Radiation Pressure Interaction Research Articles

Single-photon induced instabilities in a cavity electromechanical device

Cavity-electromechanical systems are extensively used for sensing and controlling the vibrations of mechanical resonators down to their quantum limit. The nonlinear radiation-pressure interaction in these systems could result in an unstable response of the mechanical resonator showing features such as frequency-combs, period-doubling bifurcations and chaos. However, due to weak light-matter interaction, typically these effects appear at very high driving strengths. By using polariton modes formed by a strongly coupled flux-tunable transmon and a microwave cavity, here we demonstrate an electromechanical device and achieve a single-photon coupling rate g0/2π\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\left({g}_{0}/2\\pi \\right)$$\\end{document} of 160 kHz, which is nearly 4% of the mechanical frequency ωm. Due to large g0/ωm ratio, the device shows an unstable mechanical response resulting in frequency combs in sub-single photon limit. We systematically investigate the boundary of the unstable response and identify two important regimes governed by the optomechanical backaction and the nonlinearity of the electromagnetic mode. Such an improvement in the single-photon coupling rate and the observations of microwave frequency combs at single-photon levels may have applications in the quantum control of the motional states and critical parametric sensing. Our experiments strongly suggest the requirement of newer approaches to understand instabilities.

Modeling photothermal effects in high power optical resonators used for coherent levitation

Radiation pressure can be used to enable optomechanical control and manipulation of the quantum state of a mechanical oscillator. Optomechanical interaction can also be mediated by photothermal effects which, although frequently overlooked, may compete with radiation pressure interaction. Understanding of how these phenomena affect the coherent exchange of information between optical and mechanical degrees of freedom is often underdeveloped, particularly in mesoscale high-power systems where photothermal effects can fully dominate the interaction. Here we report an effective theoretical model to predict and successfully reconstruct the dynamics of a unique optomechanical system: a cavity-enhanced setup for macroscopic optical levitation, where a free-standing mirror acts as the optomechanical oscillator. We decompose the photothermal interaction into two opposing light-induced effects, photothermal expansion, and thermo-optic effects. We then reconstruct a heuristic model that links the intracavity field to four types of cavity length changes caused by acoustic (), centre of mass (), photothermal () and thermo-optic () displacements. This offers refined predictions with a higher degree of agreement with experimental results. Our work provides a means to precisely model the photothermal effect of high power optomechanical systems, as well as for developing more precise photothermal modeling of photonics systems for precision sensing and quantum measurements.

Cavity Quantum Optomechanical Nonlinearities and Position Measurement beyond the Breakdown of the Linearized Approximation.

Several optomechanics experiments are now entering the highly sought nonlinear regime where optomechanical interactions are large even for low light levels. Within this regime, new quantum phenomena and improved performance may be achieved; however, a corresponding theoretical formalism of cavity quantum optomechanics that captures the nonlinearities of both the radiation-pressure interaction and the cavity response is needed to unlock these capabilities. Here, we develop such a nonlinear cavity quantum optomechanical framework, which we then utilize to propose how position measurement can be performed beyond the breakdown of the linearized approximation. Our proposal utilizes optical general-dyne detection, ranging from single to dual homodyne, to obtain mechanical position information imprinted onto both the optical amplitude and phase quadratures and enables both pulsed and continuous modes of operation. These cavity optomechanical nonlinearities are now being confronted in a growing number of experiments, and our framework will allow a range of advances to be made in, e.g., quantum metrology, explorations of the standard quantum limit, and quantum measurement and control.

Optomechanical Cooling and Inertial Sensing at Low Frequencies

An inertial sensor design is proposed in this paper to achieve high sensitivity and large dynamic range in the subhertz-frequency regime. High acceleration sensitivity is obtained by combining optical cavity readout systems with monolithically fabricated mechanical resonators. A high-sensitivity heterodyne interferometer simultaneously monitors the test mass with an extensive dynamic range for low-stiffness resonators. The bandwidth is tuned by optical feedback cooling to the test mass via radiation pressure interaction using an intensity-modulated laser. The transfer gain of the feedback system is analyzed to optimize system parameters towards the minimum cooling temperature that can be achieved. To practically implement the inertial sensor, we propose a dynamic cooling mechanism to improve cooling efficiency while operating at low optical power levels. The overall system layout presents an integrated design that is compact and lightweight.

Analog Quantum Control of Magnonic Cat States on a Chip by a Superconducting Qubit.

