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Quantum Pressure Waves in Superfluids (QPWS)

Jincheng Zhang

Published Aug 17, 2026• 0 citations
Publisher

Abstract

In conventional fluids, acoustic excitations are described by the propagation of pressure and density fluctuations obeying the linearized Euler equations. In contrast, a superfluid—being a macroscopic quantum state with zero viscosity—supports excitations that are governed by the Gross–Pitaevskii equation and exhibit a linear dispersion at low momenta. Here we propose a novel type of excitation in superfluids, which we term "quantum pressure waves" (QPWs). A QPW is a localized, solitonic modulation of the quantum pressure term that appears in the Madelung formulation of the Gross–Pitaevskii equation. Unlike ordinary sound, a QPW does not carry a classical pressure gradient but instead represents a self‑consistent rearrangement of the quantum potential that propagates without dissipation. We develop an analytic theory of QPWs, derive their dispersion relation, and discuss their stability properties. The existence of QPWs suggests a new class of quantum fluid dynamics and points toward possible experimental observation in ultracold atomic gases.

DOI
10.5281/zenodo.21973016

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In conventional fluids, acoustic excitations are described by the propagation of pressure and density fluctuations obeying the linearized Euler equations. In contrast, a superfluid—being a macroscopic quantum state with zero viscosity—supports excitations that are governed by the Gross–Pitaevskii equation and exhibit a linear dispersion at low momenta. Here we propose a novel type of excitation in superfluids, which we term "quantum pressure waves" (QPWs). A QPW is a localized, solitonic modulation of the quantum pressure term that appears in the Madelung formulation of the Gross–Pitaevskii equation. Unlike ordinary sound, a QPW does not carry a classical pressure gradient but instead represents a self‑consistent rearrangement of the quantum potential that propagates without dissipation. We develop an analytic theory of QPWs, derive their dispersion relation, and discuss their stability properties. The existence of QPWs suggests a new class of quantum fluid dynamics and points toward possible experimental observation in ultracold atomic gases.
Sound propagation in quantum droplets differs from that in conventional Bose-Einstein condensates (BECs) because of their self-bound nature and the role of quantum fluctuations. We investigate sound propagation in one-dimensional quantum droplets formed by a symmetric Bose-Bose mixture, focusing on finite-size and confinement effects. Using the extended Gross-Pitaevskii equation, we extract the sound velocity from the real-time propagation of localized density perturbations and compare it with the low-energy excitation spectrum. We find that, unlike in a conventional BEC, the sound velocity of a finite droplet is strongly affected by its density profile and quantum-pressure contribution. It decreases with increasing particle number as the droplet evolves from a Gaussian-like to a flat-top profile, approaching the bulk quantum-droplet value. In contrast, external harmonic confinement compresses the droplet and enhances the sound velocity, driving the system toward the acoustic behavior of a trapped BEC. Our results establish sound propagation as a sensitive probe of finite-size effects and the crossover between self-bound quantum droplets and conventional Bose gases, and suggest a feasible route for experimental observation in ultracold 39^{39}39K droplets.
The concept of pressure in quantum fluids has traditionally been treated as a static scalar quantity derived from macroscopic equations of state. In this work we introduce a dynamic, frequency-resolved pressure field P(ω) that captures the intrinsic oscillatory stresses within a quantum liquid. This Quantum Liquid Pressure Spectrum (QLPS) framework derives from the fundamental commutation relations of the field operators and the continuity equation for mass and momentum. We present a systematic derivation of P(ω), illustrate its dependence on the excitation spectrum, and discuss its implications for superfluid helium, ultracold Fermi gases, and potential applications in quantum sensing and precision metrology. The QLPS concept reveals a previously inaccessible quantum variable that may provide a new handle on the collective excitations and phase transitions in strongly correlated quantum fluids, offering a pathway toward novel quantum technologies and a deeper understanding of quantum many-body physics.
