Session B45: Optomechanics at the Quantum Limit

Sideband cooling micromechanical motion to the quantum ground state

Accessing the full quantum nature of a macroscopic mechanical oscillator first requires elimination of its classical, thermal motion. The flourishing field of cavity opto- and electromechanics provides a nearly ideal architecture for both preparation and detection of mechanical motion at the quantum level. We realize such a system by coupling the motion of an aluminum membrane to the resonance frequency of a superconducting, microwave circuit. By exciting the microwave circuit below its resonance frequency, we damp and cool the membrane motion with radiation pressure forces, analogous to laser cooling of trapped ions. The microwave excitation serves not only to cool, but also to monitor the displacement of the drum. A nearly shot-noise limited, microwave Josephson parametric amplifier is used to detect the mechanical sidebands of this microwave excitation and quantify the thermal motion of the oscillator as it is cooled with radiation pressure forces to its quantum ground state.   

Cavity Cooling of A Mechanical Resonator in Amorphous Systems

The quantum backaction force generated by a cavity coupled with a mechanical resonator can be exploited to achieve sideband cooling of the mechanical mode. By applying a red-detuned driving, the quantum ground state of the mechanical mode can be reached in the resolved-sideband regime, which has recently be demonstrated in experiments. However, in many of these materials, surface defects or adsorbates can couple with the mechanical mode and impair the cavity cooling. These defects can be treated as quantum two-level system (TLS). The mechanical vibration changes the local strain tensor and generates coupling with the TLS via the deformation potential. In this work, we study the cavity cooling of the mechanical mode in the presence of a TLS. By applying the adiabatic elimination technique widely used in quantum optics, we derive the cooling master equation for the resonator-TLS system in the eigenbasis of this system. Our results show that the stationary phonon number depends non- monotonically on the energy of the TLS. We also show that the cooling depends strongly on the decoherence rate of the TLS.   

Quantum Interactions of a Torsional Nanomechanical Resonator with a Single Spin

While the motions of macroscopic objects may ultimately be governed by quantum mechanics, the distinctive features of quantum mechanics can be hidden by thermal excitations and coupling to the environment. We present a system consisting of a torsional nanomechanical resonator with quantum behavior introduced to the system by coupling the resonator with a single spin through a uniform external magnetic field. The spin originates from a nitrogen vacancy (NV) center in a diamond nanocrystal which is positioned on the resonator. The quadratic coupling is maximized by utilizing a low moment of inertia resonator and an avoided level crossing. This coupling results in quantum non-demolition (QND) measurements of the resonator and spin states, enabling a bridge between the quantum and classical worlds. Furthermore, it provides a high-fidelity readout of the NV center spin and a potential means of observing the discrete states of the resonator. We will describe the potential for these measurements and report on the experimental progress made towards observing this coupling in the torsional resonator-NV system.   

Characterization of an oscillator's mechanical impedance using photon pressure

In recent years, there has been much progress in coupling optical cavities to mechanical oscillators, especially in the pursuit of the quantum ground state of a macroscopic oscillator. Photon pressure due to reflection is of particular interest, and such experiments must be carefully designed to minimize competing contributions. Typically, such unwanted contributions are estimated or modeled. We describe an experimental approach to place an upper bound on unwanted contributions. A fiber coupled superluminous light emitting diode is modulated at an optical power of 6.5 mW rms, driving a highly reflective cantilever at a displacement of over 10 nm rms at resonance (Q=4900) in vacuum (10-5 Torr). The optomechanical transfer function is measured and fit to a simple harmonic oscillator model. The stiffness of the oscillator determined from the fit (k=16.6 +/- 1.3 N/m) is found to be in good agreement with that obtained by calibration against our SI-traceable nanoindenter (k=17.4 +/- 0.5 N/m). We characterize the modal stiffness, mass, and dissipation of the first two eigenmodes of our oscillator with SI traceability. The quantitative agreement in our experiment indicates that our oscillator is actuated by photon pressure, and that all other contributions to the force must sum to less than 11{\%}.   

