Optomechanically induced transparency

Coherent interaction of laser radiation with multilevel atoms and molecules can lead to quantum interference in the electronic excitation pathways. A prominent example observed in atomic three-level-systems is the phenomenon of electromagnetically induced transparency (EIT), in which a control laser induces a narrow spectral transparency window for a weak probe laser beam. The concomitant rapid variation of the refractive index in this spectral window can give rise to dramatic reduction of the group velocity of a propagating pulse of probe light. Dynamic control of EIT via the control laser enables even a complete stop, that is, storage, of probe light pulses in the atomic medium. Here, we demonstrate optomechanically induced transparency (OMIT)--formally equivalent to EIT--in a cavity optomechanical system operating in the resolved sideband regime. A control laser tuned to the lower motional sideband of the cavity resonance induces a dipole-like interaction of optical and mechanical degrees of freedom. Under these conditions, the destructive interference of excitation pathways for an intracavity probe field gives rise to a window of transparency when a two-photon resonance condition is met. As a salient feature of EIT, the power of the control laser determines the width and depth of the probe transparency window. OMIT could therefore provide a new approach for delaying, slowing and storing light pulses in long-lived mechanical excitations of optomechanical systems, whose optical and mechanical properties can be tailored in almost arbitrary ways in the micro- and nano-optomechanical platforms developed to date

Process tomography of field damping and measurement of Fock state lifetimes by quantum non-demolition photon counting in a cavity

The relaxation of a quantum field stored in a high-$Q$ superconducting cavity is monitored by non-resonant Rydberg atoms. The field, subjected to repetitive quantum non-demolition (QND) photon counting, undergoes jumps between photon number states. We select ensembles of field realizations evolving from a given Fock state and reconstruct the subsequent evolution of their photon number distributions. We realize in this way a tomography of the photon number relaxation process yielding all the jump rates between Fock states. The damping rates of the $n$ photon states ($0\leq n \leq 7$) are found to increase linearly with $n$. The results are in excellent agreement with theory including a small thermal contribution

Reconstruction of non-classical cavity field states with snapshots of their decoherence

The state of a microscopic system encodes its complete quantum description, from which the probabilities of all measurement outcomes are inferred. Being a statistical concept, the state cannot be obtained from a single system realization, but can instea

Sub-nanometer active seismic isolator control

Ambitious projects such as the design of the future Compact Linear Collider (CLIC) require challenging parameters and technologies. Stabilization of the CLIC particle beam is one of these challenges. Ground motion (GM) is the main source of beam misalignment. Beam dynamics controls are however efficient only at low frequency (<4Hz), due to the sampling of the beam at 50 Hz. Hence, ground motion mitigation techniques such as active stabilization are required. This paper shows a dedicated prototype able to manage vibration at a sub-nanometer scale. The use of cutting edge sensor technology is however very challenging for control applications as they are usually used for measurement purposes. Limiting factors such as sensor dynamics and noise lead to a performance optimization problem. The current state of the art in GM measurement and GM mitigation techniques is pointed out and shows limits of the technologies. The proposed active device is then described and a realistic model of the process has been established. A dedicated controller design combining feedforward and feedback techniques is presented and theoretical results in terms of Power Spectral Density (PSD) of displacement are compared to real time experimental results obtained with a rapid control prototyping tool

Pulsed quantum optomechanics

Studying mechanical resonators via radiation pressure offers a rich avenue for the exploration of quantum mechanical behavior in a macroscopic regime. However, quantum state preparation and especially quantum state reconstruction of mechanical oscillators remains a significant challenge. Here we propose a scheme to realize quantum state tomography, squeezing and state purification of a mechanical resonator using short optical pulses. The scheme presented allows observation of mechanical quantum features despite preparation from a thermal state and is shown to be experimentally feasible using optical microcavities. Our framework thus provides a promising means to explore the quantum nature of massive mechanical oscillators and can be applied to other systems such as trapped ions.Comment: 9 pages, 4 figure

Active vibration isolation system for CLIC final focus

International audienceWith pinpoint accuracy, the next generation of Linear Collider such as CLIC will collide electron and positron beams at a centre of mass energy of 3 TeV with a desired peak luminosity of 2*1034 cm-2s-1. One of the many challenging features of CLIC is its ability to collide beams at the sub-nanometer scale at the Interaction Point (IP). Such a high level of accuracy could only be achieved by integrating Active Vibration Isolation systems (AVI) upstream of the collision to prevent the main source of vibration: Ground Motion (GM). Complementary control systems downstream of the collision (Interaction Point FeedBack (IPFB), Orbit FeedBack (OFB)) allow low frequency vibration rejection. This paper focuses on a dedicated AVI table designed for the last focusing quadrupole (QD0) where the specifications are the most stringent. Combining FeedForward (FF) and FeedBack (FB) techniques, the prototype is able to reduce GM down to 0.6 nm RMS(4Hz) experimentally without any load. These performances couldn't be achieved without cutting edge-technology such as sub-nanometer piezo actuators, ultra-low noise accelerometers and seismometers and an accurate guidance system. The whole AVI system is described in details. Further developments concern the integration of the final focusing magnet above the AVI table, first as part of the simulation with its dynamical model, and finally, as a realistic prototype

Determination of the vacuum optomechanical coupling rate using frequency noise calibration

The strength of optomechanical interactions in a cavity optomechanical system can be quantified by a vacuum coupling rate \vcr analogous to cavity quantum electrodynamics. This single figure of merit removes the ambiguity in the frequently quoted coupling parameter defining the frequency shift for a given mechanical displacement, and the effective mass of the mechanical mode. Here we demonstrate and verify a straightforward experimental technique to derive the vacuum optomechanical coupling rate. It only requires applying a known frequency modulation of the employed electromagnetic probe field and knowledge of the mechanical oscillator's occupation. The method is experimentally verified for a micromechanical mode in a toroidal whispering-gallery-resonator and a nanomechanical oscillator coupled to a toroidal cavity via its near field.Comment: 11 pages, 2 figure

Quantum properties of the three-mode squeezed operator: triply concurrent parametric amplifiers

In this paper, we study the quantum properties of the three-mode squeezed operator. This operator is constructed from the optical parametric oscillator based on the three concurrent $\chi^{(2)}$ nonlinearities. We give a complete treatment for this operator including the symmetric and asymmetric nonlinearities cases. The action of the operator on the number and coherent states are studied in the framework of squeezing, second-order correlation function, Cauchy-Schwartz inequality and single-mode quasiprobability function. The nonclassical effects are remarkable in all these quantities. We show that the nonclassical effects generated by the asymmetric case--for certain values of the system parameters--are greater than those of the symmetric one. This reflects the important role for the asymmetry in the system. Moreover, the system can generate different types of the Schr\"odinger-cat states.Comment: 21 pages, 14 figures; comments are most welcom