In recent years microfabricated microwave cavities have been extremely successful in a wide variety of detector applications. In this article we focus this technology on the challenge of quantum-limited displacement detection of a macroscopic object. We measure the displacement of a nanomechanical beam by capacitively coupling its position to the resonant frequency of a superconducting transmission-line microwave cavity. With our device we realize near state-of-the-art mechanical force sensitivity (3 $\rm{aN/\sqrt{Hz}}$) and thus add to only a handful of techniques able to measure thermomechanical motion at 10's of milliKelvin temperatures. Our measurement imprecision reaches a promising 30 times the expected imprecision at the standard quantum limit, and we quantify our ability to extract measurement backaction from our results as well as elucidate the important steps that will be required to progress towards the full quantum limit with this new detector.
We propose a scheme able to entangle at the steady state a nanomechanical resonator with a microwave cavity mode of a driven superconducting coplanar waveguide. The nanomechanical resonator is capacitively coupled with the central conductor of the waveguide and stationary entanglement is achievable up to temperatures of tens of milliKelvin.
A scheme is presented for entangling two separated nanomechanical oscillators by injecting broad band squeezed vacuum light and laser light into the ring cavity. We work in the resolved sideband regime. We find that in order to obtain the maximum entanglement of the two oscillators, the squeezing parameter of the input light should be about 1. We report significant entanglement over a very wide range of power levels of the pump and temperatures of the environment.
We measure the response and thermal motion of a high-Q nanomechanical oscillator coupled to a superconducting microwave cavity in the resolved-sideband regime where the oscillator's resonance frequency exceeds the cavity's linewidth. The coupling between the microwave field and mechanical motion is strong enough for radiation pressure to overwhelm the intrinsic mechanical damping. This radiation-pressure damping cools the fundamental mechanical mode by a factor of 5 below the thermal equilibrium temperature in a dilution refrigerator to a phonon occupancy of 140 quanta.
We theoretically study the transmission of a weak probe field under the influence of a strong pump field in a coupled nanomechanical resonator-superconducting microwave cavity system. Using the standard input-output theory, we find that both pulse delay (slow light effect) and advancement (fast light effect) of the probe field can appear in this coupled system provided that we choose the suitable detuning of the pump field from cavity resonance. The magnitude of the delay (advancement) can be tuned continuously by adjusting the power of the pump field. This technique demonstrates great potenti…
We propose a scheme able to generate stationary continuous variable entanglement between an optical and a microwave cavity mode by means of their common interaction with a micro-mechanical resonator. We show that when both cavities are intensely driven one can generate bipartite entanglement between any pair of the tripartite system, and that, due to entanglement sharing, optical-microwave entanglement is efficiently generated at the expense of microwave-mechanical and opto-mechanical entanglement.
We study how an optical parametric amplifier inside the cavity can affect the normal mode splitting behavior of the coupled movable mirror and the cavity field. We work in the resolved sideband regime. The spectra exhibit a double-peak structure as the parametric gain is increased. Moreover, for a fixed parametric gain, the double-peak structure of the spectrum is more pronounced with increasing the input laser power. We give results for mode splitting. The widths of the split lines are sensitive to parametric gain.
