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arXiv:2606.12794

Beyond-Third-Order Quantum Coherence in Two-Dimensional Spectroscopy via Order-Selective Isolation

Xue Zhang, De-Ran Zhang, Hui Dong

quant-phphysics.opticsSubmitted Jun 11, 2026• Announced Jun 12, 2026• 0 citations
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Abstract

A central challenge in nonlinear spectroscopy is the order-selective readout of weak higher-order responses that spectrally overlap with dominant lower-order signals. This bottleneck is particularly severe in two-dimensional (2D) spectroscopy, where extending conventional phase-cycling schemes to higher orders rapidly increases measurement and analysis complexity. Here we introduce a computation-assisted strategy that combines rotating-frame acquisition with a frame-shift tracking algorithm to separate signals by their frame-dependent spectral shifts. In a rubidium vapor experiment, we use this approach to isolate a 7th-order nonlinear contribution from coexisting 3rd-order components, enabling direct access to higher-order quantum-coherence dynamics without sacrificing operation at comparatively high pulse intensities. The method is broadly compatible with multidimensional spectroscopy platforms and provides a practical route to probing many-body and collective ultrafast dynamics beyond third order.

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12 pages, 5 figures

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A central challenge in nonlinear spectroscopy is the order-selective readout of weak higher-order responses that spectrally overlap with dominant lower-order signals. This bottleneck is particularly severe in two-dimensional (2D) spectroscopy, where extending conventional phase-cycling schemes to higher orders rapidly increases measurement and analysis complexity. Here we introduce a computation-assisted strategy that combines rotating-frame acquisition with a frame-shift tracking algorithm to separate signals by their frame-dependent spectral shifts. In a rubidium vapor experiment, we use this approach to isolate a 7th-order nonlinear contribution from coexisting 3rd-order components, enabling direct access to higher-order quantum-coherence dynamics without sacrificing operation at comparatively high pulse intensities. The method is broadly compatible with multidimensional spectroscopy platforms and provides a practical route to probing many-body and collective ultrafast dynamics beyond third order.
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Multidimensional coherent spectroscopy is a powerful tool for understanding the ultrafast dynamics of complex quantum systems. To fully characterize the nonlinear optical response of a system, multiple pulse sequences must be recorded and quantitatively compared. We present a new single-scan method that enables rapid and parallel acquisition of all unique pulse sequences corresponding to first- and third-order degenerate wave-mixing processes. Signals are recorded with shot-noise limited detection, enabling acquisition times of ~2 minutes with ~100 zs phase stability and ~8 orders of dynamic range, in a collinear geometry, on a single-pixel detector. We demonstrate this method using quantum well excitons, and quantitative analysis reveals new insights into the bosonic nature of excitons. This scheme may enable rapid and scalable analysis of unique chemical signatures, metrology of optical susceptibilities, nonperturbative coherent control, and the implementation of quantum information protocols using multidimensional spectroscopy.
Two-dimensional electronic coherence spectroscopy (ECS) is an important method to study the coupling between distinct optical modes of a material system. Such studies often involve excitation using a sequence of phased ultrashort laser pulses. In conventional approaches, the delays between pulse temporal envelopes must be precisely monitored or maintained. Here, we introduce a new experimental scheme for phase-selective nonlinear ECS, which combines acousto-optic phase modulation with ultrashort laser excitation to produce intensity modulated nonlinear fluorescence signals. We isolate specific nonlinear signal contributions by synchronous detection, with respect to appropriately constructed references. Our method effectively decouples the relative temporal phases from the pulse envelopes of a collinear train of four sequential pulses. We thus achieve a robust and high signal-to-noise scheme for phase-selective ECS to investigate the resonant nonlinear optical response of photoluminescent systems. We demonstrate the validity of our method using a model quantum three-level system-atomic Rb vapor. Moreover, we show how our measurements determine the resonant complex-valued third-order susceptibility.
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Nonlinear spectroscopy is a cornerstone of quantum science, providing unique access to multi-point correlations, quantum coherence, and couplings that are invisible to linear methods. However, classical simulation of these phenomena is fundamentally limited by the exponential growth of the Hilbert space, and practical quantum algorithms for the nonlinear regime have remained largely unexplored. Here, we present a unified quantum algorithmic framework for computing nnn-th order nonlinear spectroscopies. By reformulating multi-time responses as a weighted sum of expectation values at finite pump amplitudes via a generalized parameter shift rule, our approach bypasses the costly evaluation of high-order commutators and time-dependent operator expansions. This reformulation enables efficient execution via real-time evolution on current quantum hardware, ensuring inherent noise resilience. We validate the framework on IBM's superconducting quantum processors, successfully obtain higher-order response functions of a 12-qubit XXZ spin-chain. Furthermore, the versatility of our method is demonstrated by resolving quasi-particle excitation spectra in spin-liquids and identifying interaction-induced cross-peaks in atomic systems. Our results establish a practical and scalable pathway for probing complex quantum dynamics on near-term quantum devices, extending the reach of quantum simulation into the nonlinear domain.