In this paper we study a system consisting of two nearly degenerate mechanical modes that couple to a single mode of an optical cavity. We show that this coupling leads to nearly complete (99.5%) hybridization of the two mechanical modes into a bright mode that experiences strong optomechanical interactions and a dark mode that experiences almost no optomechanical interactions. We use this hybridization to transfer energy between the mechanical modes with 40% efficiency.PACS numbers: 42.50. Wk, 42.81.Wg, 42.60.Da, 85.85.+j, Optomechanical systems, in which electromagnetic resonators interact with mechanical resonators, offer a platform for studying a wide range of nonlinear and quantum effects. These systems have been studied in the context of quantum-limited detection of forces and displacements, the production of nonclassical states of light, synchronization and chaotic dynamics, and tests of quantum mechanics with massive degrees of freedom. [1] Optomechanical systems are usually modeled as a single optical mode that is parametrically coupled to a single mechanical mode. This simple model accurately describes many experiments; however, real devices invariably consist of multiple optical and mechanical modes. The presence of multiple modes can provide important capabilities, including new types of optomechanical interactions, robust means for detecting quantum effects, and the ability to transfer quantum states between different systems. [2][3][4][5][6][7][8][9][10][11][12][13] One important class of multimode optomechanical systems consists of devices in which a single optical mode couples to multiple mechanical modes. This situation arises naturally when an optomechanical device with wellseparated optical resonances is driven by a single laser beam. Within the usual weak-coupling description of optomechanics the undriven optical modes are irrelevant, and only the driven mode needs to be considered. [14][15][16] Mechanical modes, on the other hand, cannot be ignored just because they are not driven. This is because any optical mode can be detuned (to some degree) by the displacement of any of the devices' mechanical modes. As a result the effective Hamiltonian for such a device will involve one optical mode coupled to many mechanical modes.In such a system, the motion of a given mechanical mode will modulate the intracavity optical field, which will in turn drive the other mechanical modes. This can be thought of as an optically mediated coupling between the mechanical modes. This intermode coupling can be neglected for mechanical modes whose resonance frequencies are well separated. However, mechanical resonators with * alexey.shkarin@yale.edu some degree of symmetry will have some nearly degenerate modes, and for these modes this coupling can be important.In this paper we demonstrate that the optomechanical coupling between one optical mode and two mechanical modes causes the mechanical modes to nearly fully (99.5%) hybridize into bright and dark states. We then transfer classical mechanical energy betwee...

We describe an optomechanical device consisting of a fiber-based optical cavity containing a silicon nitiride membrane. In comparison with typical free-space cavities, the fiber-cavity's small mode size (10 µm waist, 80 µm length) allows the use of smaller, lighter membranes and increases the cavity-membrane linear coupling to 3 GHz/nm and the quadratic coupling to 20 GHz/nm 2 . This device is also intrinsically fiber-coupled and uses glass ferrules for passive alignment. These improvements will greatly simplify the use of optomechanical systems, particularly in cryogenic settings. At room temperature, we expect these devices to be able to detect the shot noise of radiation pressure.In quantum mechanics, a measurement of one variable is accompanied by back-action on the conjugate variable. In the particular case of an optical displacement measurement, the quantum back-action is radiation pressure shot noise (RPSN) 1,2 , the Poissonian noise in the momentum transferred by reflecting photons.When a high-finesse cavity is used to increase the sensitivity of the displacement measurement, the RPSN is also increased. The connection between increased cavity finesse, increased measurement sensitivity, and increased RPSN can be understood qualitatively by noting that the number of times each photon interacts with a mechanical element inside a cavity is approximately equal to the cavity finesse.In the field of optomechanics, floppy mechanical elements are integrated into high-finesse optical cavities in order to observe various quantum effects, including RPSN 3,4 . The goal of observing RPSN is motivated by basic questions about quantum measurements, as well as by the fact that RPSN is expected to limit the performance of next-generation gravitational-wave observatories (though squeezed light can be used to mitigate the effect) 5,6 . To date, RPSN has not been observed in solid-state optomechanical devices, largely because it has been obscured by the thermal Langevin force that produces Brownian motion 7 . While it has been proposed that correlation measurements can be used to distinguish RPSN in the presence of a much larger Langevin force 7,8 , such a measurement would be simplified by increasing the RPSN relative to the thermal Langevin force. There is an additional motivation for increasing the RPSN: the optomechanical generation of squeezed light (e.g. for improving the performance of gravitational-wave observatories) requires a setup in which the RPSN dominates over the Langevin force 9,10 . Increasing the effect of RPSN in comparison to thermal motion involves optimizing both the mechanical system a) Electronic mail: nathan.flowers-jacobs@yale.edu = 82 A 2n /κ when the laser is resonant with the cavity and the mechanical resonance frequency ω m is much less than the cavity FWHM linewidth κ (the "bad cavity" limit). Thus, the RPSN force is increased by increasing the optomechanical coupling A = dω cav /dx, increasing the average number of photons stored in the cavityn, and decreasing κ.In this paper, we present a n...