We propose to directly and quantum-coherently couple a superconducting transmon qubit to magnons-the quanta of the collective spin excitations, in a nearby magnetic particle. The magnet's stray field couples to the qubit via a superconducting quantum interference device. We predict a resonant magnon-qubit exchange and a nonlinear radiation-pressure interaction that are both stronger than dissipation rates and tunable by an external flux bias. We additionally demonstrate a quantum control scheme that generates magnon-qubit entanglement and magnonic Schrödinger cat states with high fidelity.

Two-mode Schrödinger-cat states with nonlinear optomechanics: generation and verification of non-Gaussian mechanical entanglement

Cavity quantum optomechanics has emerged as a new platform for quantum science and technology with applications ranging from quantum-information processing to tests of the foundations of physics. Of crucial importance for optomechanics is the generation and verification of non-Gaussian states of motion and a key outstanding challenge is the observation of a canonical two-mode Schrödinger-cat state in the displacement of two mechanical oscillators. In this work, we introduce a pulsed approach that utilizes the nonlinearity of the radiation–pressure interaction combined with photon-counting measurements to generate this entangled non-Gaussian mechanical state, and, importantly, describe a protocol using subsequent pulsed interactions to verify the non-Gaussian entanglement generated. Our pulsed verification protocol allows quadrature moments of the two mechanical oscillators to be measured up to any finite order providing a toolset for experimental characterisation of bipartite mechanical quantum states and allowing a broad range of inseparability criteria to be evaluated. Key experimental factors, such as optical loss and open-system dynamics, are carefully analyzed and we show that the scheme is feasible with only minor improvements to current experiments that operate outside the resolved-sideband regime. Our scheme provides a new avenue for quantum experiments with entangled mechanical oscillators and offers significant potential for further research and development that utilizes such non-Gaussian states for quantum-information and sensing applications, and for studying the quantum-to-classical transition.

Hybridized Frequency Combs in Multimode Cavity Electromechanical System.

The cavity electromechanical devices with radiation-pressure interaction induced Kerr-like nonlinearity are promising candidates to generate microwave frequency combs. We construct a silicon-nitride membrane based superconducting cavity electromechanical device and study two mechanical modes synergistic frequency combs. Around the threshold of intracavity field instability, we first show independent frequency combs with tooth spacing equal to each mechanical mode frequency. At the overlap boundaries of these two individual mechanical mode mediated instability thresholds, we observe hybridization of frequency combs based on the cavity field mediated indirect coupling between these two mechanical modes. The spectrum lines turn out to be unequally spaced, but can be recognized in combinations of the coexisting frequency combs. Beyond the boundary, the comb reverts to the single mode case, and which mechanical mode frequency will the tooth spacing be depends on the mode competition. Our work demonstrates mechanical mode competition enabled switchability of frequency comb tooth spacing and can be extended to other devices with multiple nonlinearities.

Nonreciprocal coupling induced entanglement enhancement in a double-cavity optomechanical system

We investigate the quantum entanglement in a double-cavity optomechanical system consisting of an optomechanical cavity and an auxiliary cavity, where the optomechanical cavity mode couples with the mechanical mode via radiation-pressure interaction, and simultaneously couples with the auxiliary cavity mode via nonreciprocal coupling. We study the entanglement between the mechanical oscillator and the cavity modes when the two cavities are reciprocally or nonreciprocally coupled. The logarithmic negativity () is adopted to describe the entanglement degree between the mechanical mode and the optomechanical cavity mode (the auxiliary cavity mode). We find that both and have maximum values in the case of reciprocal coupling. By using nonreciprocal coupling, and can exceed those maximum values, and a wider detuning region where the entanglement exists can be obtained. Moreover, the entanglement robustness with respect to the environment temperature is also effectively enhanced.

Strong Coupling Optomechanics Mediated by a Qubit in the Dispersive Regime.

Cavity optomechanics represents a flexible platform for the implementation of quantum technologies, useful in particular for the realization of quantum interfaces, quantum sensors and quantum information processing. However, the dispersive, radiation–pressure interaction between the mechanical and the electromagnetic modes is typically very weak, harnessing up to now the demonstration of interesting nonlinear dynamics and quantum control at the single photon level. It has already been shown both theoretically and experimentally that if the interaction is mediated by a Josephson circuit, one can have an effective dynamics corresponding to a huge enhancement of the single-photon optomechanical coupling. Here we analyze in detail this phenomenon in the general case when the cavity mode and the mechanical mode interact via an off-resonant qubit. Using a Schrieffer–Wolff approximation treatment, we determine the regime where this tripartite hybrid system behaves as an effective cavity optomechanical system in the strong coupling regime.

