Generation of circular polarized high-order harmonics from single color quantum light

TL;DR

The paper demonstrates that single-color, elliptically polarized light with squeezing can drive high-harmonic generation in regimes forbidden classically by ellipticity and produce highly elliptically polarized harmonics. By modeling the driving field as a coherent component plus a displaced squeezed vacuum with ellipticity $A$ and squeezing phase $oldsymbol{oldsymbol{ extphi}}$, the authors connect the HHG spectrum $S(oldsymbol{ ext{ω}})$ and photon statistics $g^{(2)}(0)$ to the quantum fluctuations of the driver via Husimi functions and the semiclassical dipole response. Key findings show that squeezing orientation and ellipticity shape the HHG cutoff, enabling near-circular harmonic emission from a single-color drive, and that the emitted harmonics exhibit strong super-Poissonian statistics, $g^{(2)}(0)\, ext{can}\, ext{exceed}$ $10^3$ in some regimes. Depletion effects are shown to stabilize the system, capping the growth of $g^{(2)}(0)$ and influencing propagation, making squeezed-light HHG a dual-use tool for probing non-classical light and generating highly elliptical harmonics with single-color driving.

Abstract

The atomic response to an ultra-intense driving field produces a characteristic high-harmonic spectrum featuring a rapid drop in intensity for the lower harmonics, followed by a plateau and a sharp cutoff. This response vanishes for circularly polarized classical drivers -- a limitation that can be overcome by introducing quantum features into the driving field. In this work, we show that squeezed highly elliptically polarized drivers not only enable the high-harmonic generation (HHG) process in classically forbidden regimes of large ellipticity, but also yield highly elliptical harmonic radiation with pronounced super-Poissonian photon statistics. Moreover, we show that the HHG spectral features encode information about the quantum nature of the driving field, revealing the presence of its squeezed field fluctuations. By analyzing the HHG spectral intensity dependence as a function of the driver's ellipticity and squeezing orientation, we identify a means to probe the driving field's quantum properties that intrinsically lie in the high-photon number regime.

Figures (8)

• Figure 1: Schematic illustration of the use of bright squeezed elliptically polarized light to characterize the driving field properties and generate highly elliptically polarized harmonic radiation. We consider configurations where one linear polarization component (here the $\perp$-component) is a displaced squeezed vacuum state, while the other (the $\parallel$-component) remains a coherent state. By varying the the driver's ellipticity and consequently the squeezing orientation, specified by $\phi$, one can control the intensity, ellipticity, and photon statistics of the emitted radiation.
• Figure 2: (a) Normalized intensity of harmonic orders $q = 17,19$ and $21$ against the squeezing angle $\phi$ for $A = 0.9$, with the inset plot showing the Fourier transform of the obtained signals. The FT is obtained by taking into account that the pattern in $\Delta S_{q,A}(\phi)$ repeats itself every $2\pi$ due to the recurring squeezing directions. (b) Normalized intensity difference between amplitude and phase squeezing directions for different harmonic orders against the driver's ellipticity $A$. Calculations have been performed over five optical cycles of a monochromatic field with set $\overline{\varepsilon}_\parallel = 0.053$ a.u., $\omega_L = 0.057$ a.u., $I_{\text{sq},\perp} = 10^{-5}$ a.u., using $I_p = 0.5$ a.u. (hydrogen) for the ionization potential.
• Figure 3: Ellipticity against the harmonic order and the driver's ellipticity in the case of (a) amplitude squeezing and (b) phase squeezing applied to the driving field. The same conditions as those in Fig. \ref{['Fig:Driver:Charac']} are considered here.
• Figure 4: Second-order autocorrelation function $g_{\mu,q}^{(2)}(0)$ as a function of the harmonic order $q$, with the colors indicating the driving field ellipticity. Solid (dashed) curves correspond to the $\mu = \parallel$ ($\mu = \perp$) polarization component, with the different colors denoting. The dotted thin black line marks the value $g^{(2)}(0)=1$. The same conditions as those in Fig. \ref{['Fig:Driver:Charac']} are used here.
• Figure 5: High harmonic generation spectrum for (a) phase and (b) squeezed drivers of different ellipticities $A$. Calculations have been performed over five optical cycles of a monochromatic field with set $\overline{\varepsilon}_\parallel = 0.053$ a.u., $\omega_L = 0.057$ a.u., $I_{\text{sq},\perp} = 10^{-5}$ a.u., using an ionization potential $I_p = 0.5$ a.u. (hydrogen).