose-Einstein condensate in a periodic potential we obtain unequal tunnelling rates for the two directions of tunnelling. With increasing nonlinearity, tunnelling from the ground state to the excited state is enhanced, whereas in the opposite direction it is suppressed. These findings are confirmed by numerical simulations of the condensate dynamics. Measuring the tunnelling rates for a condensate of rubidium atoms in an optical lattice, we have found experimental evidence for this asymmetry. We discuss the limitations of our approach and possible future experiments.

Rydberg excitation dynamics of a 87-Rb cold atom cloud is investigated in an effective one-dimensional geometry. We measure the excitation dynamics and the full counting statistics for resonant and off-resonant excitation to the 70S state. While for a resonant laser excitation the counting distributions have a strong sub-Poissonian character, we find strongly bimodal counting distributions in the off-resonant regime. The n-th central moments, up to n = 4, of the counting distributions are derived from the measured counting distributions.

One of the most striking features of the strong interactions between Rydberg atoms is the dipole blockade effect, which allows only a single excitation to the Rydberg state within the volume of the blockade sphere. Here we present a method that spatially visualizes this phenomenon in an inhomogeneous gas of ultra-cold rubidium atoms. In our experiment we scan the position of one of the excitation lasers across the cold cloud and determine the number of Rydberg excitations detected as a function of position. Comparing this distribution to the one obtained for the number of ions created by a two-photon ionization process via the intermediate 5P level, we demonstrate that the blockade effect modifies the width of the Rydberg excitation profile. Furthermore, we study the dynamics of the Rydberg excitation and find that the timescale for the excitation depends on the atomic density at the beam position., Comment: 4 pages, 4 figures

Ultra-cold gases excited to strongly interacting Rydberg states are a promising system for quantum simulations of many-body systems. For off-resonant excitation of such systems in the dissipative regime, highly correlated many-body states exhibiting, among other characteristics, intermittency and multi-modal counting distributions are expected to be created. So far, experiments with Rydberg atoms have been carried out in the resonant, non-dissipative regime. Here we realize a dissipative gas of rubidium Rydberg atoms and measure its full counting statistics for both resonant and off-resonant excitation. We find strongly bimodal counting distributions in the off-resonant regime that are compatible with intermittency due to the coexistence of dynamical phases. Moreover, we measure the phase diagram of the system and find good agreement with recent theoretical predictions. Our results pave the way towards detailed studies of many-body effects in Rydberg gases., Comment: 12 pages, 5 figures

We present experimental results on the preparation of a desired quantum state in a two-level system with the maximum possible fidelity using driving protocols ranging from generalizations of the linear Landau-Zener protocol to transitionless driving protocols that ensure perfect following of the instantaneous adiabatic ground state. We also study the minimum time needed to achieve a target fidelity and explore and compare the robustness of some of the protocols against parameter variations simulating a possible experimental uncertainty. In our experiments, we realize a two-level model system using Bose-Einstein condensates inside optical lattices, but the results of our investigation should hold for any quantum system that can be approximated by a two-level system. DOI: 10.1103/PhysRevA.87.012116

A fundamental requirement in quantum information processing and in many other areas of science is the capability of precisely controlling a quantum system by preparing a quantum state with the highest fidelity and/or in the fastest possible way. Here we present an experimental investigation of a two level system, characterized by a time-dependent Landau-Zener Hamiltonian, aiming to test general and optimal high-fidelity control protocols. The experiment is based on a Bose-Einstein condensate (BEC) loaded into an optical lattice, then accelerated, which provides a high degree of control over the experimental parameters. We implement generalized Landau-Zener sweeps, comparing them with the well-known linear Landau-Zener sweep. We drive the system from an initial state to a final state with fidelity close to unity in the shortest possible time (quantum brachistochrone), thus reaching the ultimate speed limit imposed by quantum mechanics. On the opposite extreme of the quantum control spectrum, the aim is not to minimize the total transition time but to maximize the adiabaticity during the time-evolution, the system being constrained to the adiabatic ground state at any time. We implement such transitionless superadiabatic protocols by an appropriate transformation of the Hamiltonian parameters. This transformation is general and independent of the physical system.

