12 pages, 3 figures, brief review submitted to Journal of Modern Optics, for the proceedings of the "Physics of Quantum Electronics" conference (Snowbird, 2008)
We review the quantum theory of cooling of a mechanical oscillator subject to the radiation pressure force due to light circulating inside a driven optical cavity. Such optomechanical setups have been used recently in a series of experiments by various groups to cool mechanical oscillators (such as cantilevers) by factors reaching $10^{5}$, and they may soon go to the ground state of mechanical motion. We emphasize the importance of the sideband-resolved regime for ground state cooling, where the cavity ring-down rate is smaller than the mechanical frequency. Moreover, we illustrate the strong coupling regime, where the cooling rate exceeds the cavity ring-down rate and where the driven cavity resonance and the mechanical oscillation hybridize.
In general, ground state cooling using optomechanical interaction is realized in the regime where optical dissipation is higher than mechanical dissipation. Here, we demonstrate that optomechanical ground state cooling in a continuous optomechanical system is possible by using backward Brillouin scattering while mechanical dissipation exceeds optical dissipation which is the common case in optical waveguides. The cooling is achieved in an anti-Stokes backward Brillouin process by modulating the intensity of the optomechanical coupling via a pulsed pump to suppress heating processes in the stro…
We analyze the performance of optomechanical cooling of a mechanical resonator in the presence of a degenerate optical parametric amplifier within the optomechanical cavity, which squeezes the cavity light. We demonstrate that this allows to significantly enhance the cooling efficiency via the coherent suppression of Stokes scattering. The enhanced cooling occurs also far from the resolved sideband regime, and we show that this cooling scheme can be more efficient than schemes realized by injecting a squeezed field into the optomechanical cavity.
We theoretically study the laser cooling of cavity optomechanics when the mechanical resonance frequency and damping depend on time. In the regime of weak optomechanical coupling we extend the theory of laser cooling using an adiabatic approximation. We discuss the modifications of the cooling dynamics and compare it with numerical simulations in a wide range of modulation frequencies.
A pulsed cooling scheme for optomechanical systems is presented that is capable of cooling at much faster rates, shorter overall cooling times, and for a wider set of experimental scenarios than is possible by conventional methods. The proposed scheme can be implemented for both strongly and weakly coupled optomechanical systems in both weakly and highly dissipative cavities. We study analytically its underlying working mechanism, which is based on interferometric control of optomechanical interactions, and we demonstrate its efficiency with pulse sequences that are obtained by using methods f…
We propose a scheme in which the cooling of a mechanical resonator is achieved by exposing the optomechanical system to a non-Markovian environment. Because of the backflow from the non-Markovian environment, the phonon number can go beyond the conventional cooling limit in a Markovian environment. Utilizing the spectrum density obtained in the recent experiment [Nature Communications 6, 7606 (2015)], we show that the cooling process is highly effective in a non-Markovian environment. The analysis of the cooling mechanism in a non-Markovian environment reveals that the non-Markovian memory eff…
Cavity opto-mechanical cooling via radiation pressure dynamical backaction enables ground state cooling of mechanical oscillators, provided the laser exhibits sufficiently low phase noise. Here, we investigate and measure the excess phase noise of widely tunable external cavity diode lasers, which have been used in a range of recent nano-optomechanical experiments, including ground-state cooling. We report significant excess frequency noise, with peak values on the order of 10^7 rad^2 Hz near 3.5 GHz, attributed to the diode lasers' relaxation oscillations. The measurements reveal that even at…
Optomechanical cooling of levitated dielectric particles represents a promising new approach in the quest to cool small mechanical resonators towards their quantum ground state. We investigate two-mode cooling of levitated nanospheres in a self-trapping regime. We identify a rich structure of split sidebands (by a mechanism unrelated to usual strong-coupling effects) and strong cooling even when one mode is blue detuned. We show the best regimes occur when both optical fields cooperatively cool and trap the nanosphere, where cooling rates are over an order of magnitude faster compared to corre…
We propose a quantum interference cooling scheme for a nano-mechanical resonator (NAMR) in a hybrid optomechanical system, where the atoms are trapped in an optomechanical cavity, coupling to an additional optical cavity. The absorption of the optomechanical resonator can be modified by quantum interference effects induced by the atom-cavity and cavity-cavity couplings independently. With the employment of the quantum interference, the desired transition for cooling is enhanced, along with the heating suppression due to the undesired transition. As a result, the NAMR vibration can be cooled do…
We propose a simple optomechanical model in which a mechanical oscillator quadrature could be "cooled" well below its equilibrium temperature by applying a suitable feedback to drive the orthogonal quadrature by means of the homodyne current of the radiation field used to probe its position.
