We present a theoretical study of optomechanical systems in which the mechanical resonator modulates both the resonant frequency (dispersive coupling) and the decay rates (dissipative coupling) of the optical cavity. We extend the generic dispersive framework to a more general case in which the dissipative coupling is split between its external and intrinsic contribution. We report a complete analysis of the influence of each kind of optical losses (intrinsic and external) on the three coupling mechanisms and highlight the interest of each external decay rate regime. The basic tools to experimentally identify the three couplings and their relative influence on the optical response are presented. We demonstrate the general expression of the optical spring effect and optomechanical damping. Comparison between experimental measurements in photonic crystal systems from the literature and our theoretical modal yields good agreement.
The recent demonstration of cooling of a macroscopic silicon nitride membrane based on dissipative coupling makes dissipatively coupled optomechanical systems as promising candidates for squeezing. We theoretically show that such a system in a cavity on resonance can yield good squeezing which is comparable to that produced by dispersive coupling. We also report the squeezing resulting from the combined effects of dispersive and dissipative couplings and thus the device can be operated in one regime or the other. We derive the maximal frequency and quadrature angles to observe squeezing for gi…
Optomechanical system with tunable dissipative and dispersive couplings
State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University（山西大学光电研究所量子光学与量子光学器件国家重点实验室）；Collaborative Innovation Center of Extreme Optics, Shanxi University（山西大学极端光学协同创新中心）
Combination of dissipative and dispersive coupling in the cavity optomechanical systems
Faculty of Physics, M.V. Lomonosov Moscow State University（莫斯科国立大学物理系）；Quantum Technology Centre, M.V. Lomonosov Moscow State University（莫斯科国立大学量子技术中心）
We describe the strong optomechanical dynamical interactions in ultrahigh-Q/V slot-type photonic crystal cavities. The dispersive coupling is based on a mode-gap photonic crystal cavities with light localization in an air mode with 0.02(lambda/n)3 modal volumes while preserving optical cavity Q up to 5 x 106. The mechanical mode is modeled to have fundamental resonance omega_m/2pi of 460 MHz and a quality factor Qm estimated at 12,000. For this slot-type optomechanical cavity, the dispersive coupling gom is numerically computed at up to 940 GHz/nm (Lom of 202 nm) for the fundamental optomechan…
Periodically structured materials can sustain both optical and mechanical excitations which are tailored by the geometry. Here we analyze the properties of dispersively coupled planar photonic and phononic crystals: optomechanical crystals. In particular, the properties of co-resonant optical and mechanical cavities in quasi-1D (patterned nanobeam) and quasi-2D (patterned membrane) geometries are studied. It is shown that the mechanical Q and optomechanical coupling in these structures can vary by many orders of magnitude with modest changes in geometry. An intuitive picture is developed based…
In this work, we study the dispersive coupling between optical quasi-bound-states in the continuum at telecom wavelengths and GHz-mechanical modes in high-index wavelength-sized disks. We show that such cavities can display values of the optomechanical coupling rate on par with optomechanical crystal cavities ($g_{0}/2π\backsimeq$ 800 kHz). Interestingly, optomechanical coupling of optical resonances with mechanical modes at frequencies well above 10 GHz seems attainable. We also show that mechanical leakage in the substrate can be extremely reduced by placing the disk over a thin silica pedes…
We present the design of a femtogram L3-nanobeam photonic crystal cavity for optomechanical studies. Two symmetric nanobeams are created by placing three air slots in a silicon photonic crystal slab where three holes are removed. The optical quality factor (Q) is optimized up to 52,000. The nanobeams' mechanical frequencies are higher than 600 MHz due to their femtogram effective modal masses. The optical and mechanical modes are dispersively coupled with a vacuum optomechanical coupling rate g0/2pi exceeding 200 kHz. The anchor-loss-limited mechanical Q of the differential beam mode is evalua…
We investigate a hybrid optomechanical system in which a membrane oscillator is coupled to a collective spin of ground states of an intracavity $Λ$-type three-level atomic medium. The cavity field response is greatly modified by atomic coherence and the anomalous dispersion generated by two Raman pumping beams near two-photon resonance. The optomechanical interaction, therefore radiation pressure force, is substantially enhanced due to superluminal propagation of photons in the cavity. Such improvement facilitates ground-state cooling of the mechanical oscillator with room temperature thermal …
In this paper we study cavity optomechanical systems in which the position of a mechanical oscillator modulates both the resonance frequency (dispersive coupling) and the linewidth (dissipative coupling) of a cavity mode. Using a quantum noise approach we calculate the optical damping and the optically-induced frequency shift. We find that dissipatively coupled systems feature two parameter regions providing amplification and two parameter regions providing cooling. To investigate the strong-coupling regime, we solve the linearized equations of motion exactly and calculate the mechanical and o…
