Levitated Sphere Research Articles

Modulating nonreciprocal transmission in levitated magnomechanical systems

In this paper, we propose a model of a dual cavity magnomechanical system with two levitated yttrium iron garnet spheres to investigate nonreciprocal transmission of a microwave field. We use an external Coulomb force to bias the steady-state position of the sphere levitated in each microwave cavity, thereby establishing an independent and controllable effective couplings between the cavity modes and the magnon modes. This can break the symmetry of the system and serve as the basis for nonreciprocal transmission in this system. We demonstrated how to achieve the system nonreciprocity with an extremely high isolation ratio and flexible controllability by appropriately selecting the suspended positions of the levitated spheres, which are related to the external bias forces. We also analyze in detail the influence of the cavity detunings and the driving power on the bias-force-induced nonreciprocity. Our study provides an effective approach to manipulating flexibly nonreciprocal transmission of a microwave field and may have potential implications for the development of future nonreciprocal transmission devices.

Design of non‐contact capacitive displacement detection methods for magnetic levitated sphere

AbstractTo meet the demand for non‐contact displacement detection of magnetic levitation spheres, single‐ended and differential variable electrode distance capacitance displacement detection schemes are designed in this paper. For these two schemes, finite element simulation models are established in COMSOL Multiphysics software to obtain the relationship between the test capacitance and the displacement of the magnetic levitation sphere. In the single‐ended scheme, there is a non‐linear relationship between the test capacitance and the position of the levitated sphere, and this non‐linearity becomes more significant as the sphere moves away from the electrode plate. In contrast, in the differential scheme, the test capacitance and the displacement of the levitated sphere follow a linear relationship, but the test sensitivity decreases with the expansion of the measuring range. The simulation results of the differential scheme have been verified by building a spherical displacement detection simulator, and thanks to the mature development of capacitive detection circuits, the scheme is expected to achieve better than nanoscale displacement detection resolution in the 6.6 mm displacement range of a magnetic levitation sphere in the future.

Magnomechanically induced transparency and tunable slow-fast light via a levitated micromagnet

In this paper, we theoretically investigate the magnomechanically induced transparency (MIT) phenomenon and slow-fast light propagation in a microwave cavity-magnomechanical system which includes a levitated ferromagnetic sphere. Magnetic dipole interaction determines the interaction between the photon, magnon, and center of mass motion of the cavity-magnomechanical system. As a result, we find that apart from coupling strength, which has an important role in MIT, the levitated ferromagnetic sphere’s position provides us a parameter to manipulate the width of the transparency window. In addition, the control field’s frequency has crucial influences on the MIT. Also this hybrid magnonic system allows us to demonstrate MIT in both the strong coupling and intermediate coupling regimes. More interestingly, we demonstrate tunable slow and fast light in this hybrid magnonic system. In other words, we show that the group delay can be adjusted by varying the control field’s frequency, the sphere position, and the magnon-photon coupling strength. These parameters have an influence on the transformation from slow to fast light propagation and vice versa. Based on the recent experimental advancements, our results provide the possibility to engineer hybrid magnonic systems with levitated particles for the light propagation, and the quantum measurements and sensing of physical quantities.

Model-based feedforward control for an optimized manipulation of acoustically levitated spheres

We present a simple dynamic model for predicting the manipulation behavior of an acoustically levitated sphere. The model allows for the calculation of the sphere position over time, which is demonstrated for two manipulation strategies: a straight motion with a constant manipulation velocity and a straight motion in which the sphere acceleration follows a cosine function. The dynamic model as well as the manipulation strategies is verified experimentally in an acoustic levitator system consisting of an array of 16 by 16 ultrasonic transducers emitting at 40 kHz and an opposing reflector. In this system, a glass sphere of a diameter of 2 mm is manipulated horizontally by controlling the phases of the transducers. The sphere motion is recorded using a high-speed camera, and a tracking algorithm is used for capturing the sphere position over time. Moreover, a model predictive control algorithm is applied on a path-following problem to move the sphere along a given reference trajectory by means of a model-based optimal feedforward control. The proposed dynamic model as well as the methodology presented in this paper enables faster manipulation speeds with reduced oscillations during object movement.

