First Observation of Bright Solitons in Bulk Superfluid He4

Abstract

The existence of bright solitons in bulk superfluid 4 He is demonstrated by time-resolved shadowgraph imaging experiments and density functional theory (DFT) calculations. The initial liquid compression that leads to the creation of non-linear waves is produced by rapidly expanding plasma from laser ablation. After the leading dissipative period, these waves transform into bright solitons, which exhibit three characteristic features: dispersionless propagation, negligible interaction in twowave collision, and direct dependence between soliton amplitude and the propagation velocity. The experimental observations are supported by DFT calculations, which show rapid evolution of the initially compressed liquid into bright solitons. At high amplitudes, solitons become unstable and break down into dispersive shock waves.PACS numbers: 67.25. D-,67.25.bf, 67.85.dt Solitons are localized non-linear waves in a medium, which do not disperse as a function of time and exhibit no interaction during a two-wave collision. After their discovery in the early eighteen hundreds, solitons have been observed in many different media, which exhibit pronounced non-linear response. In recent years, solitons have become an intense field of research due to their important applications in areas such as plasma physics, electronics, biology, and optics [1]. Mathematical description of solitons can be formulated in terms of model dependent non-linear partial differential equations (e.g., the non-linear Schrödinger equation). In general, it has been established that non-linear excitations (i.e., shock waves and solitons) exhibit distinct dependency between their amplitude and propagation velocity [1]. Solitons in thin4 He films adsorbed on solid substrates have been studied extensively by both experiments [2][3][4][5] and theory [6][7][8][9]. The film thickness is typically only a few atomic layers, which supports the propagation of third sound [10]. When the film is driven by a sufficiently large amplitude excitation, the response of the system becomes non-linear and typically follows the Kortewegde Vries (KdV) equation [4,7]. The KdV equation is known to support solitonic solutions, which has been confirmed experimentally for helium films in the previously mentioned references. Solitons have also been observed experimentally in related systems such as Bose-Einstein condensates (BEC) and 3 He (magnetic solitons) [11][12][13][14][15][16][17][18][19][20]. In the former case, experimental observations have been successfully modeled by the Gross-Pitaevskii (GP) equation [21][22][23]. However, bright solitons have not been observed in bulk superfluid 4 He up to date. Such observation would not only provide important details of the underlying non-linear response of this quantum liquid, but it would also allow for the study of soliton dynamics (including dissipation) over much longer propagation distances and times than currently possible in BECs.Studies of non-linear excitations in bulk superfluid helium are scarce. Most experiments have concentr...

Study of shock waves and solitons in bulk superfluid He4

“…As described in more detail previously, 26,29,35 our experiment uses a 355 nm laser pulse (frequency tripled Continuum Minilite-II Nd-YAG laser, 9 ns pulse length) focused down to ca. 100 µm diam.…”

“…The initial compression along the z-axis for the simulation was constructed as proposed earlier: 29,44 ρ(z, 0…”

“…The parameters entering this function are: ρ 0 the bulk density (0.0218360Å −3 at 0 K), ∆ρ the average amplitude of the initial compression, λ c = 3.58Å, and function Θ w (z) = 1 inside the spatial window of width w and zero elsewhere. 29 The latter defines the overall width of the initial layered structure, which, in the experiments, would be created by the rapidly expanding plasma. Here we have used w = 700 nm to generate the initial condition for the simulations.…”

“…26 Recently, bright solitons were finally observed in bulk superfluid 4 He, which were formed as a by-product of high-amplitude shock wave decay. 29 For solitons in BECs, the experimental observations have been successfully modeled by using the Gross-Pitaevskii (GP) theory. [30][31][32] Despite this promising success, however, the GP equation is a very poor model for more dense quantum liquids such as superfluid 4 He.…”

“…33,34 Recently, OT-DFT was also used to model soliton propagation in superfluid helium to support the experimental observations. 29 In this work, we report on the properties of shock waves and bright solitons in bulk superfluid 4 He. We provide experimental data for shock wave velocity decay, amplitudevelocity decay relationship, compare these results with OT-DFT, and finally establish the soliton limit.…”