Squeezing of $X$ waves with orbital angular momentum

Multilevel quantum protocols may potentially supersede standard quantum optical polarization-encoded protocols in terms of amount of information transmission and security. However, for free-space telecommunications, we do not have tools for limiting loss due to diffraction and perturbations, as, for example, turbulence in air. Here we study propagation invariant quantum $X$ waves with angular momentum; this representation expresses the electromagnetic field as a quantum gas of weakly interacting bosons. The resulting spatiotemporal quantized light pulses are not subject to diffraction and dispersion, and are intrinsically resilient to disturbances in propagation. We show that spontaneous down-conversion generates squeezed $X$ waves useful for quantum protocols. Surprisingly, the orbital angular momentum affects the squeezing angle, and we predict the existence of a characteristic axicon aperture for maximal squeezing. These results may boost the applications in free space of quantum optical transmission and multilevel quantum protocols, and may also be relevant for novel kinds of interferometers, such as satellite-based gravitational wave detectors.

Figure 1

(a) Plot of the normalized squeezing parameter modulus $|{\xi }_m^{\left(N\right)}|=\mathrm{\Delta }|{\xi }_m|/\left(\pi \chi c\right)$ in function of the normalized velocity $\tilde{v}/{\omega }^{\prime \prime }$. (b),(c) Quadrature space representation of the squeezed down-converted state in the case of odd [panel (b)] and even [panel (c)] values of the OAM parameter $m$ with a normalized velocity $\tilde{v}/{\omega }^{\prime \prime }=3$ and fixing the time $t$ so that $\pi \chi ct/\mathrm{\Delta }=1$.