Emulation of the dynamics of bound electron exposed to strong oscillatory laser field with Bose-Einstein Condensates

TL;DR

This work demonstrates a one-dimensional Bose-Einstein condensate in a finite Gaussian well as a quantum emulator for bound-electron dynamics under a strong oscillatory drive. It solves the Gross-Pitaevskii equation using imaginary-time ground-state preparation and a second-order split-operator method for real-time evolution to track density, momentum, and energy-space occupation, as well as high-harmonic generation spectra. The study reveals that diffusion and continuum occupation depend on drive amplitude $F$, cycle count $n_c$, and interaction strength $g$: rapid driving can suppress diffusion and localization persists in momentum space, while stronger interactions promote continuum occupation and enhance HHG yields by orders of magnitude. These findings highlight the potential of ultracold-atom systems to simulate ultrafast strong-field physics and to elucidate how interactions regulate non-equilibrium dynamical processes.

Abstract

This paper employs a Bose-Einstein condensates to simulate the dynamical response of bound electrons in a strongly oscillating pulsed laser field. We investigate the excitation dynamics of Bose-Einstein condensates with repulsive interaction confined in a potential well with finite depth and width driven by a strong oscillatory pulse field. By numerically solving the Gross-Pitaevskii equation with Crank-Nicolson method and split operator method, we obtain the time-dependent wavefunction and therefore the evolution of density distribution in real space and that in momentum space, and the occupation distribution in energy space. It is shown that cold atoms with weak interaction oscillate as a whole body in a finite space when the amplitude of pulse drive is not strong enough. During the evolution atoms occupy the bound states with larger probability. Increasing the driving strength or atomic interactions promotes the excitation of atoms into continuum states and their diffusion out of the potential well, leading to complex structures or even interference-like patterns in the momentum distribution. The number of cycles in the pulse envelope plays a crucial role in the dynamical behavior: High-frequency driving can suppress diffusion and maintain localization. Furthermore, repulsive atomic interactions can enhance high-harmonic generation yields by several orders of magnitude. This study offers a new perspective for quantum simulations of ultrafast dynamics in strong fields and reveals the regulatory role of interactions in condensates on non-equilibrium dynamical processes.

Figures (7)

• Figure 1: Evolution of density distribution in real space and momentum space for different cycle numbers $n_c$. The calculation parameters are set as $F=1$, $g=1$. From top to bottom, the cycle numbers are (a) and (b) $n_c=2$, (c) and (d) $n_c=4$, (e) and (f) $n_c=12$. In this and all subsequent figures, the white dashed line represents the driving field $E(t) = F \sin^2 (\omega t/2 n_c) \sin(\omega t)$.
• Figure 2: Evolution of the density distribution and momentum distribution with $F=1$ and $g=10$. (a) and (b) correspond to $n_c=2$, (c) and (d) $n_c=4$, (e) and (f) $n_c=12$. To enhance the visibility of the driving field curves, the amplitude of the driving field in the density distribution plots has been amplified by a factor of 10. This adjustment applies specifically to the white dashed lines in panels (a), (c), and (e), while the driving field curves in the momentum distribution plots remain unchanged.
• Figure 3: Evolution of the density distribution and momentum distribution with $F=10$ and $g=1$. (a) and (b) correspond to $n_c=2$, (c) and (d) $n_c=4$, (e) and (f) $n_c=12$. To enhance the visibility of the driving field curves, the amplitude of the driving field in the density distribution plots has been amplified by a factor of 5. This adjustment applies specifically to the white dashed lines in panels (a), (c), and (e).
• Figure 4: Evolution of the occupation distribution for continuum states and bound states under different interaction strengths, with $F=1$ and $n_c=4$. (a) and (b) show the evolution of occupation distribution for continuum states and bound states, respectively, at $g=1$. (c) and (d) show the evolution of occupation distribution for continuum states and bound states, respectively, at $g=10$. The vertical axis represents the energy of different eigenstates. In (b) and (d), there are a total of 10 discrete bound state energy levels. The portion with energy $\ge 0$ represents the sum of occupation numbers of all continuum states.
• Figure 5: Evolution of the occupation distribution for continuum states and bound states under different cycle numbers, with $F=10$ and $g=1$. (a) and (b) show the evolution of occupation distribution for continuum states and bound states, respectively, at $n_c=2$. (c) and (d) show the evolution of occupation distribution for continuum states and bound states, respectively, at $n_c=12$. The plotting method used in this figure is the same as that in Fig. \ref{['fig4']}.