Hyperloss from coherent spatial-mode mixing in quantum-correlated networks

Abstract

Quantum-correlated networks distribute quantum resources such as squeezed and entangled states. These states are central to modern quantum technology, including photonic quantum computing, quantum communications, non-destructive biological sensing and gravitational-wave detection. Even for squeezed states of light - the most robust quantum-correlated resource - loss-induced decoherence remains the dominant obstacle to strong quantum advantage in in large-scale interferometric and networked quantum systems. Common design assumption in these applications is treating mismatches between spatial modes as a small, incoherent loss. Here we show that this picture can fail: coherent spatial-mode mixing with higher-order spatial modes can produce an apparent loss exceeding 100% relative to the initial squeezing, a regime we term hyperloss. We experimentally demonstrate hyperloss in a minimal two-node quantum network: with only 8% mode mismatch, a 5.8dB squeezed state is converted into an effectively thermal state with no quadrature squeezing, eliminating the quantum advantage. Because the effect is coherent, it is controllable: lost correlations can be recovered by tuning differential spatial-mode phases (e.g., Gouy-/propagation-phase). We demonstrate this recovery experimentally, not only eliminating the hyperloss, but even significantly suppressing the mode mismatch loss, with 15% geometric mismatch acting like only ~2.8% effective loss. Hyperloss is a design-limiting mechanism for all quantum networks with squeezed light, from from photonic quantum processors to large-scale interferometers and distributed quantum-sensing networks. Our results provide a practical route to avoid hyperloss and turn mode mismatch into an explicit, phase-aware design parameter for future quantum technologies.

Figures (8)

• Figure 1: Top: Quantum optical network in a block diagram with multiple nodes that couple several optical modes and three examples of such networks (center to right): a photonic quantum computer, a multimode fiber in a quantum communications or sensing system, and a gravitational-wave detector. Bottom: Two types of coupling nodes that act as spatial mode-mixers: a simple beam-splitter (left) and an optical cavity (right). In both cases, the main mode and the displaced auxiliary mode interfere to produce a higher-order spatial mode upon reflection (center).
• Figure 2: Physical picture behind the hyperloss effect. Top: Field amplitude of the vacuum (left) and the squeezed (right) states as a function of time; and the uncertainty of the measurement record plotted in the phase space with two orthogonal quadratures $\hat{X}_0$ and $\hat{X}_{\pi/2}$. Bottom: Mode-coupling leading to interference between different modes and the resulting decoherence effects in the detected noise. The bottom left part demonstrates the mode-mixing at two interference points (cavities or beam-splitters), forming an effective Mach-Zehnder interferometer. Squeezed field in the FM couples to the vacuum field in the HOM. The green crosses are used to keep track of the phase of the state. Upon coupling to the HOM at the first interface, squeezed field acquires a relative phase $\phi_1$, which depends on the parameters of the coupler. After propagation, HOM rotates in phase space due to the Gouy phase $\phi_\text{G}$. Upon coupling at the second interface, FM and HOM have some phase delay, leads to destructive or constructive interference between the coupled fields. Depending on the relative phase, we highlight three special cases (center): when the ellipses end up perfectly aligned, squeezing is fully coherently restored, despite experiencing two mismatches. Fully squeezed noise is observed upon detection. When the ellipses are exactly $\pi$ relative to each other, correlations are completely canceled, and the measured state is at the shot noise level. When the phase is $\pi/2$, anti-squeezing from HOM couples to squeezed quadrature, producing significantly thermal state with increased noise on the detector. This is the hyperloss effect.
• Figure 3: Top row: power loss from the cold SMM effect on the coherent light field versus the FM-HOM differential phase. The baseline (violet) shows the loss level when mode mismatch is treated as direct optical loss. The second row: minimal quadrature variance versus the FM-HOM differential phase, relative to shot noise. Two regimes are shown: the hyperloss (left) and recovery (right). In the hyperloss regime, all squeezing is lost and the state is thermal-like with $\approx 1.5\,$dB noise above shot noise level. In the recovery regime the noise variance drops below the baseline. Up to 5.2 dB of initial 5.8 dB squeezing is recovered, so $\approx 15\,\%$ mismatch acts like only $\approx 2.8\,\%$ effective loss. The phase-space illustrations of the measured states are shown as insets, see Fig. \ref{['fig:2']} for details. The third row: the full data set, out of which the second row is a slice at 3.75 MHz (white line). Shown is the minimal noise variance versus measurement frequency and FM-HOM differential phase. Bottom row: theoretical simulation captures the observed behavior using independently measured parameters, with the propagation Gouy phase and the detuning of first cavity being the fit parameters.
• Figure 4: Left: A simplified setup highlighting the main components of the experiment: the introduced mismatch of $\pm$ 8 % (red background), the cavity setup (green background), and the homodyne detection system (blue background). The experiment uses Laguerre-Gauss modes (LG$_{00}$ and LG$_{01}$) to realize the fundamental and higher-order spatial modes. The first set of lenses creates +8 % mismatch at a cavity 1, and the second set of lenses compensates it at cavity 2, resulting in pure LG$_{00}$ mode at the homodyne detector. Right: A detailed setup, additionally including auxiliary components such as a control beam to assist in aligning the squeezed beam via the diagnostic setup and a stabilization beam for cavity 1.
• Figure 5: Top: Phase response of cavity 1's resonance peak at different length stabilization points. Bottom: Resonance peaks of 1064 nm (monitored at photodiode 2) and 532 nm (monitored at photodiode 1) for cavity 1. Different modes of 532 nm were optimized to achieve various differential phases between the fundamental and higher-order modes in response to the 1064 nm resonance peak.