We propose an optomechanical dissipation engineering scheme by introducing an ancillary mechanical mode with a large decay rate to control the density of states of the optical mode. The effective linewidth of the optical mode can be reduced or broadened, manifesting the dissipation engineering. To prove the ability of our scheme in improving the performances of the optomechanical system, we studied optomechanical entanglement and phonon cooling. It is demonstrated that the optomechanical entanglement overwhelmed by thermal phonon excitations could be restored via dissipation engineering. For t…
We present a theoretical scheme for ground state cooling of a mechanical resonator in a membrane-in-middle optomechanical system (OMS) driven by two red-detuned drive fields. The details of dynamical evolution of OMS are provided, and the effect of system conditions on cooling results are systematically studied. Most importantly, the setups with two drives are found to be capable of achieving better cooling results than the theoretical cooling limit with single cavity. Even an improvement by one order of thermal phonon number is possible with proper combination of the cavity damping rate and d…
We discuss how the optomechanical coupling provided by radiation pressure can be used to cool macroscopic collective degrees of freedom, as vibrational modes of movable mirrors. Cooling is achieved using a phase-sensitive feedback-loop which effectively overdamps the mirrors motion without increasing the thermal noise. Feedback results able to bring macroscopic objects down to the quantum limit. In particular, it is possible to achieve squeezing and entanglement.
We demonstrate cavity sideband cooling of a single collective motional mode of an atomic ensemble down to a mean phonon occupation number of 2.0(-0.3/+0.9). Both this minimum occupation number and the observed cooling rate are in good agreement with an optomechanical model. The cooling rate constant is proportional to the total photon scattering rate by the ensemble, demonstrating the cooperative character of the light-emission-induced cooling process. We deduce fundamental limits to cavity-cooling either the collective mode or, sympathetically, the single-atom degrees of freedom.
We propose and analyze theoretically a cavity optomechanical analog of a heat pump that uses a polariton fluid to cool mechanical modes coupled to a single pre-cooled phonon mode via external modulation of the substrate of the mechanical resonator. This approach permits to cool phonon modes of arbitrary frequencies not limited by the cavity-optical field detuning deep into the quantum regime from room temperature.
We propose to cool a mechanical resonator close to its ground state via an electromagnetically-induced-transparency- (EIT-) like cooling mechanism in a double-cavity optomechanical system, where an additional cavity couples to the original one in the standard optomechanical system. By choosing optimal parameters such that the cooling process of the mechanical resonator corresponds to the maximum value of the optical fluctuation spectrum and the heating process to the minimum one, the mechanical resonator can be cooled with the final mean phonon number less than that at the absence of the addit…
A scheme is presented to optimize the optomechanical cooling of mechanical resonator in instability regime. Based on the stability analysis, we uncovered a distinct bistable effect of photons and phonons, which can be used to realize a strong nonlinear effect even in the single-photon weak coupling regime. Considering the experimental realization, we investigate the sideband cooling in bistable regime with and without quantum nonlinearity. It is shown that the fluctuation of the steady state phonons can be excellently suppressed at a rather low level due to the anti-rotating-wave effect, and i…
We develop a theory of optomechanical cooling with a squeezed input light field. We show that Stokes heating transitions can be \emph{fully} suppressed when the driving field is squeezed below the vacuum noise level at an appropriately selected squeezing phase and for a finite amount of squeezing. The quantum backaction limit to laser cooling can be therefore moved down to zero and the resulting final temperature is then solely determined by the ratio between the thermal phonon number and the optomechanical cooperativity parameter, independently of the actual values of the cavity linewidth and…
We theoretically study the radiation-induced interaction between the mechanical motion of an oscillating mirror and a remotely trapped atomic cloud. When illuminated by continuous-wave radiation, the mirror motion will induce red and blue sideband radiation, which respectively increases and reduces motional excitation. We find that by suitably driving $Λ$-level atoms, the mirror correlation with a specific radiation sideband could be converted from the outgoing to the incoming radiation. Such process allows us to manipulate the heating and cooling effects. Particularly, we develop an optomecha…
Ground-state cooling of mechanical resonators is an important task in quantum optomechanics, because it is a necessary prerequisite for creation, manipulation, and application of macroscopic mechanical coherence. Here, we propose a transient-state scheme to accelerate ground-state cooling of a mechanical resonator in a three-mode loop-coupled optomechanical system via shortcuts to adiabaticity (STA). We consider four kinds of coupling protocols and calculate the evolution of the mean phonon number of the mechanical resonator in both the adiabatic and STA cases. We verify that the ground-state …
Cooling mechanical resonators is of great importance for both fundamental study and applied science. We investigate the hybrid optomechanical cooling with a three-level atomic ensemble fixed in a strong excited optical cavity. By using the quantum noise approach, we find the upper bound of the noise spectrum and further present three optimal parameter conditions, which can yield a small heating coefficient, a large cooling coefficient, and thus a small final phonon number. Moreover, through the covariance matrix approach, results of numerical simulation are obtained, which are consistent with …
