Space-Time Quantum Metasurfaces

Metasurfaces have recently entered the realm of quantum photonics, enabling manipulation of quantum light using a compact nanophotonic platform. Realizing the full potential of metasurfaces at the deepest quantum level requires the ability to tune coherent light-matter interactions continuously in space and time. Here, we introduce the concept of space-time quantum metasurfaces for arbitrary control of the spectral, spatial, and spin properties of nonclassical light using a compact photonic platform. We show that space-time quantum metasurfaces allow on-demand tailoring of entanglement among all degrees of freedom of a single photon. We also show that spatiotemporal modulation induces asymmetry at the fundamental level of quantum fluctuations, resulting in the generation of steered and vortex photon pairs out of vacuum. Space-time quantum metasurfaces have the potential to enable novel photonic functionalities, such as encoding quantum information into high-dimensional color qudits using designer modulation protocols, sculpting multispectral and multispatial modes in spontaneous emission, and generating reconfigurable hyperentanglement for high-capacity quantum communications.

Figure 1

Conceptual representations of space-time quantum metasurfaces. (a) A dielectric STQM with all-optical refractive index modulation induces color-spin-path hyperentanglement on a single photon. (b) A graphene-disk STQM with electro-optical modulation generates entangled vortex photon pairs out of the quantum vacuum.

Figure 2

(a) Modulation amplitudes of polarizability tensor components normalized to the meta-atom volume for $\mathrm{\Delta }\epsilon /{\epsilon }_{um}=1\%$ of an optical all-dielectric STQM designed for maximal cross-polarized transmission at 1550 nm under normal incidence. Inset: anisotropic amorphous Si meta-atom with $L_1=950\mathrm{nm}$, $L_2=435\mathrm{nm}$, $h=300\mathrm{nm}$, $w=200\mathrm{nm}$, and square unit cell with period $P=1200\mathrm{nm}$. (b) Conversion probability of a linearly polarized input photon into an output photon in frequency harmonic ${\omega }_{\mathrm{in}}+p\mathrm{\Omega }$ and momentum harmonic $p\mathit{\beta }+q{\mathit{\beta }}_g$ versus polarizability modulation depth. Density matrices of input (c) and output photons feature (d) spin-path entanglement, (e) color-path entanglement, and (f) color-spin-path hyperentanglement. Parameters are ${\omega }_{\mathrm{in}}/2\pi =193\mathrm{THz}$, $\mathrm{\Omega }/2\pi =10\mathrm{THz}$, $|\mathit{\beta }|=|{\mathit{\beta }}_g|=0.01{\omega }_{\mathrm{in}}/c$, 1 ps interaction time, and ${\alpha }_{um}^{(cr)}=0.6\mu {\mathrm{m}}^3$ [23].

Figure 3

Steered quantum vacuum from a graphene-disk STQM. The first column contains density polar plots of emitted circularly polarized radiation for various momentum kicks $c\beta /\mathrm{\Omega }$ equal to 0 (a), 0.3 (b), 0.38 (c), and 0.5 (d). The areas to the right (left) of the vertical solid line correspond to the emission spectrum of the high- (low-)frequency photon in a pair. The second and third columns show the corresponding spherical polar plots. Parameters are $\mathrm{\Omega }/2\pi =10\mathrm{THz}$, $\mathrm{\Delta }{E}_F/E_F=1\%$, $n_{MS}={10}^3{\mathrm{mm}}^{-2}$, $D=5\mu \mathrm{m}$, and $\mu ={10}^4{\mathrm{cm}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$.

Figure 4

Spectral weight function for (a) linear and (b) rotating synthetic phase. Solid lines in (b) correspond to a finite radius metasurface ($\mathrm{\Omega }R/c=30$) and dashed line is the $\ell =0$ case for an infinite metasurface. Angular-momentum spectra for finite radius metasurface for the (c) low- and (d) high-frequency photon. (e) Spectral photoproduction rate for null synthetic phase for a graphene-disk STQM. Inset: unmodulated electric polarizability ${\alpha }_{um}(\omega )$ (solid) and modulation amplitude $\mathrm{\Delta }\alpha (\omega )$ (dashed) in units of $\mu m^3$. (f) Emission rate for linear synthetic phase. The black thick curve joins peaks of maximal emission and the thin black curve ${\omega }_{\mathrm{res}}(E_F)=(\mathrm{\Omega }+c\beta )/2$ is its projection on the $\beta -E_F$ plane. Parameters are the same as in Fig. 3.