在自由空间中，空时波包所能达到的最大差分群时延是多少？
What is the maximum differential group delay achievable by a space-time wave packet in free space?
摘要：
具有严格时空谱相关性的“时空”波包$-$传播不变脉冲光束$-$在自由空间中的群速度可以取任意值。在这里，我们从理论上和实验上研究的最大可实现的群延迟，现实的有限能量时空波包可以实现相对于一个参考脉冲以光速行进。我们发现，这种延迟是完全由光谱的不确定性之间的关联的空间频率和波长的波包时空频谱$-$，而不是由光束的大小，带宽，或脉冲宽度。我们的实验表明，时空波包的传播是由光谱的不确定性引起的“导频包络”，在真空中传播的群速度等于光速。空时波包和导频包络之间的时间走离将最大可实现差分群延迟限制到导频包络的宽度。在这个导频包络内，时空波包可以以任意的群速度局部传播，但不会违反相对论因果关系，因为超光速和亚光速时空波包的前沿或后沿一旦到达包络边缘就分别被抑制。使用脉冲宽度$\sim$ 4 ps和$\sim$ 20 pm的光谱不确定性，我们测量的最大差分群延迟约为$\pm$ 150 ps，超过以前报道的测量至少三个数量级。
英文摘要：
The group velocity of 'space-time' wave packets $-$ propagation-invariant pulsed beams endowed with tight spatio-temporal spectral correlations $-$ can take on arbitrary values in free space. Here we investigate theoretically and experimentally the maximum achievable group delay that realistic finite-energy space-time wave packets can achieve with respect to a reference pulse traveling at the speed of light. We find that this delay is determined solely by the spectral uncertainty in the association between the spatial frequencies and wavelengths underlying the wave packet spatio-temporal spectrum $-$ and not by the beam size, bandwidth, or pulse width. We show experimentally that the propagation of space-time wave packets is delimited by a spectral-uncertainty-induced `pilot envelope' that travels at a group velocity equal to the speed of light in vacuum. Temporal walk-off between the space-time wave packet and the pilot envelope limits the maximum achievable differential group delay to the width of the pilot envelope. Within this pilot envelope, the space-time wave packet can locally travel at an arbitrary group velocity and yet not violate relativistic causality because the leading or trailing edge of superluminal and subluminal space-time wave packets, respectively, are suppressed once they reach the envelope edge. Using pulses of width $\sim$4ps and a spectral uncertainty of $\sim$ 20 pm, we measure maximum differential group delays of approximately $\pm$ 150 ps, which exceed previously reported measurements by at least three orders of magnitude.
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