Optomechanical systems show tremendous promise for high sensitivity sensing of forces and modification of mechanical properties via light. For example, similar to neutral atoms and trapped ions, laser cooling of mechanical motion by radiation pressure can take single mechanical modes to their ground state. Conventional optomechanical cooling is able to introduce additional damping channel to mechanical motion, while keeping its thermal noise at the same level, and as a consequence, the effective temperature of the mechanical mode is lowered. However, the ratio of temperature to quality factor …
Ground-state cooling of mechanical motion by coupling to a driven optical cavity has been demonstrated in various optomechanical systems. In our work, we provide a so far missing thermodynamic performance analysis of optomechanical sideband cooling in terms of a heat valve. As performance quantifiers, we examine not only the lowest reachable effective temperature (phonon number) but also the evacuated-heat flow as an equivalent to the cooling power of a standard refrigerator, as well as appropriate thermodynamic efficiencies, which all can be experimentally inferred from measurements of the ca…
In the usual optomechanical cooling, even if the system has no thermal component, it still has a quantum limit-known as the quantum backaction limit (QBL)-on the minimum phonon number related to shot noise. By studying the side-band cooling regime in optomechanical system (OMS), we find that the cooling can be improved significantly when the frequency modulation (FM) that can suppress the Stokes heating processes is introduced into the system. We analyze and demonstrate the reasons of the phonon number below the QBL redefined in the whole stable region of the standard OMSs. The above analyses …
Cooling to the motional ground state is an important first step in the preparation of nonclassical states of mesoscopic mechanical oscillators. Light-mediated coupling to a remote atomic ensemble has been proposed as a method to reach the ground state for low frequency oscillators. The ground state can also be reached using optical measurement followed by feedback control. Here we investigate the possibility of enhanced cooling by combining these two approaches. The combination, in general, outperforms either individual technique, though atomic ensemble-based cooling and feedback cooling each …
The dark-mode effect is a stubborn obstacle for ground-state cooling of multiple degenerate mechanical modes optomechanically coupled to a common cavity-field mode. Here we propose an auxiliary-cavity-mode method for simultaneous ground-state cooling of two degenerate or near-degenerate mechanical modes by breaking the dark mode. We find that the introduction of the auxiliary cavity mode not only breaks the dark-mode effect, but also provides a new cooling channel to extract the thermal excitations stored in the dark mode. Moreover, we study the general physical-coupling configurations for bre…
We report on cooling the center-of-mass motion of a nanoparticle due to a purely quadratic coupling between its motion and the optical field of a high finesse cavity. The resulting interaction gives rise to a Van der Pol nonlinear damping, which is analogous to conventional parametric feedback where the cavity provides passive feedback without measurement. We show experimentally that like feedback cooling the resulting energy distribution is strongly nonthermal and can be controlled by the nonlinear damping of the cavity. As quadratic coupling has a prominent role in proposed protocols to gene…
Cooling a mesoscopic mechanical oscillator to its quantum ground state is elementary for the preparation and control of low entropy quantum states of large scale objects. Here, we pre-cool a 70-MHz micromechanical silica oscillator to an occupancy below 200 quanta by thermalizing it with a 600-mK cold 3He gas. Two-level system induced damping via structural defect states is shown to be strongly reduced, and simultaneously serves as novel thermometry method to independently quantify excess heating due to the cooling laser. We demonstrate that dynamical backaction sideband cooling can reduce the…
We obtain a master equation for a parametrically driven optomechanical cavity. We use a more correct dissipation model that accounts for the modification of the quasienergy spectrum caused by the driving. When the natural frequency of the mechanical object oscillates periodically around its mean value, the master equation with the improved dissipation model is expressed using Floquet operators. We apply the corresponding master equation to model the laser cooling of the mechanical object. Using an adiabatic approximation, an analytical expression for the number of excitations of the mechanical…
We investigate the effects of atomic collisions as well as optomechanical mirror-field coupling on the optical bistability in a hybrid system consisting of a Bose-Einstein condensate inside a driven optical cavity with a moving end mirror. It is shown that the bistability of the system can be controlled by the s-wave scattering frequency which can provide the possibility of realizing a controllable optical switch. On the other hand, by studying the effect of the Bogoliubov mode, as a secondary mechanical mode relative to the mirror vibrations, on the cooling process as well as the bipartite mi…
We consider a cavity optomechanical cooling configuration consisting of a mechanical resonator (denoted as resonator b) and an electromagnetic resonator (denoted as resonator a), which are coupled in such a way that the effective resonance frequency of resonator a depends linearly on the displacement of resonator b. We study whether back-reaction effects in such a configuration can be efficiently employed for suppression of decoherence. To that end, we consider the case where the mechanical resonator is prepared in a superposition of two coherent states and evaluate the rate of decoherence. We…
Effects of Quadratic Optomechanical Coupling on Bipartite Entanglements, Mechanical Ground-State Cooling and Squeezing in an Electro-Optomechanical System
Dynamical back-action cooling of phonons in optomechanical systems having one optical mode is well studied. Systems with two optical modes have the potential to reach significantly higher cooling rate through resonant enhancement of both pump and scattered light. Here we experimentally investigate the role of dual optical densities of states on optomechanical cooling, and the deviation from theory caused by thermal locking to the pump laser. Using this, we demonstrate a room temperature system operating very close to the strong coupling regime, where saturation of cooling is anticipated.
