Fluctuation amplification engineering in multimode Raman-cavity systems

TL;DR

The work addresses fluctuation engineering in multimode Raman–cavity hybrids with many Raman-active and cavity modes. Using Placzek's Raman–light coupling, a stabilized multimode Hamiltonian with a quartic photon term $g_4$ and open-system Truncated Wigner Approximation, it analyzes how photon and phonon dispersions shape fluctuations. In the flat-band limit the collective cavity fluctuations scale as $\sqrt{N}$ and Raman fluctuations are attenuated, with an effective coupling capturing this enhancement in a single-mode picture. When bands are dispersive, the study reveals nonreciprocal control and mode-specific amplification that can exceed $\sqrt{N}$ in selected modes, offering potential for quantum sensing and THz spectroscopy.

Abstract

Parametric amplification is a key ingredient of a wide range of phenomena, from the classical to the quantum domain. Although such phenomena have been demonstrated in non-equilibrium settings, their use for fluctuation engineering has been put forth in Raman-cavity hybrids only recently. In this work, we generalize fluctuation engineering to a multi-mode scenario in which multiple Raman-active modes interact nonlinearly with multiple cavity modes. We demonstrate the emergence of resonant and non-resonant collective fluctuations that can be non-reciprocally controlled by engineering the band dispersion of photons and phonons. As an example we show how Raman fluctuations can be selectively attenuated by tuning the photonic bandgap or even nonresonantly amplified, in marked contrast to the single-mode scenario. We also identify a regime in which the amplification of cavity fluctuations in a specific mode is boosted, surpassing a $\sqrt{N}$ scaling with increasing number of $N$ Raman and cavity modes. Our study reveals the key role of multi-mode interactions on fluctuations in nonlinear cavity-matter hybrids. Noise engineering through different photon and phonon dispersions, as demonstrated here, could be leveraged for the design of novel quantum sensing platforms and advanced spectroscopy in the THz regime.

Figures (7)

• Figure 1: Raman-active modes coupled to light fluctuations of a photonic crystal. (a) Sketch of a Raman-active material on top of a photonic crystal (PC). The red arrows represent an example of THz Raman-active phonon oscillations. Specifically, breathing (arrows to the left) and shearing (arrows to the right) modes that couple to light fluctuations of PC. (b) Schematic of Raman phonon dispersion (green) and the photonic crystal dispersion (magenta). (c) Vertex interaction of strength $g_{kq}/\sqrt{N}$, where one Raman mode converts to two photonic modes by conserving momentum. This process is also illustrated by arrows in (b). $N$ is the number of unit cells.
• Figure 2: Modification of the Raman and cavity field variances in each mode (different colors) as a function of the photonic band gap $\omega_0^c$. Amplification of photonic fluctuations ($\delta V(E_k)>0$) and attenuation of Raman fluctuations ($\delta V(Q_k)<0$) occur for $\omega_0^c\approx\omega_0^R/2$. Both, the phonon and photon bands are considered perfectly flat. We use $g=0.04\omega_0^R$, $\kappa=\gamma=0.02\omega_0^R$, $g_4=0.01\omega_0^R$ and $N=11$. The black lines show the results for a single-mode case with $\frac{g}{\sqrt{N}}$ coupling (thin dashed line) and with $\sqrt{N}$-times larger effective coupling $g_{\mathrm{eff}}=g$ (wide dashed line).
• Figure 3: Modification of the variance of the Raman fluctuations $\delta V(Q_k)$ (a) and variance of the photonic fluctuations $\delta V(E_k)$ (b) as a function of the photonic band gap $\omega_c^0$. The different colors indicate the six different modes with $k\ge0$ (see text). We consider a perfectly flat photon dispersion whereas the Raman dispersion is considered to be quadratic in $k$ with a bandwidth $\delta\omega_k^R=\omega_0^R$. The vertical dashed lines in (a) indicate the resonant condition $2\omega_0^c=\omega_k^R$ for the different Raman modes $k$. The rest of parameters are as in Fig. \ref{['fig:amplification']}.
• Figure 4: Same as Fig. \ref{['fig:Ramandispersion']} but considering a flat Raman dispersion and a quadratic cavity dispersion with a bandwidth $\delta\omega_c^k=\omega_0^R$ (see main text). The vertical dashed lines at $\omega_0^c=0.5\omega_0^R$ indicate the threshold above which resonances are not possible (gray zones). The horizontal dashed line in the lower panel (b) marks the maximum value of $\delta V(E_k)$ that can be obtained by considering a collective enhancement factor of $\sqrt{N}$ on the coupling, i.e. the maximum cavity fluctuation value reached in Fig. \ref{['fig:amplification']} for perfectly flat bands. Notice the different scale in the vertical axis in the lower panel compared to the vertical axes of all previous figures.
• Figure 5: Thermal cavity and Raman fluctuations. (a) Variance of the cavity field in each $k$ mode (different colors) in the presence of multiple Raman modes (solid lines). The variance of the cavity field in the absence of Raman fluctuations is shown with thin dotted lines for reference. The difference between these variances is shown in the inset. (b) Change in the variance of the Raman coordinate, in each $k$ mode, with respect to the variance of the Raman coordinate in the absence of cavity fluctuations. The difference of the variance of the Raman coordinate with respect to the variance of the cavity field in the interacting regime is shown in the inset (see text). The phonon and photon bands are considered flat and $\hbar \omega_0^R= 0.5k_B T.$ The rest of the parameters are as in Fig. \ref{['fig:amplification']}