Quantum optomechanical system in a Mach-Zehnder interferometer

We consider an oscillating micromirror replacing one of the two fixed mirrors of a Mach-Zehnder interferometer. In this ideal optical set-up the quantum oscillator is subjected to the radiation pressure interaction of travelling light waves, no cavity is involved. This configuration shows that squeezed light can be generated by pure scattering on a quantum system, without involving a cavity. The squeezing can be detected at the output ports of the interferometer either by direct detection or by measuring the spectrum of the difference current. We use the Hudson-Parthasarathy equation to model the global evolution. It can describe the scattering of photons and the resulting radiation pressure interaction on the quantum oscillator. It allows to consider also the interaction with a thermal bath. In this way we have a unitary dynamics giving the evolution of oscillator and fields. The Bose fields of quantum stochastic calculus and the related generalized Weyl operators allow to describe the whole optical circuit. By working in the Heisenberg picture, the quantum Langevin equations for position and momentum and the output fields arise, which are used to describe the monitoring in continuous time of the light at the output ports. In the case of strong laser and weak radiation pressure interaction highly non-classical light is produced, and this can be revealed either by direct detection (a negative Mandel Q-parameter is found), either by the intensity spectrum of the difference current of two photodetector; in the second case a nearly complete cancellation of the shot noise can be reached. In this last case it appears that the Mach-Zehnder configuration together with the detection of the difference current corresponds to an homodyne detection scheme, so that we can say that the apparatus is measuring the spectrum of squeezing.

Heat transfer mediated by the dynamical Casimir effect in an optomechanical system

Heat transfer in an optomechanical system consisting of one optical cavity and two movable mirrors with or without a laser field is studied by using the quantum master-equation method. The radiation-pressure interaction between the cavity and the mirrors contains the single-photon optomechanical coupling (SPOC) and the dynamical Casimir effect (DCE). When the laser is not applied to the cavity, the heat transfer is induced by a nonlocal interaction between mirrors that builds up only due to the presence of the DCE. Once the monochromatic field is turned on, both the SPOC and the DCE can be used to modify the energy transfer process. In both cases, the heat transfer can be drastically enhanced at resonant conditions manifested by the DCE. Our results can motivate further studies to actively control heat transfer mediated by the DCE in optomechanical devices.

Absolute Determination of the Single-Photon Optomechanical Coupling Rate via a Hopf Bifurcation

We establish a method for the determination of the single-photon optomechanical coupling rate, which characterizes the radiation pressure interaction in an optomechanical system. The estimation of the rate with which a mechanical oscillator, initially in a thermal state, undergoes a Hopf bifurcation, and reaches a limit cycle, allows us to determine the single-photon optomechanical coupling rate in a simple and consistent way. Most importantly, and in contrast to other methods, our method does not rely on knowledge of the system's bath temperature and on a calibration of the signal. We provide the theoretical framework, and experimentally validate this method, providing a procedure for the full characterization of an optomechanical system, which could be extended outside cavity optomechanics, whenever a resonator is driven into a limit cycle by the appropriate interaction with another degree of freedom.

Mechanical oscillator thermometry in the nonlinear optomechanical regime

Optomechanical systems are promising platforms for controlled light-matter interactions. They are capable of providing several fundamental and practical novel features when the mechanical oscillator is cooled down to nearly reach its ground state. In this framework, measuring the effective temperature of the oscillator is perhaps the most relevant step in the characterization of those systems. In conventional schemes, the cavity is driven strongly, and the overall system is well-described by a linear (Gaussian preserving) Hamiltonian. Here, we depart from this regime by considering an undriven optomechanical system via non-Gaussian radiation-pressure interaction. To measure the temperature of the mechanical oscillator, initially in a thermal state, we use light as a probe to coherently interact with it and create an entangled state. We show that the optical probe gets a nonlinear phase, resulting from the non-Gaussian interaction, and undergoes an incoherent phase diffusion process. To efficiently infer the temperature from the entangled light-matter state, we propose using a nonlinear Kerr medium before a homodyne detector. Remarkably, placing the Kerr medium enhances the precision to nearly saturate the ultimate quantum bound given by the quantum Fisher information. Furthermore, it also simplifies the thermometry procedure as it makes the choice of the homodyne local phase independent of the temperature, which avoids the need for adaptive sensing protocols.