Optomechanical systems couple an electromagnetic cavity to a mechanical resonator which is typically formed from a solid object. The range of phenomena accessible to these systems depends on the properties of the mechanical resonator and on the manner in which it couples to the cavity fields. In both respects, a mechanical resonator formed from superfluid liquid helium offers several appealing features: low electromagnetic absorption, high thermal conductivity, vanishing viscosity, well-understood mechanical loss, and in situ alignment with cryogenic cavities. In addition, it offers degrees of freedom that differ qualitatively from those of a solid. Here, we describe an optomechanical system consisting of a miniature optical cavity filled with superfluid helium. The cavity mirrors define optical and mechanical modes with near-perfect overlap, resulting in an optomechanical coupling rate ~ 3 kHz. This coupling is used to drive the superfluid; it is also used to observe the superfluid's thermal motion, resolving a mean phonon number as low as 11.Light confined in a cavity exerts forces on the components that form the cavity. These forces can excite mechanical vibrations in the cavity components, and these vibrations can alter the propagation of light in the cavity. This interplay between electromagnetic (EM) and mechanical degrees of freedom is the basis of cavity optomechanics. It gives rise to a variety of nonlinear phenomena in both the EM and mechanical domains, and provides means for controlling and sensing EM fields and mechanical oscillators. 1 If the optomechanical interaction is approximately unitary, it can provide access to quantum effects in the optical and mechanical degrees of freedom. 1 Optomechanical systems have been used to observe quantum effects which are remarkable in that they are associated with the motion of massive objects. 2,3,4,5,6,7,8,9,10,11,12 They have also been proposed for use in a range of quantum information and sensing applications. 13,14,15,16,17,18,19,20,21,22 Realizing these goals typically requires strong optomechanical coupling, weak EM and mechanical loss, efficient cooling to cryogenic temperatures, and reduced influence from technical noise.To date, nearly all optomechanical devices have used solid objects as mechanical oscillators.However, liquid oscillators offer potential advantages. A liquid can conformally fill a hollow EM cavity, 23 allowing for near-perfect overlap between the cavity's EM modes and the normal modes of the liquid body's vibrations. In addition, the liquid's composition can be changed in situ, an important feature for applications in fluidic sensing. 24 However, most liquids face two important obstacles to operation in or near the quantum regime: their viscosity results in strong mechanical losses, and they solidify when cooled to cryogenic temperatures. Liquid helium is exceptional in both respects, as it does not solidify under its own vapor pressure and possesses zero viscosity in its purely superfluid state. In addition, liquid He has low EM lo...

We measure the noise added by an atomic point contact operated as a displacement detector. With a microwave technique, we increase the measurement speed of atomic point contacts by a factor of 500. The measurement is then fast enough to detect the resonant motion of a nanomechanical beam at frequencies up to 60 MHz and sensitive enough to observe the random thermal motion of the beam at 250 mK. We demonstrate a shot-noise limited imprecision of 2.3 fm/square root[Hz] and observe a 78 aN/square root[Hz] backaction force, yielding a total uncertainty in the beam's displacement that is 42 times the standard-quantum limit.