Dissipative and dispersive optomechanical couplings are experimentally observed in a photonic crystal split-beam nanocavity optimized for detecting nanoscale sources of torque. Dissipative coupling of up to approximately $500$ MHz/nm and dispersive coupling of $2$ GHz/nm enable measurements of sub-pg torsional and cantilever-like mechanical resonances with a thermally-limited torque detection sensitivity of 1.2$\times 10^{-20} \text{N} \, \text{m}/\sqrt{\text{Hz}}$ in ambient conditions and 1.3$\times 10^{-21} \text{N} \, \text{m}/\sqrt{\text{Hz}}$ in low vacuum. Interference between optomecha…
Resonant photoelastic coupling in semiconductor nanostructures opens new perspectives for strongly enhanced light-sound interaction in optomechanical resonators. One potential problem, however, is the reduction of the cavity Q-factor induced by dissipation when the resonance is approached. We show in this letter that cavity-polariton mediation in the light-matter process overcomes this limitation allowing for a strongly enhanced photon-phonon coupling without significant lifetime reduction in the strongly-coupled regime. Huge optomechanical coupling factors in the PetaHz/nm range are envisaged…
Despite the several novel features arising from the dissipative optomechanical coupling, such effect remains vastly unexplored due to the lack of a simple formalism that captures non-Hermiticity in optomechanical systems. In this Letter, we show that quasinormal-mode-based perturbation theory is capable of correctly predicting both dispersive and dissipative optomechanical couplings. We validate our model through simulations and also by comparison with experimental results reported in the literature. Finally, we apply this formalism to plasmonic systems, used for molecular optomechanics, where…
We introduce a passively-aligned, flexure-tuned cavity optomechanical system in which a membrane is positioned microns from one end mirror of a Fabry-Perot optical cavity. By displacing the membrane through gentle flexure of its silicon supporting frame (i.e., to ~80 m radius of curvature (ROC)), we gain access to the full range of available optomechanical couplings, finding also that the optical spectrum exhibits none of the abrupt discontinuities normally found in "membrane-in-the-middle" (MIM) systems. More aggressive flexure (3 m ROC) enables >15 microns membrane travel, milliradian tilt t…
Micro- and nanoscale optical or microwave cavities are used in a wide range of classical applications and quantum science experiments, ranging from precision measurements, laser technologies to quantum control of mechanical motion. The dissipative photon loss via absorption, present to some extent in any optical cavity, is known to introduce thermo-optical effects and thereby impose fundamental limits on precision measurements. Here, we theoretically and experimentally reveal that such dissipative photon absorption can result in quantum feedback via in-loop field detection of the absorbed opti…
Motivated by the increasing interest in the properties of multimode optomechanical devices, here we study a system in which a driven mode of a large-area optical cavity is despersively coupled to a deformable mechanical element. Two different models naturally appear in such scenario, for which we predict the formation of periodic patterns, localized structures (cavity solitons), and domain walls, among other complex nonlinear phenomena. Further, we propose a realistic design based on intracavity membranes where our models can be studied experimentally. Apart from its relevance to the field of …
Cooling of mesoscopic mechanical resonators represents a primary concern in cavity optomechanics. Here in the strong optomechanical coupling regime, we propose to dynamically control the cavity dissipation, which is able to significantly accelerate the cooling process while strongly suppressing the heating noise. Furthermore, the dynamic control is capable of overcoming quantum backaction and reducing the cooling limit by several orders of magnitude. The dynamic dissipation control provides new insights for tailoring the optomechanical interaction and offers the prospect of exploring macroscop…
Dissipative optomechanics has some advantages in cooling compared to the conventional dispersion dominated systems. Here, we study the optical response of a cantilever-like, silica, microsphere pendulum, evanescently coupled to a fiber taper. In a whispering gallery mode resonator the cavity mode and motion of the pendulum result in both dispersive and dissipative optomechanical interactions. This unique mechanism leads to an experimentally observable, asymmetric response function of the transduction spectrum which can be explained using coupled-mode theory. The optomechanical transduction, an…
Tunable evanescent coupling is used to modify the optomechanical interactions within a split-beam photonic crystal nanocavity. An optical fiber taper probe is used to renormalize the optical nanocavity field and introduce a dissipative optomechanical coupling channel, reconfiguring and enhancing coupling between the optical and mechanical resonances of the device. Positioning of the fiber taper allows preferential coupling to specific mechanical modes and provides a mechanism for tuning the optomechanical interaction between dissipative and dispersive coupling regimes.
