Critical evaluation of attosecond time delays retrieved from photoelectron streaking measurements

A photoelectron streaking experiment which was conceived as a means to extract the electron wave packet of single-photon ionization has also been employed to retrieve time delays in the fundamental photoemission processes. The discrepancies between the time delays thus measured and those from many sophisticated theoretical calculations have generated a great deal of controversy in recent years. Here we present a careful examination of the methods that were used to retrieve the time delays and demonstrate the difficulty of achieving an accuracy of the retrieved time delays of a few to tens of attoseconds in typical streaking measurements. The difficulty owes more to the lower sensitivity of the streaking spectra to the phase of the photoionization transition dipole than to the spectral phase of the attosecond light pulse in the experiment. The retrieved time delay contains extra errors when the attochirp of the attosecond pulse is large so that the dipole phase becomes negligible compared to it.

Figure 1

(a) SFA-simulated Ne spectrogram for a 190-as transform-limited (TL) XUV pulse. (b) Spectrogram for a 280-as chirped XUV. In these simulations the peak of the XUV envelope and the peak of the IR field overlap at $\tau =0$. A negative $\tau$ means that the XUV comes before the IR. (c) Input dipole amplitude and (d) dipole phase for Ne $2p$ and $2s$ ionization channels, calculated using the SAE model potential given in Ref. [23].

Figure 2

(a) FROG-CRAB retrieved spectral phases of the $2p$ and $2s$ wave packets for the case of the transform-limited (TL) XUV, compared with the input XUV phase. (b) Retrieved wave-packet phases for the case of the chirped XUV. (c) Retrieved Wigner delay difference $\mathrm{\Delta }{\tau }_{2p\left(2s\right)}^W$ for both cases compared with the input data. In the energy domain both XUV pulses are centered at 105 eV, with an FWHM bandwidth of 9 eV.

Figure 3

(a) SFA simulated spectrogram of Ar and Ne using a transform-limited (TL) 160-as XUV pulse. (b) Simulated spectrogram using a 80-as XUV pulse. In both cases the Ar spectrogram has been multiplied by a factor of 10 and shifted upward by 60 eV. (c) Input dipole amplitude and (d) dipole phase for $\mathrm{Ar}\left(3p\right)$ and $\mathrm{Ne}\left(2p\right)$ ionization, calculated using the SAE model given in Ref. [23].

Figure 4

FROG-CRAB retrieved Wigner time delay between the ionization of Ar and that of Ne $\mathrm{\Delta }{\tau }_{\mathrm{Ar}\left(\mathrm{Ne}\right)}^W$ for various energy shifts $E_{\mathrm{shift}}$, compared with the input value. (a) Using an 160-as transform-limited (TL) XUV, centered at 60 eV, with an FWHM bandwidth of 11.5 eV. (b) Using an 80-as TL XUV, centered at 60 eV, with an FWHM bandwidth of 23 eV.

Figure 5

SFA simulated spectrograms: (a) Ne target, 80-as transform-limited (TL) XUV; (b) Ne target, 130-as chirped XUV; (c) Ar target, 80-as TL XUV; (d) Ar target, 130-as chirped XUV.

Figure 6

(a) Retrieved XUV spectral phase and (b) retrieved XUV temporal envelope compared with the input value, for the case of the transform-limited XUV. (c, d) Similar plots, but for the case of the chirped XUV. XUV pulses are extracted from Ne spectrograms using FROG-CRAB.

Figure 7

Retrieved IR field from the Ne spectrogram with transform-limited XUV. (a) Solid black line: retrieved IR through direct fitting. Dot-dashed blue line: output IR field from FROG-CRAB by setting $p_0=1.68$. Dashed red line: input IR field. (b) Zoomed-in plot of (a) near $t=0$.

Figure 8

Wigner delay of Ar. Solid blue line: retrieved by fitting for the case of 80-as transform-limited (TL) XUV. Solid green line: retrieved by fitting for the case of 130-as chirped XUV. Dot-dashed black line: retrieved from FROG-CRAB in Sec. 3 for the case of 80-as TL XUV, by choosing $E_{\mathrm{shift}}=80$ eV and using the input Ne dipole. Dashed red line: input data. In the energy domain the XUV pulses are centered at 60 eV, with an FWHM bandwidth of 23 eV.

Figure 9

(a) Wigner delays for the two artificial targets compared with the Wigner delay of the input Ar target. (b) Photoelectron spectra for these targets at $\tau =0$ fs. (c) Photoelectron spectra at $\tau =-0.64$ fs.

Figure 10

Wigner delay of Ar retrieved by the fitting approach compared with the input value. We have added 5% or 10% random errors to the original Ne and Ar spectrograms, Figs. 5 and 5, as the new input data.

Figure 11

(a) Dipole amplitude; (b) dipole phase; (c) corresponding Wigner delay of the Ne atom calculated using the SAE model potential given by Green [31] compared with that calculated using Tong and Lin's potential [23].

Figure 12

(a) XUV pulse retrieved by FROG-CRAB. (b) IR field retrieved by the fitting method from the Ne spectrogram [Fig. 5]. (c) Wigner delay of Ar extracted by the fitting method from Fig. 5. Solid green line: retrieved using Green's potential for Ne. Dot-dashed blue line: retrieved using Lin's potential for Ne as a comparison. Dashed red line: input values.

Figure 13

(a) SFA and (b) TDSE simulated Ne spectrograms. (c) SFA and (d) TDSE simulated Ar spectrograms. A 160-as transform-limited XUV pulse is used, which is centered at 40 eV, with an FWHM bandwidth of 11.5 eV.

Figure 14

(a) Retrieved XUV spectral phase and (b) retrieved XUV temporal envelope compared with the input value, for the case of the transform-limited XUV. (c, d) Similar plots, but for the case of the chirped XUV. XUV pulses are extracted from low-energy Ne spectrograms simulated by solving TDSE.

Figure 15

(a) Amplitude and (b) phase of the retrieved photoelectron wave packets of Ar and Ne as functions of the photon energy $\mathrm{\Omega }$, compared with the amplitude and phase of the input XUV pulse. Wave packets are retrieved using FROG-CRAB from combined Ar and Ne spectrograms simulated by TDSE. (c) Time delay between the ionization of Ar and that of Ne. Solid blue line: by taking the energy derivative of the phase difference between the two retrieved wave packets in (b). Solid green line: after subtracting the positive CLC term $\mathrm{\Delta }{\tau }_{\mathrm{Ar}\left(\mathrm{Ne}\right)}^{\mathrm{CLC}}\left(\mathrm{\Omega }\right)$. Dashed red line: input Wigner delay between Ar and Ne. The input XUV pulse is transform-limited (TL) with an FWHM duration of 160 as. In the energy domain it is centered at 40 eV, with an FWHM bandwidth of 11.5 eV.

Figure 16

(a) Retrieved IR field from the Ne spectrogram simulated by TDSE. Solid black line: retrieved IR by fitting. Dot-dashed blue line: output IR field from FROG-CRAB by setting $p_0=1.16$. Dashed red line: input IR field. (b) Photoionization time delay of Ar. Solid blue line: retrieved from the Ar spectrogram simulated by TDSE through GA fitting. Solid green line: after subtracting the negative CLC term ${\tau }_{\mathrm{Ar}}^{\mathrm{CLC}}\left(\mathrm{\Omega }\right)$. Dot-dashed black line: retrieved by FROG-CRAB, using the input Ne dipole. Dashed red line: input Wigner delay of Ar.