Fluctuation-induced symmetry breaking in high harmonic generation for bicircular quantum light

Abstract

Symmetries are ubiquitous in physics and play a pivotal role in light-matter interactions, where they determine the selection rules governing allowed atomic transitions and define the associated conserved quantities. For the up-conversion process of high harmonic generation, the symmetries of the driving field determine the allowed frequencies and the polarization properties of the resulting harmonics. As a consequence, it is possible to establish classical selection rules when the process is driven by coherent radiation. In this work, we show that fluctuation-induced symmetry breaking in the driving field leads to the appearance of otherwise forbidden harmonics. This is achieved by considering bicircular quantum light, and demonstrate that the enhanced quantum fluctuations due to squeezing in the driving field break the classical selection rules. To this end, we develop a quantum optical description of the dynamical symmetries in the process of high harmonic generation, revealing corrections to the classical selection rules. Moreover, we show that the new harmonics show squeezing-like signatures in their photon statistics, allowing them to be clearly distinguished from classical thermal fluctuations.

The paper asks how quantum fluctuations modify dynamical-symmetry selection rules in high-harmonic generation (HHG). For an isotropic medium driven by counter-rotating coherent fields at $\omega$ and $2\omega$, threefold dynamical symmetry permits only $q=3n\pm1$, with alternating helicity. The configuration studied adds squeezing to one linearly polarized component of a driving mode while preserving the bicircular mean field. A quantum-optical description of polarization rotations and time translations shows that the squeezed field’s variance does not retain the mean field’s symmetry. Under strong-field, low-depletion approximations, each harmonic is represented as a Husimi-weighted mixture of coherent states whose amplitudes follow from semiclassical dipole responses. Calculations for hydrogen at $\omega=0.057$ a.u. and coherent field amplitudes $E_0=0.037$ a.u. predict emission at previously forbidden orders $q=3n$, plus opposite-helicity contributions at classically allowed orders. Photon-exchange arguments incorporating both helicities of the squeezed linear component explain the additional channels. For weak symmetry-breaking responses that scale linearly with the fluctuating amplitude, strongly squeezed driving yields $g^{(2)}(0)\approx3$ in fluctuation-induced channels, versus approximately $2$ for the thermal comparison; native allowed channels remain approximately Poissonian. These values change when stronger fluctuations probe nonlinear response. The supplement explicitly identifies individual harmonic states as classical coherent-state mixtures, despite their squeezing-like intensity statistics. The treatment assumes dipole coupling, a single active electron, ground-state return, negligible dipole correlations, and a single-atom response. Extensions to other media and the full quantum-state implications remain open.