Andreev Optoelectronics

TL;DR

This work develops a minimal model for coupling light to Andreev bound states in semiconductor-based SNS junctions, revealing two optical absorption resonances and a novel anomalous absorption mechanism that can populate an occupied ABS. By integrating out high-energy quasiparticles, the authors derive an effective optical–microwave transduction Hamiltonian, enabling coherent conversion between optical and microwave photons via the ABS. Using realistic Al–InAs parameters, they demonstrate phase-dependent absorption features and quantify the transduction pathways, highlighting the sensitivity of coupling to wavefunction overlaps and junction geometry. The results establish Andreev optoelectronics as a new platform that merges circuit quantum electrodynamics with quantum optics, enabling time-resolved control of Andreev parity and potential integration with quantum information protocols.

Abstract

Superconducting weak-link junctions host electron--hole hybridized excitations called Andreev bound states. These have attracted significant interest for the role they play in the device microelectronic operation and for quantum information applications. Andreev physics has so far been synonymous with the microwave range. However, the maturation of superconductor--semiconductor hybrid junctions opens the door to the characterization, and manipulation, of Andreev states by light. Here we introduce a model for light--Andreev interaction, with distinct features: Electrons transitioning into Andreev levels can sidestep Pauli exclusion, resulting in two optical absorption resonances separated by twice the bound state energy. One resonance populates the Andreev state and the other empties it; pumping both resets the junction and prevents saturation. Given their natural microwave coupling, we show how Andreev bound states can operate as optical--to--microwave transducers. We illustrate these effects with realistic device parameters. Our results highlight the possibilities in the new field of Andreev optoelectronics.

Figures (5)

• Figure 1: Sketch of the proposed device band structure and absorption spectrum (not to scale). A doped semiconductor (N, middle segment) with a conduction band Fermi surface (dark pink) is sandwiched between two superconducting leads (S, side segments). In the leads, superconducting pairing opens a gap $2\Delta$ (cyan) around the Fermi level $E_F$. Far below, the semiconductor valence band is completely filled. A local potential (black dipper) separates a discrete trapped state from the band continuum. Light (red wavy arrow) kicks (black solid arrow) the trapped valence electron into the conduction band. At energies $<\Delta$, this electron (filled circle) hybridizes with a hole below the Fermi surface (empty circle) to form a circulating Andreev bound state (purple). The hole portion of the ABS allows the occupied ABS to absorb a second photoexcited electron (dashed black arrow), which we refer to as anomalous absorption. After the two transitions, the junction is reset; in the process, a Cooper pair (blue circles) was photo-injected into one lead. The electron and hole comprising the ABS have kinetic energies $\pm E_A$ relative to the Fermi level, so the absorption resonances of the junction in the empty and occupied states are separated by $2E_A$. The trapped valence orbital overlaps with the leads' conduction band (cut away for clarity) so decays at some rate $\Gamma_h$ which sets the absorption resonance line widths.
• Figure 2: Absorption spectrum versus junction phase $\varphi$. Junction parameters are given in the text. $\hbar\nu_0 = E_0 + E_F$ is the transition frequency from the trapped valence state to the Fermi energy. The right panel shows line cuts at $\varphi/\pi=1/2,1$. The dashed curves indicate the contribution of the valence band continuum edge.
• Figure 3: Andreev optical-to-microwave transduction. (a) Circuit electrodynamics diagram. The SNS junction (cyan/pink/cyan) is embedded in an electromagnetic environment with equivalent circuit representation. The junction phase is set by an external bias $\varphi_0$ and further modulated by the phase fluctuations $\hat{\varphi}^{\newline}$ of a microwave resonance $\omega_m$ (blue). A classical idler beam (black) provides the energy to convert microwave photons to optical photons (red) and vice versa. An electrostatic side gate tunes the semiconductor doping and/or valence impurity state; the ABS also couples to microwave gate charge fluctuations $\hat{Q}^{\newline}$, not pursued in this work. (b) Schematic level diagram. A detuned optical photon $\nu_{ph}$ (red) excites the junction into a virtual state (dashed black). This could be the Andreev level (purple, detuning $\delta_A$) or other quasiparticle states, like the above-gap continuum (cyan, detuning $\delta_\mathrm{qp}$). Emitting a microwave photon (blue) to the environment modulates the junction phase by $\sim \varphi_\mathrm{zpf}$. Since the ABS energy and wavefunction depend on phase, this scatters the virtual state to the new Andreev level. If $\delta_\mathrm{qp}$ is large, the quasiparticle-mediated transitions are captured in a renormalized dipole element $\mathcal{D}_e + \partial_\varphi\mathcal{D}_e\hat{\varphi}^{\newline}$. Finally, the idler drive (black) de-excites the ABS. (c) Transduction amplitudes for transitions via a virtual ABS (purple) or the other quasiparticle states (pink), corresponding to the numerators in Eq. \ref{['eq:transduction_Rabi']}. Note that the former, $\propto \partial_\varphi E_A$, enters Eq. \ref{['eq:transduction_Rabi']} augmented by a factor $\sim \Delta/\hbar\omega_m \gg 1$. Same device parameters as Fig. \ref{['fig:absorption']}.
• Figure 4: Absorption spectra and transduction amplitudes versus phase, for the indicated junction length $L$ and barrier position $L_Z$. The top right panel is a reproduction of Figs. \ref{['fig:absorption']} and \ref{['fig:transduction']} of the main text. Other parameters same as in the main text. Note the absorption color scale is not shared across panels.
• Figure 5: Continuation of Fig. \ref{['fig:extra_params_1']}.