= Attosecond streaking
<Attosecond streaking> uses a synchronized reference <electric field> to change a <photoelectron>'s outgoing <momentum>. Scanning relative delay produces an <energy>-versus-delay distribution. A short emission interval samples only a small part of the reference cycle; a longer interval samples a range of kicks and can broaden or reshape the distribution.
For an explicit classical limit, use the <electric dipole> approximation and choose the <magnetic vector potential> $A(t)$ along the detection axis with $E(t)=-dA/dt$ and $A(\infty)=0$. Neglect the residual <ion>'s <Coulomb force>. An <Electron> released at $t_i$ with mechanical <momentum> $p_0$ obeys
$$
p_f=p_0-eA(t_i),\qquad
K_f=\frac{[p_0-eA(t_i)]^2}{2m}.
$$
Indeed, integrating $\dot p=-eE=e\dot A$ from release to the end of the field gives the stated minus sign. The useful clock variable here is $A$, rather than the instantaneous $E$ itself. If $A$ is nearly linear across a narrow emission window with temporal <standard deviation> $\sigma_t$, and initial <momentum> is sharp, then
$$
\sigma_p\simeq e|E(t_i)|\sigma_t.
$$
This local mapping fails near a zero of $E$, where first-order timing sensitivity vanishes. A real inversion must include the incident bandwidth, initial <photoelectron> distribution, collection angles and target–field response.
For an original dimensionless example in <atomic units>, choose $p_0=2$, $m=e=1$ and $A(t_i)=0.10$. Then $p_f=1.9$ and $K_f=1.805$, compared with initial <kinetic energy> $2$. Reversing $A$ gives $K_f=2.205$: the shifts are asymmetric because of the $A^2/2$ term. A measurement that keeps only the term linear in $A$ would miss $0.005$ in both cases.
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