Experimental investigation of walking drops: Wave field and interaction with slit structures

While bouncing walking silicone oil droplets (walkers) do show many quantumlike phenomena, the original, most intriguing, double-slit experiment with walkers has been shown to be an overinterpretation of data. Several experiments and numerical simulations have proven that for at least some parameter region there is no randomness. Still, true randomness was claimed to be observed in an experiment on chaotically bouncing walkers. Also, most of the available phase space has not been investigated. The main goal of this paper is therefore to look for true interference and chaos in the entire phase space. Recently, we made an extensive investigation of drops interacting with slits, but still in a limited range. However, the outcome was always deterministic and only incidentally mimicked the statistics of the corresponding quantum case. We also showed that the extra interference, already seen by others, in the double-slit case was caused by reflection of waves from the outlet of the unused slit after passage and thus was not a true double-slit effect. A new theoretical treatment of bouncing drop dynamics has since given analytic relations for the associated wave field, leading to a proposal for criteria for the possible occurrence of true interference in the double-slit experiment. Satisfying these criteria, requires working close to the onset of the Faraday instability, with two spatial conditions favoring slow walkers, and a temporal condition favoring fast walkers. The regions of high velocity, where the walkers bounce periodically, and of very low velocity, with chaotically bouncing walkers, have not been comprehensively investigated so far. We have therefore looked at these regions, probing the limits for interaction with slits. Furthermore, noting that a short transit time is essential to fulfill the criteria, experiments were done using double-slit barriers only 0.5 and 2 mm broad. Nowhere was true interference or a chaotic response found. As the theory has implications for many of the observed quantumlike phenomena involving walkers as, e.g., tunneling and interaction between drops, we have measured the spatial and temporal decay of the wave field. A comparison with the theory shows very good agreement but leads to a reformulation of the above-mentioned criteria.

Interaction of wave-driven particles with slit structures

Just over a decade ago Couder and Fort [Phys. Rev. Lett. 97, 154101 (2006)PRLTAO0031-900710.1103/PhysRevLett.97.154101] published a provocative paper suggesting that a classical system might be able to simulate the truly fundamental quantum mechanical single- and double-slit experiment. The system they investigated was that of an oil droplet walking on a vibrated oil surface. Their results have since been challenged by Andersen et al. [Phys. Rev. E 92, 013006 (2015)PLEEE81539-375510.1103/PhysRevE.92.013006] by pointing to insufficient statistical support and a lack of experimental control over critical parameters. Here we show that the randomness in the original experiment is an artifact of lack of control. We present experimental data from an extensive scan of the parameter space of the system including the use of different size slits and tight control of critical parameters. For the single-slit we find very diverse samples of interference-like patterns but all causal by nature. This also holds for the double-slit. However, an extra interference effect appears here. The origin of this is investigated by blocking either the inlet or the outlet of one slit. Hereby we show that the extra interference is solely due to back-scatter of the associated wave field from the outlet of the slit not passed by the droplet. Recently Pucci et al. [J. Fluid Mech. 835, 1136 (2018)JFLSA70022-112010.1017/jfm.2017.790] using a much broader slit also showed that the classical system is basically causal. They, too, observed the extra interference effect for the double-slit. However, the reason behind was not determined. Moreover they claimed the existence of a chaotic regime just below the cri- tical acceleration for spontaneous generation of Faraday surface waves. Our measurements do not support the validity of this claim. However, the drop dynamics turns out to have an interesting multifaceted interaction with the slit structure.

Double-slit experiment with single wave-driven particles and its relation to quantum mechanics

In a thought-provoking paper, Couder and Fort [Phys. Rev. Lett. 97, 154101 (2006)] describe a version of the famous double-slit experiment performed with droplets bouncing on a vertically vibrated fluid surface. In the experiment, an interference pattern in the single-particle statistics is found even though it is possible to determine unambiguously which slit the walking droplet passes. Here we argue, however, that the single-particle statistics in such an experiment will be fundamentally different from the single-particle statistics of quantum mechanics. Quantum mechanical interference takes place between different classical paths with precise amplitude and phase relations. In the double-slit experiment with walking droplets, these relations are lost since one of the paths is singled out by the droplet. To support our conclusions, we have carried out our own double-slit experiment, and our results, in particular the long and variable slit passage times of the droplets, cast strong doubt on the feasibility of the interference claimed by Couder and Fort. To understand theoretically the limitations of wave-driven particle systems as analogs to quantum mechanics, we introduce a Schrödinger equation with a source term originating from a localized particle that generates a wave while being simultaneously guided by it. We show that the ensuing particle-wave dynamics can capture some characteristics of quantum mechanics such as orbital quantization. However, the particle-wave dynamics can not reproduce quantum mechanics in general, and we show that the single-particle statistics for our model in a double-slit experiment with an additional splitter plate differs qualitatively from that of quantum mechanics.

