Optical Manipulation of Bipolarons in a System with Nonlinear Electron-Phonon Coupling

K. Kovač, D. Golež, M. Mierzejewski, and J. Bonča

Phys. Rev. Lett. 132, 106001 – Published 4 March 2024

Abstract

We investigate full quantum mechanical evolution of two electrons nonlinearly coupled to quantum phonons and simulate the dynamical response of the system subject to a short spatially uniform optical pulse that couples to dipole-active vibrational modes. Nonlinear electron-phonon coupling can either soften or stiffen the phonon frequency in the presence of electron density. In the former case, an external optical pulse tuned just below the phonon frequency generates attraction between electrons and leads to a long-lived bound state even after the optical pulse is switched off. It originates from a dynamical modification of the self-trapping potential that induces a metastable state. By increasing the pulse frequency, the attractive electron-electron interaction changes to repulsive. Two sequential optical pulses with different frequencies can switch between attractive and repulsive interaction. Finally, we show that the pulse-induced binding of electrons is shown to be efficient also for weakly dispersive optical phonons, in the presence anharmonic phonon spectrum and in two dimensions.

Received 4 May 2023
Revised 12 September 2023
Accepted 13 February 2024

DOI:https://doi.org/10.1103/PhysRevLett.132.106001

Physics Subject Headings (PhySH)

Cooper pairs Electron-phonon coupling Lattice dynamics Optical phonons Pairing mechanisms Superconducting phase transition Ultrafast phenomena

1-dimensional systems Nonequilibrium systems

Holstein model Ultrafast pump-probe spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

K. Kovač ¹, D. Golež^1,2, M. Mierzejewski ³, and J. Bonča^1,2

¹J. Stefan Institute, 1000 Ljubljana, Slovenia
²Faculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana, Slovenia
³Department of Theoretical Physics, Faculty of Fundamental Problems of Technology, Wrocław University of Science and Technology, 50-370 Wrocław, Poland

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Issue

Vol. 132, Iss. 10 — 8 March 2024

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Images

Figure 1
Different expectation values for 1D system: (a) the density-density correlation function in the ground state $g (j, t = 0)$ and time-averaged $\bar{g} (j)$ in the time interval [45–150] after the pulse $V (t)$ with amplitude $A_{p} = 0.06$ , $σ = 15$ , $t_{0} = 30$ , and frequency $ω_{d} / ω_{0} = 0.9$ ; (b) the total energy $E (t) = ⟨ H ⟩_{t}$ , the kinetic energy $E_{kin} (t) = ⟨ H_{kin} ⟩_{t}$ and EP coupling energy $E_{g_{2}} (t) = ⟨ H_{g_{2}} ⟩_{t}$ where $H_{kin}$ and $H_{g_{2}}$ represent the first and the second term in Eq. (1), respectively; (c) the total number of phonon excitations $N_{pho} = ⟨ \sum_{j} a_{j}^{†} a_{j} ⟩_{t}$ at different pulse amplitudes $A_{p}$ ; (d) the average particle distance $\bar{d}$ ; (e) the density-density correlation function $g (j, t)$ ; (f) the number of phonons as a function of the interelectron distance $γ (j, t)$ ; in (e) and (f) we used $A_{p} = 0.06$ and the shape of the pulse $V (t)$ is depicted with a blue line, while its vertical scale is in arbitrary units. In all figures, the driving frequency is $ω_{d} / ω_{0} = 0.9$ and the electron-phonon coupling is $g_{2} = - 0.12$ .
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Figure 2
(a) and (b) Magnitude of the effective potential $| v (j, t) |$ computed with two distinct driving frequencies $ω_{d} / ω_{0} = 0.9$ and 1.1, respectively. Note that the sign of $v (j, t)$ is strictly negative since $g_{2} = - 0.12$ ; (c) the effective potential in the ground state, $v (j, 0)$ , and time-averaged $\bar{v} (j)$ for two distinct $ω_{d}$ . Time averages were performed in the same interval as in Fig. 1; (d) time-averaged $\bar{v} (j)$ for different $ω_{d}$ . We have used the pulse amplitude $A_{p} = 0.06$ while the other parameters are identical to those used in Fig. 1.
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Figure 3
(a) and (c) The time–averaged density-density correlation function $\bar{g} (j)$ computed using different driving frequencies $ω_{d}$ for $g_{2} = - 0.12$ and 0.12, respectively; (b) and (d) Time-averaged phonon distribution function $\bar{γ} (j)$ . In all cases the time averages were performed in the same interval as in Figs. 1 and 2. We have used the pulse amplitude $A_{p} = 0.06$ while the rest of parameters are identical to those used in Fig. 1.
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Figure 4
(a) $g (x, y, t = 0)$ computed in the ground state at $ω_{0} = 1$ , $g_{2} = - 0.12$ for the 2D version of the model in Eq. (1); (b) Time-averaged $\bar{g} (x, y)$ where time averages have been performed in the time interval $t \in [45, 150]$ ; to facilitate comparison between results computed before and after driving, we have rescaled the density plots so that the largest value of $\bar{g} (x, y)$ is set to unity; (c) the average distance between particles $\bar{d} (t) = \sum_{x, y} \sqrt{x^{2} + y^{2}} g (x, y, t)$ . We have used $N_{h} = 12$ while the size of the Hilbert space was $N_{st}^{2 D} \sim 2.6 \times 10^{6}$ and the rest of parameters of the model are the same as in the 1D case. For the driving field we have used the following parameters $ω_{d} / ω_{0} = 1.18$ , $A = 0.1$ , $σ = 15$ , $t_{0} = 30$ .
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