Macroscopic Mechanical Oscillators Research Articles

Acoustic Torsional Mechanical Oscillator Driven by Wave‐Matter Orbital Angular Momentum Transfer with Quality Factor >1000

AbstractThe experimental realization of a macroscopic mechanical oscillator driven by the nondissipative transfer of angular momentum from sound waves to matter is presented, with quality factor up to Q ≈ 2000. This performance is two orders of magnitude higher than previously reported values Q ≈ 10. This result is achieved through the use of a monolithic metallic torsional pendulum and improved assembling method of the constitutive parts of the apparatus. This allows a substantial reduction of the internal losses associated with the imaginary part of the complex shear modulus compared with previous attempts using photocurable resin materials.

Manipulating bipartite and tripartite quantum correlations of mechanical oscillators via optomechanical interaction.

The entanglement of macroscopic mechanical oscillators is always an interesting domain. How to entangle multiple mechanical oscillators is still not well answered. In this paper, we investigate the bipartite and tripartite quantum correlations among three distinct mechanical oscillators interacting with one cavity pumped by a multi-tone driving laser. Floquet cavity modes, resulting from different frequency components of the multi-tone driven cavity, are used to construct channels for quantum correlations between mechanical oscillators. By modulating the effective optomechanical coupling, we can manipulate the mechanical entanglement and EPR steering. The numerical results show that the two-tone driving widely employed is not enough to generate tripartite entanglement, while three- and four-tone driving can be employed to generate and enhance genuine tripartite entanglement. All bipartite entanglement can also be modulated. In addition, we demonstrate the monogamous relation of tripartite EPR steering and manipulate the asymmetry of steering. This work provides a method for manipulating the quantum correlation among multiple macroscopic objects.

Measurement-Based Control of Quantum Entanglement and Steering in a Distant Magnomechanical System

In this paper, we propose a scheme for measurement-based control of hybrid Einstein–Podolsky–Rosen (EPR) entanglement and steering between distant macroscopic mechanical oscillator and yttrium iron garnet (YIG) sphere in a system of an electromechanical cavity unidirectionally coupled to an electromagnonical cavity. We reveal that when the output of the electromagnonical cavity is continuously monitored by homodyne detection, not only the phonon–magnon entanglement and steering but also the purities of the phononic, magnonic and phonon–magnon states are considerably enhanced. We also find that the measurement can effectively retrieve the magnon-to-phonon steering, which is not yet obtained in the absence of the measurement. We show that unconditional phonon–magnon entanglement and steering can be achieved by introducing indirect feedback to drive the magnon and mechanical subsystems. The long-distance macroscopic hybrid entanglement and steering can be useful for, e.g., fundamental tests for quantum mechanics and quantum networks.

Macroscopic mechanical oscillator is herded into a Schrödinger cat state

A new demonstration of a famous thought experiment has coaxed a classical 16 µg cluster of atoms to behave like a quantum object.

Dynamical bipartite and tripartite entanglement of mechanical oscillators in an optomechanical array

We theoretically propose a method to generate tripartite entanglement of three mechanical oscillators in an optomechanical array. We consider a system comprised of three bichromatically driven optomechanical systems which are coupled to each other via Coulomb interaction of the mechanical oscillators. We show that, for small Coulomb coupling strength, steady tripartite entanglement of the three mechanical oscillators with time periodicity can be generated due to the combined effect of the two-tone drivings and the Coulomb coupling. At large Coulomb coupling strength, the tripartite entanglement exhibits steady entanglement sudden death and revival. The duration of entanglement death during one period can be controlled by the Coulomb coupling strength. The tripartite entanglement is robust against the mechanical thermal noise. Our paper provides us a route for exploring and exploiting controllable and robust multipartite entanglement among macroscopic mechanical oscillators.

Generation of quintupartite entanglement with an atom-assisted dual-cavity optomechanical system

We present a proposal to generate quintupartite entanglement with an optomechanical dual-cavity containing an ensemble of Λ-type three-level atoms. By solving the Heisenberg-Langevin equations, we show that entanglement among the two cavity fields, two mechanical oscillators, and atoms can be realized via atomic coherence and cavity field radiation pressure. In addition, within the experimentally available range of parameters, the larger the input laser power, atomic ensemble number, and quality factors of the cavity and mechanical oscillators, and the smaller the environmental temperature, the stronger the multipartite entanglement. This atom-cavity-optomechanical hybrid system provides an efficient and convenient platform for quantum states exchange between macroscopic (mechanical oscillators) and microscopic (atoms, photons) matters, and may find promising applications in realistic quantum information processing.