Saturation of shape instabilities in single-bubble sonoluminescence

Excitation of shape instabilities represents one route to bubble death in single-bubble sonoluminescence. This feature is satisfactorily explained by an expansion to first order in the amplitude of a shape distortion in the form of a spherical harmonic. By taking the expansion to second order, it is found that regions of parameter space exist where the exponential growth into bubble disruption is checked and a saturated stable state of shape distortion is possible. Experimental evidence provided by Mie scattering is presented, and a possible connection to simultaneous spatially anisotropic light emission is discussed.

Concomitance in single bubble sonoluminescence of period doubling in emission and shape distortion

We report the first direct observation for a single stable sonoluminescing bubble of a shape instability. Furthermore we show that stable saturation of the shape distortion caused by the instability for a certain range of parameters is experimentally possible and furthermore is directly linked to the curious phenomenon of flash by flash period doubling of the sonoluminescent emission as the afterbounce instability causing the shape distortion is always period doubled whenever the emission is & vice versa.

Segregation in water-based stable single-bubble sonoluminescence

A long-standing issue in the field of long-time-stable, water-based, single-bubble sonoluminescence has been the close similarity of the spectra to that of blackbody radiation, the question being whether the similarity is just a weird coincidence, with the bubbles being, on the whole, transparent to their own radiation. One mechanism that has been suggested is the generation of a shock or, at least, a compression wave in the gas of the bubble. A footprint of such a wave would be segregation of species. We have investigated spectra from bubbles seeded with various mixtures of helium or neon with xenon or argon using a transformation, specific to our experimental setup and spectrometer, that was shown to allow for a single-parameter characterization of the spectra in some simpler situations. The surprising result of this investigation is that although no trace of segregation is found, the radiation seems to be highly thermalized in all cases.

Data collapse of the spectra of water-based stable single-bubble sonoluminescence

In the early days of stable single-bubble sonoluminescence, it was strongly debated whether the emission was blackbody radiation or whether the bubble was transparent to its own radiation (volume emission). Presently, the volume emission picture is nearly universally accepted. We present new measurements of spectra with apparent color temperatures ranging from 6000 to 21 000 K. We show through data collapse that within experimental uncertainty, apart from a constant, the spectra of strongly driven stable single-bubble sonoluminescence in water can be written as the product between a universal function of wavelength and a functional form that only depends on wavelength and apparent temperature but has no reference to any other parameter specific to the experimental situation. This remarkable result does question our theoretical understanding of the state of the plasma in the interior of strongly driven stable sonoluminescent bubbles.

Stability of a sonoluminescing nitrogen bubble in chilled water

Bubbles are levitated in a resonator driven by an ultrasound wave. Their highly nonlinear oscillations feature a strong collapse, where fluidlike densities and temperatures of several thousand degrees Kelvin are reached, resulting in the emission of ultrashort light pulses. Previous experiments and theories explained the observed stable bubble dynamic and emission on long time scales with the requirement of a noble gas. Recent experiments reveal stable sonoluminescent emission of nitrogen bubbles in chilled water without the presence of a noble gas. Numerical calculations show that a diffusive and dissociative equilibrium can be reached when the temperature within a nitrogen bubble is limited due to the presence of water vapor. Calculated stability lines agree with published experimental results. The results show that noble-gas-free stable single bubble sonoluminescence of nitrogen bubbles is possible.