We describe a cavity QED analogue for the coupling system of a spin and a nanomechanical resonator with a magnetic tip. For the quantized nanomechanical resonator, a spin-boson model for this coupling system can refer to a Jaynes-Cummings(JC) or an anti-JC model. These observations predict some quantum optical phenomena, such as squeezing and "collapse-revival" in the single oscillation mode of the nanomechanical resonator when it is initially prepared in the quasi-classical state. By modulating the phase of RF magnetic field one can switch the system between the JC and anti-JC model, which pr…
Cavity-enhanced radiation pressure coupling between optical and mechanical degrees of freedom allows quantum-limited position measurements and gives rise to dynamical backaction enabling amplification and cooling of mechanical motion. Here we demonstrate purely dispersive coupling of high Q nanomechanical oscillators to an ultra-high finesse optical microresonator via its evanescent field, extending cavity optomechanics to nanomechanical oscillators. Dynamical backaction mediated by the optical dipole force is observed, leading to laser-like coherent nanomechanical oscillations solely due to r…
We demonstrate the existence of the phenomenon of the inverse electromagnetically induced transparency (IEIT) in an opto mechanical system consisting of a nanomechanical mirror placed in an optical cavity. We show that two weak counter-propagating identical classical probe fields can be completely absorbed by the system in the presence of a strong coupling field so that the output probe fields are zero. The light is completely confined inside the cavity and the energy of the incoming probe fields is shared between the cavity field and creation of a coherent phonon and resides primarily in one …
We study the effect of a strong coupling field on the absorptive property of a ring cavity with two mirrors oscillating at slightly different frequencies to a weak probe field. We observe double electromagnetically induced transparency windows separated by an absorption peak at line center in the output probe field under the action of a strong coupling field. We find that increasing driving power can broaden the two transparency windows, which results in narrowing of the central absorption peak. At high driving power, the linewidth of the sharp central absorption peak is approximately equal to…
We study a parametrically-driven nanomechanical resonator capacitively coupled to a microwave cavity. If the nanoresonator can be cooled to near its quantum ground state then quantum squeezing of a quadrature of the nanoresonator motion becomes feasible. We consider the adiabatic limit in which the cavity mode is slaved to the nanoresonator mode. By driving the cavity on its red-detuned sideband, the squeezing can be coupled into the microwave field at the cavity resonance. The red-detuned sideband drive is also compatible with the goal of ground state cooling. Squeezing of the output microwav…
We show how the coherent oscillations of a nanomechanical resonator can be entangled with a microwave cavity in the form of a superconducting coplanar resonator. Dissipation is included and realistic values for experimental parameters are estimated.
We propose and study an "intrinsic probing" approach, without introducing any external detector, to mimic cavity QED effects in a qubit-nanomechanical resonator system. This metallic nanomechanical resonator can act as an intrinsic detector when a weak driving current passes through it. The nanomechanical resonator acts as both the cavity and the detector. A cavity QED-like effect is demonstrated by the correlation spectrum of the electromotive force between the two ends of the nanomechanical resonator. Using the quantum regression theorem and perturbation theory, we analytically calculate the…
Spontaneous synchronization is a significant collective behavior of weakly coupled systems. Due to their inherent nonlinear nature, optomechanical systems can exhibit self-sustained oscillations which can be exploited for synchronizing different mechanical resonators. In this paper, we explore the synchronization dynamics of two membranes coupled to a common optical field within a cavity, and pumped with a strong blue-detuned laser drive. We focus on the system quantum dynamics in the parameter regime corresponding to synchronization of the classical motion of the two membranes. With an approp…
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 oscill…
The inherently nonlinear interaction between light and motion in cavity optomechanical systems has experimentally been studied in a linearized description in all except highly driven cases. Here we demonstrate a nanoscale optomechanical system, in which the interaction between light and motion is so large (single-photon cooperativity $C_0 \approx 10^3$) that thermal motion induces optical frequency fluctuations larger than the intrinsic optical linewidth. The system thereby operates in a fully nonlinear regime, which pronouncedly impacts the optical response, displacement measurement, and radi…
We consider a nanomechanical analogue of a nonlinear interferometer, consisting of two parallel, flexural nanomechanical resonators, each with an intrinsic Duffing nonlinearity and with a switchable beamsplitter-like coupling between them. We calculate the precision with which the strength of the nonlinearity can be estimated and show that it scales as $1/n^{3/2}$, where $n$ is the mean phonon number of the initial state. This result holds even in the presence of dissipation, but assumes the ability to make measurements of the quadrature components of the nanoresonators.