Vortex Shedding from a Microsphere Oscillating in Superfluid ^4He at mK Temperatures and from a Laser Beam Moving in a Bose–Einstein Condensate

Turbulent drag of an oscillating microsphere that is levitating in superfluid ^4He at mK temperatures, is unstable slightly above a critical velocity amplitude v_c. The lifetime tau of the turbulent state is determined by the number n of vortices shed per half-period. It is found that this number is identical to the superfluid Reynolds number. The possibility of moving a levitating sphere through superfluid ^3He at microkelvin temperatures is considered. A laser beam moving through a Bose–Einstein condensate (BEC) (as observed by other authors) also produces vortices in the BEC. In particular, in either case, a linear dependence of the shedding frequency f_v on Delta v = v - v_c is observed, where v is the velocity amplitude of the sphere or the constant velocity of the laser beam above v_c for the onset of turbulent flow: f_v = a ,Delta v, where the coefficient a is proportional to the oscillation frequency omega above some characteristic frequency omega _k and assumes a finite value for steady motion omega rightarrow 0. A relation between the superfluid Reynolds number and the superfluid Strouhal number is presented that is different from classical turbulence.

Intensive Cavity-Magnomechanical Cooling of a Levitated Macromagnet.

We describe microwave cavity-magnomechanical center-of-mass cooling of a levitated magnetic sphere. The standing magnetic component of the electromagnetic wave within a microwave cavity exerts a dynamical force on a magnonic crystalline sphere and dissipates the mechanical energy through scattering into the magnon mode. The coupling is established by the magnetic dipole interaction and enriched by the collective spin motion. We find that the final cooled phonon occupation achieved is an intensive property independent of the mass and size of the sphere, in contrast to standard optomechanical couplings. This is of particular importance for testing quantum mechanics with macroscopic objects.

Design of a system for controlling a levitating sphere in superfluid 3He at extremely low temperatures

We present a new mechanical probe to study the properties of superfluid 3He at microkelvin temperatures down to 100 μK. The setup consists of a set of coils for levitating a superconducting sphere and controlling its motion in a wide variety of regimes. In particular, the realisation of motion of a levitating body at a uniform velocity presents both an experimental challenge and a promising direction into the study of the edge states in topological superfluid 3He-B. We include the theoretical study of the device stability and simulations to illustrate the capabilities of the control system.

Optical rotation of levitated spheres in high vacuum

A circularly polarized laser beam is used to levitate and control the rotation of microspheres in high vacuum. At low pressure, rotation frequencies as high as 6 MHz are observed for birefringent vaterite spheres, limited by centrifugal stresses. Due to the extremely low damping in high vacuum, controlled optical rotation of amorphous SiO$_2$ spheres is also observed at rates above several MHz. At $10^{-7}$ mbar, a damping time of $6\times10^4$ s is measured for a $10\ \mu$m diameter SiO$_2$ sphere. No additional damping mechanisms are observed above gas damping, indicating that even longer damping times may be possible with operation at lower pressure. The controlled optical rotation of microspheres at MHz frequencies with low damping, including for materials that are not intrinsically birefringent, provides a new tool for performing precision measurements using optically levitated systems.

A two-year analysis of the iOSG-24 superconducting gravimeter at the low noise underground laboratory (LSBB URL) of Rustrel, France: Environmental noise estimate

Since July 2015 a Superconducting Gravimeter (SG) of the latest generation, the iOSG-24, has been recording continuously the time-varying gravity field at the low noise underground laboratory (LSBB URL) of Rustrel, France. This instrument designed for observatory purpose has a levitated Niobium sphere weighting 17.7 g instead of 4.3 g. The advantage of increasing the mass of the sphere is to reduce the thermal noise due to Brownian motion inside the sensor. A comparison of the noise levels shows that the combination of this iOSG-24 with the environmental condition at the LSBB makes this site one of the quietest worldwide SG sites. Parallel measurements with an absolute FG5 gravimeter give a calibration factor of −451 ± 3 nm/s2/V and a negligible linear drift is observed 3 months after the installation. Tidal analyses are consistent with theoretical predictions and have shown a strong S1 thermal wave. Influence of the hydrological water content, mostly related to the Fontaine de Vaucluse catchment, is clearly visible on the SG residuals after tides removal. However the hydrological influence modelled using the MERRA2 products does not fully explain the observed noise level at periods between 1 and 10 days. Longer gravimetric time-series are necessary to further study the seasonal hydrological effects.