Converting microwave and telecom photons with a silicon photonic nanomechanical interface

Practical quantum networks require low-loss and noise-resilient optical interconnects as well as non-Gaussian resources for entanglement distillation and distributed quantum computation. The latter could be provided by superconducting circuits but existing solutions to interface the microwave and optical domains lack either scalability or efficiency, and in most cases the conversion noise is not known. In this work we utilize the unique opportunities of silicon photonics, cavity optomechanics and superconducting circuits to demonstrate a fully integrated, coherent transducer interfacing the microwave X and the telecom S bands with a total (internal) bidirectional transduction efficiency of 1.2% (135%) at millikelvin temperatures. The coupling relies solely on the radiation pressure interaction mediated by the femtometer-scale motion of two silicon nanobeams reaching a Vπ as low as 16 μV for sub-nanowatt pump powers. Without the associated optomechanical gain, we achieve a total (internal) pure conversion efficiency of up to 0.019% (1.6%), relevant for future noise-free operation on this qubit-compatible platform.

World Beyond Black Holes

To understand the physics of Black Holes, it is important to understand the first law in Physics which controls our entire universe. This is the law of “Perfect Equilibrium”. Within the entire universe there is always a prefect equilibrium between all the physical forces like gravity, forces of inertia, radiation pressure and Electro-Magnetic Interaction forces at any time, in any direction and at any space coordinate. This is the fundamental law in physics on which also the existence of a Black Hole has been grounded. This new theory will explain the forces within a beam of light interacting with gravity while the beam of light propagates within the gravitational field generated by a black hole. When we look at modern Physics, we can only be impressed by an enormous amount of knowledge and a complete New World of technical applications. We now live in the century of the impressive victory of the new science and the new technology over the old-fashioned world and the old-fashioned way of thinking. Great shifts in the way of thinking and the technological achievements are mostly characterized by an important scientific publication in a century that changes everything in that century. We can recognize the century of Isaac Newton who triggered in 1687 the seismic shift in thinking with his famous publication “Philisophiae Naturalis Principia Mathematica” (Mathematical Principles of Natural Philosophy). We recognize the century of James Clerk Maxwell who triggered in 1865 the large shift in thinking with his famous publication “A Dynamical Theory of the Electromagnetic Field”. We recognize the century of Albert Einstein who triggered in 1905 the large changings in thinking with his famous theory of Special Relativity represented in his publication “On the Electrodynamics of Moving Bodies”. Manifesting a “New Theory” and a “New Way of Thinking” with important contributions of Hendrik Lorentz, Henri Poincaré and Hermann Minkowski. It is recognizable that with the sudden change in thinking in a new period, a new kind of mutual common sense and a general agreement by many scientists of the new theory and the new way of thinking arises. The “New Theory” will be protected by common sense and mutual agreement. This new way of thinking settles down in the scientific society and become immovable. Other options disappear and simply do not exist anymore. Which will make it almost impossible for the following “New Theory” to rise. The “New Theory” which will be introduced in this article has been based on the fundamental principle of “Perfect Equilibrium within the Universe”. A fundamental universal principle in Physics which has already been expressed by Newton’s famous 3 equations, published in 1687 in “Philosophiae Naturalis Principia Mathematica. Newton’s famous Equations in 3 dimensions will be published in this article in an extension into 4 dimensions. Newton’s 4-dimensional law in the 3 spatial dimensions results in an improved version of the classical Maxwell Equations and Newton’s law in the 4th dimension (time) results in the quantum mechanical Schrödinger wave equation (at non-relativistic velocities) and the relativistic Dirac equation.

The World Beyond Black Holes

To understand the physics of Black Holes, it is important to understand the first law in Physics which controls our entire universe. This is the law of “Perfect Equilibrium”. Within the entire universe there is always a prefect equilibrium between all the physical forces like gravity, forces of inertia, radiation pressure and Electro-Magnetic Interaction forces at any time, in any direction and at any space coordinate. This is the fundamental law in physics on which also the existence of a Black Hole has been grounded. This new theory will explain the forces within a beam of light interacting with gravity while the beam of light propagates within the gravitational field generated by a black hole. When we look at modern Physics, we can only be impressed by an enormous amount of knowledge and a complete New World of technical applications. We now live in the century of the impressive victory of the new science and the new technology over the old-fashioned world and the old-fashioned way of thinking. Great shifts in the way of thinking and the technological achievements are mostly characterized by an important scientific publication in a century that changes everything in that century. We can recognize the century of Isaac Newton who triggered in 1687 the seismic shift in thinking with his famous publication “Philisophiae Naturalis Principia Mathematica” (Mathematical Principles of Natural Philosophy). We recognize the century of James Clerk Maxwell who triggered in 1865 the large shift in thinking with his famous publication “A Dynamical Theory of the Electromagnetic Field”. We recognize the century of Albert Einstein who triggered in 1905 the large changings in thinking with his famous theory of Special Relativity represented in his publication “On the Electrodynamics of Moving Bodies”. Manifesting a “New Theory” and a “New Way of Thinking” with important contributions of Hendrik Lorentz, Henri Poincaré and Hermann Minkowski. It is recognizable that with the sudden change in thinking in a new period, a new kind of mutual common sense and a general agreement by many scientists of the new theory and the new way of thinking arises. The “New Theory” will be protected by common sense and mutual agreement. This new way of thinking settles down in the scientific society and become immovable. Other options disappear and simply do not exist anymore. Which will make it almost impossible for the following “New Theory” to rise. The “New Theory” which will be introduced in this article has been based on the fundamental principle of “Perfect Equilibrium within the Universe”. A fundamental universal principle in Physics which has already been expressed by Newton’s famous 3 equations, published in 1687 in “Philosophiae Naturalis Principia Mathematica. Newton’s famous Equations in 3 dimensions will be published in this article in an extension into 4 dimensions. Newton’s 4-dimensional law in the 3 spatial dimensions results in an improved version of the classical Maxwell Equations and Newton’s law in the 4th dimension (time) results in the quantum mechanical Schrödinger wave equation (at non-relativistic velocities) and the relativistic Dirac equation.