We show that the stable optical rigidity can be obtained in a Fabry-Perot cavity with dissipative optomechanical coupling and with detuned pump, corresponding conditions are formulated. An optical detection of a weak classical mechanical force with usage of this rigidity is analyzed. The sensitivity of small force measurement can be better than the standard quantum limit (SQL).
Optomechanical coupling between a light field and the motion of a cavity mirror via radiation pressure plays an important role for the exploration of macroscopic quantum physics and for the detection of gravitational waves (GWs). It has been used to cool mechanical oscillators into their quantum ground states and has been considered to boost the sensitivity of GW detectors, e.g. via the optical spring effect. Here, we present the experimental characterization of generalized, that is, dispersive and dissipative optomechanical coupling, with a macroscopic (1.5mm)^2-sized silicon nitride (SiN) me…
We present an experimental study of an optomechanical system formed by a vibrating thin semi-transparent membrane within a high-finesse optical cavity. We show that the coupling between the optical cavity modes and the vibrational modes of the membrane can be tuned by varying the membrane position and orientation. In particular we demonstrate a large quadratic dispersive optomechanical coupling in correspondence with avoided crossings between optical cavity modes weakly coupled by scattering at the membrane surface. The experimental results are well explained by a first order perturbation trea…
The synchronization of coherent states of light has long been an important subject of basic research and technology. Recently, a new concept for analog computers has emerged where this synchronization process can be exploited to solve computationally hard problems - potentially faster and more energy-efficient than what can be achieved with conventional computer technology today. The unit cell of such systems consists of two coherent centers that are coupled to one another in a controlled manner. Here, we experimentally characterize and analyze the synchronization process of two photon Bose-Ei…
In whispering gallery mode resonator sensing applications, the conventional way to detect a change in the parameter to be measured is by observing the steady state transmission spectrum through the coupling waveguide. Alternatively, cavity ring-up spectroscopy (CRUS) sensing can be achieved transiently. In this work, we investigate CRUS using coupled mode equations and find analytical solutions with a large spectral broadening approximation of the input pulse. The relationships between the frequency detuning, coupling gap and ring-up peak height are determined and experimentally verified using…
We propose an optomechanical laser based on III-V compounds which exhibits self-pulsation in the presence of a dissipative optomechanical coupling. In such a laser cavity, radiation pressure drives the mechanical degree of freedom and its back-action is caused by the mechanical modulation of the cavity loss rate. Our numerical analysis shows that even in a wideband gain material, such dissipative coupling couples the mechanical oscillation with the laser relaxation oscillations process. Laser self-pulsation is observed for mechanical frequencies below the laser relaxation oscillation frequency…
Exceptional points (EPs) represent a distinct type of spectral singularity in non-Hermitian systems, and intriguing physics concepts have been studied with optical EPs recently. As a system beyond photonics, the mechanical oscillators coupling with many physical systems are expected to be further exploited EPs for mechanical sensing, topology energy transfer, nonreciprocal dynamics etc. In this study, we demonstrated on-chip mechanical EPs with a silicon optomechanical zipper cavity, wherein two near-degenerate mechanical breathing modes are coupled via a single co-localized optical mode. By t…
Dissipative coupling, dispersive coupling and their combination in the cavity-less opto-mechanical systems
Faculty of Physics, M.V. Lomonosov Moscow State University（莫斯科国立大学物理系）；Quantum Technology Centre, M.V. Lomonosov Moscow State University（莫斯科国立大学量子技术中心）
Synthetic magnetism has been used to control charge neutral excitations for applications ranging from classical beam steering to quantum simulation. In optomechanics, radiation-pressure-induced parametric coupling between optical (photon) and mechanical (phonon) excitations may be used to break time-reversal symmetry, providing the prerequisite for synthetic magnetism. Here we design and fabricate a silicon optomechanical circuit with both optical and mechanical connectivity between two optomechanical cavities. Driving the two cavities with phase-correlated laser light results in a synthetic m…
Numerical calculation of modes in dispersive and absorptive systems is performed using the finite element method. The dispersion is tackled in the frame of an extension of Maxwell's equations where auxiliary fields are added to the electromagnetic field. This method is applied to multi-domain cavities and photonic crystals including Drude and Drude-Lorentz metals. Numerical results are compared to analytical solutions for simple cavities and to previous results of the literature for photonic crystals, showing excellent agreement. The advantages of the developed method lie on the versatility of…
