Quantum effects of radiation pressure are expected to limit the sensitivity of second-generation gravitational-wave interferometers. Though ubiquitous, such effects are so weak that they haven't been experimentally demonstrated yet. Using a high-finesse optical cavity and a classical intensity noise, we have demonstrated radiation-pressure induced correlations between two optical beams sent into the same moving mirror cavity. Our scheme can be extended down to the quantum level and has applications both in high-sensitivity measurements and in quantum optics.
In this work we have considered a simple mechanical oscillator interacting with a single mode optical field inside a cavity in the generalized uncertainty principle framework (GUP). Our aim is to calculate the modified noise spectrum and observe the effects of the GUP. The commutation relation that we have considered has an extra linear order momentum term along with a quadratic order term. Confronting our theoretical results with the observational results, we observe that we get a much tighter bound on the GUP parameters from the noise spectrum using the values of the system parameters from d…
We combine matter-wave interferometry and cavity optomechanics to propose a coherent matter--light interface based on mechanical motion at the quantum level. We demonstrate a mechanism that is able to transfer non-classical features imprinted on the state of a matter-wave system to an optomechanical device, transducing them into distinctive interference fringes. This provides a reliable tool for the inference of quantum coherence in the particle beam. Moreover, we discuss how our system allows for intriguing perspectives, paving the way to the construction of a device for the encoding of quant…
Probing gravitational interaction between milligram optomechanical oscillators operating in the quantum regime
Istituto Nazionale di Fisica Nucleare, TIFPA（意大利国家核物理研究所，TIFPA）；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）；Physics Division, School of Science and Technology, Università di Camerino（卡梅里诺大学理学院物理系）；INFN, Sezione di Perugia（意大利国家核物理研究所，佩鲁加分部）；LENS（激光工程与应用科学欧洲研究中心）；Dipartimento di Fisica e Astronomia, Università di Firenze（佛罗伦萨大学物理与天文学系）；INFN, Sezione di Firenze（意大利国家核物理研究所，佛罗伦萨分部）；CNR-INO（意大利国家研究委员会-光学研究所）
We determine the theoretical limits to squeezing-enhanced measurement sensitivity of mechanical motion in a cavity optomechanical system. The motion of a mechanical resonator is transduced onto quadrature fluctuations of a cavity optical field and a measurement is performed on the optical field exiting the cavity. We compare measurement sensitivities obtained with coherent probing and quantum-enhanced probing of the mechanical motion, i.e. the coherent probe field carries vacuum states and quadrature squeezed vacuum states at sideband frequencies, respectively. We find that quantum-enhanced pr…
Hybrid optomechanical systems are emerging as a fruitful architecture for quantum technologies. Hence, determining the relevant atom-light and light-mechanics couplings is an essential task in such systems. The fingerprint of these couplings is left in the global state of the system during non-equilibrium dynamics. However, in practice, performing measurements on the entire system is not feasible, and thus, one has to rely on partial access to one of the subsystems, namely the atom, the light, or the mechanics. Here, we perform a comprehensive analysis to determine the optimal subsystem for pr…
We present a way of measuring with high precision the anharmonicity of a quantum oscillator coupled to an optical field via radiation pressure. Our protocol uses a sequence of pulsed interactions to perform a loop in the phase space of the mechanical oscillator, which is prepared in a thermal state. We show how the optical field acquires a phase depending on the anharmonicity. Remarkably, one only needs small initial cooling of the mechanical motion to probe even small anharmonicities. Finally, by applying tools from quantum estimation theory, we calculate the ultimate bound on the estimation …
We propose here a setup to generate and evaluate the entanglement between two mechanical resonators in a cavity optomechanical setting. As in previous proposals, our scheme includes two driving pumps allowing for the generation of two-mode mechanical squeezing. In addition, we include here four additional probing tones, which allow for the separate evaluation of the collective mechanical quadratures required to estimate the Duan quantity, thus allowing us to infer whether the mechanical resonators are entangled.