The concept of pressure in quantum fluids has traditionally been treated as a static scalar quantity derived from macroscopic equations of state. In this work we introduce a dynamic, frequency-resolved pressure field P(ω) that captures the intrinsic oscillatory stresses within a quantum liquid. This Quantum Liquid Pressure Spectrum (QLPS) framework derives from the fundamental commutation relations of the field operators and the continuity equation for mass and momentum. We present a systematic derivation of P(ω), illustrate its dependence on the excitation spectrum, and discuss its implications for superfluid helium, ultracold Fermi gases, and potential applications in quantum sensing and precision metrology. The QLPS concept reveals a previously inaccessible quantum variable that may provide a new handle on the collective excitations and phase transitions in strongly correlated quantum fluids, offering a pathway toward novel quantum technologies and a deeper understanding of quantum many-body physics.
In many-body quantum systems at ultra‑low temperatures, the collective behavior of particles can give rise to exotic states of matter such as superfluids and quantum liquids. These states exhibit macroscopic quantum coherence and support topological excitations, yet their internal mechanical response has traditionally been described only by local thermodynamic variables such as pressure, density, and temperature. In this work we introduce the concept of a topological pressure field, denoted PT(x)P_T(x)PT​(x), which captures the influence of non‑trivial topological order on the local mechanical pressure within a quantum liquid. The proposed field is derived from a gauge‑invariant formulation of the quantum stress tensor that incorporates Berry curvature and Chern‑Simons terms. We show that PT(x)P_T(x)PT​(x) is non‑zero only in regions where the quantum state hosts topological defects such as quantized vortices or skyrmion‑like textures. Using a simplified model of a two‑dimensional superfluid film, we calculate the spatial profile of PT(x)P_T(x)PT​(x) around a vortex core and predict measurable deviations from the classical pressure distribution. The existence of PT(x)P_T(x)PT​(x) implies that quantum liquids possess an additional mechanical degree of freedom that is purely topological. This insight opens a pathway to experimentally detect topological pressure via precision pressure sensors in superfluid helium or cold‑atom Bose‑Einstein condensates, and suggests new avenues for engineering quantum fluid devices that exploit topological mechanics.
Superfluidity describes the ability of quantum matter to flow without friction. Due to its fundamental role in many transport phenomena, it is crucial to understand the robustness of superfluid properties to external perturbations. Here, we theoretically study the effects of speckle disorder on the propagation of sound waves in a two-dimensional Bose-Einstein condensate at zero temperature. We numerically solve the Gross-Pitaevskii equation in the presence of disorder and employ a superfluid hydrodynamic approach to elucidate the role of the compressibility and superfluid fraction in the propagation of sound. A key result is that disorder reduces the superfluid fraction and hence the speed of sound; it also introduces damping and mode coupling. In the limit of weak disorder, the predictions for the speed of sound and its damping rate are well reproduced by a quadratic perturbation theory. The hydrodynamic description is valid over a wide range of parameters, while discrepancies become evident if the disorder becomes too strong, the effect being more significant for disorder applied in only one spatial direction. Our predictions are well within the reach of state-of-the-art cold-atom experiments and carry over to more general disorder potentials.
Superfluidity is a macroscopic quantum phenomenon, which shows up below a critical temperature and leads to a peculiar behavior of matter, with frictionless flow, the formation of quantized vortices, and the quenching of the moment of inertia being intriguing examples. A remarkable explanation for many phenomena exhibited by a superfluid at finite temperature can be given in terms of a two-fluid mixture comprised of a normal component that behaves like a usual fluid and a superfluid component with zero viscosity and zero entropy. Important examples of superfluid systems are liquid helium and neutron stars. More recently, ultracold atomic gases have emerged as new superfluid systems with unprecedented possibilities to control interactions and external confinement. Here we report the first observation of `second sound' in an ultracold Fermi gas with resonant interactions. Second sound is a striking manifestation of the two-component nature of a superfluid and corresponds to an entropy wave, where the superfluid and the non-superfluid components oscillate in opposite phase, different from ordinary sound (`first sound'), where they oscillate in phase. The speed of second sound depends explicitly on the value of the superfluid fraction, a quantity sensitive to the spectrum of elementary excitations. Our measurements allow us to extract the temperature dependence of the superfluid fraction, which in strongly interacting quantum gases has been an inaccessible quantity so far.