Raman-type laser excitation of a trapped atom allows one to realize the quantum mechanical counterpart of phenomena of nonlinear optics, such as Kerr-type nonlinearities, parametric amplification, and multi-mode mixing. Additionally, huge nonlinearities emerge from the interference of the atomic wave function with the laser waves. They lead to a partitioning of the phase space accompanied by a significantly different action of the time evolution in neighboring phase-space zones. For example, a nonlinearly modified coherent "displacement" of the motional quantum state may induce strong amplitude squeezing and quantum interferences.
Quantum control of engineered mechanical oscillators can be achieved by coupling the oscillator to an auxiliary degree of freedom, provided that the coherent rate of energy exchange exceeds the decoherence rate of each of the two sub-systems. We achieve such quantum-coherent coupling between the mechanical and optical modes of a micro-optomechanical system. Simultaneously, the mechanical oscillator is cooled to an average occupancy of n = 1.7 \pm 0.1 motional quanta. Pulsed optical excitation reveals the exchange of energy between the optical light field and the micromechanical oscillator in t…
We present a quantum-mechanical analysis of a nonlinear interferometer that achieves optical switching via cross-phase modulation resulting from the Kerr effect. We show how it performs as a very precise optical regenerator, highly improving the transmitted bit-error rate in the presence of loss.
We study an optomechanical system in which a microwave field and an optical field are coupled to a common mechanical resonator. We explore methods that use these mechanical resonators to store quantum mechanical states and to transduce states between the electromagnetic resonators from the perspective of the effect of mechanical decoherence. Besides being of fundamental interest, this coherent quantum state transfer could have important practical implications in the field of quantum information science, as it potentially allows one to overcome intrinsic limitations of both microwave and optica…
Witnessing quantumness in mesoscopic objects is an important milestone for both quantum technologies and foundational reasons. Cavity optomechanics offers the ideal system to achieve this by combing high precision optical measurements with mechanical oscillators. However, mechanical quantumness can only be established if the behaviour is incompatible with any classical description of an oscillator. After explicitly considering classical and hybrid quantum-classical descriptions of an optomechanical system, we rule out squeezing of the optical field as such a witness by showing it is also predi…
We study the quantum dynamics of an optomechanical setup comprising two optical modes and one mechanical mode. We show that the same system can undergo a Dicke-Hepp-Lieb superradiant type phase transition. We found that the coupling between the momentum quadratures of the two optical fields give rise to a new critical point. We show that selective energy exchange between any two modes is possible by coherent control of the coupling parameters. In addition we also demonstrate the occurrence of Normal Mode Splitting (NMS) in the mechanical displacement spectrum.
We describe an experiment in which a laser beam is sent into a high-finesse optical cavity with a mirror coated on a mechanical resonator. We show that the reflected light is very sensitive to small mirror displacements. We have observed the Brownian motion of the resonator with a very high sensitivity.
Rapid advances are being made toward optically cooling a single mode of a micro-mechanical system to its quantum ground state and observing quantum behavior at macroscopic scales. Reaching this regime in room-temperature environments requires a stringent condition on the mechanical quality factor $Q_m$ and frequency $f_m$, $Q_{m}f_{m}{\gtrsim}k_{B}T_{bath}/h$, which so far has been marginally satisfied only in a small number of systems. Here we propose and analyze a new class of systems that should enable unprecedented $Q_{m}f_m$ values. The technique is based upon using optical forces to "tra…
