Superradiant phononic emission from the analog spin ergoregion in a two-component Bose-Einstein condensate

TL;DR

This work uses an analog gravity framework to analyze ergoregion instabilities in rotating, two-component Bose-Einstein condensates with a vortex. By separating excitations into density and spin branches and exploiting a finite coherent coupling, the authors reveal both core-localized and extended spin-mode instabilities, including robust superradiant-like emission when spin ergoregions extend far from the vortex core. The study combines local-density reasoning, Bogoliubov spectra analysis, and 2D Gross-Pitaevskii simulations to identify parameter regimes where long-wavelength spin modes drive the instability, offering a clear path to experimental realization in atomic and photonic two-component fluids. Overall, the results establish two-component BECs as versatile analog models for rotating spacetime dynamics and invite future exploration of nonlinear saturation and quantum correlations in superradiant phonon emission.

Abstract

We make use of an analog gravity perspective to obtain a physical understanding of hydrodynamic instabilities stemming from the presence of quantized vortices in two-component atomic condensates and of their relation to ergoregion instabilities of rotating massive objects in gravitation. In addition to the localized instabilities related to vortex splitting, configurations displaying dynamically unstable modes that extend well outside the vortex core are found. In this case, the superradiant scattering process involves phonon emission into the much wider ergoregion of spin modes, so the physics most closely resembles the one of rotating massive objects. Our results confirm the potential of two-component condensates as analog models of rotating space-times in different regimes of gravitational interest.

Figures (9)

• Figure 1: Comparison between the density and spin sound speed (red and blue line respectively), and the flow velocity (dashed black line) in a vortex configuration. The location of the ergosurface for density (spin) excitations, indicated by the dotted red (blue) line, is found as the intersection between $|\mathbf{v}(r)|$ and $c_d(r)$ [$c_s(r)$]. All velocities are normalized to the large-distance value of the speed of density sound, $c_d^\infty \equiv c_d(r\to\infty)$. The plot is obtained using the numerically calculated density profile of a vortex of charge $L=2$; interactions are set to $g_{12}=0.93 g$, giving $c_d/c_s=\xi_s/\xi_d \sim 5.25$.
• Figure 2: Properties of the dispersion relation in the LDA \ref{['bogodispM']} (obtained with $L=2,M=1,g_{12}/g= 0.93,\Omega = 0$, $\mu_d/\mu_s = 27.5$). (a-c) Plot of the dispersion at different radii, showing the availability of positive and negative norm modes at a generic frequency $\omega$, indicated by the red horizontal line: solid (dotted) black lines refer to the upper (lower) branch. (d) Plot of the maximum frequency of the lower branch (black line) and minimum frequency of the upper branch (red line); the red (gray) area indicates the region of the plot where positive (negative) energy modes are available. The white area represents the centrifugal gap. The dashed black line indicates the spin ergosurface location, given by \ref{['ergoposition']}.
• Figure 3: Bogoliubov spectrum for $M=1$ spin excitations on top of a $L=1$ (panels a-c) or $L=2$ (panels d-f) vortex located at the center of a harmonically trapped mixture of TF radius $R=30\xi_d$. Panels (c) and (f) show, together with the radial profile of the BEC density (grey dashed line), an example of the real-space profile of the particle $|u(x)|$ (black solid line) and antiparticle $|v(x)|$ (red solid line) components of the dynamically unstable mode for $g_{12}=0.75 g$.
• Figure 4: Bogoliubov spectrum for $M=2$ (panels a-d) and $M=3$ (panels e-g) spin excitations on top of an $L=2$ vortex in a harmonically trapped mixture of TF radius $R=30\xi_d$. Two dynamical instabilities are present in the $M=2$ channel: the real-space profile of the particle (black solid line) and antiparticle (red solid line) components of these modes is shown in panels (c) and (d) for $g_{12}=0.75 g$ and $g_{12}=0.95$, respectively. The main difference between the two modes is in the localization of the antiparticle component, which dominates up to $r_- \sim 3\xi_d$ for the former, and up to $r_-\sim 14\xi_d$ for the latter; indeed, according to our LDA treatment, lower frequency modes are more extended. Remarkably, the low frequency mode is only present for $g_{12}\sim g$. The $M=3$ channel shows a single instability: an example of the real-space profile of the mode is shown in panel (g) for $g_{12}=0.81 g$.
• Figure 5: Dynamics of the vortex splitting instability. Real time evolution of a $L=1$ vortex with $R=21\xi_d$ and $g_{12}=0.8g$. For these parameters, the growth rate of the $M=1$ unstable mode, whose real-space profile is shown in panel (c), is $\Gamma/\mu \simeq 0.014$. Panels (a1-a6): total density $n = n_1+n_2$, measured in units of the peak Thomas-Fermi density $2 n_\text{TF}(r=0) = 2\mu/(g+g_{12})$. Panels (b1-b6): polarization, $Z = (n_1-n_2)/n$. Each column is computed at the time indicated by one of red dots in panel (d), which shows the temporal evolution of the standard deviation of the spin density $\delta n= n_1-n_2$ (black solid line), compared with the analytical exponential growth $\exp(\Gamma t)$ (blue dashed line).