We study theoretically nonlinear effects arising from the presence of a Kerr-down conversion nonlinear crystal inside an optomechanical cavity. For this system we investigate the influences of the two nonlinearities, i.e., the Kerr nonlinearity and the parametric gain, on the dynamics of the oscillating mirror, the intensity and the squeezing spectra of the transmitted field, and the steady-state mirror-field entanglement. We show that in comparison with a bare optomechanical cavity, the combination of the cavity energy shift due to the Kerr nonlinearity and increase in the intracavity photon …
We investigate the resonant enhancement of nonlinear interactions in a three-mode cavity optomechanical system with two mechanical oscillators. By using the Keldysh Green's function technique we find that nonlinear effects on the cavity density of states can be greatly enhanced by the resonant scattering of two phononic polaritons, due to their small effective dissipation. In the large detuning limit and taking into account an upper bound on the achievable dressed coupling, the optimal point for probing the nonlinear effect is obtained, showing that such three-mode system can exhibit prominent…
Measurement-based control has emerged as an important technique to prepare mechanical resonators in pure quantum states for applications in quantum information processing and quantum sensing. Conventionally this has required two separate channels, one for probing the motion and another one acting back on the resonator. In this work, we analyze and experimentally demonstrate a technique of single-laser feedback cooling, where one laser is used for both probing and controlling the mechanical motion. We show using an analytical model and experiments that feedback cooling is feasible in this mode …
We analytically study the optomechanically induced transparency (OMIT) in the $N$-cavity system with the \textit{N}th cavity driven by pump, probing laser fields and the \textit{1}st cavity coupled to mechanical oscillator. We also consider that one atom could be trapped in the \textit{i}th cavity. Instead of only illustrating the OMIT in such a system, we are interested in how the number of OMIT windows is influenced by the cavities and the atom and what roles the atom could play in different cavities. In the resolved sideband regime, we find that, the number of cavities precisely determines …
Probing the boundary between classical and quantum mechanics has been one of the central themes in modern physics. Recently, experiments to precisely measure the force acting on milligram scale oscillators with optical cavities are attracting interest as promising tools to test quantum mechanics, decoherence mechanisms, and gravitational physics. In this paper, we review the present status of experiments using milligram scale optomechanical systems. We compare the feasibility of reaching the quantum regime with a pendulum, torsion pendulum, and optically levitated mirror. Considerations for de…
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…
We analyze the optomechanics of an atomic Bose-Einstein condensate interacting with the optical lattice inside a laser-pumped optical cavity and subject to a uniform bias force such as gravity. An atomic wave packet in a tilted lattice undergoes Bloch oscillations; in a cavity the backaction of the atoms on the light leads to a time-dependent modulation of the intracavity lattice at the Bloch frequency. When the Bloch frequency is on the order of the cavity damping rate we find transport of the atoms either up or down the lattice. The transport dynamics can be interpreted as a manifestation of…
Recent advances in the development of modern quantum technologies have opened the possibility of studying the interplay between spontaneous parametric down-conversion and optomechanics, two of the most fundamental nonlinear optical processes. Apart from practical reasons, such scenario is very interesting from a fundamental point of view, because it allows exploring the optomechanical interaction in the presence of a strongly quantum-correlated field, the spontaneously down-converted mode. In this work we analyze such problem from two approximate but valuable perspectives: the classical limit …
We present the optical and mechanical properties of high-Q fused silica microtoroidal resonators at cryogenic temperatures (down to 1.6 K). A thermally induced optical multistability is observed and theoretically described; it serves to characterize quantitatively the static heating induced by light absorption. Moreover the influence of structural defect states in glass on the toroid mechanical properties is observed and the resulting implications of cavity optomechanical systems on the study of mechanical dissipation discussed.
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.
Degenerate optomechanical parametric oscillators are optical resonators in which a mechanical degree of freedom is coupled to a cavity mode that is nonlinearly amplified via parametric down-conversion of an external pumping laser. Below a critical pumping power the down-converted field is purely quantum-mechanical, making the theoretical description of such systems very challenging. Here we introduce a theoretical approach that is capable of describing this regime, even at the critical point itself. We find that the down-converted field can induce significant mechanical cooling and identify th…
We derive a standard quantum limit for probing mechanical energy quantization in a class of systems with mechanical modes parametrically coupled to external degrees of freedom. To resolve a single mechanical quantum, it requires a strong-coupling regime -- the decay rate of external degrees of freedom is smaller than the parametric coupling rate. In the case for cavity-assisted optomechanical systems, e.g. the one proposed by Thompson et al., zero-point motion of the mechanical oscillator needs to be comparable to linear dynamical range of the optical system which is characterized by the optic…
This paper is concerned with quantum dynamics of a system coupled to a critical reservoir. In this context, we employ the Dicke model which is known to exhibit a super radiant quantum phase transition (QPT) and we allow one of the mirrors to move under a linear restoring force. The electromagnetic field couples to the movable mirror though radiation pressure just like in typical optomechanical setups. We show that, in the thermodynamical limit, the super-radiant phase induces a classical driving force on the mirror without causing decoherence.
