Photon-Blockade Analogue Nonreciprocal Absorption in Spatiotemporal Metasurfaces

Abstract

Controlling the flow of electromagnetic energy is essential for advancing quantum technologies. We introduce a spatiotemporally modulated superconducting metasurface that exhibits photon-blockade-analogue nonreciprocal absorption. In this system, the frequency of incident radiation is matched to the modulation frequency of the metasurface, enabling one-way directional absorption. Forward-traveling waves undergo resonant coupling to higher-order Floquet harmonics and are absorbed within the slab, while backward-traveling waves transmit freely without interaction. This behavior arises from classical wave interference and harmonic conversion in a space-time periodic medium, a classical analogue of quantum photon blockade. We present a design based on a superconductor-semiconductor metasurface incorporating cascaded Josephson field-effect transistors (JoFETs) for millikelvin-temperature operation. Our analysis includes the system Hamiltonian, Floquet band structure, isofrequency diagrams, and full-wave simulations demonstrating strong nonreciprocal absorption. These findings establish a pathway toward compact, nonreciprocal superconducting devices for quantum information processing and microwave photonics.

Figures (5)

• Figure 1: Nonreciprocal absorption in superconducting spatiotemporal metasurfaces, where the space-time modulation and incident wave share the same frequency ($\omega_\text{s}=\omega_0$). The system comprises space-time-modulated nonlinear unit cells coupled together. a) Incidence from the left port ($L_\text{in}$): Energy transition to higher states occur due to the strong interaction and one-way coherency with the nonlinear left-to-right traveling space-time modulation, resulting in zero transmission to the right port ($R_\text{out}=0$). b) Illustration of the physical mechanism for incidence from the right port ($R_\text{in}$): Free passage of wave to the left port ($L_\text{out}=R_\text{in}$) occurs due to the lack of transition to higher energy states and weak interaction with the opposite-direction traveling nonlinear space-time modulation, resulting in full transmission of waves.
• Figure 2: Superconductor-semiconductor quantum spatiotemporal metasurface. (a) One-way absorption functionality. (b) Circuit model of the metasurface, consisting of an array of spatiotemporally-modulated gate-controlled Josephson field-effect transistors (JoFETs).
• Figure 3: Experimental prototype design. (a) Schematic of the space-time-modulated superconductor-semiconductor Josephson field-effect transistors (JoFETs). (b) Metasurface architecture composing a 2D array of gated superconductor-semiconductor hybrid modulated JoFETs in space and time via the yellow-color modulation line.
• Figure 4: Band structure of the superconductor-semiconductor spatiotemporal quantum metasurface computed using Eq. \ref{['eqa:det_gen']}. (a) The $\omega - \kappa$ diagram illustrates strong nonreciprocity at $\omega_0/\omega_\text{s} = 1$. Here, all higher-order forward ($+z$ direction) traveling space-time harmonics converge at $\kappa_n/\kappa_\text{s} = 1$, resulting in the absorption of energy from the fundamental harmonic and transitioning the system from $\omega_0$ to higher frequency states, denoted as $\omega_m$. In contrast, the higher-order backward ($-z$ direction) traveling space-time harmonics are spatially separated, preventing any energy transition from $\omega_0$ to higher states. (b) The $k_x - \kappa_n$ isofrequency diagram at $\omega_0/\omega_\text{s} = 1$ further demonstrates the nonreciprocity of the metasurface, where all forward higher-order harmonics are clustered at $\kappa_n/\kappa_\text{s} = 1$, effectively absorbing the energy of the fundamental harmonic. The group velocity vector $v_{\text{g},n}$ indicates that these harmonics propagate along the $+z$ direction, parallel to the metasurface boundary, rather than being transmitted outside the metasurface.
• Figure 5: Nonreciprocal absorption in spatiotemporal superconductor-semiconductor quantum metasurfaces. (a) and (b) Field distribution (top) and frequency spectrum (bottom) for $E_y$, demonstrating (a) strong absorption of the incident beam from the left at $55^\circ$, and (b) full transmission of the incident beam from the right at $125^\circ$ to the left at $55^\circ$. (c) and (d) Field distribution for $H_z$, demonstrating (c) strong absorption of the incident beam from the left at $55^\circ$, and (d) full transmission of the incident beam from the right at $125^\circ$ to the left at $55^\circ$.