Effects of horizontal acceleration on the superconducting gravimeter CT #036 at Ishigakijima, Japan

In the gravity sensor of a superconducting gravimeter, a superconducting sphere as a test mass is levitated in a magnetic field. Such a sensor is susceptible to applied horizontal as well as vertical acceleration, because the translational degrees of freedom of the mass are not perfectly limited to the vertical direction. In the case of the superconducting gravimeter CT #036 installed at Ishigakijima, Japan, horizontal ground acceleration excited by the movements of a nearby VLBI antenna induces systematic step noise within the gravity recordings. We investigate this effect in terms of the static and dynamic properties of the gravity sensor using data from a collocated seismometer. It is shown that this effect can be effectively modeled by the coupling between the horizontal and vertical components in the gravity sensor. It is also found that the mechanical eigenfrequency for horizontal translation of the levitating sphere is approximately 3 Hz.

Experimental determination of the dynamics of an acoustically levitated sphere

Levitation of solids and liquids by ultrasonic standing waves is a promising technique to manipulate materials without contact. When a small particle is introduced in certain areas of a standing wave field, the acoustic radiation force pushes the particle to the pressure node. This movement is followed by oscillations of the levitated particle. Aiming to investigate the particle oscillations in acoustic levitation, this paper presents the experimental and numerical characterization of the dynamic behavior of a levitated sphere. To obtain the experimental response, a small sphere is lifted by the acoustic radiation force. After the sphere lift, it presents a damped oscillatory behavior, which is recorded by a high speed camera. To model this behavior, a mass-spring-damper system is proposed. In this model, the acoustic radiation force that acts on the sphere is theoretically predicted by the Gor'kov theory and the viscous forces are modeled by two damping terms, one term proportional to the square of the velocity and another term proportional to the particle velocity. The proposed model was experimentally verified by using different values of sound pressure amplitude. The comparison between numerical and experimental results shows that the model can accurately describe the oscillatory behavior of the sphere in an acoustic levitator.

Experimental study of the oscillation of spheres in an acoustic levitator.

The spontaneous oscillation of solid spheres in a single-axis acoustic levitator is experimentally investigated by using a high speed camera to record the position of the levitated sphere as a function of time. The oscillations in the axial and radial directions are systematically studied by changing the sphere density and the acoustic pressure amplitude. In order to interpret the experimental results, a simple model based on a spring-mass system is applied in the analysis of the sphere oscillatory behavior. This model requires the knowledge of the acoustic pressure distribution, which was obtained numerically by using a linear finite element method (FEM). Additionally, the linear acoustic pressure distribution obtained by FEM was compared with that measured with a laser Doppler vibrometer. The comparison between numerical and experimental pressure distributions shows good agreement for low values of pressure amplitude. When the pressure amplitude is increased, the acoustic pressure distribution becomes nonlinear, producing harmonics of the fundamental frequency. The experimental results of the spheres oscillations for low pressure amplitudes are consistent with the results predicted by the simple model based on a spring-mass system.

Long-term production of butyric acid through immobilization ofClostridium tyrobutyricumin a moving fibrous-bed bioreactor (MFBB)

BACKGROUND Butyric acid is an important chemical with wide industrial applications, but large-scale bio-production still requires an efficient bioprocess. For this purpose, one novel moving fibrous-bed bioreactor (MFBB) was developed in this work for economical production of butyric acid. RESULTS The cells of Clostridium tyrobutyricum were immobilized on a fibrous matrix packed in porous levitated sphere carriers. Each carrier was packed with a fiber quantity 2 cm × 6 cm (0.42 g) and was rotated at 100 rpm in a stirred-tank fermentor having pH and temperature controls. Batch and repeated-batch fermentations were carried out to produce butyric acid with a high yield (0.48 ± 0.015 g g-1). Subsequent fed-batch fermentation using the MFBB resulted in a high concentration of butyric acid (65.4 ± 1.4 g L-1). This novel MFBB could be employed to produce high concentration butyric acid (64.5 ± 1.2 g L-1) by a simple repeated-batch addition of a high concentration of glucose (>100 g L-1). CONCLUSIONS The MFBB system developed could practically and economically produce butyric acid from glucose for long-term operation. © 2013 Society of Chemical Industry

Behavior of Ultrasonically Levitated Object above Reflector Hole

Using an axis-symmetric model comprising a flat reflector with a hole and a piston vibrator, we simulate the radiation force acting on a small object levitated near the hole, and predict that the position of the object shifts from the center line of the hole. We also experimentally investigate the behavior of a levitated polystyrene sphere approaching the hole. As predicted, the sphere avoids approaching the hole with some distance, depending on the reflector/vibrator interval and the hole diameter. We believe that this effect is useful in discriminating the droplets to be dispensed from those that should not be dispensed.