Second mode of recycling together with period doubling links single-bubble and multibubble sonoluminescence

We report the existence of a second type of recycling mode that occurs for air-seeded bubbles. Observation of period doubling in both the stable, the first type, and the second type of recycling mode, together with simultaneous measurement of the relative phase of light emission compared to the drive, shows that the instability boundaries of period doubling and bubble extinction are mainly determined by the bubble size irregardless of the gas composition. The second type mode seems to represent a link between single-bubble and multibubble sonoluminescence.

Size of the light-emitting region in a sonoluminescing bubble

The size of the light-emitting region is a key parameter toward understanding the light-emitting processes in a sonoluminescing bubble. Here we present measurements of interference effects from particles with a diameter of approximately 2 microm situated 6-10 microm from a sonoluminescing bubble. From the angular size of the pattern and from an estimated distance to the particles we conclude that the light-emitting region of a sonoluminescing bubble is smaller than commonly believed [see, e.g., Nature (London) 398, 402 (1999)]. We argue that an upper limit of the size of the light-emitting region is approximately 200 nm.

Parametric dependence of single-bubble sonoluminescence spectra

We present experimental spectra of single sonoluminescing bubble in water at different dissolved argon concentrations and excitation levels. All the relevant experimental conditions are either measured directly or derived from measured quantities for each spectrum, thus the parametric dependence of the spectra can be analyzed. To characterize the data in a given wavelength interval we fitted the shape of the spectra with the Planck function. The effective temperatures obtained from these fits lie in the range 12,000-18,000 K, practically independent of the expansion ratio, while the intensity normalized by the volume of the bubble increases with the expansion ratio as a power law. The effective temperatures decrease with the pressure amplitude for each argon concentration, while the light intensity, measured with a photomultiplier tube, increases. These observations suggest that the increased energy input due to the higher pressure amplitudes results in an increased number of less energetic photons as compared to the case of a lower excitation level.

Direct observation of period-doubled nonspherical states in single-bubble sonoluminescence

We present direct observations of period doubling in the flash to flash pulse heights in single-bubble sonoluminescence. States involved are stable, spherically symmetry broken. Observations are made using seven detectors distributed in the equatorial plane of the bubble. Contrary to earlier experiments by Holt et al. [Phys. Rev. Lett. 72, 1376 (1994)], where period doubling was observed in the time intervals between flashes but not in the pulse heights, we observe period doubling in pulse heights, but no corresponding period doubling is seen in the time intervals. In parameter space the period doubling is observed below the n=2 shape instability boundary line where extinction is shown to take place.

Alternative method to deduce bubble dynamics in single-bubble sonoluminescence experiments

In this paper we present an experimental approach that allows to deduce the important dynamical parameters of single sonoluminescing bubbles (pressure amplitude, ambient radius, radius-time curve). The technique is based on a few previously confirmed theoretical assumptions and requires the knowledge of quantities such as the amplitude of the electric excitation and the phase of the flashes in the acoustic period. These quantities are easily measurable by a digital oscilloscope, avoiding the cost of the expensive lasers or ultrafast cameras of previous methods. We show the technique in a particular example and compare the results with conventional Mie scattering. We find that within the experimental uncertainties these two techniques provide similar results.

Stable nonspherical bubble collapse including period doubling in sonoluminescence

We present observations of stable spherical symmetry broken states in single bubble sonoluminescence including observations of period doubled states. States observed involve both spatially oriented states and states with a tumbling symmetry axis. The observations are made using a fiber based four-channel correlation scheme. The measurements are made both with and without narrow band optical filters. The symmetry broken states are seen in all cases even using a 650+/-40-nm filter. This fact may be used to distinguish between different theories for the light emission. Prior to the measurements reported here, theoretical attempts to explain observations of period doubling bifurcation phenomena in single bubble sonoluminescence were centered on radially bifurcated collapses. The present experiments show unequivocally that the observations are primarily a result of breaking the spherical symmetry in the bubble collapse. Period doubling will at most show up as secondary effects in the total light output, if at all.

Period-doubling bifurcations from breaking the spherical symmetry in sonoluminescence: experimental verification

Using a fiber-based four-channel correlation scheme to investigate spatial and temporal correlations, we show that observations of period-doubling phenomena in single bubble sonoluminescence are primarily a result of spontaneously breaking the spherical symmetry in the bubble collapse and, at most, may show up as secondary effects in the flash-to-flash spatially integrated light output.