Optical self-cooling of a membrane oscillator in a cavity optomechanical experiment at room temperature
Università di Firenze（佛罗伦萨大学）；Institute of Materials for Electronics and Magnetism, Nanoscience-Trento-FBK Division（电子与磁性材料研究所，纳米科学-特伦托-FBK分部）；Istituto Nazionale di Fisica Nucleare (INFN), Trento Institute for Fundamental Physics and Application（意大利国家核物理研究所（INFN），特伦托基础物理与应用研究所）；CNR-INO（意大利国家研究委员会-光学研究所）；INFN, Sezione di Firenze（意大利国家核物理研究所，佛罗伦萨分部）；Delft University of Technology（代尔夫特理工大学）
Optomechanical cooling is a prerequisite for many exotic applications promised by modern quantum technology and it is crucial to achieve it in short times, in order to minimize the undesirable effects of the environment. We formulate cavity optomechanical cooling as a minimum-time optimal control problem on anti-de Sitter space of appropriate dimension and use the Legendre pseudospectral optimization method to find the minimum time and the corresponding optimal control, for various values of the maximum coupling rate between the cavity field and the mechanical resonator. The present framework …
The interaction of a single-mode field with both a weak Kerr medium and a parametric nonlinearity in an intrinsically nonlinear optomechanical system is studied. The nonlinearities due to the optomechanical coupling and Kerr-down conversion lead to the bistability and tristability in the mean intracavity photon number. Also, our work demonstrates that the lower bound of the resolved sideband regime and the minimum attainable phonon number can be less than that of a bare cavity by controlling the parametric nonlinearity and the phase of the driving field. Moreover, we find that in the system un…
Multimode optomechanical systems are an emerging platform for studying fundamental aspects of matter near the quantum ground state and are useful in sensitive sensing and measurement applications. We study optomechanical cooling in a system where two nearly degenerate mechanical oscillators are coupled to a single microwave cavity. Due to an optically mediated coupling the two oscillators hybridize into a bright mode with strong optomechanical cooling rate and a dark mode nearly decoupled from the system. We find that at high coupling, sideband cooling of the dark mode is strongly suppressed. …
Ground state cooling of massive mechanical objects remains a difficult task restricted by the unresolved mechanical sidebands. We propose an optomechanically-induced-transparency cooling scheme to achieve ground state cooling of mechanical motion without the resolved sideband condition in a pure optomechanical system with two mechanical modes coupled to the same optical cavity mode. We show that ground state cooling is achievable for sideband resolution $ω_{m}/κ$ as low as 0.003. This provides a new route for quantum manipulation of massive macroscopic devices and high-precision measurements.
We demonstrate the optomechanical cooling of a tapered optical nanofiber by coupling the polarization of light to the mechanical angular momentum of the system. The coupling is enabled by birefringence in the fiber and does not make use of an optical resonator. We find evidence for cooling in the distribution of thermally driven amplitude fluctuations and the noise spectrum of the torsional modes. Our proof-of-principle demonstration shows cavity-less cooling of the torsional degree of freedom of a macroscopically extended nanofiber.