We study generation of two-dimensional dispersive shock waves and oblique dark solitons upon interaction of tilted plane waves with negative refractive index defects embedded into defocusing material with linear gain and two-photon absorption. Different evolution regimes are encountered including the formation of well-localized disturbances for input tilts below critical one, and generation of extended shock waves containing multiple intensity oscillations in the "upstream" region and gradually vanishing oblique dark solitons in "downstream" region for input tilts exceeding critical one. The g…
We study a system of interacting matter quasiparticles strongly coupled to photons inside an optomechanical cavity. The resulting normal modes of the system are represented by hybrid polaritonic quasiparticles, which acquire effective nonlinearity. Its strength is influenced by the presence of the mechanical mode and depends on the resonance frequency of the cavity. This leads to an interactive type of optomechanical coupling, being distinct from the previously studied dispersive and dissipative couplings in optomechanical systems. The emergent interactive coupling is shown to generate effecti…
Within the framework of a phenomenological quantization scheme, we present the quantization of the electromagnetic field in the presence of a moving absorptive and dispersive magneto-dielectric slab (MDS) with uniform velocity in the direction parallel to its interface. We derive the quantum input-output relations for the case that quantum states propagate perpendicularly to the moving MDS.We thoroughly investigate the impact of the motion of the movingMDS on quantum properties of the incident states. To illustrate this, by modeling the dispersive and dissipative effects of the slab by the Lor…
Macroscopic mechanical objects and electromagnetic degrees of freedom couple to each other via radiation pressure. Optomechanical systems with sufficiently strong coupling are predicted to exhibit quantum effects and are a topic of considerable interest. Devices reaching this regime would offer new types of control of the quantum state of both light and matter and would provide a new arena in which to explore the boundary between quantum and classical physics. Experiments to date have achieved sufficient optomechanical coupling to laser-cool mechanical devices but have not yet reached the quan…
We investigate theoretically the generation of nonlinear dissipative structures in optomechanical (OM) systems containing discrete arrays of mechanical resonators. We consider both hybrid models in which the optical system is a continuous multimode field, as it would happen in an OM cavity containing an array of micro-mirrors, and also fully discrete models in which each mechanical resonator interacts with a single optical mode, making contact with Ludwig & Marquardt [Phys. Rev. Lett. 101, 073603 (2013)]. Also, we study the connections between both types of models and continuous OM models. Whi…
The interaction between dielectric particles and a laser-driven optical cavity gives rise to both conservative and dissipative dynamics, which can be used to levitate, trap and cool nanoparticles. We analytically and numerically study a two-mode setup in which the optical potentials along the cavity axis cancel, so that the resulting dynamics is almost purely dissipative. For appropriate detunings of the laser-drives, this dissipative optomechanical dynamics can be used to sort particles according to their size, to rectify their velocities and to enhance transverse cooling.
In cavity optomechanics, nanomechanical motion couples to a localized optical mode. The regime of single-photon strong coupling is reached when the optical shift induced by a single phonon becomes comparable to the cavity linewidth. We consider a setup in this regime comprising two optical modes and one mechanical mode. For mechanical frequencies nearly resonant to the optical level splitting, we find the photon-phonon and the photon-photon interactions to be significantly enhanced. In addition to dispersive phonon detection in a novel regime, this offers the prospect of optomechanical photon …
Laser cooling of mesoscopic mechanical resonators is of great interest for both fundamental studies and practical applications. We provide a general framework to describe the cavity-assisted backaction cooling in the strong coupling regime. By studying the cooling dynamics, we find that the temporal evolution of mean phonon number oscillates as a function of the optomechanical coupling strength depending on frequency mixing. The further analytical result reveals that the optimal cooling limit is obtained when the system eigenmodes satisfy the frequency matching condition. The reduced instantan…
Vibrating nano- and micromechanical resonators have been the subject of research aiming at ultrasensitive mass sensors for mass spectrometry, chemical analysis and biomedical diagnosis. Unfortunately, their merits diminish dramatically in liquids due to dissipative mechanisms like viscosity and acoustic losses. A push towards faster and lighter miniaturized nanodevices would enable improved performances, provided dissipation was controlled and novel techniques were available to efficiently drive and read-out their minute displacement. Here we report on a nano-optomechanical approach to this pr…
