Nonlinear dynamics of a microelectromechanical mirror in an optical resonance cavity

One of the reasons for the recent rising interest in electromagnetically induced transparency (EIT) in multilevel atomic systems [1] is its potential application in enhancing nonlinear optical processes. Several experiments were carried out recently to show that the atomic coherence effect in multi-level atomic systems could reduce absorption and enhance frequency conversion and four-wave mixing processes [2, 3]. On the other hand, when two level atoms are put into an optical cavity, many nonlinear processes, such as optical bistability and instability, occur. Recently, several theoretical papers proposed switching effects in three-level and four-level atomic systems with and without an optical cavity [4, 5]. These nonlinear optical effects are caused by enhanced Kerr-nonlinearity and dramatic changes in the dispersion slope due to atomic coherence in such multi-level atomic systems. Recently, we have measured the enhanced Kerr-nonlinear index of refraction n 2 of three-level A-type atoms by using an optical ring cavity and found a large modification of n 2 as functions of the frequency detunings of the probe and coupling lasers. We also observed self-pulsation of cavity transmission when the coupling frequency is tuned to atomic resonance and the probe frequency is detuned from resonance by a few MHz. In this paper, we report such observation and discuss its physical mechanism.

This thesis investigates the direct measurement of the thermal noise spectral distribution. Long base line gravitational wave detectors, being commissioned around the world, are limited in sensitivity in the intermediate frequencies by the thermal noise. These detectors are utilising suspended test mirrors for the detection of gravitational waves by measuring their relative displacement. One of the fundamental noise sources in these detectors is the thermally induced displacement of the suspension onto and within the mirrors. This thermally induced motion of the test mirrors limits the displacement sensitivity of the gravitational wave detectors. Knowledge of the spectral behavior of thermal noise over a wide frequency range will improve predictions and understanding of the behavior of the suspension and test mirrors. ¶ In this thesis the direct measurement of the thermal noise spectral distribution of a mechanical flexure resonator is described. The mechanical flexure resonator is an unidirectional ’wobbly table’ made from copper-beryllium, which hinges around four thin flexures 15 mm wide, 1 mm high and ~116 µm thick. The mechanical flexure resonator has a resonant frequency of 192 Hz, with a quality factor of ~3000. ¶ ...

Resonant intracavity four-wave mixing in a composite atom–cavity system

Summary form only given. We present our recent results in measuring the nonlinear Kerr index of refraction of multi-level rubidium atoms inside an optical ring cavity. By using a similar experimental arrangement as we used previously to demonstrate cavity linewidth narrowing due to EIT inside an optical ring cavity, we can measure the nonlinear coefficient χ/sup (3)/ through the asymmetric transmission profile of the ring cavity. By measuring the degree of asymmetry, we can obtain the Kerr nonlinear index of refraction directly, without worrying about contributions from linear absorption. Our preliminary results indicate a significant enhancement of Kerr nonlinearity due to atomic coherence at near-resonance conditions. We present our experimental results and their comparison with theoretical calculations. We discuss the implications of this enhanced nonlinear Kerr index of refraction to nonlinear optical processes in an optical cavity.

We demonstrate a method of light phase shift measurement using a high-finesse optical ring cavity which exhibits reduced phase noise due to cavity length fluctuations. Two laser beams with a frequency difference of one cavity free spectral range are simultaneously resonant with the cavity, demonstrating noise correlations in the error signals due to the common-mode cavity length fluctuations. The differential error signal shows a 30 dB reduction in cavity noise down to the noise floor in a frequency range up to half the cavity linewidth (~ 30 kHz). Various noise sources are analyzed and their contributions to the noise floor are evaluated. Additionally, we apply this noise-reduced phase shift measurement scheme in a simulated spin-squeezing experiment where we have achieved a factor of 40 improvement in phase sensitivity with a phase resolution of 0.7 mrad, which may remove one important barrier against attaining highly spin-squeezed states. The demonstrated method provides a flexible situation by using an optical ring cavity and two independent beams. This method can find direct application to nondestructive measurements in quantum systems, such as for the generation of spin-squeezed states in atom interferometers and atomic clocks.

Development of optical resonant cavities for laser-Compton scattering

Trajectory optimization method based on ellipse model for dynamic motion control of piezoelectric transducer in an optical resonance cavity

Indefinite media with mixed signs of dielectric tensor elements possess unbounded equifrequency surfaces that have been utilized for diverse applications such as superimaging, enhanced spontaneous emission, and thermal radiation. One particularly interesting application of indefinite media is an optical cavity supporting anomalous scaling laws. In this Letter, we show that by replacing an indefinite medium with magnetized plasma one can construct a tunable indefinite cavity. The magnetized plasma model is based on realistic semiconductor material properties at terahertz frequencies that show hyperbolic dispersion in a certain frequency regime. The hyperbolic dispersion features are utilized for the design of optical cavities. Dramatically different sizes of cavities can support the same resonance mode at the same frequency. For a cavity of fixed size, the anomalous scaling law between the resonance frequency and mode number is confirmed. The resonance frequency can be strongly modulated by changing the strength of the applied magnetic field. The proposed model provides active controllability of terahertz resonances on the deep subwavelength scale with realistic semiconductor materials.

