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.

Figures (9)

• Figure 1: (a) Schematic figure of BQL leading to symmetry breaking in the field, and hence the observation of classically forbidden harmonics induced by the quantum fluctuations of the field. (b) Lissajous figures of the BQL for amplitude and phase squeezed $2 \omega$ field. The dark blue lines show the mean field value, following the dynamical symmetry, while the shaded region indicates the field fluctuations breaking the symmetry.
• Figure 2: (a), (b) HHG spectra resolved along the right- and left-circular polarization components, respectively. The black dashed lines indicate the positions of the classically allowed harmonics for each polarization component: (a) $3n-1$ and (b) $3n + 1$. (c) Helicity as a function of the squeezing intensity, with the dashed lines highlighting the classically allowed harmonics. The atomic medium is hydrogen ($I_p = 0.5$ a.u.), the driving frequency is $\omega_L = 0.057$ a.u., and the bicircular coherent field amplitudes are set to $E_0 = 0.037$ a.u.
• Figure 3: Equal time intensity correlation function $g^{(2)}(0)$ for a squeezed driver [(a),(b)] and a thermal state [(c)]. Panel (a) shows the $g^{(2)}(0)$ for different harmonic orders, resolved into $R$- and $L$-polarization components (red and blue, respectively), for a squeezing intensity $I_{\text{squ}} = 10^{-8}$ a.u. Panel (b) displays $g^{(2)}(0)$ for two selected harmonic orders as a function of the squeezing intensity. Panel (c) is analogous to (a), but for a thermal state with $I_{\text{th}} = 10^{-9}$ a.u. The atomic medium is hydrogen ($I_p = 0.5$ a.u.), the driving frequency is $\omega_L = 0.057$ a.u., and the bicircular coherent field amplitudes are set to $E_0 = 0.037$ a.u.
• Figure 4: Lissajous figures for two values of the electric field sampled symmetrically around the maxima of $Q(\alpha)$. Each panel shows a different driving field configuration: (a) and (b) correspond to the case where amplitude and phase squeezing are applied to the $2\omega$ field, respectively, while panels (c) and (d) show the case where it is applied to the $\omega$ field instead.
• Figure 5: HHG spectra obtained when applying the linearly polarized squeezing to the $\omega$ (left panels) and to the $2\omega$ (right panels) field contribution. The first row displays the spectra evaluated along the RCP component, while the second row when evaluated along the LCP component. The black dashed vertical lines highlight the locatiton of the classically allowed harmonics. The atomic medium is hydrogen ($I_p = 0.5$ a.u.), the driving frequency is $\omega_L = 0.057$ a.u., and the bicircular component field amplitudes are set to $E_0 = 0.037$ a.u.