Many applications of quantum information processing (QIP) require distribution of quantum states in networks, both within and between distant nodes. Optical quantum states are uniquely suited for this purpose, as they propagate with ultralow attenuation and are resilient to ubiquitous thermal noise. Mechanical systems are then envisioned as versatile interfaces between photons and a variety of solid-state QIP platforms. Here, we demonstrate a key step towards this vision, and generate entanglement between two propagating optical modes, by coupling them to the same, cryogenic mechanical system.…
We experimentally demonstrate the high-sensitivity optical monitoring of a micro-mechanical resonator and its cooling by active control. Coating a low-loss mirror upon the resonator, we have built an optomechanical sensor based on a very high-finesse cavity (30000). We have measured the thermal noise of the resonator with a quantum-limited sensitivity at the 10^-19 m/rootHz level, and cooled the resonator down to 5K by a cold-damping technique. Applications of our setup range from quantum optics experiments to the experimental demonstration of the quantum ground state of a macroscopic mechanic…
Nonclassical states of macroscopic objects are promising for ultrasensitive metrology as well as testing quantum mechanics. In this work, we investigate dissipative mechanical quantum state engineering in an optically levitated nanodiamond. First, we study single-mode mechanical squeezed states by magnetically coupling the mechanical motion to a dressed three-level system provided by a Nitrogen-vacancy center in the nanoparticle. Quantum coherence between the dressed levels is created via microwave fields to induce a two-phonon transition, which results in mechanical squeezing. Remarkably, we …
We apply the strategy of the back action evading measurement of a quadrature component of mechanical motion of a test mass to detection of a classical force acting on the mass (Science, 209, (1980) 547) and study both classical and quantum limitations of the technique. We are considering a resonant displacement transducer interrogated with a dichromatic optical pump as a model system in this study. The transducer is represented by a Fabry Perot cavity with a totally reflecting movable end mirror the resonant force of interest acts upon. The cavity is pumped with two coherent optical carriers e…
Hybrid quantum systems exhibiting coupled optical, spin, and mechanical degrees of freedom can serve as a platform for sensing, or as a bus to mediate interactions between qubits with disparate energy scales. These systems are also creating opportunities to test foundational ideas in quantum mechanics, including direct observations of the quantum regime in macroscopic objects. Here, we make use of angular momentum conservation to study the dynamics of a pair of paramagnetic centers featuring different spin numbers in the presence of a properly tuned external magnetic field. We examine the inte…
We investigate theoretically the mechanical effects of light on atoms trapped by an external potential, whose dipole transition couples to the mode of an optical resonator and is driven by a laser. We derive an analytical expression for the quantum center-of-mass dynamics, which is valid in presence of a tight external potential. This equation has broad validity and allows for a transparent interpretation of the individual scattering processes leading to cooling. We show that the dynamics are a competition of the mechanical effects of the cavity and of the laser photons, which may mutually int…
Parametric coupling of optical and mechanical degrees of freedom forms the basis of many ultra-sensitive measurements of both force and mechanical displacement. An optical cavity with a mechanically compliant boundary enhances the optomechanical interaction, but also gives rise to qualitatively new coupled dynamics. As early as 1967, in a pioneering work, V. Braginsky analyzed theoretically the role of radiation pressure in the interferometric measurement process, but it has remained experimentally unexplored for many decades. Here, we use whispering-gallery-mode (WGM) optical microresonators …
We explore theoretically the optical response properties in an optomechanical system under electromagneti- cally induced transparency condition but with the mechanical resonator being driven by an additional coherent field. In this configuration, more complex quantum coherent and interference phenomena occur. In partic- ular, we find that the probe transmission spectra depend on the total phase of the applied fields. Our study also provides an efficient way to control propagation of amplification.