Generation of Strong Mechanical–Mechanical Entanglement by Pump Modulation

AbstractThe implementation of strong quantum entanglement between two macroscopic mechanical oscillators is a longstanding pursued goal in fundamental research or applied science. Here, an effective scheme is proposed to generate strong mechanical–mechanical entanglement in a double‐oscillator optomechanical system via only introducing the sole amplitude‐modulated pattern into the pump field instead without the requirement of any extra techniques. Based on two mechanical oscillators with identical or different frequencies, a specific kind of amplitude‐modulated pump field is respectively designed, which successfully manipulates the mechanical oscillators into the highly entangled two‐mode squeezed state. The maximum value of the logarithmic negativity that quantifies the generated entanglement reaches about 9 ebits in the appropriate parameter regime, which greatly surpasses the bound 1 ebits on the maximal stationary entanglement from the two‐mode parametric interaction. Moreover, the obtained entanglement can be detected via resorting to an ancillary cavity mode with homodyne detection technique. Compared with the previous congeneric schemes, this scheme involves fewer modulation techniques and may provide a new perspective to effectively manipulate the mechanical quantum states in optomechanical systems utilizing the time‐dependent modulation.

Einstein-Podolsky-Rosen entanglement and asymmetric steering between distant macroscopic mechanical and magnonic systems

We propose a deterministic scheme for establishing hybrid Einstein-Podolsky-Rosen (EPR) entanglement channel between a macroscopic mechanical oscillator and a magnon mode in a distant yttrium-iron-garnet (YIG) sphere across about ten gigahertz of frequency difference. The system consists of a driven electromechanical cavity which is unidirectionally coupled to a distant electromagnonical cavity inside which a YIG sphere is placed. We find that far beyond the sideband-resolved regime in the electromechanical subsystem, stationary phonon-magnon EPR entanglement can be achieved. This is realized by utilizing the output field of the electromechanical cavity being an intermediary which distributes the electromechanical entanglement to the magnons, thus establishing a remote phonon-magnon entanglement. The EPR entanglement is strong enough such that phonon-magnon quantum steering can be attainable in an asymmetric manner. This long-distance macroscopic hybrid EPR entanglement and steering enable potential applications not only in fundamental tests of quantum mechanics at the macro scale, but also in quantum networking and one-sided device-independent quantum cryptography based on magnonics and electromechanics.

Mechanical squeezing in a dissipative optomechanical system with two driving tones

The squeezed state of a macroscopic mechanical oscillator can be exploited to enhance the sensitivity of precision measurements. Here, we theoretically demonstrate that the displacement squeezing of a mechanical oscillator in a dissipative optomechanical system can be generated by the use of two driving tones tuned to the first upper and lower mechanical sidebands. We find that the displacement squeezing of the mechanical oscillator is determined by the powers of the two driving tones and the temperature of the environment. Even when the temperature of the environment is as high as 20 mK, the mechanical squeezing beyond 3 dB can be achieved. Moreover, we show that the mechanical squeezing can be detected by directly measuring the cavity output spectrum.

Non-classical energy squeezing of a macroscopic mechanical oscillator

Optomechanics and electromechanics have made it possible to prepare macroscopic mechanical oscillators in their quantum ground states, in quadrature squeezed states, and in entangled states of motion. In addition to coaxing ever larger and more tangible objects into a regime of quantum behavior, this new capability has encouraged ideas of using mechanical oscillators in the processing and communication of quantum information and as precision force sensors operating beyond the standard quantum limit. But the effectively linear interaction between motion and light or electricity precludes access to the broader class of quantum states of motion, such as cat states or energy squeezed states. Indeed, early optomechanical proposals noted the possibility to escape this restriction by creating strong quadratic coupling of motion to light. Although there have been experimental demonstrations of quadratically coupled optomechanical systems, these have not yet accessed nonclassical states of motion. Here we create nonclassical states by quadratically coupling motion to the energy levels of a Cooper-pair box (CPB) qubit. By monitoring the qubit's transition frequency, we detect the oscillator's phonon distribution rather than its position. Through microwave frequency drives that change both the state of the oscillator and qubit, we then dissipatively stabilize the oscillator in a state with a large mean phonon number of 43 and sub-Poissonian number fluctuations of approximately 3. In this energy squeezed state we observe a striking feature of the quadratic coupling: the recoil of the mechanical oscillator caused by qubit transitions, closely analogous to the vibronic transitions in molecules.