Stroboscopic quantum optomechanics

We consider an optomechanical cavity that is driven stroboscopically by a train of short pulses. By suitably choosing the inter-pulse spacing we show that ground-state cooling and mechanical squeezing can be achieved, even in the presence of mechanical dissipation and for moderate radiation-pressure interaction. We provide a full quantum-mechanical treatment of stroboscopic backaction-evading measurements, for which we give a simple analytic insight, and discuss preparation and verification of squeezed mechanical states. We further consider stroboscopic driving of a pair of non-interacting mechanical resonators coupled to a common cavity field, and show that they can be simultaneously cooled and entangled. Stroboscopic quantum optomechanics extends measurement-based quantum control of mechanical systems beyond the good-cavity limit.

Efficient microwave frequency conversion mediated by a photonics compatible silicon nitride nanobeam oscillator

Microelectromechanical systems and integrated photonics provide the basis for many reliable and compact circuit elements in modern communication systems. Electro-opto-mechanical devices are currently one of the leading approaches to realize ultra-sensitive, low-loss transducers for an emerging quantum information technology. Here we present an on-chip microwave frequency converter based on a planar aluminum on silicon nitride platform that is compatible with slot-mode coupled photonic crystal cavities. We show efficient frequency conversion between two propagating microwave modes mediated by the radiation pressure interaction with a metalized dielectric nanobeam oscillator. We achieve bidirectional coherent conversion with a total device efficiency of up to ∼60%, a dynamic range of 2 × 109 photons/s and an instantaneous bandwidth of up to 1.7 kHz. A high fidelity quantum state transfer would be possible if the drive dependent output noise of currently ∼14 photons s−1 Hz−1 is further reduced. Such a silicon nitride based transducer is in situ reconfigurable and could be used for on-chip classical and quantum signal routing and filtering, both for microwave and hybrid microwave-optical applications.

Single-photon quantum regime of artificial radiation pressure on a surface acoustic wave resonator

Electromagnetic fields carry momentum, which upon reflection on matter gives rise to the radiation pressure of photons. The radiation pressure has recently been utilized in cavity optomechanics for controlling mechanical motions of macroscopic objects at the quantum limit. However, because of the weakness of the interaction, attempts so far had to use a strong coherent drive to reach the quantum limit. Therefore, the single-photon quantum regime, where even the presence of a totally off-resonant single photon alters the quantum state of the mechanical mode significantly, is one of the next milestones in cavity optomechanics. Here we demonstrate an artificial realization of the radiation pressure of microwave photons acting on phonons in a surface acoustic wave resonator. The order-of-magnitude enhancement of the interaction strength originates in the well-tailored, strong, second-order nonlinearity of a superconducting Josephson junction circuit. The synthetic radiation pressure interaction adds a key element to the quantum optomechanical toolbox and can be applied to quantum information interfaces between electromagnetic and mechanical degrees of freedom.

Optomechanical generation of a mechanical catlike state by phonon subtraction

We propose a scheme to prepare a macroscopic mechanical oscillator in a catlike state, close to a coherent state superposition. The mechanical oscillator, coupled by radiation-pressure interaction to a field in an optical cavity, is first prepared close to a squeezed vacuum state using a reservoir engineering technique. The system is then probed using a short optical pulse tuned to the lower motional sideband of the cavity resonance, realizing a photon-phonon swap interaction. A photon number measurement of the photons emerging from the cavity then conditions a phonon-subtracted catlike state with a negative Wigner distribution exhibiting separated peaks and multiple interference fringes. We show that this scheme is feasible using state-of-the-art photonic crystal optomechanical system.