Multi-stability in an optomechanical system with two-component Bose-Einstein condensate

We investigate a system consisting of a two-component Bose-Einstein condensate interacting dispersively with a Fabry-Perot optical cavity where the two components of the condensate are resonantly coupled to each other by another classical field. The key feature of this system is that the atomic motional degrees of freedom and the internal pseudo-spin degrees of freedom are coupled to the cavity field simultaneously, hence an effective spin-orbital coupling within the condensate is induced by the cavity. The interplay among the atomic center-of-mass motion, the atomic collective spin and the cavity field leads to a strong nonlinearity, resulting in multi-stable behavior in both matter wave and light wave at the few-photon level.   

Optomechanical down-conversion

One of the central interactions in quantum optics is two-mode squeezing, also known as down-conversion. It has been used in a multitude of pioneering experiments to demonstrate non-classical states of light and it is at the heart of generating quantum entanglement in optical fields. Here we demonstrate first experimental results towards the optomechanical analogue, in which an optical and a mechanical mode interact via a two-mode squeezing operation. In addition, we make use of the fact that large optomechanical coupling strengths provide access to an interaction regime beyond the rotating wave approximation. This allows for simultaneous cooling of the mechanical mode, which will eventually enable the preparation of pure initial mechanical states and is hence an important precondition to achieve the envisioned optomechanical entanglement.   

Photothermally induced dynamics in partially coated loaded microcantilevers

Cooling of microcantilevers in a Fabry-Perot cavity either by radiation pressure or using the photothermal effect has attracted significant attention lately. We present ongoing experimental results on partially coated microcantilevers which are either loaded ( gold sphere) or have a coating only at the tip. In particular, we will compare the results with that of recent work on fully coated cantilevers.   

Micro-optomechanical trampoline resonators

Recently, micro-optomechanical devices have been proposed for implementation of experiments ranging from non-demolition measurements of phonon number to creation of macroscopic quantum superpositions. All have strenuous requirements on optical finesse, mechanical quality factor, and temperature. We present a set of devices composed of dielectric mirrors on Si$_{3}$N$_{4}$ trampoline resonators. We describe the fabrication process and present data on finesse and quality factor.   

Proposal for detecting measurement-induced entanglement between remote mechanical oscillators

In optomechanical systems where an optical cavity mode interacts with a mechanical oscillator, the light leaking out of the cavity has sidebands at the mechanical frequency. The photon statistics of these sidebands contain information about the mechanical oscillator. We consider driving two similar optical cavities, containing one mechanical system each, in such a way that the mechanical oscillators are laser cooled close to the ground state. When the output fields of the two cavities are made indistinguishable by combining them on a beamsplitter, the detection of sideband photons can lead to measurement-induced entanglement between the two non-interacting mechanical oscillators. We show how this short-lived entanglement between remote mechanical oscillators can be verified through measurements of higher-order coherences of the optical output field.   

Investigation of radiation pressure shot-noise in a microwave circuit optomechanical system

We examine the possibility of measuring the radiation pressure shot-noise of microwave light. When the motion of a nanomechanical oscillator is coupled to the microwave energy stored in a resonant circuit, the oscillator experiences a radiation pressure force. That force must have a random component associated with the quantum nature of the microwave field, a mechanical manifestation of the microwave photon. The variance of this random component increases with increasing circuit excitation power. Until recently, reaching powers where radiation pressure shot-noise would dominate over other random forces was unfeasible due to relatively weak optomechanical coupling and technical power limitations of microwave circuits. However, the recent advent of a mechanical oscillator coupled strongly to a microwave circuit [1] will enable exploration of this regime. We discuss the most favorable circuit parameters and measurement strategy for studying radiation pressure shot-noise. \\[4pt] [1] J. D. Teufel, et al, Circuit cavity electromechanics in the strong coupling regime, arXiv:1011.3067v1.   