The dipole blockade of Rydberg excitations is a hallmark of the strong interactions between atoms in these high-lying quantum states. One of the consequences of the dipole blockade is the suppression of fluctuations in the counting statistics of Rydberg excitations, of which some evidence has been found in previous experiments. Here we present experimental results on the dynamics and the counting statistics of Rydberg excitations of ultra-cold Rubidium atoms both on and off resonance, which exhibit sub- and super-Poissonian counting statistics, respectively. We compare our results with numerical simulations using a novel theoretical model based on Dicke states of Rydberg atoms including dipole-dipole interactions, finding good agreement between experiment and theory., Comment: accepted for publication in PRL; 10 pages, 4 figures (including Supplemental Material)

The ability to accurately control a quantum system is a fundamental requirement in many areas of modern science such as quantum information processing and the coherent manipulation of molecular systems. It is usually necessary to realize these quantum manipulations in the shortest possible time in order to minimize decoherence, and with a large stability against fluctuations of the control parameters. While optimizing a protocol for speed leads to a natural lower bound in the form of the quantum speed limit rooted in the Heisenberg uncertainty principle, stability against parameter variations typically requires adiabatic following of the system. The ultimate goal in quantum control is to prepare a desired state with 100% fidelity. Here we experimentally implement optimal control schemes that achieve nearly perfect fidelity for a two-level quantum system realized with Bose-Einstein condensates in optical lattices. By suitably tailoring the time-dependence of the system's parameters, we transform an initial quantum state into a desired final state through a short-cut protocol reaching the maximum speed compatible with the laws of quantum mechanics. In the opposite limit we implement the recently proposed transitionless superadiabatic protocols, in which the system perfectly follows the instantaneous adiabatic ground state. We demonstrate that superadiabatic protocols are extremely robust against parameter variations, making them useful for practical applications., 17 pages, 4 figures

Rydberg excitation of an elongated Bose-Einstein condensate is performed. We show how the dipole-blockade mechanism restricts the number of Rydberg atoms it is possible to excite in such a cloud. Using the super-atom model we then look at the feasibility of observing coherent effects in even stricter geometries, one dimensional optical lattices

We experimentally realize Rydberg excitations in Bose-Einstein condensates of rubidium atoms loaded into quasi-one-dimensional traps and in optical lattices. Our results for condensates expanded to different sizes in the one-dimensional trap agree well with the intuitive picture of a chain of Rydberg excitations. We also find that the Rydberg excitations in the optical lattice do not destroy the phase coherence of the condensate, and our results in that system agree with the picture of localized collective Rydberg excitations including nearest-neighbor blockade.

Two-photon ionization of Rubidium atoms in a magneto-optical trap and a Bose-Einstein condensate (BEC) is experimentally investigated. Using 100 ns laser pulses, we detect single ions photoionized from the condenstate with a 35(10)% efficiency. The measurements are performed using a quartz cell with external electrodes, allowing large optical access for BECs and optical lattices., Comment: 14 pages, 7 figures

We report a comparison between two absolute gravimeters: the LNE-SYRTE cold atoms gravimeter and FG5#220 of Leibniz Universit\"at of Hannover. They rely on different principles of operation: atomic and optical interferometry. Both are movable which enabled them to participated to the last International Comparison of Absolute Gravimeters (ICAG'09) at BIPM. Immediately after, their bilateral comparison took place in the LNE watt balance laboratory and showed an agreement of 4.3 +/- 6.4 {\mu}Gal.

International audience; We demonstrate a scheme for realizing a compact cold atom gravimeter. The use of a hollow pyramidal configuration allows to achieve all functions: trapping, interferometer and detection with a unique laser beam leading to a drastic reduction in complexity and volume. In particular, we demonstrate a relative sensitivity to acceleration of gravity (g) of 1.7 × 10-7 at one second, with a moderate laser power of 50 mW. This simple geometry combined to such a high sensitivity opens wide perspectives for practical applications (P. Bouyer and A. Landragin, patent n° FR2009/000252, 2009).

International audience; We demonstrate the realization of a scheme for cold-atom gravimetry based on the recently demonstrated use of double-diffraction beam splitters [T. Lévèque, A. Gauguet, F. Michaud, F. Pereira Dos Santos, and A. Landragin, Phys. Rev. Lett. 103, 080405 (2009)], where the use of two retro-reflected Raman beams allows symmetric diffraction in ±ℏkeff momenta. Although in principle restricted to the case of zero Doppler shift, for which the two pairs of Raman beams are simultaneously resonant, such diffraction pulses can remain efficient on atoms with nonzero velocity, such as in a gravimeter, when the frequency of one of the two Raman laser sources is modulated. Such pulses are used to realize an interferometer insensitive to laser phase noise and some of the dominant systematics. This approach reduces the technical requirements and would allow the realization of a simple atomic gravimeter. A sensitivity of 1.2×10-7g per shot is demonstrated.

We have measured the spin-forbidden decay rate from $(3s3d){^{1}D}_{2}\ensuremath{\rightarrow}(3s3p){^{3}P}_{2,1}$ in $^{24}\text{M}\text{g}$ atoms trapped in a magneto-optical trap. The total decay rate, summing up both exit channels $(3s3p){^{3}P}_{1}$ and $(3s3p){^{3}P}_{2}$, yields $196\ifmmode\pm\else\textpm\fi{}10\text{ }{\text{s}}^{\ensuremath{-}1}$ in excellent agreement with resent relativistic many-body calculations of Porsev et al. [Phys. Rev. A 64, 012508 (2001)]. The characterization of this decay channel is important as it may limit the performance of quantum optics experiments carried out with this ladder system as well as two-photon cooling experiments currently explored in several groups.

