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arXiv:2508.04398 · Physical Review A

Anomalous Doppler effect in two-component Bose-Einstein condensates

Tomasz Zawiślak, S. Stringari, Alessio Recati

Published Nov 12, 2025• 0 citations
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Abstract

We show that two-component Bose-Einstein condensed mixtures, in presence of a persistent current, exhibit a nontrivial Doppler shift of the sound velocities. The peculiarity is due to the interspecies interaction and the possibility of generating a counterflow persistent current. Analytical predictions are derived using superfluid hydrodynamics. While the existence of anomalous Doppler shifts at finite temperature has been discussed a long time ago in the case of superfluid $^{4}\mathrm{He}$, an experimental verification of the effect is still missing. For this reason, we also propose a protocol for the measurement of the Doppler shifts, based on the density-density response function. The dynamical protocol is simulated by means of coupled Gross-Pitaevskii equations.

DOI
10.1103/yc6t-13d4

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We show that two-component Bose-Einstein condensed mixtures, in presence of a persistent current, exhibit a nontrivial Doppler shift of the sound velocities. The peculiarity is due to the interspecies interaction and the possibility of generating a counterflow persistent current. Analytical predictions are derived using superfluid hydrodynamics. While the existence of anomalous Doppler shifts at finite temperature has been discussed a long time ago in the case of superfluid 4He^{4}\mathrm{He}4He, an experimental verification of the effect is still missing. For this reason, we also propose a protocol for the measurement of the Doppler shifts, based on the density-density response function. The dynamical protocol is simulated by means of coupled Gross-Pitaevskii equations.
By employing the formalism of hydrodynamics, we derive novel analytic predictions for the Doppler effect in superfluids with broken Galilean invariance and hosting persistent currents at zero temperature. We consider two scenarios: when Galilean invariance is broken explicitly (by external potentials) and spontaneously, as it happens in a supersolid. In the former case, the presence of a stationary current affects the propagation of sound via an anomalous Doppler term proportional to the density derivative of the superfluid fraction. In supersolids, where, according to Goldstone theorem, distinct sounds of hybrid superfluid and crystal nature can propagate, the Doppler effect can be very different for each sound. Quantitative estimates of the Doppler shifts are obtained for Bose-Einstein condensed atomic gases, described by Gross-Pitaevskii theory. The estimates are obtained both calculating the thermodynamic parameters entering the hydrodynamic results and from full time-dependent simulations.
Abstract. The creation and propagation of sound waves in two-component Bose-Einstein condensates (BEC) are investigated and a new method of wave generation in binary BEC mixtures is proposed. The method is based on a fast change of the interspecies interaction constant and is illustrated for two experimental settings: a drop-like condensate immersed into a second large repulsive condensate, and a binary mixture of two homogeneous repulsive BEC’s. A mathematical model based on the linearized coupled Gross-Pitaevskii equations is developed and explicit formulae for the space and time dependence of sound waves are provided. Comparison of the analytical and numerical results shows excellent agreement, confirming the validity of the proposed approach. PACS numbers: 03.75.Kk Submitted to: J. Phys. B: At. Mol. Phys. Matter sound waves in two-component Bose-Einstein condensates 2 1.
Superfluid and dissipative regimes in the dynamics of a two-component quasi-one-dimensional Bose–Einstein condensate (BEC) with unequal atom numbers in the two components have been explored. The system supports localized waves of the symbiotic type owing to the same-species repulsion and cross-species attraction. The minority BEC component moves through the majority component and creates excitations. To quantify the emerging excitations, we introduce a time-dependent function called disturbance. Through numerical simulations of the coupled Gross–Pitaevskii equations with periodic boundary conditions, we have identified a critical velocity of the localized wave, above which a transition from the superfluid to dissipative regime occurs, as evidenced by a sharp increase in the disturbance function. The factors responsible for the discrepancy between the actual critical velocity and the speed of sound, expected from theoretical arguments, have been discussed.
We study the dynamics of two-component atomic Bose gases initially in a mixture encountering a sudden quench of the interspecies interactions. The dynamics above the critical temperature Tc{T}_{c}Tc​ is studied using a leading-order large-NNN approximation that predicted a phase transition from mixing to phase separation as a function of the interspecies coupling. Here, we explore the dynamics of this phase transition following a quench and compare our results to those found at zero temperature using the time-dependent Gross-Pitaevskii equations which ignore quantum and thermal fluctuations. In the regime above Tc{T}_{c}Tc​ where no condensate is present, however, the time evolution of the densities following the quench exhibits features similar to those found at zero temperature where only the condensates contribute to the densities. When the interspecies interaction jumps above the critical value, we observe dynamical transitions from a homogeneous mixture to a phase-separated structure for both cases. Our simulations suggest that at temperatures above Tc{T}_{c}Tc​ where no condensate is present this dynamical transition should still be observable in experiments.
The Doppler effect, the shift in the frequency of sound due to motion, is present in both classical gases and quantum superfluids. Here, we perform an in situ , minimally destructive measurement, of the persistent current in a ring-shaped, superfluid Bose–Einstein condensate using the Doppler effect. Phonon modes generated in this condensate have their frequencies Doppler shifted by a persistent current. This frequency shift will cause a standing-wave phonon mode to be 'dragged' along with the persistent current. By measuring this precession, one can extract the background flow velocity. This technique will find utility in experiments where the winding number is important, such as in emerging 'atomtronic' devices.
We study a mixture of two superfluids with density–density and current–current (Andreev–Bashkin) interspecies interactions. The Andreev–Bashkin coupling gives rise to a dissipationless drag (or entrainment) between the two superfluids. Within the quantum hydrodynamics approximation, we study the relations between speeds of sound, susceptibilities and static structure factors, in a generic model in which the density and spin dynamics decouple. Due to translational invariance, the density channel does not feel the drag. The spin channel, instead, does not satisfy the usual Bijl–Feynman relation, since the f-sum rule is not exhausted by the spin phonons. The very same effect on one dimensional Bose mixtures and their Luttinger liquid description is analysed within perturbation theory. Using diffusion quantum Monte Carlo simulations of a system of dipolar gases in a double layer configuration, we confirm the general results. Given the recent advances in measuring the counterflow instability, we also study the effect of the entrainment on the dynamical stability of a superfluid mixture with non-zero relative velocity.