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Sound emission and annihilations in a programmable quantum vortex collider

Abstract

In quantum fluids, the quantization of circulation forbids the diffusion of a vortex swirling flow seen in classical viscous fluids. Yet, accelerating quantum vortices may lose their energy into acoustic radiations1,2, similar to the way electric charges decelerate on emitting photons. The dissipation of vortex energy underlies central problems in quantum hydrodynamics3, such as the decay of quantum turbulence, highly relevant to systems as varied as neutron stars, superfluid helium and atomic condensates4,5. A deep understanding of the elementary mechanisms behind irreversible vortex dynamics has been a goal for decades3,6, but it is complicated by the shortage of conclusive experimental signatures7. Here we address this challenge by realizing a programmable vortex collider in a planar, homogeneous atomic Fermi superfluid with tunable inter-particle interactions. We create on-demand vortex configurations and monitor their evolution, taking advantage of the accessible time and length scales of ultracold Fermi gases8,9. Engineering collisions within and between vortex–antivortex pairs allows us to decouple relaxation of the vortex energy due to sound emission and that due to interactions with normal fluid (that is, mutual friction). We directly visualize how the annihilation of vortex dipoles radiates a sound pulse. Further, our few-vortex experiments extending across different superfluid regimes reveal non-universal dissipative dynamics, suggesting that fermionic quasiparticles localized inside the vortex core contribute significantly to dissipation, thereby opening the route to exploring new pathways for quantum turbulence decay, vortex by vortex.

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Fig. 1: Deterministic generation and frictional dissipation of single vortex dipoles.
Fig. 2: Arbitrary vortex collisions on demand.
Fig. 3: Dissipation and annihilation in two-dipole collisions.
Fig. 4: Direct observation of the sound emission from dipole–dipole annihilation events.

Data availability

The data that support the figures within this paper are available from the corresponding author upon reasonable request.

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Acknowledgements

We thank C. F. Barenghi, A. Bulgac, P. Magierski, F. Marino, M. McNeil Forbes, N. P. Proukakis, G. Wlazłowski and the Quantum Gases group at LENS for fruitful discussions, and N. Cooper for careful reading of the manuscript. This work was supported by the European Research Council under grant agreement no. 307032, the EPSRC under grant no. EP/R005192/1, the Italian Ministry of University and Research under the PRIN2017 project CEnTraL, and the EU’s Horizon 2020 research and innovation programme under Marie Skłodowska-Curie grant agreement no. 843303.

Author information

Authors and Affiliations

Authors

Contributions

W.J.K., G.D.P., F.S. and G.R. conceived the study. W.J.K., G.D.P., A.M.F. and F.S. performed the experiments. W.J.K. and G.D.P. analysed the experimental data. K.X. and L.G. carried out numerical simulations. All authors contributed to the interpretation of the results and to the writing of the manuscript.

Corresponding author

Correspondence to W. J. Kwon.

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Competing interests

The authors declare no competing interests.

Additional information

Extended data

is available for this paper at https://doi.org/10.1038/s41586-021-04047-4.

Peer review information Nature thanks Ashton Bradley, Maren Mossman, Davide Proment and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Fig. 1. In situ profiles of homogeneous sample and an individual vortex.

a, In-plane density profile of a UFG sample from a single experimental shot, along with centred vertical and horizontal cuts averaged over 15 different experimental realizations. b, In situ vortex profile (inset) and its integrated radial profile (symbols) in a BEC sample. The image consists of the average of 10 experimental realisations. The measured radial profile is fitted with a Lorentzian function (solid line), yielding a width of 0.87(6) µm. This matches the expected value ξ 0.68 µm, once the optical resolution of the imaging system is taken into account (see text).

Extended Data Fig. 2 Orbiting motion of a large vortex dipole in UFGs.

a, A single dipole of d ≈ 12 µm orbiting the homogeneous unitary Fermi gas of radius R = 45 µm. It rectilinearly crosses the cloud and then orbits it immediately adjacent to the boundary, in stark contrast to the observation of a vortex dipole shrinking and expanding during its propagation in a harmonic trap due to density inhomogeneity37. Each image is a single experimental shot. b, A trajectory obtained from the identical realisations of a. The hold time t varies from 0 to 500 ms with time intervals of 50 ms. The light red × signs (blue +) indicate single realisations of each vortex (antivortex) for the given t. The red (blue) circles represent the averaged positions of the vortices (antivortices) at the given t. Error bars indicate standard deviation over about 20 experimental measurements. After one orbit 500 − 550 ms, a survival probability of a vortex dipole decreases below 50%, probably due to interaction with the boundary.

