Multiply quantized vortex spectroscopy in a quantum fluid of light

Abstract

The formation of quantized vortices is a unifying feature of quantum mechanical systems, making it a premier means for fundamental and comparative studies of different quantum fluids. Being excited states of motion, vortices are normally unstable towards relaxation into lower energy states. However, here we exploit the driven-dissipative nature of polaritonic fluids of light to create stationary, multiply charged vortices. We measure the spectrum of collective excitations and observe negative energy modes at the core and positive energy modes at large radii. Their coexistence at the same frequency normally causes the dynamical instability, but here intrinsic losses stabilize the system, allowing for phase pinning by the pump on macroscopic scales. We observe generic features of quantized vortices in quantum fluids and other rotating geometries like astrophysical compact objects, opening the way to the study of generic amplification phenomena.

Figures (3)

• Figure 1: MQV generation and mean-field measurements. (a) Schematic of the experimental setup. A continuous-wave laser with a helical wavefront pumps a microcavity near resonance, forming a MQV. A flat-phase reference beam, interferes with photonic signal exiting the cavity, allowing the full polariton field reconstruction by OAI SM. (b), (c) Amplitude and phase of the polariton field. (d) Azimuthally averaged velocity components $v_r$ (green), $v_\theta$ (orange) and $\sqrt{\hbar gn/m^{\star}}$ (blue). Shaded areas represent one standard deviation over the azimuthal angle. The black dashed line at $5µm$ marks the approximate lower bound for the validity of the azimuthal average (inside that radius, the SQVs make the profile highly inhomogeneous azimuthally). Vertical dashed purple lines: radii at which the Bogoliubov spectrum is shown in Fig. \ref{['fig:w_m_disp']}.
• Figure 2: Spatially resolved Bogoliubov spectrum. (a)- (d) WKB spectrum $\hbar\omega_\mathrm{B}$ at $r = 6$, $9$, $18$, and $27µm$. Solid line, $p=0$ mode; shaded area, $|p|>0$ modes. (e) - (h) $(\hbar\omega, m)$ probe transmission intensity normalized radius by radius at $r = 6$, $9$, $18$, and $27µm$, plotted in dashed purple lines in Fig. \ref{['fig:mean_field']} (d). For a given $r$, each pixel value is obtained by summing the squared probe amplitude over the interval $[r - 3µm, r + 3µm]$. (i)-(k) Normalized probe amplitude for $m=-8$ at three different $\hbar\omega$ with correspondingly color-coded star labels in the inset of (g).
• Figure 3: Effective potential model. (a) $(\hbar\omega$--$r)$ probe transmission intensity for $m = -4$. (b) Focus on the core modes. Right, integrated transmission for $r < 20~\mu\mathrm{m}$; bottom, azimuthally averaged probe intensity of the $p_0$ (red) and $p_1$ (blue) modes. Note that the $p_0$ mode saturates the detector for $r < 6µm$; these data points exceed 1 in arbitrary units and are omitted. (c) - (d) Rescaled density of the $p_1$ and $p_0$ modes for $m=-4$. (e)- (m) $(\hbar\omega$--$r)$ probe transmission intensity for different $m\in[-12,6]$ (common color scale). White line, azimuthal average of $\mathrm{min}\{\hbar\omega_B^+\}$, corresponding to $V_m(r)$\ref{['eq:eff_pot']}; shaded area, one standard deviation. Note that panels (h) - (j) are saturated under the chosen color scale to capture all features of interest.