Levitated Quantum Nano-Magneto-Mechanical Systems

Quantum nanomechanical sysems have attracted much attention as they provide new macroscopic platforms for the study of quantum mechanics but may also have applications in ultra-sensitive sensing, high precision measurements and in quantum computing. \noindent In this work we study the control and cooling of a quantum nanomechanical system which is magnetically levitated via the Meissner effect. Supercurrents in nano-sized superconducting loops give rise to a motional restoring force (trap), when placed in an highly inhomogenous magnetic field and can yield complete trapping of all translational and rotational motions of the levitated nano-object with motional oscillation frequencies $\nu\sim 10-100$MHz. As the supercurrents experience little damping this system will possess unprecendented motional quality factors, with $Q_{motion}\sim 10^9-10^{13}$, and motional superposition states may remain coherent for days. We describe how to execute sideband cooling through inductive coupling to a nearby flux qubit, cooling the mechanical motion close to the ground state.   

Measurement of Casimir force with transparent conducting oxides

The Casimir force plays an important role in micro- and nano electro mechanical systems (MEMS and NEMS) fabrication, because it can easily exceed the electrostatic forces used for actuating the systems at small electrode separation distances. The reduction of the Casimir force in devices is a complicated problem that needs to be scientifically investigated to open opportunities for the full exploitation of MEMS and NEMS technology. One of the ways to tune the Casimir force is to properly choose the materials of which the interacting surfaces are made. According to the Lifshitz theory, the interaction between two objects depends on their dielectric permittivity. In that case the transparent dielectrics attract less than reflective materials. This can be used to decrease the Casimir force when the design requires a smaller short range interaction. To achieve low Casimir forces and avoid uncontrolled electrostatic forces as present in dielectrics, transparent but conductive materials can be used. An ideal choice is conductive Indium Oxide such as very low doped Indium Tin Oxide (ITO). In this report we present the results of the Casimir force using transparent electrodes such as Indium Tin Oxide coated SiO$_{2}$ plate.   

Precision measurements of the Casimir force at Low temperatures

We will present research involving the precision measurement of the Casimir force at low temperatures. The role of material losses in this force and its incorporation into the Lifshitz theory remains unresolved. The Casimir force results from the modification of the zero point photon spectrum due to the presence of boundaries. The problem arises when the Casimir force is calculated at non zero temperature, where the role of thermal photons have to be included to that of the zero point photons. We plan to address this problem by measuring the Casimir force for different materials as a function of the temperature. Currently we are involved in making precision measurements of the Casmir force at 6K, 77K, and 300K with a micro cantilever based system that we have designed and built at UC-Riverside. The high sensitivity of this instrument will provide us with the resolution to advance our understanding of the interactions of both virtual photons and real photons when confined to a semi-infinite cavity made out of real metals. The constructed apparatus will also provide a deeper understanding of the role vacuum fluctuations play when the cavity constituents are made of a combination of dielectric, superconductor, and metal surfaces.   

Strong interactions of single atoms and photons near a dielectric boundary

Quantum control of strong interactions between a single atom and photon has been achieved within the setting of cavity quantum electrodynamics (cQED). To move beyond proof-of-principle experiments involving one or two conventional optical cavities to more complex scalable systems that employ $N > 1$ microscopic resonators requires localization of atoms on distance scales $\sim 100$ nm from a resonator's surface where an atom can be strongly coupled to a single intracavity photon while at the same time experiencing significant radiative interactions with the dielectric boundaries of the resonator. As an initial step into this new regime of cQED, we use real-time detection and high-bandwidth feedback to select and monitor motion of single Cesium atoms through the evanescent field of a microtoroid\footnote{D. J. Alton, \textit{et al,} \textit{Nature Physics} (2010); available as arXiv:1011.0740.}. Direct temporal and spectral measurements coupled with simulations reveal both the significant role of Casimir-Polder attraction and the manifestly quantum nature of the atom-cavity dynamics, here in a regime of strong coupling, setting the stage for trapping atoms near micro- and nano-scopic optical resonators.   

Distinct single photons strongly interacting at a single atom in a waveguide

We propose a waveguide QED system where two distinct single photons can interact strongly. The system consists of a single ladder-type three level atom coupled to a waveguide. We show that the nonlinear interaction can be tremendously enhanced by the strong coupling of the cascade atomic transitions to the waveguide mode simultaneously. As a result, a control photon tuned to the upper transition induces a $\pi$ phase shift and tunneling of a probe photon tuned to the otherwise reflective lower transition. Waveguide QED schemes could be an alternative to high quality cavities or dense atomic ensembles in quantum information processing.