Cui Xu 2024a - Revision history

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Rimni at 13:35, 18 June 2024

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Rimni: /* 3. Results and discussion */

2024-06-18T11:24:24Z

‎3. Results and discussion

Rimni at 11:11, 18 June 2024

2024-06-18T11:11:12Z

Rimni at 11:07, 18 June 2024

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 ==Time-resolved subcycle and intercycle interference influencedmomentum shift in nonadiabatic tunnelling ionization==
 ==Mengyao Xu<sup>1</sup>==
 ''<sup>1</sup>School of Physics and Electronic Engineering, Jiangsu University, Zhenjiang''

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 ==Time-resolved subcycle and intercycle interference influencedmomentum shift in nonadiabatic tunnelling ionization==

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 ==Abstract==
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 Momentum shift is an important sign of nonadiabatic tunnelling ionization process. To investigate the mechanism of momentum shift, we use the strong-field approximation theory to track the formation of ionization momentum spectra of hydrogen atom under the action of different laser pulses in the time domain. By observing the ionization momentum spectra of different structures over time, we find that the momentum shift is formed by the continuous interference and evolution of ionization signals. Meanwhile, we further analyze how subcycle and intercycle interference influence the formation of momentum shift. Before the duration is long enough for intercycle interference to emerge, momentum shift grows smoothly. Our findings reveal different intrinsic mechanisms for the formation of momentum shift in many-cycle and few-cycle laser pulses, showing that subcycle interference plays a dominant role in the former while intercycle interference is critical in the latter. This work lays the foundation for a deeper understanding of the nonadiabatic tunnelling process and makes the regulation of momentum shift possible.

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 ==Time-resolved subcycle and intercycle interference influencedmomentum shift in nonadiabatic tunnelling ionization==

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 ''<sup>1</sup>School of Physics and Electronic Engineering, Jiangsu University, Zhenjiang''
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 ==Abstract==
 Momentum shift is an important sign of nonadiabatic tunnelling ionization process. To investigate the mechanism of momentum shift, we use the strong-field approximation theory to track the formation of ionization momentum spectra of hydrogen atom under the action of different laser pulses in the time domain. By observing the ionization momentum spectra of different structures over time, we find that the momentum shift is formed by the continuous interference and evolution of ionization signals. Meanwhile, we further analyze how subcycle and intercycle interference influence the formation of momentum shift. Before the duration is long enough for intercycle interference to emerge, momentum shift grows smoothly. Our findings reveal different intrinsic mechanisms for the formation of momentum shift in many-cycle and few-cycle laser pulses, showing that subcycle interference plays a dominant role in the former while intercycle interference is critical in the latter. This work lays the foundation for a deeper understanding of the nonadiabatic tunnelling process and makes the regulation of momentum shift possible.

