Chiral cavity-induced quantum phase transitions in a quantum ring

TL;DR

The paper demonstrates a gyrotropic-cavity–induced quantum phase transition in a quantum ring, where vacuum fluctuations of the two circularly polarized cavity modes generate an Aharonov-Bohm–like step change in the ground-state current as the light–matter coupling grows in the ultrastrong regime. A dimensionless, angular-momentum–resolved Hamiltonian is derived, revealing block structure labeled by total angular momentum $j$ and a critical coupling $g_{0}^{\star}$ for transitions from $j=0$ to $j=\pm1$. Finite-temperature effects and driven-dissipative dynamics are analyzed, showing signatures in emitted light such as a discontinuity in the second-order autocorrelation $g_{2}(0)$ at the level crossing, making the transition experimentally accessible via spectroscopy and photon statistics. These results point to vacuum-fluctuation–driven topological-like transitions and provide a potential pathway for cavity-assisted material engineering in the ultrastrong coupling regime.

Abstract

We consider a quantum ring placed in a gyrotropic cavity characterized by the energy splitting between the left and right circularly polarized modes. We show that despite the absence of constant magnetic field penetrating through the ring, in the regime of the ultrastrong light matter coupling, the total current in the ground state changes discontinuously with the light matter coupling in the direct analogy with the Aharonov-Bohm ring. We consider the driven-dissipative of the system and show that the discontinuous change of the total angular momentum can be directly probed via the spectral and statical properties of the radiation emitted by the system under weak coherent drive.

Figures (6)

• Figure 1: One-dimensional ring of radius $R$ (red) embedded in a Fabry-Perot chiral cavity of length $D$ formed by ferromagnetic mirrors in the presence of photons (blue) with energy $\hbar\omega_{\sigma}$ and circular polarization $\sigma=\pm$ propagating in the $z$-direction.
• Figure 2: Critical light-matter coupling $g_{0}^{\star}$ at which a transition $j=0\rightarrow j=\pm1$ occurs as a function of the frequency $\omega_{\pm}$. Low values of $g_{0}^{\star}$ are obtained for large detuning, while keeping one frequency small.
• Figure 3: Ground state current $\ev{\operatorname{J}}^{(j)}$ as a function of the light-matter coupling $g_{0}$, for $\omega=5\pi/16\approx0.982$ (top) and $\omega=0.3$ (bot.) with $\sigma=+1$, for different total angular momenta $-5\le j\le 5$.
• Figure 4: Quantum phase transition in the expectation value of the angular momentum as a function of the light-matter coupling $g_{0}$ and dimensionless temperature $T$ for $\omega=5\pi/16$, $\sigma=+1$. Top: total angular momentum $\langle\hat{\mathrm{j}}\rangle$. Bottom left: photonic angular momentum $\langle\hat{\mathrm{J}}_{p}\rangle$. Bottom right: electronic angular momentum $\langle\hat{\mathrm{L}}\rangle$. The values would be inverted for $\sigma=-1$.
• Figure 5: (Upper panel): dependence of the three lowest eigenergies of the closed system on the coupling parameter $g_+$. The value of $\tilde{\omega}_+=0.2$. (Lower panel) dependence of the output intensity and second order temporal correlation function $g_2(0)$ for the open system periodically driven with frequency $\omega_p=0.2$ and corresponding field amplitude $\Omega_p=0.6$. The decay rate is $\gamma=0.1$.