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…
Institute of Science and Technology Austria (ISTA)（奥地利科学技术研究所）；Institute for Theoretical Physics, Eberhard Karls Universität Tübingen（蒂宾根大学理论物理研究所）；Naturwissenschaftlich-Technische Fakultät, Universität Siegen（锡根大学自然科学技术学院）；Department of Physics and Astronomy, University College London（伦敦大学学院物理与天文系）；ZARM, University of Bremen（不来梅大学ZARM中心）
The coherent quantum noise cancellation (CQNC) strategy has been performed in the single-mode optomechanical systems to promote an ultra-sensitive metrology protocol to break the standard quantum limit. The key idea of CQNC is that the backaction noises arising from radiation pressure and driving can be offset by coupling the optical mode to a near-resonant ancillary mode. In this work, a continuous weak-force sensing under CQNC is developed in a double-mode optomechanical system consisted of two optical modes with distinct frequencies and a mechanical mode. In particular, under the asymmetric…
A strategy for generating entanglement in two separated optomechanical oscillators is analysed, using entangled radiation produced from downconversion and stored in an initiating cavity. We show that the use of pulsed entanglement with optimally shaped temporal modes can efficiently transfer quantum entanglement into a mechanical mode, then remove it after a fixed waiting time for measurement. This protocol could provide new avenues to test for bounds on decoherence in massive systems that are spatially separated, as originally suggested by Wendell Furry [1] not long after the discussion by Ei…
We study a Fermi gas with strong, tunable interactions dispersively coupled to a high-finesse cavity. Upon probing the system along the cavity axis, we observe a strong optomechanical Kerr nonlinearity originating from the density response of the gas to the intracavity field and measure it as a function of interaction strength. We find that the zero-frequency density response function of the Fermi gas increases by a factor of two from the Bardeen-Cooper-Schrieffer to the Bose-Einstein condensate regime. The results are in quantitative agreement with a theory based on operator-product expansion…
Entangled continuous variable (CV) Gaussian states with different wavelengths plays a central role in recent CV-based approaches to quantum network, quantum information processing and quantum metrology. Typically, experiments demonstrating CV entanglement exploit the optical parametric frequency down conversion. Due to the probabilistic nature of photon pair generation, the entanglement involving the post-selection of photonic qubits is limited to at most three colors. Here We theoretically present a scheme for the deterministic generation of entanglement among bright multicolor CV Gaussian st…
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 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 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…
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…
We consider an optomechanical cavity made by two moving mirrors which contains a Kerr-down conversion nonlinear crystal. We show that the coherent oscillations of the two mechanical oscil- lators can lead to splitting in the electromagnetically induced transparency (EIT) resonance, and appearance of an absorption peak within the transparency window. In this configuration the coher- ent induced splitting of EIT is similar to driving a hyperfine transition in an atomic Lambda-type three-level system by a radio-frequency or microwave field. Also, we show that the presence of non- linearity provid…
Entanglement had played a crucial role in developing frontier technologies as a critical resource, for instance, in quantum teleportation and quantum sensing schemes. Notably, thanks to the ability to cool down the vibrational modes of mechanical oscillators to its quantum regime, entanglement between mechanical modes and the production of nonclassical mechanical states have emerged as central resources for quantum technological applications. Thus, proposing deterministic schemes to achieve those tasks is of paramount importance. While the dominant scheme for bipartite mechanical entanglement …
We study enhanced sensing of optomechanically induced nonlinearity (OMIN) in a cavity-waveguide coupled system. The Hamiltonian of the system is anti-PT symmetric with the two involved cavities being dissipatively coupled via the waveguide. When a weak waveguide-mediated coherent coupling is introduced, the anti-PT symmetry may break down. However, we find a strong bistable response of the cavity intensity to the OMIN near the cavity resonance, benefiting from linewidth suppression caused by the vacuum induced coherence. The joint effect of optical bistability and the linewidth suppression is …
We explore the possibility of achieving a significant nonlinear phase shift among photons propagating in nanoscale waveguides exploiting interactions among photons that are mediated by vibrational modes and induced through Stimulated Brillouin Scattering (SBS). We introduce a configuration that allows slowing down the photons by several orders of magnitude via SBS involving sound waves and two pump fields. We extract the conditions for maintaining vanishing amplitude gain or loss for slowly propagating photons while keeping the influence of thermal phonons to the minimum. The nonlinear phase a…
We derive a general expression that quantifies the total entanglement production rate in continuous variable systems, where a source emits two entangled Gaussian beams with arbitrary correlators.This expression is especially useful for situations where the source emits an arbitrary frequency spectrum,e.g. when cavities are involved. To exemplify its meaning and potential, we apply it to a four-mode optomechanical setup that enables the simultaneous up- and down-conversion of photons from a drive laser into entangled photon pairs. This setup is efficient in that both the drive and the optomecha…