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 |style="text-align: center;padding:10px;"| [[Image:Draft_Xu_669609640-image76.png|600px]]
 |-
-| style="background:#efefef;text-align:justify;padding:10px;font-size: 85%;"| '''Figure 4'''. (Color online) Final PMD of hydrogen atom exposed to OTC laser pulse when the pulse duration is: (a)  <math display="inline">\tau =1.8</math>T. (b)  <math display="inline">\tau =2.1</math>T. (c)  <math display="inline">\tau =2.3</math>T. (d)  <math display="inline">\tau =2.6</math>T with  <math display="inline">T=\frac{2\pi }{\omega }</math>,  <math display="inline">\omega =0.057a.u.</math> and the intensity  <math display="inline">I=3.5\times {10}^{14}\mbox{ W/cm}^2</math>. The white dots mark the most probable momentum corresponding to the peak electric field and black triangles mark the most probable momentum corresponding to the maximum ionization rate. The white dotted lines indicate the magnitude of the momentum shift  <math display="inline">\Delta P</math>. The small image in the lower right corner of (c) and (d) shows an enlargement of the marked area with a white dashed box
+| style="background:#efefef;text-align:justify;padding:10px;font-size: 85%;"| '''Figure 4'''. (Color online) Final PMD of hydrogen atom exposed to OTC laser pulse when the pulse duration is: (a)  <math display="inline">\tau =1.8T</math>. (b)  <math display="inline">\tau =2.1T</math>. (c)  <math display="inline">\tau =2.3T</math>. (d)  <math display="inline">\tau =2.6T</math> with  <math display="inline">T=\frac{2\pi }{\omega }</math>,  <math display="inline">\omega =0.057a.u.</math> and the intensity  <math display="inline">I=3.5\times {10}^{14}\mbox{ W/cm}^2</math>. The white dots mark the most probable momentum corresponding to the peak electric field and black triangles mark the most probable momentum corresponding to the maximum ionization rate. The white dotted lines indicate the magnitude of the momentum shift  <math display="inline">\Delta P</math>. The small image in the lower right corner of (c) and (d) shows an enlargement of the marked area with a white dashed box
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 Obviously, the interference fringes depend strongly on the duration of an OTC laser pulse. When the duration is short enough, the momentum spectrum only involves simple crescent structures as shown in [[#img-4|Figure 4]](a) and (b), telling us that subcycle interference is in effect. As the number of cycles increases, the structures of the PMDs become more and more complex. In [[#img-4|Figure 4]](c), we can slightly find the ATI-like cyclic structures upon the crescent structures. While in [[#img-4|Figure 4]](d), ATI-like cyclic structures are already very obvious. This evolution can be attributed to the gradual emerging of intercycle interference. At the same time, it can be observed that, the momentum shift  <math display="inline">\Delta p</math> also evolves with the duration.
-In order to unfold the trend of  <math display="inline">\Delta p</math> more accurately, we present the momentum shift  <math display="inline">\Delta p</math> with respect to the laser pulse duration in [[#img-5|Figure 5]]. The momentum shift depends sensitively on the pulse duration. We can find that, the trends are the same when the duration varies from  <math display="inline">\tau =1.7</math>T to  <math display="inline">\tau =2.1</math>T and from  <math display="inline">\tau =2.3</math>T to  <math display="inline">\tau =2.7</math>T. However, an obvious difference appears between  <math display="inline">\tau =2.1</math>T and  <math display="inline">\tau =2.3</math>T (red circle), where  <math display="inline">\Delta p</math> decreases sharply as had happened in [[#img-3|Figure 3]]. What is more important, when the duration ranges from  <math display="inline">\tau =2.1</math>T to  <math display="inline">\tau =2.3</math>T, the interference type ICI is emerging significantly as shown in [[#img-4|Figure 4]]. This correspondence further illustrates that the interference type is influencing the momentum shift synchronously.
+In order to unfold the trend of  <math display="inline">\Delta p</math> more accurately, we present the momentum shift  <math display="inline">\Delta p</math> with respect to the laser pulse duration in [[#img-5|Figure 5]]. The momentum shift depends sensitively on the pulse duration. We can find that, the trends are the same when the duration varies from  <math display="inline">\tau =1.7T</math> to  <math display="inline">\tau =2.1T</math> and from  <math display="inline">\tau =2.3T</math> to  <math display="inline">\tau =2.7T</math>. However, an obvious difference appears between  <math display="inline">\tau =2.1T</math> and  <math display="inline">\tau =2.3T</math> (red circle), where  <math display="inline">\Delta p</math> decreases sharply as had happened in [[#img-3|Figure 3]]. What is more important, when the duration ranges from  <math display="inline">\tau =2.1T</math> to  <math display="inline">\tau =2.3T</math>, the interference type ICI is emerging significantly as shown in [[#img-4|Figure 4]]. This correspondence further illustrates that the interference type is influencing the momentum shift synchronously.
 <div id='img-5'></div>