Radiation pressure measurement using a macroscopic oscillator in an ambient environment

In contrast to current efforts to quantify the radiation pressure of light using nano-micromechanical resonators in cryogenic conditions, we proposed and experimentally demonstrated the radiation pressure measurement in ambient conditions by utilizing a macroscopic mechanical longitudinal oscillator with an effective mass of the order of 20 g. The light pressure on a mirror attached to the oscillator was recorded in a Michelson interferometer and results showed, within the experimental accuracy of 3.9%, a good agreement with the harmonic oscillator model without free parameters.

Quantum-feedback-controlled macroscopic quantum nonlocality in cavity optomechanics

In this paper, we propose a continuous measurement and feedback scheme to achieve strong Einstein–Podolsky–Rosen (EPR) steering and Bell nonlocality of two macroscopic mechanical oscillators in cavity optomechanics. Our system consists of two optomechanical cavities in which two cavity fields are coupled to each other via nondegenerate parametric downconversion. The two cavity output fields are subject to continuous Bell-like homodyne detection and the detection currents are fed back to drive the cavity fields. It is found that when the feedback is absent, the two mechanical oscillators can only be prepared in steady weakly entangled states which however do not display EPR steering and Bell nonlocality, due to the so-called 3 dB limit. But when the feedback is present, it is found that the mechanical entanglement is considerably enhanced such that strong mechanical steering and Bell nonlocality can be obtained in the steady-state regime. We analytically reveal that this is because the feedback drives the mechanical oscillators into a steady approximate two-mode squeezed vacuum state, with arbitrary squeezing in principle. It is shown that the feedback can also obviously improve the purity of the nonclassical mechanical states. The dependences of the mechanical quantum nonlocality on the feedback strength and thermal fluctuations are studied, and it is found that Bell nonlocality is much more vulnerable to thermal noise than EPR steerable nonlocality.

Entanglement between distant macroscopic mechanical and spin systems

Entanglement is an essential property of multipartite quantum systems, characterized by the inseparability of quantum states of objects regardless of their spatial separation. Generation of entanglement between increasingly macroscopic and disparate systems is an ongoing effort in quantum science, as it enables hybrid quantum networks, quantum-enhanced sensing and probing of the fundamental limits of quantum theory. The disparity of hybrid systems and the vulnerability of quantum correlations have thus far hampered the generation of macroscopic hybrid entanglement. Here, we generate an entangled state between the motion of a macroscopic mechanical oscillator and a collective atomic spin oscillator, as witnessed by an Einstein–Podolsky–Rosen variance below the separability limit, 0.83 ± 0.02 < 1. The mechanical oscillator is a millimetre-size dielectric membrane and the spin oscillator is an ensemble of 109 atoms in a magnetic field. Light propagating through the two spatially separated systems generates entanglement because the collective spin plays the role of an effective negative-mass reference frame and provides—under ideal circumstances—a back-action-free subspace; in the experiment, quantum back-action is suppressed by 4.6 dB. Einstein–Podolsky–Rosen entanglement between a millimetre-size mechanical membrane oscillator and a collective atomic spin oscillator formed by an ensemble of caesium atoms is achieved, although the two systems are spatially separated by one metre.

Probing quantum gravity effects with quantum mechanical oscillators

Phenomenological models aiming to join gravity and quantum mechanics often predict effects that are potentially measurable in refined low-energy experiments. For instance, modified commutation relations between position and momentum, that account for a minimal scale length, yield a dynamics that can be codified in additional Hamiltonian terms. When applied to the paradigmatic case of a mechanical oscillator, such terms, at the lowest order in the deformation parameter, introduce a weak intrinsic nonlinearity and, consequently, deviations from the classical trajectory. This point of view has stimulated several experimental proposals and realizations, leading to meaningful upper limits to the deformation parameter. All such experiments are based on classical mechanical oscillators, i.e., excited from a thermal state. We remark indeed that decoherence, that plays a major role in distinguishing the classical from the quantum behavior of (macroscopic) systems, is not usually included in phenomenological quantum gravity models. However, it would not be surprising if peculiar features that are predicted by considering the joined roles of gravity and quantum physics should manifest themselves just on purely quantum objects. On the basis of this consideration, we propose experiments aiming to observe possible quantum gravity effects on macroscopic mechanical oscillators that are preliminary prepared in a high purity state, and we report on the status of their realization.Graphical abstract

Mechanical Squeezing via Fast Continuous Measurement.