The temperature dependence of the asymmetry between Stokes and anti-Stokes Raman scattering can be exploited for self-calibrating, optically-based thermometry. In the context of cavity optomechanics, we observe the cavity-enhanced scattering of light interacting with the standing-wave drumhead modes of a silicon nitride membrane mechanical resonator. The ratio of the amplitude of Stokes to anti-Stokes scattered light is used to measure temperatures of optically-cooled mechanical modes down to the level of a few vibrational quanta. We demonstrate that the Raman-ratio technique is able to measur…
Optical measurement of the motion of a 940 kHz mechanical resonance of a silicon nitride nanostring resonator is demonstrated with a read out noise imprecision reaching 37 dB below that of the resonator's zero-point fluctuations. Via intensity modulation of the optical probe laser, radiation pressure feedback is used to cool and damp the mechanical mode from an initial room temperature occupancy of $\bar{n}_{b} = 6.5 \times 10^6$ ($T_{b}=295$K) down to a phonon occupation of $\langle n \rangle = 66 \pm 10$, representing a mode temperature of $T_{m} \approx 3$mK. The five decades of cooling is …
We apply the formalism of quantum estimation theory to extract information about potential collapse mechanisms of the continuous spontaneous localisation (CSL) form. In order to estimate the strength with which the field responsible for the CSL mechanism couples to massive systems, we consider the optomechanical interaction between a mechanical resonator and a cavity field. Our estimation strategy passes through the probing of either the state of the oscillator or that of the electromagnetic field that drives its motion. In particular, we concentrate on all-optical measurements, such as homody…
The spectral-temporal correlation and the correlation time of a biphoton wavepacket generated in the process of parametric down-conversion (PDC), is of great importance for a broad range of quantum experiments. We utilise an integrated PDC source to generate biphotons with different types of spectral-temporal correlations and probe their respective correlation times. The outcomes confirms that the correlation time is independent of the coherence time of the pump light, and it is only determined by the waveguide length and its dispersion properties. Furthermore, we investigate the properties of…
Recent experimental progress in table-top experiments or gravitational-wave interferometers has enlightened the unique displacement sensitivity offered by optical interferometry. As the mirrors move in response to radiation pressure, higher power operation, though crucial for further sensitivity enhancement, will however increase quantum effects of radiation pressure, or even jeopardize the stable operation of the detuned cavities proposed for next-generation interferometers. The appearance of such optomechanical instabilities is the result of the nonlinear interplay between the motion of the …
We study cavity optomechanics of a mixture of ultracold atoms with tunable nonlinear collisions. We show that atomic collisions provide linear couplings between fictitious condensate oscillators, leading to possibilities of achieving a globally coupled quantum optomechanical network with an integrated atom chip. Potential applications range from simulating collective nonequilibrium dynamics in fields well past physics to probing unique properties of quantum mixtures.
We present a complete theory for laser cooling of a macroscopic radio-frequency LC electrical circuit by means of an optoelectromechanical system, consisting of an optical cavity dispersively coupled to a nanomechanical oscillator, which is in turn capacitively coupled to the LC circuit of interest. We determine the optimal parameter regime where the LC resonator can be cooled down to its quantum ground state, which requires a large optomechanical cooperativity, and a larger electromechanical cooperativity. Moreover, comparable optomechanical and electromechanical coupling rates are preferable…
Optomechanics, which explores the fundamental coupling between light and mechanical motion, has made important advances in both exploring and manipulating macroscopic mechanical oscillators down to the quantum level. However, dynamical effects related to the vectorial nature of the optomechanical interaction remain to be investigated. Here we study a nanowire with sub-wavelength dimensions strongly coupled to a tightly focused beam of light, enabling ultrasensitive readout of the nanoresonators dynamics. We experimentally determine the vectorial structure of the optomechanical interaction and …
We propose a feasible scheme to cool down a mechanical resonator (MR) in a three-mirror cavity optomechanical system with controllable external optical drives. Under the Born-Oppenheimer (BO) approximation, the whole dynamics of the mechanical resonator and cavities is reduced to that of a time-dependent harmonic oscillator, whose effective frequency can be controlled through the optical driving fields. The fast cooling of the MR can be realized by controlling the amplitude of the optical drives. Significantly, we further show that the ground-state cooling may be achieved via the three-mirror …
We establish the emergence of chaotic motion in optomechanical systems. Chaos appears at negative detuning for experimentally accessible values of the pump power and other system parameters. We describe the sequence of period doubling bifurcations that leads to chaos, and state the experimentally observable signatures in the optical spectrum. In addition to the semi-classical dynamics we analyze the possibility of chaotic motion in the quantum regime. We find that quantum mechanics protects the optomechanical system against irregular dynamics, such that simple periodic orbits reappear and repl…
Cavity optomechanics provides a unique platform for controlling micromechanical systems by means of optical fields that crosses the classical-quantum boundary to achieve solid foundations for quantum technologies. Currently, optomechanical resonators have become promising candidates for the development of precisely controlled nano-motors, ultrasensitive sensors and robust quantum information processors. For all these applications, a crucial requirement is to cool the mechanical resonators down to their quantum ground states. In this paper, we present a novel cooling scheme to further cool a mi…