Optomechanical cooling of levitated spheres with doubly resonant fields

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 corresponding single-sideband cooling rates.

Time-Optimal Control Supported by PD in Real-Time

The Magnetic Levitation System (MLS) is ideal for modelling because it is frictionless. With a model well-fitted to the system one can generate adjoint equations and solve both the state and adjoint differential sets numerically to obtain the time-optimal sequences corresponding to the desired initial and final positions of the levitating sphere. This action is repeated for a broad set of the sphere position differences. The resulting bang-bang controls are associated with the sphere levels and stored in the computer memory. Each sphere level is equipped with an appropriately tuned PD controller to maintain levitation. This means that the damping and elasticity coefficients are sustained at the values close to each other despite changes of the distance between the sphere and electromagnet. In this way the time-optimal, open-loop control applied for the position change aided by the PD controller at steady states becomes a variable control structure and appears to be the correct and rapid strategy to experiment with MLS in the real-time.

Matrix method for acoustic levitation simulation

A matrix method is presented for simulating acoustic levitators. A typical acoustic levitator consists of an ultrasonic transducer and a reflector. The matrix method is used to determine the potential for acoustic radiation force that acts on a small sphere in the standing wave field produced by the levitator. The method is based on the Rayleigh integral and it takes into account the multiple reflections that occur between the transducer and the reflector. The potential for acoustic radiation force obtained by the matrix method is validated by comparing the matrix method results with those obtained by the finite element method when using an axisymmetric model of a single-axis acoustic levitator. After validation, the method is applied in the simulation of a noncontact manipulation system consisting of two 37.9-kHz Langevin-type transducers and a plane reflector. The manipulation system allows control of the horizontal position of a small levitated sphere from -6 mm to 6 mm, which is done by changing the phase difference between the two transducers. The horizontal position of the sphere predicted by the matrix method agrees with the horizontal positions measured experimentally with a charge-coupled device camera. The main advantage of the matrix method is that it allows simulation of non-symmetric acoustic levitators without requiring much computational effort.

New method for laser driven ion acceleration with isolated, mass-limited targets

Abstract A new technique to investigate laser driven ion acceleration with fully isolated, mass-limited glass spheres with a diameter down to 8 μ m is presented. A Paul trap was used to prepare a levitating glass sphere for the interaction with a laser pulse of relativistic intensity. Narrow-bandwidth energy spectra of protons and oxygen ions have been observed and were attributed to specific acceleration field dynamics in case of the spherical target geometry. A general limiting mechanism has been found that explains the experimentally observed ion energies for the mass-limited target.

Neural adapted controller learned on-line in real-time

Abstract An adapted controller consisting of a PD structure aided by a neural network is considered. It is dedicated to an unstable magnetic levitation system (MLS) to maintain a levitated sphere in the real-time. The main motivation is to create a self-tuning intelligent device that can easily change the controller parameter estimates based on adaptive update rules. How to formulate these rules in order to not disturb or ruin the system stability is the most serious question. This issue is discussed and verified by real-time experiments carried out at our apparatus that enables to vary its parameters. The neural network learned on-line guarantees the robustness of the control despite the system parameter are changed and disturbances are introduced. One can expect a better stabilizing performance as well.

Is the instrumental drift of superconducting gravimeters a linear or exponential function of time?

The instrumental drift of the superconducting gravimeter in Membach, Belgium, is estimated using 9 years of co-located and episodic absolute gravity measurements. We show that the best model of the long-term drift of the SG-C021 is an exponential. The thermal levelers used to compensate tilts are unlikely to induce the observed drift. Rather, the capacitance bridge, magnetic variations, gas adsorption on the levitating sphere, or helium gas pressure variations around it are most likely the possible combined causes of the observed instrumental drift. In practice, either linear or exponential drift models are equivalent as long as the record duration does not exceed 10 years. For longer records, this study demonstrates that an exponential models the drift better than a simple linear trend.