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Dynamic charge oscillation in a quantum conductor driven by ultrashort voltage pulses

Lucas Mazzella, Seddik Ouacel, Inès Safi

Abstract

Time-dependent driving with ultrashort voltage pulses brings quantum conductors into the non-adiabatic transport regime, where novel dynamical effects emerge. An example of this physics occurs in interferometric systems, where the transmitted charge oscillates as a function of the charge injected by an ultrashort voltage pulse. This behavior has been predicted in a variety of setups, including Fabry-Pérot and Mach-Zehnder interferometers, and more recently in quantum dots. It is commonly interpreted as resulting from interference between different propagating paths taken by the injected excitation. In this letter, we fully generalize the derivation of such dynamic charge oscillations beyond interferometric devices for a generic quantum conductor with the single assumption that its DC current is sublinear at large bias. Strikingly, they also extend perturbatively to strongly correlated conductors, showing in particular their robustness against arbitrarily strong Coulomb interactions. To illustrate the generality of our approach, we analyze in detail the case of a quantum point contact in the fractional quantum Hall regime, which fulfills the sublinearity condition. We demonstrate that this non-interferometric system exhibit dynamic charge oscillation. Finally, we propose a complementary interpretation of this phenomenon, rooted in the photo-assisted probabilities associated with the voltage pulse.

Dynamic charge oscillation in a quantum conductor driven by ultrashort voltage pulses

Abstract

Time-dependent driving with ultrashort voltage pulses brings quantum conductors into the non-adiabatic transport regime, where novel dynamical effects emerge. An example of this physics occurs in interferometric systems, where the transmitted charge oscillates as a function of the charge injected by an ultrashort voltage pulse. This behavior has been predicted in a variety of setups, including Fabry-Pérot and Mach-Zehnder interferometers, and more recently in quantum dots. It is commonly interpreted as resulting from interference between different propagating paths taken by the injected excitation. In this letter, we fully generalize the derivation of such dynamic charge oscillations beyond interferometric devices for a generic quantum conductor with the single assumption that its DC current is sublinear at large bias. Strikingly, they also extend perturbatively to strongly correlated conductors, showing in particular their robustness against arbitrarily strong Coulomb interactions. To illustrate the generality of our approach, we analyze in detail the case of a quantum point contact in the fractional quantum Hall regime, which fulfills the sublinearity condition. We demonstrate that this non-interferometric system exhibit dynamic charge oscillation. Finally, we propose a complementary interpretation of this phenomenon, rooted in the photo-assisted probabilities associated with the voltage pulse.
Paper Structure (12 sections, 24 equations, 3 figures)

This paper contains 12 sections, 24 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Quantum conductor in the short pulse limit
  3. Quantum point contact in the fractional quantum hall regime
  4. Driven regime.
  5. Numerical results
  6. Interpretation of dynamic charge oscillations
  7. Conclusion
  8. Expressions for $|p_l|^2$ in the short-pulse limit
  9. Validity of the weak backscattering regime in the fractional quantum Hall (FQH) effect
  10. DC regime
  11. AC regime
  12. Adiabatic limit

Figures (3)

  • Figure 1: Schematic of a QPC in the FQH edges. Electrons are injected by a periodic train of voltage pulses $V(t)$ applied to an Ohmic contact, inducing the backscattered charge $\bar{n}$.
  • Figure 2: DC backscattering current at the QPC with $R$ = 0.01, $\nu=\delta= 1/3$ and ${\omega_{\mathrm{th}}} = 0.01\cdot\omega_c$. The green dotted line represents the equilibrium regime $\omega \ll \omega_{\mathrm{th}}$. The blue dotted line represents the non-equilibrium regime $\omega\gg \omega_{\mathrm{th}}$.
  • Figure 3: Backscattered charge $\bar{n}$ as a function of the injected charge $q$ for Lorentzian pulses of various widths $\tau$ at $R$ = 0.01, $\nu$= 1/3, $\delta$ = 1/3, ${\omega_{\mathrm{th}}} = 0.01\,\omega_c$ and $\Omega_{0} = 10^{-3}\,\omega_c$. Solid gray line: adiabatic limit. Solid black line: ultrashort pulse limit given by Eq. \ref{['eq3:I_ph_final']}.