All-optical logic gates for extreme ultraviolet switching via attosecond four-wave mixing

TL;DR

This work extends all-optical logic switching into the extreme ultraviolet by employing carrier-envelope phase (CEP) controlled, noncollinear four-wave mixing (FWM) between one attosecond XUV pulse and two few-cycle NIR pulses in a gas target, using helium doubly-excited states as a testbed. A hybrid TDSE multi-emitter model simulates the CEP-dependent FWM signals and reveals that strong-field NIR driving induces Rabi cycling, significantly enhancing CEP sensitivity and enabling robust, spatially separated XUV outputs. By optimizing CEP input bases, the study demonstrates a complete set of logic gates—X(N)OR, (N)AND, and (N)OR—with switching contrasts ranging from $3.6$ to $10.4$, and identifies specific divergence-ROI regions that maximize gate performance. The results establish a feasible, CEP-controlled XUV logic framework with potential extensions to other targets and quantum logic, paving the way for ultrafast photonic computation in the XUV and beyond.

Abstract

All-optical logic-gate-based switching is a prerequisite for photonic computing. This article introduces a logic-gate protocol for noncollinear four-wave mixing (FWM) of one attosecond extreme ultraviolet (XUV) with two few-femtosecond near infrared (NIR) pulses. Simulations show that the NIR carrier-envelope phases (CEPs) alter the spatial distribution of the XUV FWM emission, using doubly-excited states of gas-phase helium as an example. A complete set of logic gates$-$X(N)OR, (N)AND, and (N)OR$-$is realized for the 2s3p FWM signal at 63.66 eV with switching contrasts of 3.6 to 10.4. This theoretical study extends all-optical logic switching to the XUV and x-ray regimes and opens a new pathway for ultrafast photonic logic.

Figures (7)

• Figure 1: Attosecond four-wave-mixing scheme. (a) Experimental setup for attosecond FWM logic switching. An attosecond XUV pulse is focused together with two time-delayed ($\tau$) few-cycle pulses NIR$_{1,2}$ into a gas-phase target. Afterwards, a thin metal filter cleans the XUV signals from the residual NIR pulses. Due to the noncollinear angle of the NIR beams with respect to the XUV beam, the resulting FWM beams are spatially separated from the on-axis attosecond transient absorption (ATA) beam. A grating spectrally disperses the XUV beams, e.g., the FWM signal into its Rydberg series. (b) Pulse sequence. The XUV pulse precedes the NIR pulse pair by $\tau$. (c) CEP-dependent FWM intensity. The measured FWM intensity of one resonance is binned and measured with respect to its dependence on the NIR CEPs $\Phi_{1,2}$.
• Figure 2: Four-wave-mixing simulation scheme. The noncollinear angle ($2\Theta$) between the NIR$_{1,2}$ beams results in a periodically modulated (along the y-axis) electric-field superposition in the target volume. The gas-phase target is approximated as a one-dimensional emitter chain along the y direction. Solving the TDSE for the input XUV field in combination with the space- and time-dependent NIR field superposition results in a time-dependent dipole moment $D(y,t)$ that differs on the 10 µm-scale of the NIR field modulations. The resulting electric near-field signal $\mathcal{E}^{near}_{XUV}(y,\omega)$ is propagated via a Fourier transform (FFT) into the far field. The far-field divergence-dependent XUV-intensity spectrogram $I_{FWM}(\varphi,\omega)$ is the measurement observable in Fig. 1.
• Figure 3: FWM simulation applied to doubly-excited states in helium. (a) Few-level model scheme of helium. A broadband attosecond XUV pulse populates the bright states 2s2p and 2s3p, located above the first ionization threshold ($E_{IP}$). The NIR$_{1,2}$ pulses lead to FWM emissions by a $\Lambda$- (dashed orange) or $V$-coupling (solid red) scheme via the 2p$^2$ dark state. The rainbow-colored bar indicates the spectral bandwidth of the NIR pulses. (b) FWM simulation for a noncollinear input angle of $\Theta = 2^{\circ}$, an intensity of $I(NIR_{1,2}) = 1 \times 10^{10}$ W/cm$^{2}$, CEP values of $\Phi_{1,2} = 0$, and a time delay of $\tau = 10$ fs. In the following, the focus is on the highlighted, lower-right 2s3p FWM signal.
• Figure 4: Strong-field effects on the helium 2s3p lower FWM emission. Simulated FWM emission in the low-intensity [$I(NIR_{1,2}) = 1.0 \times 10^{10}$ W/cm$^{2}$] limit for CEPs (a) $\Phi_{1,2} = \pi/2$ and (b) $\Phi_{1,2} = 0$. (c) NIR$_{1,2}$-intensity dependence of the photon-energy binned FWM divergence distribution for $\Phi_{1,2} = 0$. FWM emission in the high-intensity [$I(NIR_{1,2}) = 1.3 \times 10^{12}$ W/cm$^{2}$] regime for (d) $\Phi_{1,2} = 0$ and (e) $\Phi_{1,2} = \pi/2$. The dashed black lines in (d) and (e) indicate the divergence region of interest.
• Figure 5: Simulated population evolution for one central on-axis emitter in the (a) low- [$I(NIR_{1,2}) = 1.0 \times 10^{10}$ W/cm$^{2}$] and (b) high-intensity [$I(NIR_{1,2}) = 1.3 \times 10^{12}$ W/cm$^{2}$] regimes. The electric-field envelope of the NIR pulses is given as shaded red area while the attosecond XUV pulse is centered around 0 fs.