We determine the quantum mechanical limits to inertial mass-sensing based on nanomechanical systems. We first consider a harmonically oscillating cantilever whose vibration frequency is changed by mass accretion at its surface. We show that its zero-point fluctuations limit the mass sensitivity, for attainable parameters, to about an electron mass. In contrast to the case of a classical cantilever, we find the mass sensitivity of the quantum mechanical cantilever is independent of its resonant frequency in a certain parameter regime at low temperatures. We then consider an optomechanical setup…
We analyze the quantum information processing capability of a superconducting transmon circuit used to mediate interactions between quantum information stored in a collection of phononic crystal cavity resonators. Having only a single processing element to be controlled externally makes this approach significantly less hardware-intensive than traditional architectures with individual control of each qubit. Moreover, when compared with the commonly considered alternative approach using coplanar waveguide or 3d cavity microwave resonators for storage, the nanomechanical resonators offer both ver…
We propose and analyze a hybrid device by integrating a microscale diamond beam with a single built-in nitrogen-vacancy (NV) center spin to a superconducting coplanar waveguide (CPW) cavity. We find that under an ac electric field the quantized motion of the diamond beam can strongly couple to the single cavity photons via dielectric interaction. Together with the strong spin-motion interaction via a large magnetic field gradient, it provides a hybrid quantum device where the dia- mond resonator can strongly couple both to the single microwave cavity photons and to the single NV center spin. T…
We propose and experimentally demonstrate a technique for coupling phonons out of an optomechanical crystal cavity. By designing a perturbation that breaks a symmetry in the elastic structure, we selectively induce phonon leakage without affecting the optical properties. It is shown experimentally via cryogenic measurements that the proposed cavity perturbation causes loss of phonons into mechanical waves on the surface of silicon, while leaving photon lifetimes unaffected. This demonstrates that phonon leakage can be engineered in on-chip optomechanical systems. We experimentally observe larg…
We present a scheme for photonic transistors based on photons and phonons in a cavity electromechanical system, which is consisted of a superconducting microwave cavity coupled to a nanomechanical resonator. Control of the propagation of photons is achieved through the interaction of microwave field (photons) and nanomechanical vibrations (phonons). By calculating the transmission spectrum of the signal field, we show that the signal field can be efficiently attenuated or amplified, depending on the power of a second `gating'(pump) field. This scheme may be a promising candidate for single-pho…
Spin-mechanics studies interactions between spin systems and mechanical vibrations in a nanomechanical resonator and explores their potential applications in quantum information processing. In this tutorial, we summarize various types of spin-mechanical resonators and discuss both the cavity-QED-like and the trapped-ion-like spin-mechanical coupling processes. The implementation of these processes using negatively charged nitrogen vacancy and silicon vacancy centers in diamond is reviewed. Prospects for reaching the full quantum regime of spin-mechanics, in which quantum control can occur at t…
We introduce an approach to quantum information processing where the information is stored in the motional degrees of freedom of nanomechanical devices. The qubits of our approach are formed by the two lowest energy levels of mechanical resonators which are tuned to be strongly anharmonic by suitable electrostatic fields. Single qubit rotations are conducted by radio frequency voltage pulses that are applied to individual resonators. Two qubit entangling gates in turn are implemented via a coupling of two qubits to a common optical resonance of a high finesse cavity. We find that gate fideliti…
We demonstrate a transducer of nanomechanical motion based on cavity enhanced optical near-fields capable of achieving a shot-noise limited imprecision more than 10 dB below the standard quantum limit (SQL). Residual background due to fundamental thermodynamical frequency fluctuations allows a total imprecision 3 dB below the SQL at room temperature (corresponding to 600 am/Hz^(1/2) in absolute units) and is known to reduce to negligible values for moderate cryogenic temperatures. The transducer operates deeply in the quantum backaction dominated regime, prerequisite for exploring quantum back…
We present optical sideband spectroscopy measurements of a mesoscopic mechanical oscillator cooled near its quantum ground state. The mechanical oscillator, corresponding to a 3.99GHz acoustic mode of a patterned silicon nanobeam, is coupled via radiation pressure to a pair of co-localized 200THz optical modes. The mechanical mode is cooled close to its quantum ground state from a bath temperature of 18K using radiation pressure back-action stemming from the optical pumping of one of the optical cavity resonances. An optical probe beam, resonant with the second optical cavity resonance, is use…