We solve the problem addressed by Landau and Lifshitz in 1958, and Oughstun and Sherman of determining the dynamical losses in a purely dissipative dielectric media. We develop concrete notions of macroscopic free energy and losses as energy which is reversible and irreversible, respectively, in the medium-field interaction. We define the reversible and irreversible energies and outline the derivation of said quantities. We examine the implications of our definition and it's auxiliary quantity, the reversal field, for the single Lorentz oscillator model of a medium. We show that for this model…
Solving the challenging problem of the amplification and generation of an electromagnetic field in nanostructures enables to implement many properties of the electromagnetic field at the nanoscale in novel practical applications. A first-principles quantum mechanical consideration of such a problem is sufficiently restricted by the exponentially large number of degrees of freedom, and does not allow the electromagnetic field dynamics to be described if it involves a high number of interacting atoms and modes of the electromagnetic field. Conversely, the classical description of electromagnetic…
Dissipative Kerr solitons are self-sustaining optical wavepackets in resonators. They use the Kerr nonlinearity to both compensate dispersion and to offset optical loss. Besides providing insights into nonlinear resonator physics, they can be applied in frequency metrology, precision clocks, and spectroscopy. Like other optical solitons, the dissipative Kerr soliton can radiate power in the form of a dispersive wave through a process that is the optical analogue of Cherenkov radiation. Dispersive waves typically consist of an ensemble of optical modes. A limiting case is demonstrated in which …
Optomechanical devices sensitively transduce and actuate motion of nanomechanical structures using light. Single--crystal diamond promises to improve the performance of optomechanical devices, while also providing opportunities to interface nanomechanics with diamond color center spins and related quantum technologies. Here we demonstrate dissipative waveguide--optomechanical coupling exceeding 35 GHz/nm to diamond nanobeams supporting both optical waveguide modes and mechanical resonances, and use this optomechanical coupling to measure nanobeam displacement with a sensitivity of $9.5$ fm/$\s…
We present a novel locking scheme for active length-stabilization and frequency detuning of a cavity optomechanical device based on the optical spring effect. The scheme can be used as an alternative to the Pound-Drever-Hall locking technique but in contrast doesn't require signal processing on time-scales of the cavity decay rate. It is therefore particularly suited for stabilizing micro cavities, where this time-scale can be extremely fast. The error signal is generated through the optical spring effect, i.e. the detuning-dependent frequency-shift of a nanomechanical oscillator that is dispe…
We study a hybrid system formed from an optomechanical resonator and a cavity mode strongly coupled to an excitonic transition inside a quantum well. We show that due to the mixing of cavity photon and exciton states, the emergent quasiparticles - polaritons - possess coupling to the mechanical mode of both dispersive and dissipative nature. We calculate the occupancies of polariton modes and reveal bistable behavior, which deviates from conventional Kerr nonlinearity or dispersive coupling cases due to the dissipative coupling. The described system serves as a good candidate for future polari…
The design of highly wavelength tunable semiconductor laser structures is presented. The system is based on a one dimensional photonic crystal cavity consisting of two patterned, doubly-clamped nanobeams, otherwise known as a "zipper" cavity. Zipper cavities are highly dispersive with respect to the gap between nanobeams in which extremely strong radiation pressure forces exist. Schemes for controlling the zipper cavity wavelength both optically and electrically are presented. Tuning ranges as high as 75nm are achieved for a nominal design wavelength of 1.3micron. Sensitivity of the mechanical…
The process of soliton Cherenkov radiation (also known as dispersive wave emission) in microresonator frequency combs plays a critical role in generating broadband and coherent microcomb spectra. Here, we report the observation of symmetry breaking in the group velocity of counter-propagating dissipative Kerr solitons, induced by polychromatic soliton Cherenkov radiation. Results show that in the presence of higher-order dispersion, the temporal arrangement of a multi-soliton state affects its group velocity, an effect which originates from the interference between multiple radiative tails emi…
In this letter we theoretically investigate the formation of localized temporal dissipative structures, and their corresponding frequency combs in doubly resonant dispersive optical parametric oscillators. We derive a nonlocal mean field model, and show that domain wall locking allows for the formation of stable coherent optical frequency combs.
New resonant emission of dispersive waves by oscillating solitary structures is considered analytically and numerically. The resonance condition for the radiation is derived and it is demonstrated that the predicted resonances match the spectral lines observed in numerical simulations perfectly. The complex recoil of the radiation on the soliton dynamics is discussed.
