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The Josephson effects in superconductors have received attention both as an aid to scientific understanding and for their technological importance1. Analogous effects, including Josephson oscillations, have been observed2,3 in superfluid 3He below 1 mK. However, detection of oscillations at the Josephson frequency in superfluid 4He has remained elusive until now, despite almost four decades of attempts4.

Superconductors and superfluids are both described by a macroscopic wave function that includes amplitude and phase, φ. A chemical-potential difference, Δµ=µ2−µ1, between two baths of superfluid separated by an aperture causes the phase difference, Δφ=φ2−φ1, to change in accordance with the Josephson–Anderson phase-evolution equation

where ħ is Planck's constant (h) divided by 2π and where Δµ/m4=ΔP/ρ−SΔT (and m4 is the mass of the 4He atom, ΔP is the pressure difference, ρ is the mass density, S is the entropy per unit mass, and ΔT is the temperature difference). A non-zero Δφ results in a superfluid current, I(Δφ), through the aperture. If I(Δφ) is periodic for 2π, a constant Δµ causes current to oscillate through the aperture at the Josephson frequency fj=Δµ/h. The periodicity in I(Δφ) can occur if the aperture acts like an ideal weak link3,5, in which case I(Δφ)∝sin(Δφ), or by the generation of 2π phase slips6, in which case I(Δφ) is expected to follow a sawtooth waveform.

The experimental set-up is shown in Fig. 1a (for methods, see supplementary information). We used an electrostatically driven diaphragm2 to apply an initial pressure step between two baths of superfluid separated by an aperture array. The array consisted of 65×65 nominally 70-nm apertures spaced on a 3-µm square lattice in a 50-nm-thick silicon nitride membrane. After the pressure step, fluid flowed through the array and the chemical-potential difference relaxed to zero. When the output of a diaphragm position sensor, which monitored fluid flow, was connected to a set of headphones, we heard a clear whistling sound that passed from high to low frequency (audio recording in supplementary information).

Figure 1: Quantum oscillations in 4He.
figure 1

a, Experimental cell (see supplementary information for details). b, Whistle frequency plotted against the initial pressure, ΔP0=ρΔµ0/m4. Temperature is in the range where, if Tλ is the superfluid transition temperature, Tλ−T is 1.7−2.9 mK. A fit (solid line) to the data gives a slope of 78 Hz mPa−1 , with a systematic uncertainty of 20% arising from our pressure calibration. This agrees with the Josephson frequency relation fj=Δµ/h value of 68.7 Hz mPa−1. The oscillation is still present down to at least 150 mK below Tλ, where the healing length is much smaller than the aperture diameter and I(Δφ) is linear. The oscillation is presumably due to periodic 2π phase slips.

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By using Fourier transform methods, we extracted the frequency and amplitude of this whistle as a function of time throughout the transient. Immediately after the pressure step is applied, the temperatures on either side of the aperture array are equal and the entire Δµ is determined by the initial pressure head, ΔP0. Figure 1b shows that the initial frequency is proportional to the initial chemical-potential difference. The slope of the line agrees, within the systematic error of our pressure calibration, with the Josephson frequency formula (fj=m4ΔP0/ρh).

Oscillations resulting from 2π phase slips are expected to have a velocity amplitude κ/2l, where κ=h/m4 is the circulation quantum and l is an effective length for one aperture7. If, in addition, the oscillation in each of the N apertures occurs coherently, the amplitude of the diaphragm-displacement Fourier component at fj is

where A is the area of the diaphragm, a is the area of a single aperture, and ρs is the superfluid density. The factor α would be 2/π for a sawtooth waveform, or unity for a sinusoid of the same peak amplitude. We find α≈0.6, independent of temperature in the range where, if Tλ is the superfluid transition temperature, Tλ−T is between 1.7 and 2.9 mK.

We conclude that the oscillation is a coherent phenomenon involving all the apertures in the array, and is possibly sawtooth in waveform. This coherence is remarkable, because earlier work using a single aperture showed that thermal fluctuations in the phase-slip nucleation process destroy time coherence in the rate of phase slippage, so that no Josephson oscillation exists8. However, it seems that thermal fluctuations are suppressed for an array — an observation that calls for further investigation9.

We have found that superfluid 4He in an array of small apertures behaves quantum coherently, oscillating at the Josephson frequency. Because these oscillations appear in 4He at a temperature 2,000 times higher than in superfluid 3He, it may be possible to build sensitive rotation sensors using much simpler technology than previously believed10,11,12,13. This could find application in rotational seismology, geodesy and tests of general relativity.