Pulsed optomechanical measurements enable squeezing, non-classical state creation and backaction-free sensing. We demonstrate pulsed measurement of a cryogenic nanomechanical resonator with record precision close to the quantum regime. We use these to prepare thermally squeezed and purified conditional mechanical states, and to perform full state tomography. These demonstrations exploit large photon-phonon coupling in a nanophotonic cavity to reach a single-pulse imprecision of 9 times the mechanical zero-point amplitude $x_\mathrm{zpf}$. We study the effect of other mechanical modes which lim…
We propose an active mechanism for coupling the quantized mode of a nanomechanical resonator to the persistent current in the loop of a superconducting Josephson junction (or phase slip) flux qubit. This coupling is independently controlled by an external coupling magnetic field. The whole system forms a novel solid-state cavity quantum electrodynamics (QED) architecture in the strong coupling limit. This architecture can be used to demonstrate quantum optics phenomena and coherently manipulate the qubit for quantum information processing. The coupling mechanism is applicable for more generali…
We consider a theoretical model for a nonlinear nanomechanical resonator coupled to a superconducting microwave resonator. The nanomechanical resonator is driven parametrically at twice its resonance frequency, while the superconducting microwave resonator is driven with two tones that differ in frequency by an amount equal to the parametric driving frequency. We show that the semi-classical approximation of this system has an interesting fixed point bifurcation structure. In the semi-classical dynamics a transition from stable fixed points to limit cycles is observed as one moves from positiv…
Recently, the design of a white-light-cavity has been proposed using negative dispersion in an intra-cavity medium to make the cavity resonate over a large range of frequencies and still maintain a high cavity build-up. This paper presents the demonstration of this effect in a free-space cavity. The negative dispersion of the intra-cavity medium is caused by bi-frequency Raman gain in an atomic vapor cell. A significantly broad cavity response over a bandwidth greater than 20 MHz has been observed. The experimental results agree well with the theoretical model, taking into account effects of r…
We theoretically study the coupling of Bose-Einstein condensed atoms to the mechanical oscillations of a nanoscale cantilever with a magnetic tip. This is an experimentally viable hybrid quantum system which allows one to explore the interface of quantum optics and condensed matter physics. We propose an experiment where easily detectable atomic spin-flips are induced by the cantilever motion. This can be used to probe thermal oscillations of the cantilever with the atoms. At low cantilever temperatures, as realized in recent experiments, the backaction of the atoms onto the cantilever is sign…
We study a resonator coupled to a generic detector and calculate the noise spectra of the two sub-systems. We describe the coupled system by a closed, linear, set of Langevin equations and derive a general form for the finite frequency noise of both the resonator and the detector. The resonator spectrum is the well-known thermal form with an effective damping, frequency shift and diffusion term. In contrast, the detector noise shows a rather striking Fano-like resonance, i.e. there is a resonance at the renormalized frequency, and an anti-resonance at the bare resonator frequency. As examples …
We theoretically investigate the generation of atom-light entanglement via Raman superradiance in an optical cavity, and show how this can be used to enhance the sensitivity of atom interferometry. We model a realistic optical cavity, and show that by careful temporal shaping of the optical local oscillator used to measure the light emitted from the cavity, information in the optical mode can be combined with the signal from the atom interferometer to reduce the quantum noise, and thus increase the sensitivity. It was found in Phys. Rev. Lett. 110, 053002 (2013) that an atomic `seed' was requi…
Atomic Kapitza-Dirac (KD) scattering in the classical standing wave of lights is widely used to make the laser-pulsed atom interferometers. In this theoretical work, we show that the dielectric nanoparticle can be used as a weak light source to generate atomic KD scattering and make atom interferometer. We consider a cavity system consisting of atoms and a single nanoparticle, where the nanoparticle is illuminated by the external laser pulses. Atoms and the cavity mirrors are not illuminated by the laser beam, so nanoparticle acts as a pulsed source to excite the cavity mode which non-resonant…
We propose an enhanced optical interferometer based on tailored non-classical light generated by nonlinear dynamics and projective measurements in a three-level atom cavity QED system. A coherent state in the cavity becomes dynamically entangled with two ground states of the atom and is transformed to a macroscopic superposition state via a projective measurement on the atom. We show that the resulting highly non-classical state can improve interferometric precision measurements well beyond the shot-noise limit once combined with a classical laser pulse at the input of a Mach-Zehnder interfero…
We investigate the steady-state cooling dynamics of vibrational degrees of freedom related to a nanomechanical oscillator coupled with a laser-pumped quantum dot in an optical resonator. Correlations between phonon-cooling and quantum-dot photon emission processes occur respectively when a photon laser absorption together with a vibrational phonon absorption is followed by photon emission in the optical resonator. Therefore, the detection of photons generated in the cavity mode concomitantly contribute to phonon cooling detection of the nanomechanical resonator.