We propose an approach to generate strong quantum entanglement by the controllable four wave mixing mechanism in a single cavity, weak coupling optomechanical system. The optomechanical system is driven by a strong two tone pump field and a weak signal field, simultaneously. The two tone pump field consists of a lower and an upper sideband, which couple with the optical cavity and mechanical resonator, and generate the beam splitter and two mode squeezing interactions under the rotating wave approximation. This interaction mechanism modifies the effective susceptibility of the optomechanical cavity and optomechanically induces a four wave mixing process. Strong quantum entanglement can be generated between the signal and four wave mixing fields with an entangled degree over 16 dB in realistic optomechanical systems. The generation scheme of the quantum entanglement is quite robust against thermal mechanical noise, and entanglement above 3 dB can persist at room temperature in the weak coupling regime.

Devices for measuring physical, chemical, and biological phenomena must be able to detect electrostatic charge with high accuracy. A strong interaction between an optical cavity and a mechanical resonator is accomplished by a nanophotonic optomechanical cavity, which limits the light field at the nanoscale. It offers promise for applications in precision sensing thanks to its strong optomechanical coupling and high optical quality factor cavity. Using a zipper cavity and a suspended photonic crystal nanobeam (PCN) that functions as a moveable mechanical resonator, an integrated optomechanical electrometer for electrical voltage measurement is presented here.

Optomechanics is concerned with the coupling between optical cavities and mechanical resonators. Most early works are concentrated in the physics of optomechanics in the small-displacement regime and consider one single optical cavity mode participating in the optomechanical coupling. In this article, we focus on optomechanics in the extremely-large-amplitude regime in which a mechanical resonator is coupled with multiple optical cavity modes during the oscillation. We explicitly show that the mechanical resonator can present self-sustained oscillations with limit cycles in the shape of sawtooth-edged ellipses and can exhibit dynamical multistability. By analyzing the mechanical oscillation process and the accompanying variation of the optical cavity occupation, we develop an energy-balanced condition to ensure the stability of self-sustained oscillation. The effect of the mechanical nonlinearities on the dynamics of the mechanical resonator is also investigated.

We present our experimental demonstration of controlling the cavity output intensity of one laser beam with the intensity of another laser beam in a composite system consisting of a collection of three-level ?-type rubidium atoms and an optical ring cavity. When the intensity of the controlling beam is modulated with a square waveform, the cavity output power switches on and off (with a distinction ratio better than 20:1) between two steady-state values. This all-optical switching effect is the result of combined absorption and enhanced Kerr nonlinearity near resonance in such three-level atomic systems because of atomic coherence and can find applications in optical communication and optical computation.

We develop a fully quantized model of a Bose-Einstein condensate driven by a far off-resonant pump laser which interacts with a single mode of an optical ring cavity. In the linear regime, the cavity mode exhibits spontaneous exponential gain correlated with the appearance of two atomic field side-modes. These side-modes and the cavity field are generated in a highly entangled state, characterized by thermal intensity fluctuations in the individual modes, but with two-mode correlation functions which violate certain classical inequalities. By injecting an initial coherent field into the optical cavity one can significantly decrease the intensity fluctuations at the expense of reducing the correlations, thus allowing for optical control over the quantum statistical properties of matter waves.

Raman-gain-enhanced near-field optomechanical transduction between a movable optical cavity and SiN-membrane resonator is demonstrated. The Raman gain compensates for the intrinsic loss of the cavity and amplifies the optomechanical transduction, through which the membrane vibration is sensed using a high-Q whispering-gallery-mode optical cavity evanescently. The optical Q of the cavity resonance is improved with respect to the optical pump power, which results in an increase in the optomechanically transduced vibration signals of the mechanical resonator. Our near-field optomechanical coupling approach with optical gain realizes highly sensitive displacement measurement in nano- and micro-mechanical resonators consisting of arbitrary materials and structures.

We investigate the optomechanically induced transparency in a hybrid optomechanical system, which consists of two optical cavities and a mechanical resonator. The two-level and three-level atomic ensembles are trapped in the two optical cavities, respectively. We focus on the changes in the number and width of transparency windows and the position of transparent points under different conditions influenced by various interactions. Five transparency windows can be observed when all the interactions are on. The introduction of two-level and three-level atomic ensembles can increase the number of transparency windows and also provide better flexibility for controlling the width of the transparency windows. Specifically, the two-level and three-level atomic ensembles contribute one and two transparency windows, respectively. The stronger coupling results in the larger transparency windows and movement of the transparent points. Moreover, we also study the slow/fast light phenomenon through the variation of phase and group delay. These results may contribute to the research of nonlinear optics and have potential applications in optical signal processing and communication.