Single Photon Cross-Phase Shifts Can Be Enhanced by Localization in both Frequency and Time

• URL: http://arxiv.org/abs/2606.11516v1
• Date: Tue, 09 Jun 2026 23:30:23 GMT
• Title: Single Photon Cross-Phase Shifts Can Be Enhanced by Localization in both Frequency and Time
• Abstract summary: Single-photon optical nonlinearities face a fundamental trade-off: maximum nonlinearity requires both spectral resonance (narrow bandwidth) and high peak intensity (short duration)<n>We demonstrate experimentally that this limitation does not need to exist in cases involving post-selection.<n>This work uncovers new consequences of having simultaneous knowledge of frequency and time, raising new foundational questions about how a particle behaves.
• Score: 1.5681641502558186
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Single-photon optical nonlinearities face a fundamental trade-off: maximum nonlinearity requires both spectral resonance (narrow bandwidth) and high peak intensity (short duration), constraints that are incompatible due to the time-energy uncertainty relation. We demonstrate experimentally that this limitation does not need to exist in cases involving post-selection. We measure a cross-phase shift (XPS) produced by a resonant photon from a narrow-band source that is first transmitted through a cold atomic cloud and then localized in time through detection. The peak size of this XPS is greatly enhanced compared to that of Gaussian single-photon-level pulses without post-selection, benefiting from the narrow bandwidth of the resonant prepared state and the high intensity of the post-selected state simultaneously. We measure enhancements in the peak XPS of 6$\pm$1 at an optical depth (OD) of 2.4$\pm$0.1, and our results are in qualitative agreement across a range of optical depths with the recently developed weak value theory of atomic excitation [Thompson et al., APL Quantum 2, 036108 (2025)] for such post-selected photons. This work uncovers new consequences of having simultaneous knowledge of frequency and time, raising new foundational questions about how a particle behaves, and interacts with other systems, when its preparation and post-selection are non-commuting.

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