Extended Data Fig. 3 Decay of short vortex dipoles due to self-annihilation in UFG and BCS regimes.

The dipole half-life τ for each initial d12, i.e. the time required for Nvd to drop to half of its initial value, is determined by fitting Nvd(t) with a sigmoid function 1/(1+e(tτ)), where the γ is used as the measurement uncertainty. The only exception is the shortest dipole shown in the BCS regime, which is fitted with an exponential function. The initial d12 is controlled to range from 3.4 to 6 µm (lighter colours denotes shorter dipoles). See also Fig. 1f. Error bars show the standard error of the mean over 40 experimental realisations.

Extended Data Fig. 4 Time evolution of the number of vortex dipoles Nvd during dipole-dipole collisions.

Examples of Nvd(t) for head-on (120°) collisions are shown as orange (purple) symbols in (a) BEC, (b) UFG, and (c) BCS superfluids. Each data point consists of 40 − 60 same experimental realisations and the error bar indicates the standard error of the mean. Data sets are part of those for which Pa is shown in Fig. 3f-h of the main text, and specifically: (a) din 5ξ, (b) din 16/kF, and (c) din 18/kF (head-on) and din 24/kF (120°). Shaded regions mark the time interval of vortex partner-exchange during a collision, estimated via DPV model imposing the condition 0.9 < d13(t)/d12(t) < 1.1. The drop of Nvd(t) approximately matches this interval, confirming that the observed annihilations do not stem from single-dipole self-annihilations, but are an outcome of the collision dynamics. Experimental images show typical examples of a partial annihilation for a 120° collisions (b) and a rarely observed annihilation from head-on collisions in BCS superfluids (c). Images consist of single independent experimental shots.

Extended Data Fig. 5 Vortex annihilation images for BECs and UFGs.

Additional images display the clear emission of a density excitation following vortex annihilations in head-on collisions for (a) BECs and (b) UFGs. Two vortex dipoles collide horizontally as in Fig. 4 of the main text. The images in first and second rows of (a) are obtained independently with the same experimental parameters as in Fig. 4. By measuring the ring sizes of the density pulses observed in BECs (t = 9 ms and t = 12 ms), we find that the propagation speed of the density pulse is around 4.4(3) mm/s which coincides with the speed of sound evaluated from the mean density along the tight z-direction of the cloud. Annihilation images observed in UFGs are in general not as clear as in BECs, yet a number of images showing small-amplitude density waves propagating outwards are detected. Each shot is acquired in an independent experimental realisation.

Extended Data Fig. 6 Numerical criterion for selecting the vortex interaction period.

The temporal evolution of the direction β of the velocity of vortex 1 (cf. inset) is displayed for a head-on collision with din = 4.63ξ. The shaded area indicates the interaction interval [t1, t2] during which the the dipole-dipole interaction takes place, with t1 being the last time instant where β ≈ 0° and t2 the first instant where β ≈ 90°. Inset: trajectories of the four vortices in the head-on collision. The dashed blue rectangle denotes the interaction region [t1, t2].

Extended Data Fig. 7 Time evolution of the compressible kinetic energy \({{\boldsymbol{E}}}_{{\rm{k}}}^{{\rm{c}}}\) for the head-on collision and din = 4.43ξ.

The vertical dashed lines indicate times t1 and t2, edges of the interaction interval. The increase of the compressible kinetic energy shown in Fig. 3c (inset) in the main paper is defined as \(\Delta {E}_{{\rm{k}}}^{{\rm{c}}}={E}_{{\rm{k}}}^{{\rm{c}},{\text{t}}_{2}}-{E}_{{\rm{k}}}^{{\rm{c}},{\text{t}}_{1}}\). More in detail, the initial \({E}_{{\rm{k}}}^{{\rm{c}},{\text{t}}_{1}}\) and the final \({E}_{{\rm{k}}}^{{\rm{c}},{\text{t}}_{2}}\) values of the compressible energy are extracted by computing an average value on a time interval of width δt centred at t1 and t2, respectively. This is a characteristic time interval defined as δt = din/vd corresponding to the shaded areas in the plot, where vd = ħ/Mdin is the vortex dipole velocity.

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Kwon, W.J., Del Pace, G., Xhani, K. et al. Sound emission and annihilations in a programmable quantum vortex collider. Nature 600, 64–69 (2021). https://doi.org/10.1038/s41586-021-04047-4

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