We demonstrate an accurate method for measuring the lifetime of long-lived metastable magnetic states using a magneto-optical trap (MOT). Through optical pumping, the metastable $(3s3p)\text{ }{^{3}P}_{1}$ level is populated in a standard MOT. During the optical pumping process, a fraction of the population is captured in the magnetic quadrupole field of the MOT. When the metastable atoms decay to the $(3{s}^{2})\text{ }{^{1}S}_{0}$ ground state they are recaptured into the MOT. In this system no alternative cascading transition is possible. The lifetime of the metastable level is measured directly as an exponential load time of the MOT. We have experimentally tested our method by measuring the lifetime of the $(3s3p)\text{ }{^{3}P}_{1}$ of $^{24}\text{M}\text{g}$. This lifetime has been measured numerous times previously, but with quite different results. Using our method we find the $(3s3p)\text{ }{^{3}P}_{1}$ lifetime to be $(4.4\ifmmode\pm\else\textpm\fi{}0.2)\text{ }\text{ms}$. Theoretical values point toward a lower value for the lifetime.

The excitation to high-lying Rydberg states is investigated in a sample of 87-Rb atoms undergoing the Bose-Einstein condensation phase transition, in the limit that the spatial dimensions of the condensed cloud are smaller than the (Wan-der-Waals) dipole blockade radius. We measure the number of excitations by single ion counting as a function of the dimensions of the condensed and thermal fraction. We observed a distinct decrease in the number of excitations due to the change of the atomic spatial density distribution, from the thermal cloud, through a bimodal distribution, to the condensed cloud. When only the condensed part is present, the average number of excitations measured levels off at around one which is compatible with having a single collective excitation in the condensed cloud.

A two-photon mechanism for cooling atoms below the Doppler temperature is analyzed. We consider the magnesium ladder system $(3{s}^{2})^{1}S_{0}\ensuremath{\rightarrow}(3s3p)^{1}P_{1}$ at $285.2\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ followed by the $(3s3p)^{1}P_{1}\ensuremath{\rightarrow}(3s3d)^{1}D_{2}$ transition at $880.7\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$. For the ladder system quantum coherence effects may become important. Combined with the basic two-level Doppler cooling process this allows for reduction of the atomic sample temperature by more than a factor of 10 over a broad frequency range. First experimental evidence for the two-photon cooling process is presented and compared to model calculations. Agreement between theory and experiment is excellent. In addition, by properly choosing the Rabi frequencies of the two optical transitions a velocity independent atomic dark state is observed.

By accelerating a Bose-Einstein condensate in a controlled way across the edge of the Brillouin zone of a 1D optical lattice, we investigate the stability of the condensate in the vicinity of the zone edge. Through an analysis of the visibility of the interference pattern after a time-of-flight and the widths of the interference peaks, we characterize the onset of instability as the acceleration of the lattice is decreased. We briefly discuss the significance of our results with respect to recent theoretical work., 7 pages, 3 figures; submitted to Optics Express (Focus Issue on Cold Atomic Gases in Optical Lattices)

Using a simple model for nonlinear Landau-Zener tunneling between two energy bands of a Bose-Einstein condensate in a periodic potential, we find that the tunneling rates for the two directions of tunneling are not the same. Tunneling from the ground state to the excited state is enhanced by the nonlinearity, whereas in the opposite direction it is suppressed. These findings are confirmed by numerical simulations of the condensate dynamics. Measuring the tunneling rates for a condensate of rubidium atoms in an optical lattice, we have found experimental evidence for this asymmetry., 5 pages, 3 figures

Rydberg spectroscopy of rubidium cold atoms trapped in a magneto-optical trap (MOT) was performed in a quartz cell. When electric fields acting on the atoms generated by a plate external to the cell were continuously applied, electric charges on the cell walls were created, as monitored on the Rydberg spectra. Avoiding accumulation of the charges and realizing good control over the applied electric field was instead obtained when the fields were applied only for a short time, typically a few microseconds. In a two-photon excitation via the 6(2)P state to the Rydberg state, the laser resonant with the 5(2)S-6(2)P transition photoionizes the excited state. The photoionization-created ions produce an internal electric field which deforms the excitation spectra, as monitored on the Autler-Townes absorption spectra. (C) 2010 Optical Society of America

We study synchronization of a room temperature optomechanical system formed by two resonators coupled via radiation pressure to the same driven optical cavity mode. By using stochastic Langevin equations and effective slowly-varying amplitude equations, we explore the long-time dynamics of the system. We see that thermal noise can induce significant non-Gaussian dynamical properties, including the coexistence of multi-stable synchronized limit cycles and phase diffusion. Synchronization in this optomechanical system is very robust with respect to thermal noise: in fact, even though each oscillator phase progressively diffuses over the whole limit cycle, their phase difference is locked, and such a phase correlation remains strong in the presence of thermal noise., 13 pages, 8 figures