We revisit quantum state preparation of an oscillator by continuous linear position measurement. Quite general analytical expressions are derived for the conditioned state of the oscillator. Remarkably, we predict that quantum squeezing is possible outside of both the backaction dominated and quantum coherent oscillation regimes, relaxing experimental requirements even compared to ground-state cooling. This provides a new way to generate nonclassical states of macroscopic mechanical oscillators, and opens the door to quantum sensing and tests of quantum macroscopicity at room temperature.

Cooling a Mechanical Oscillator in Opto-electro-mechanical System with Frequency Modulations

The opto-electro-mechanical system as a quantum interface between electronic information and optical information plays an important role in quantum information processing. Ground-state cooling of the macroscopic mechanical oscillator is a crucial requirement for this system in order to eliminate the effect of thermal fluctuations on transmission of information. Here, we propose a scheme of ground-state cooling for a mechanical oscillator which is coupled to an optical cavity through radiation pressure force and simultaneously coupled to a superconducting microwave cavity through an effective capacitance. Meanwhile, the periodical frequency modulations are applied to the optical mode, microwave cavity, and mechanical mode, respectively. The cooling efficiency is analyzed and cooling dynamics is simulated numerically by means of covariance matrix. The results show that the Stokes heating processes can be suppressed effectively by means of frequency modulations, and the mechanical oscillator can be cooled to near its ground-state with a higher efficiency than that of a standard optomechanical system due to the double cooling channel. Moreover, a complementary cooling effect is found between these two cooling channels, i.e., a high cooling efficiency can be achieved by cooperation between a good optical cavity and a bad microwave cavity, or vice versa. This cooperative cooling of the double channel breaks the limitation of resolved-sideband regime.

Cavity electromechanics with parametric mechanical driving

Microwave optomechanical circuits have been demonstrated to be powerful tools for both exploring fundamental physics of macroscopic mechanical oscillators, as well as being promising candidates for on-chip quantum-limited microwave devices. In most experiments so far, the mechanical oscillator is either used as a passive element and its displacement is detected using the superconducting cavity, or manipulated by intracavity fields. Here, we explore the possibility to directly and parametrically manipulate the mechanical nanobeam resonator of a cavity electromechanical system, which provides additional functionality to the toolbox of microwave optomechanics. In addition to using the cavity as an interferometer to detect parametrically modulated mechanical displacement and squeezed thermomechanical motion, we demonstrate that this approach can realize a phase-sensitive parametric amplifier for intracavity microwave photons. Future perspectives of optomechanical systems with a parametrically driven mechanical oscillator include exotic bath engineering with negative effective photon temperatures, or systems with enhanced optomechanical nonlinearities.

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.

Quantum Signature of a Squeezed Mechanical Oscillator.

Recent optomechanical experiments have observed nonclassical properties in macroscopic mechanical oscillators. A key indicator of such properties is the asymmetry in the strength of the motional sidebands produced in the probe electromagnetic field, which is originated by the noncommutativity between the oscillator ladder operators. Here we extend the analysis to a squeezed state of an oscillator embedded in an optical cavity, produced by the parametric effect originated by a suitable combination of optical fields. The motional sidebands assume a peculiar shape, related to the modified system dynamics, with asymmetric features revealing and quantifying the quantum component of the squeezed oscillator motion.

Testing the generalized uncertainty principle with macroscopic mechanical oscillators and pendulums

Recent progress in observing and manipulating mechanical oscillators at quantum regime provides new opportunities of studying fundamental physics, for example, to search for low energy signatures of quantum gravity. For example, it was recently proposed that such devices can be used to test quantum gravity effects, by detecting the change in the [x,p] commutation relation that could result from quantum gravity corrections. We show that such a correction results in a dependence of a resonant frequency of a mechanical oscillator on its amplitude, which is known as amplitude-frequency effect. By implementing this new method we measure amplitude-frequency effect for 0.3 kg ultra high-Q sapphire split-bar mechanical resonator and for 10 mg quartz bulk acoustic wave resonator. Our experiments with sapphire resonator have established the upper limit on quantum gravity correction constant for $\beta_0<5 \times10^6$ which is a factor of 6 better than previously detected. The reasonable estimates of $\beta_0$ from experiments with quartz resonators yield an even more stringent limit of $4\times10^4$. The data sets of 1936 measurement of physical pendulum period by Atkinson results in significantly stronger limitations on $\beta_0 \ll 1$. Yet, due to the lack of proper pendulum frequency stability measurement in these experiments, the exact upper bound on $\beta_0$ can not be reliably established. Moreover, pendulum based systems only allow testing a specific form of the modified commutator that depends on the mean value of momentum. The electro-mechanical oscillators to the contrary enable testing of any form of generalized uncertainty principle directly due to much higher stability and a higher degree of control.