The ground state cooling of Brillouin scattering optomechanical system is limited by defects in practical sample. In this paper, we propose a new compensatory cooling mechanism for Brillouin scattering optomechanical system with exceptional points (EPs). By using the EPs both in optical and mechanical modes, the limited cooling process is compensated effectively. The dual-EPs system, which is discovered in this work for the first time, can be induced by two defects with specific relative angles and has function of not only actively manipulating the coupling strength of optical modes but also t…
We consider the radiative trapping and cooling of a partially transmitting mirror suspended inside an optical cavity, generalizing the case of a perfectly reflecting mirror previously considered [M. Bhattacharya and P. Meystre, Phys. Rev. Lett. \textbf{99}, 073601 (2007)]. This configuration was recently used in an experiment to cool a nanometers-thick membrane [Thompson \textit{et al.}, arXiv:0707.1724v2, 2007]. The self-consistent cavity field modes of this system depend strongly on the position of the middle mirror, leading to important qualitative differences in the radiation pressure effe…
We review and study the roles of quantum and classical fluctuations in recent cavity-optomechanical experiments which have now reached the quantum regime (mechanical phonon occupancy < 1) using resolved sideband laser cooling. In particular, both the laser noise heating of the mechanical resonator and the form of the optically transduced mechanical spectra, modified by quantum and classical laser noise squashing, are derived under various measurement conditions. Using this theory, we analyze our recent ground-state laser cooling and motional sideband asymmetry experiments with nanoscale optome…
Standard optomechanical cooling methods ideally require weak coupling and cavity damping rates which enable the motional sidebands to be well resolved. If the coupling is too large then sideband-resolved cooling is unstable or the rotating wave approximation can become invalid. In this work we describe a protocol to cool a mechanical resonator coupled to a driven optical mode in an optomechanical cavity, which is also coupled to an optical mode in another auxiliary optical cavity, and both the cavities are frequency-modulated. We show that by modulating the amplitude of the drive as well, one …
Optomechanical devices have been cooled to ground-state and genuine quantum features, as well as long-predicted nonlinear phenomena, have been observed. When packing close enough more than one optomechanical unit in the same substrate the question arises as to whether collective or independent dissipation channels are the correct description of the system. Here we explore the effects arising when introducing dissipative couplings between mechanical degrees of freedom. We investigate synchronization, entanglement and cooling, finding that collective dissipation can drive synchronization even in…
We present a scheme for ground-state cooling of a mechanical resonator by simultaneously coupling it to a superconducting qubit and a cavity field. The Hamiltonian describing the hybrid system dynamics is systematically derived. The cooling process is driven by a red-detuned ac drive on the qubit and a laser drive on the optomechanical cavity. We have investigated cooling in the weak and the strong coupling regimes for both the individual system, i.e., qubit assisted cooling and optomechanical cooling, and compared them with the effective hybrid cooling. It is shown that hybrid cooling is more…
Atoms in spatially dependent light fields are attracted to local intensity maxima or minima depending on the sign of the frequency difference between the light and the atomic resonance. For light fields confined in open high-Q optical resonators the backaction of the atoms onto the light field generates dissipative dynamic opto-mechanical potentials, which can be used to cool and trap the atoms. Extending the conventional case of high field seekers to the regime of blue atom-field detuning, where the particles are low field seeking, we show that inherent nonlinear atom field dynamics still can…
We present a scheme for cooling mechanical motion to the ground state in an optomechanical system. Unlike standard sideband cooling, this scheme applies to the so-called unresolved sideband regime, where the resonance frequency of the mechanical mode is much smaller than the cavity linewidth. Ground state cooling becomes possible when assuming the presence of an additional, auxiliary mechanical mode and exploiting the effect of optomechanically induced transparency. We first consider a system where one optical cavity interacts with two mechanical modes, and show that ground state cooling of th…
Optomechanical cavities in the well-resolved-sideband regime are ideally suited for the study of a myriad of quantum phenomena with mechanical systems, including backaction-evading measurements, mechanical squeezing, and generation of non-classical states. For these experiments, the mechanical oscillator should be prepared in its ground state; residual motion beyond the zero-point motion must be negligible. The requisite cooling of the mechanical motion can be achieved using the radiation pressure of light in the cavity by selectively driving the anti-Stokes optomechanical transition. To date,…
One of the most fundamental problems in optomechanical cooling is how small the thermal phonon number of a mechanical oscillator can be achieved under the radiation pressure of a proper cavity field. Different from previous theoretical predictions, which were based on an optomechanical system's time-independent steady states, we treat such cooling as a dynamical process of driving the mechanical oscillator from its initial thermal state, due to its thermal equilibrium with the environment, to a stabilized quantum state of higher purity. We find that the stabilized thermal phonon number left in…