Multi-element systems of micro/nano-mechanical resonators offer promising prospects for enhanced optomechanical performances [1,2], and for the exploration of multi-oscillators synchronization [3]. A solution, capable of providing systems with ratio between the single-photon optomechanical coupling rate and the cavity decay rate enhanced by orders of magnitude, exploits quantum interference in multi-element optomechanical setups. Although the simplest two-membrane sandwich in an optical cavity is a paradigm for the realization of strong-coupling optomechanics, and the observation of collective mechanical effects (such as synchronization), no experimental studies of these phenomena have been reported till now. We report on the first experimental characterization of the optical, mechanical, and especially optomechanical properties of a sandwich constituted of two parallel membranes within an optical cavity [4]. The membrane-sandwich we use in our experiment is constituted of two low-stress Si 3 N 4 square membranes, with a side of 1 mm, and a thickness of 100 nm. One of the membranes is glued on a piezo, for scanning the membrane-cavity length. The whole membrane-sandwich mount is attached to another piezo to displace in a controlled way the center of mass of the two membranes inside the Fabry-Perot cavity. To estimate the optomechanical coupling strength achievable with our system, we inserted the membrane-sandwich in an optical cavity 90 mm-long, driven with a 1064 nm laser beam.

Highly excited atoms exhibit large long range dipole-dipole interaction, making them a perfect tool for studying strongly correlated quantum gases and for implementing basic elements for quantum computation with cold neutral atoms [1,2]. Here we present an experimental study of Rydberg excitations of rubidium Bose Einstein condensates loaded in a quasi-one dimensional potential (dipole trap) and in periodic potentials (optical lattices). The excitation of Rydberg atoms in periodic potentials is one of the possible paths towards reaching the scalability requirements in quantum computation devices, with quantum gates based on the dipole blockade effect [3,4].

An opto--electro--mechanical system formed by a nanomembrane capacitively coupled to an LC resonator and to an optical interferometer has been recently employed for the high--sensitive optical readout of radio frequency (RF) signals [T. Bagci, \emph{et~al.}, Nature {\bf 507}, 81 (2013)]. Here we propose and experimentally demonstrate how the bandwidth of such kind of transducer can be increased by controlling the interference between two--electromechanical interaction pathways of a two--mode mechanical system. With a proof--of--principle device \new{operating at room temperature, we achieve a sensitivity of 300 nV/Hz^(1/2) over a bandwidth of 15 kHz in the presence of radiofrequency noise, and an optimal shot-noise limited sensitivity of 10 nV/Hz^(1/2) over a bandwidth of 5 kHz. We discuss strategies for improving the performance of the device, showing that, for the same given sensitivity, a mechanical multi--mode transducer can achieve a bandwidth} significantly larger than that of a single-mode one.

Systematic effects on the stability (1.4×10−8g at 1s) and accuracy of a compact cold atoms gravimeter at SYRTE-LNE are studied with special emphasis on the effect due to light wave aberration of the Raman Lasers.

We have realized a hybrid opto-electro-mechanical system [1], consisting of a radiofrequency (rf) resonato: capacitively coupled to a nanomechanical membrane, and read-out at the shot noise level by an optica interferometer. The oscillation of the mechanical resonator can alter the capacitance of the radiofrequency resonator leading to the modulation of transmitted signal. In our setup the rf resonator is a tunable LC circui with variable resonance frequency between 100 kHz–1MHz. The quality factor of the resonator is 130. The hybrid system is obtained by capacitively coupling the LC resonator to a high stress, 1×1 mm2, 50 nm-thick stoichiometric SiN membrane, metalized with a 20 nm-thick Nb film. The distance between the metalizec membrane and the electrodes is obtained by fitting the mechanical resonance frequency shift due to applied dc voltage V according to m= ω 0 (1-CV2/2mω 0 2), where ω 0 is the zero-bias mechanical resonant frequency, m is the effective mass of the mechanical resonator, and C is a constant that depends upon the geometry of the system (Fig.1). We measured the coupling rate in two independent ways using the electronic signal as well as the reflected optical signal, both yielding a distance between membrane and electrodes of 52 μm. The coupling between the two resonators also manifests itself via Electro-Mechanically-Induced Transparency (EMIT) [1, 2] which is an interference effect analogous to Electromagnetically-Induced Transparency (EIT). We have drivei the electronic resonator with an rf signal and observed an EMIT transparency window in the transmitted signa (Fig. 2). By reducing the distance and increasing the coupling we expect to reach quantum limited detection of Π signals [3].