We consider a standard optomechanical system where a mechanical oscillator is coupled to a cavity mode through the radiation pressure interaction. The oscillator is coherently driven at its resonance frequency, whereas the cavity mode is driven below its resonance, providing optical damping of the mechanical oscillations. We study the nonlinear coherent response of the mechanical oscillator in this setup. For large mechanical amplitudes, we find that the system can display dynamical multistability if the optomechanical cooperativity exceeds a critical value. This analysis relates standard opto…
A quantum emitter coupled to a nano-mechanical oscillator is a hybrid system where a macroscopic degree of freedom is coupled to a purely quantum system. Recent progress in nanotechnology has led to the realization of such devices by embedding single artificial atoms like quantum dots or superconducting qubits into vibrating wires or membranes, opening up new perspectives for quantum information technologies and for the exploration of the quantum-classical boundary. In this letter, we show that the quantum emitter can be turned into a strikingly efficient light-controlled source of mechanical …
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…
Optical entanglement facilitated by a hot mechanical oscillator
Faculty of Physics, M.V. Lomonosov Moscow State University（莫斯科大学物理系）；Jet Propulsion Laboratory, California Institute of Technology（加州理工学院喷气推进实验室）；Faculty of Physics, Branch of M.V. Lomonosov Moscow State University in Baku（莫斯科大学巴库分校物理系）
We study the synchronization of a superconducting qubit to an external optical field via a mechanical resonator in a hybrid optoelectromechanical system. The quantum trajectory method is employed to investigate synchronization. The bistability in one of the qubit polarization vectors, where the qubit rotates about the polarization vector, is observed for a single quantum trajectory run. The rotation in one of the stable states is synced with the external optical drive. When the number of trajectories is significantly increased, the qubit no longer displays bistability. However, synchronization…
An optical network of superconducting quantum bits (qubits) is an appealing platform for quantum communication and distributed quantum computing, but developing a quantum-compatible link between the microwave and optical domains remains an outstanding challenge. Operating at $T < 100$ mK temperatures, as required for quantum electrical circuits, we demonstrate a mechanically-mediated microwave-optical converter with 47$\%$ conversion efficiency, and use a feedforward protocol to reduce added noise to 38 photons. The feedforward protocol harnesses our discovery that noise emitted from the two c…
We create an ultracold-atoms-based cavity optomechanical system in which as many as six distinguishable mechanical oscillators are prepared, and optically detected, near their ground states of motion. We demonstrate that the motional state of one oscillator can be selectively addressed while preserving neighboring oscillators near their ground states to better than 95% per excitation quantum. We also show that our system offers nanometer-scale spatial resolution of each mechanical element via optomechanical imaging. This technique enables in-situ, parallel sensing of potential landscapes, a ca…
Conversion between signals in the microwave and optical domains is of great interest both for classical telecommunication, as well as for connecting future superconducting quantum computers into a global quantum network. For quantum applications, the conversion has to be both efficient, as well as operate in a regime of minimal added classical noise. While efficient conversion has been demonstrated using mechanical transducers, they have so far all operated with a substantial thermal noise background. Here, we overcome this limitation and demonstrate coherent conversion between GHz microwave s…
The rapid development of high-Q macroscopic mechanical resonators has enabled great advances in optomechanics. Further improvements could allow for quantum-limited or quantum-enhanced applications at ambient temperature. Some of the remaining challenges include the integration of high-Q structures on a chip, while simultaneously achieving large coupling strengths through an optical read-out. Here, we present a versatile fabrication method, which allows us to build fully integrated optomechanical structures. We place a photonic crystal cavity directly above a mechanical resonator with high-Q fu…
Quantum optical measurement techniques offer a rich avenue for quantum control of mechanical oscillators via cavity optomechanics. In particular, a powerful yet little explored combination utilizes optical measurements to perform heralded non-Gaussian mechanical state preparation followed by tomography to determine the mechanical phase-space distribution. Here, we experimentally perform heralded single- and multi-phonon subtraction via photon counting to a laser-cooled mechanical thermal state with a Brillouin optomechanical system at room temperature, and use optical heterodyne detection to m…
We demonstrate electro-mechanical control of an on-chip GaAs optical beam splitter containing a quantum dot single-photon source. The beam splitter consists of two nanobeam waveguides, which form a directional coupler (DC). The splitting ratio of the DC is controlled by varying the out-of-plane separation of the two waveguides using electro-mechanical actuation. We reversibly tune the beam splitter between an initial state, with emission into both output arms, and a final state with photons emitted into a single output arm. The device represents a compact and scalable tuning approach for use i…
Using Fermat's least optical path principle the family of ray-trajectories through a special but common type of a gradient refractive index lens, n(r)=n_0+Δn R/r, is solved analytically. The solution, i.e. the ray-equation r(phi), is shown to be closely related to the famous Rutherford scattering and therefore termed photonic Rutherford scattering. It is shown that not only do these classical limits correspond, but also the wave-mechanical pictures coincide: The time-independent Schrödingier equation and the inhomogeneous Helmholz equation permit the same mapping between massive particle scatt…
A general procedure for construction of the formalism of quantum beam optics for any particle is reviewed. The quantum formalism of spin-1/2 particle beam optics is presented starting {\em ab initio} with the Dirac equation. As an example of application the case of normal magnetic quadrupole lens is discussed. In the classical limit the quantum formalism leads to the well-known Lie algebraic formalism of classical particle beam optics.