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 To further validate our conclusion, we will use more complex few-cycle OTC laser pulses as shown in [[#img-1|Figure 1]](b) with different durations to repeat the simulations discussed above. When interacting with hydrogen atom, the few-cycle OTC laser pulse will give more details of the interference type in the PMD.
-In [[#img-4|Figure 4]], final PMDs of hydrogen atom exposed to OTC laser pulses are presented, when the pulse durations are (a)  <math display="inline">\tau =1.8T</math>, (b)  <math display="inline">\tau =2.1</math>T, (c)  <math display="inline">\tau =2.3</math>T, and (d)  <math display="inline">\tau =2.6</math>T, respectively. The photon energy  <math display="inline">\omega =0.057a.u.</math>, the intensity  <math display="inline">I =3.5\times {10}^{14}W/\mbox{cm}^2</math> and the keldysh parameter  <math display="inline">\gamma \approx 1</math>, hence, nonadiabatic tunneling ionization occurs. Meanwhile, the momentum shift  <math display="inline">\Delta p</math> is marked as the same way as in [[#img-2|Figure 2]].
+In [[#img-4|Figure 4]], final PMDs of hydrogen atom exposed to OTC laser pulses are presented, when the pulse durations are (a)  <math display="inline">\tau =1.8T</math>, (b)  <math display="inline">\tau =2.1T</math>, (c)  <math display="inline">\tau =2.3T</math>, and (d)  <math display="inline">\tau =2.6T</math>, respectively. The photon energy  <math display="inline">\omega =0.057a.u.</math>, the intensity  <math display="inline">I =3.5\times {10}^{14}W/\mbox{cm}^2</math> and the keldysh parameter  <math display="inline">\gamma \approx 1</math>, hence, nonadiabatic tunneling ionization occurs. Meanwhile, the momentum shift  <math display="inline">\Delta p</math> is marked as the same way as in [[#img-2|Figure 2]].
 <div id='img-4'></div>

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 To understand the law of  <math display="inline">\Delta p</math> varing over time more deeply, we record the magnitude of  <math display="inline">\Delta p</math> at different times. In [[#img-3|Figure 3]], seven black squares guided by a solid line from left to right represent the momentum shift  <math display="inline">\Delta p</math> corresponding to seven moments from  <math display="inline">t=-T</math> to  <math display="inline">t=T</math>. Unsurprisingly, the magnitude of  <math display="inline">\Delta p</math> changs with time as expected. However, something unusual has happened here. We can see that, in [[#img-3|Figure 3]],  <math display="inline">\Delta p</math> changes smoothly overall except the area indicated with a red circle, where  <math display="inline">\Delta p</math> sharply decreases from  <math display="inline">t=\frac{1}{4}T</math> to  <math display="inline">t=\frac{1}{2}T</math>. This notable phenomenon interests us and the evolution of the interference structure in [[#img-2|Figure 2]] prompts us.
-Correspondingly, the PMDs at these two moments are presented in [[#img-2|Figure 2]](b) and (c). In [[#img-2|Figure 2]](b), we can see many crescent interference structures, which is corresponding to subcycle interference(SCI) with electron wave packets(EWPs) from different half cycle within one optical cycle. Differently, for the situation  <math display="inline">t=\frac{1}{2}T</math> ([[#img-2|Figure 2]](c)), many ATI(above-threshold ionization)-like structures emerge, this indicates that intercycle interference (ICI) with EWPs released from different laser optical cycles starts to dominate [37]. So far we can say that, the time-resolved changing of the interference type from only SCI to SCI+ICI for a 2-cycle CP laser pulse results in the drastic decrease of  <math display="inline">\Delta p</math> in [[#img-3|Figure 3]].
+Correspondingly, the PMDs at these two moments are presented in [[#img-2|Figure 2]](b) and (c). In [[#img-2|Figure 2]](b), we can see many crescent interference structures, which is corresponding to subcycle interference (SCI) with electron wave packets (EWPs) from different half cycle within one optical cycle. Differently, for the situation  <math display="inline">t=\frac{1}{2}T</math> ([[#img-2|Figure 2]](c)), many ATI (above-threshold ionization)-like structures emerge, this indicates that intercycle interference (ICI) with EWPs released from different laser optical cycles starts to dominate [37]. So far we can say that, the time-resolved changing of the interference type from only SCI to SCI+ICI for a 2-cycle CP laser pulse results in the drastic decrease of  <math display="inline">\Delta p</math> in [[#img-3|Figure 3]].
 <div id='img-3'></div>