We consider a simple model of a Josephson junction phase qubit coupled to a solid-state nanoelectromechanical resonator. This and many related qubit-resonator models are analogous to an atom in an electromagnetic cavity. When the systems are weakly coupled and nearly resonant, the dynamics is accurately described by the rotating-wave approximation (RWA) or the Jaynes-Cummings model of quantum optics. However, the desire to develop faster quantum-information-processing protocols necessitates approximate, yet analytic descriptions that are valid for more strongly coupled qubit-resonator systems.…
In the usual optomechanical systems, the stability of the systems severely limits those researches of the macroscopic quantum effects. We study an usual cavity optomechanical system where the frequency of the optical mode is shaken periodically. We find that, when the optical shaking frequency is large enough, the shake of the optical mode can stabilize the system. That means we can study the macroscopic quantum effects of the mechanical resonator even in the strong coupling region where the standard optomechanical systems are always unstable. As examples, we study the ground-state cooling of …
The shot-noise limited peak sensitivity of cavity-enhanced interferometric measurement devices, such as gravitational-wave detectors, can be improved by increasing the cavity finesse, even when comparing fixed intra-cavity light powers. For a fixed light power inside the detector, this comes at the price of a proportional reduction in the detection bandwidth. High sensitivity over a large span of signal frequencies, however, is essential for astronomical observations. It is possible to overcome this standard sensitivity-bandwidth limit using non-classical correlations in the light field. Here,…
We present a scheme for tuning and controlling nano mechanical resonators by subjecting them to electrostatic gradient fields, provided by nearby tip electrodes. We show that this approach enables access to a novel regime of optomechanics, where the intrinsic nonlinearity of the nanoresonator can be explored. In this regime, one or several laser driven cavity modes coupled to the nanoresonator and suitably adjusted gradient fields allow to control the motional state of the nanoresonator at the single phonon level. Some applications of this platform have been presented previously [New J. Phys. …
We propose a realizable experimental scheme to prepare a superposition of the vacuum and one-photon states using a typical cavity QED-setup. This is different from previous schemes, where the superposition state of the field is generated by resonant atom-field interaction and the cavity is initially empty. Here, we consider only dispersive atom-field interaction and the initial state of the cavity field is coherent. Then, we determine the parameters to prepare the desired state via atomic postselection. We also include the effect of cavity losses and detection imperfections in our analysis, ag…
We propose a quantum enhanced interferometric protocol for gravimetry and force sensing using cold atoms in an optical lattice supported by a standing-wave cavity. By loading the atoms in partially delocalized Wannier-Stark states, it is possible to cancel the undesirable inhomogeneities arising from the mismatch between the lattice and cavity fields and to generate spin squeezed states via a uniform one-axis twisting model. The quantum enhanced sensitivity of the states is combined with the subsequent application of a compound pulse sequence that allows to separate atoms by several lattice si…
Bragg interferometers, operating using pseudospin-1/2 systems composed of two momentum states, have become a mature technology for precision measurements. State-of-the-art Bragg interferometers are rapidly surpassing technical limitations and are soon expected to operate near the projection noise limit set by uncorrelated atoms. Despite the use of large numbers of atoms, their operation is governed by single-atom physics. Motivated by recent proposals and demonstrations of Raman gravimeters in cavities, we propose a scheme to squeeze directly on momentum states for surpassing the projection no…
The coherent states that describe the classical motion of a mechanical oscillator do not have well-defined energy, but are rather quantum superpositions of equally-spaced energy eigenstates. Revealing this quantized structure is only possible with an apparatus that measures the mechanical energy with a precision greater than the energy of a single phonon, $\hbarω_\text{m}$. One way to achieve this sensitivity is by engineering a strong but nonresonant interaction between the oscillator and an atom. In a system with sufficient quantum coherence, this interaction allows one to distinguish differ…
