Manipulation of resonant Auger processes using a strong bichromatic field

We theoretically investigate the effects of strong couplings in resonant Auger processes under the combination of strong resonant x-ray and nearly resonant optical pulses. The x-ray field couples the ground state with a core-excited state, while the optical field couples the core-excited state with another core-excited state of opposite parity. The Auger electron spectrum changes its shape as the intensities of the x-ray and/or optical fields increase, and at sufficiently high intensities we observe that the splitting, which is induced by the optical field, is superposed on the asymmetric splitting induced by the x-ray field in the Auger electron spectra. The asymmetric splitting itself, which is induced by the strong x-ray pulse, is persistent but modified due to the presence of the strong optical field. Moreover, through the systematic study by including or excluding the individual photoionization processes from the core-excited states and the direct photoionizaton process from the ground state, we clarify the contribution of the respective processes to the total electron yield and the Auger electron spectra. These results show that we can manipulate the resonant Auger processes through the introduction of the second core-excited state and the strong optical field.

Figure 1

Level scheme under consideration. A resonant x-ray pulse couples the ground state $|g\rangle$ and a core-excited state $|a\rangle$, and an optical pulse couples the core-excited state $|a\rangle$ and another core-excited state with opposite parity $|b\rangle$. Auger decay takes place from the core-excited states $|a\rangle$ and $|b\rangle$ into the continuum states $|f_1,{\varepsilon }_1\rangle$ and $|f_2,{\varepsilon }_2\rangle$, respectively. A direct ionization pathway, which plays a very important role in this work, is also explicitly shown. Processes (A)–(C) describe photoionization, as explained in the text.

Figure 2

The temporal profiles of the x-ray (solid) and optical (dashed) pulses. They have Gaussian shapes with FWHM of 2.4 and 20 fs, respectively.

Figure 3

Auger electron spectra in the weak intensity regime of the x-ray pulse. The optical pulse intensities are $I_{\mathrm{opt}}=0$ [solid, with processes (B) and (C)], $I_{\mathrm{opt}}={10}^{12} \mathrm{W}/\mathrm{cm}{}^2$ [dashed, with processes (B) and (C)], and $I_{\mathrm{opt}}={10}^{12} \mathrm{W}/\mathrm{cm}{}^2$ [short-dashed, with all processes (A)–(C)], respectively.

Figure 4

Auger electron spectra in the strong intensity regime of the x-ray pulse. The optical pulse intensity is $I_{\mathrm{opt}}={10}^{12} \mathrm{W}/\mathrm{cm}{}^2$. The x-ray pulse intensities are $I_x={10}^{18}$ (solid), $2\times {10}^{18}$ (dashed), $3\times {10}^{18}$ (short-dashed), $4\times {10}^{18}$ (dotted), and $5\times {10}^{18} \mathrm{W}/\mathrm{cm}{}^2$ (dot-dashed), respectively.

Figure 5

Total electron yield and the population dynamics for the system shown in Fig. 1 under different conditions. (a) Variation of the total electron yield $P_{\mathrm{tot}}$ as a function of peak intensity of the optical pulse under different conditions. Results by taking into account all photoionization processes (A)–(C) (solid), processes (B) and (C) only (dashed), processes (A) and (C) only (short-dashed), process (C) only (dotted), and all processes (A)–(C) excluded (dot-dashed) are presented. (b) Temporal dynamics of the populations in states $|g\rangle$ (solid), $|a\rangle$ (dashed), and $|b\rangle$ (short-dashed) with $I_x=5\times {10}^{18} \mathrm{W}/\mathrm{cm}{}^2$ and optical pulse off. (c) Similar to panel (b) but with optical pulse on at $I_{\mathrm{opt}}=6\times {10}^{12} \mathrm{W}/\mathrm{cm}{}^2$. Laser-induced ionization processes (A)–(C) are all excluded in both (b) and (c).

Figure 6

Influence of optical pulse intensity on the Auger electron spectra. The x-ray pulse intensity is $I_x=5\times {10}^{18} \mathrm{W}/\mathrm{cm}{}^2$ for all cases, while the optical pulse intensity is $I_{\mathrm{opt}}=0$ (dotted), $0.5\times {10}^{12}$ (dashed), $0.8\times {10}^{12}$ (short-dashed), and ${10}^{12} \mathrm{W}/\mathrm{cm}{}^2$ (solid), respectively.

Figure 7

Influence of population loss from state $|a\rangle$ through photoionization by the optical pulse [process (A)] on the Auger electron spectra. The x-ray pulse intensity is $I_x=5\times {10}^{18} \mathrm{W}/\mathrm{cm}{}^2$ for all cases. $I_{\mathrm{opt}}=0$ (dashed) with processes (B) and (C) only, $I_{\mathrm{opt}}={10}^{12} \mathrm{W}/\mathrm{cm}{}^2$ with processes (B) and (C) only (solid), and $I_{\mathrm{opt}}={10}^{12} \mathrm{W}/\mathrm{cm}{}^2$ with all processes (A)–(C) (short-dashed), respectively.

Figure 8

Influence of lifetime of state $|a\rangle$ on the Auger electron spectra. $I_x=5\times {10}^{18}$ and $I_{\mathrm{opt}}={10}^{12} \mathrm{W}/\mathrm{cm}{}^2$ for all cases. The lifetime of state $|a\rangle$ is hypothetically varied from the original value, 2.4 fs (solid) to 1.2 fs (dashed) and 5.0 fs (short-dashed), respectively.

Figure 9

Modification of the Auger electron spectra due to the interference between two competing pathways, $|g\rangle \to |a\rangle \to |f_1\rangle$ and $|g\rangle \to |f_1\rangle$ (in Fig. 1). $I_x=5\times {10}^{18} \mathrm{W}/\mathrm{cm}{}^2$ and $I_{\mathrm{opt}}={10}^{12} \mathrm{W}/\mathrm{cm}{}^2$ for all cases. To highlight the interference effect, the included photoionization processes are all processes (A)–(C) (solid), processes (A) and (B) only (dashed), process (A) only (short-dashed), and process (B) only (dot-dashed), respectively.