A matter-wave Fabry-Pérot cavity in the ultrastrong driving regime

TL;DR

The paper addresses realizing horizon-like dynamics in ultrastrongly driven cavities by swapping light and matter to create a matter-wave analogue with quasi-relativistic dispersion in an optical lattice between moving light barriers. Using a conformal map to a static cavity and a one-cycle Floquet map f, the authors observe stable and unstable fixed-point trajectories that behave like white-hole and black-hole horizons, with higher-order resonances producing multiple fixed points and phase-controlled reversals of horizon roles. Dispersion-curvature effects explain deviations from the ideal photon theory, and phase jumps enable stroboscopic time reversal, suggesting applications to pulse generation and signal processing in electro-optic platforms. Overall, the work establishes a versatile platform for exploring dynamical Casimir physics and analogue gravity phenomena in a controllable matter-wave system with potential technological implications.

Abstract

When the length of an optical cavity is modulated, theory predicts exponential concentration of energy around particular space-time trajectories. Viewed stroboscopically, photons in such a driven cavity propagate as if in a curved spacetime, with black hole and white hole event horizons corresponding to unstable and stable fixed points of the evolution. Such phenomena have resisted direct experimental realization due to the difficulty of relativistically accelerating massive cavity mirrors. We report results of an experiment which overcomes this limitation by exchanging the roles of light and matter. A matter wave endowed with quasi-relativistic dispersion is confined between two barriers made of light, one of which is periodically translated at speeds comparable to the matter wave group velocity. In this strongly-modulated cavity we observe the emergence of the predicted bright and dark fixed point trajectories, and demonstrate that changing the modulation waveform can vary the number of fixed points and exchange their stability character. We observe signatures of nontrivial dynamics beyond those predicted for photons, and attribute them to residual curvature in the dispersion relation. In addition to experimentally realizing and characterizing cavity dynamics in the ultra-strong driving regime, these results point the way to implementations of related dynamics in electro-optic materials, with potential applications in pulse generation and signal compression.

Figures (10)

• Figure 1: Emergence of stable fixed point trajectory. (a) The discrete Floquet map $f(x)$ of a cavity driven at the fundamental (light blue) and second-order (dark blue) resonances exhibits stable ($f'(x)<1$) and unstable ($f'(x)>1$) fixed points at the intersections with $f(x)=x$ (gray dashed). (b) Matter waves in the $D$ band of an optical lattice exhibit approximately linear (photonic) dispersion. (c) Lattice-trapped atoms between repulsive light sheets simulate a driven optical cavity. (d) Evolution of an initially diffuse atomic distribution in a static (top) and driven (bottom) cavity demonstrates drive-induced emergence of the stable fixed point trajectory.
• Figure 2: Convergence of Various Initial Conditions to the Stable Fixed Point Trajectory. (a) Absorption images of atomic density in the cavity over $80\,\mathrm{ms}$ for different modulation phases $\phi$, averaged over 3 repeats. The resulting trajectories are offset by $T/12$ to line up the boundary modulation and effectively scan initial position. Gray vertical lines indicate times at which the atoms' trajectory in a static cavity reflects from the upper wall, as extracted from a triangle fit. At early times, the offset trajectories are all out of phase with one another, but after several cycles of boundary modulation, they rephase. (b) The same temporally-offset absorption images overlaid on one another. An effectively uniform sampling of initial conditions coalesces onto the stable fixed point trajectory (red triangle wave) and is repelled from the unstable one (blue triangle wave) when subject to boundary modulation on the bottom wall.
• Figure 3: Stroboscopic Motion toward an Event Horizon. (a) Normalized atomic density imaged at the frequency of the boundary modulation for a range of initial conditions (modulation phases $\phi$) and averaged over 3 repeats. The red (black) dashed lines indicate the predicted (un)stable fixed points of the Floquet map. (b) Numerical simulation of a massive wavepacket initialized in the $2^\mathrm{nd}$ excited Bloch band subject to the same parameters as the experiment and to a Gaussian blur corresponding to the experimental imaging resolution. (c) Numerical simulation of $d$-band fraction. The boundary modulation imparts enough energy to the wavepacket to excite it into higher bands of the optical lattice, whose group velocities are no longer resonant with the drive (see Supplementary Information).
• Figure 4: Emergence of Multiple Stable Fixed Point Trajectories from Higher-Order Cavity Resonances. (Top) Modulating the boundary of the cavity at twice the fundamental frequency results in two stable fixed point trajectories at late times. (Bottom) Fitting the density distributions to two doubly-reflected Gaussian distributions recovers the expected $\pi$ phase difference between the two trajectories. Shaded region is one standard deviation width of the atomic cloud.
• Figure 5: Stroboscopic Time Reversal. (a) The modulation waveform $\Delta L=AL_0\cos(\Omega t-\phi(t))$ with a sharp phase step of $\pi$ after four complete drive cycles and a modulation depth $A=2.9\times10^{-2}$. (b) An atomic wavepacket initialized at the unstable fixed point initially evolves toward the stable one, but once the stable and unstable fixed points switch roles, it returns to its original trajectory. (c) Sampling stroboscopically at approximately the drive period, the wavepacket moves from one fixed point to the other and back again.