The 'optical spring' results from dynamical back-action and can be used to improve the sensitivity of cavity-enhanced gravitational-wave detectors. The effect occurs if an oscillation of the cavity length results in an oscillation of the intra-cavity light power having such a phase relation that the light's radiation pressure force amplifies the oscillation of the cavity length. Here, we analyse a Michelson interferometer whose optical-spring cavity includes an additional optical-parametric amplifier with adjustable phase. We find that the phase of the parametric pump field is a versatile para…
The interplay between coherent tunnel coupling and on-site interactions in dissipation-free bosonic systems has lead to many spectacular observations, ranging from the demonstration of number-phase uncertainty relation to quantum phase transitions. To explore the effect of dissipation and coherent drive on tunnel coupled interacting bosonic systems, we propose a device that is the quantum optical analog of a Josephson interferometer. It consists of two coherently driven linear optical cavities connected via a central cavity with a single-photon nonlinearity. The Josephson-like oscillations in …
Optomechanical cavities in the well-resolved-sideband regime are ideally suited for the study of a myriad of quantum phenomena with mechanical systems, including backaction-evading measurements, mechanical squeezing, and generation of non-classical states. For these experiments, the mechanical oscillator should be prepared in its ground state; residual motion beyond the zero-point motion must be negligible. The requisite cooling of the mechanical motion can be achieved using the radiation pressure of light in the cavity by selectively driving the anti-Stokes optomechanical transition. To date,…
We describe the design for a scalable, solid-state quantum-information-processing architecture based on the integration of GHz-frequency nanomechanical resonators with Josephson tunnel junctions, which has the potential for demonstrating a variety of single- and multi-qubit operations critical to quantum computation. The computational qubits are eigenstates of large-area, current-biased Josephson junctions, manipulated and measured using strobed external circuitry. Two or more of these phase qubits are capacitively coupled to a high-quality-factor piezoelectric nanoelectromechanical disk reson…
Setting off from the classic input-output formalism, we develop a theoretical framework to characterise the Gaussian quantum channels relating the initial correlations of an open bosonic system to those of properly identified output modes. We then proceed to apply our formalism to the case of quantum harmonic oscillators, such as the motional degrees of freedom of trapped ions or nanomechanical oscillators, interacting with travelling electromagnetic modes through cavity fields and subject to external white noise. Thus, we determine the degree of squeezing that can be transferred from an intra…
We describe a chip-based, solid-state analogue of cavity-QED utilizing acoustic phonons instead of photons. We show how long-lived and tunable acceptor impurity states in silicon nanomechanical cavities can play the role of a matter non-linearity for coherent phonons just as, e.g., the Josephson qubit plays in circuit-QED. Both strong coupling (number of Rabi oscillations ~ 100) and strong dispersive coupling (0.1-2 MHz) regimes can be reached in cavities in the 1-20 GHz range, enabling the control of single phonons, phonon-phonon interactions, dispersive phonon readout of the acceptor qubit, …
Broadband quantum noise reduction can be achieved in gravitational wave detectors by injecting frequency dependent squeezed light into the the dark port of the interferometer. This frequency dependent squeezing can be generated by combining squeezed light with external filter cavities. However, in future long baseline interferometers (LBIs), the filter cavity required to achieve the broadband squeezing has a low bandwidth -- necessitating a very long cavity to mitigate the issue from optical loss. It has been shown recently that by taking advantage of Einstein-Podolsky-Rosen (EPR) entanglement…
We carry out analysis of optomechanical system formed by moveable mirror of Fabry-Perot cavity pumped by detuned laser. Optical spring arising from detuned pump creates in the system several eigen modes which could be treated as high-Q oscillators. Modulation of laser power results in parametric modulation of oscillators spring constants thus allowing to squeeze noise in quadratures of the modes. Evidence of the squeezing could be found in the light reflected from the cavity.
