Current fluctuations in nonequilibrium open quantum systems beyond weak coupling: a reaction coordinate approach

Abstract

We investigate current fluctuations in open quantum systems beyond the weak-coupling and Markovian regimes, focusing on a coherently driven qubit strongly coupled to a structured bosonic environment. By combining full counting statistics with the reaction coordinate mapping, we develop a framework that enables the calculation of steady-state current fluctuations and their temporal correlations in the strong-coupling regime. Our analysis reveals that, unlike in weak coupling, both the average current and its fluctuations exhibit nonmonotonic dependence on the system-environment interaction strength. Notably, we identify a regime where current noise is suppressed below the classical thermodynamic uncertainty bound, coinciding with enhanced anticorrelations in quantum jump trajectories and faster system relaxation. We further show that these features are linked to nonclassical properties of the reaction coordinate mode, such as non-Gaussianity and quantum coherence. Our results provide new insights and design principles for controlling current fluctuations in quantum devices operating beyond the standard weak-coupling paradigm.

Figures (7)

• Figure 1: Reaction coordinate (RC) mapping for a coherently driven qubit strongly coupled to its environment. The RC mapping incorporates a harmonic oscillator mode into the extended system. $|0\rangle$ and $|1\rangle$ denote the qubit eigenstates in the $\sigma_z$ basis, with transition frequency $\omega_q$. The qubit couples to a drive at $\omega_d$ and the RC mode with frequency $\omega_{c}$ and coupling $\lambda$. The extended qubit-RC system interacts weakly ($\gamma$) with the residual bath at temperature $T$.
• Figure 2: Drude-Lorentz spectral density with central frequency $\omega_c = \omega_q$ and $\lambda = 0.02 \omega_q$ for different widths $\alpha = 0.01$ (blue) and $1$ (green). The sharply peaked curve for $\alpha = 0.01$ represents the strong coupling to the bath and the dashed purple curve represents the Ohmic spectral density function for the residual environment after RC mapping.
• Figure 3: (a) Average excitation current $J$ into the bath, (b) fluctuations of the excitation current $D$, (c) signal-to-noise ratio (SNR) $J^2/D$, and (d) TUR ratio $\mathcal{Q}$ as functions of interaction strength $\lambda$ for different spectral density width $\alpha = 0.01, 0.04,$ and $1$. We set $\Delta_q=0$, $\Delta_c=0$, $\Omega = 0.005$, and $n_{\rm B} = 0.01$.
• Figure 4: Average excitation current $J$ into the bath and fluctuations of the excitation current $D$ as functions of interaction strength $\lambda$, in (a) and (c) for different temperatures leading to bath occupation $n_{\rm B} = 0.01, 0.1$ and $1$, with fixed $\Omega =0.01$, and in (b) and (d) for different drive strengths $\Omega = 0.005, 0.01$ and $0.02$, with fixed $n_{\rm B} =0.01$. We set $\Delta_q=0$ and $\Delta_c=0$.
• Figure 5: Average excitation current $J$, diffusion coefficient $D$, dynamical activity $K$, and $D-K$ as functions of interaction strength $\lambda$, in (a) and (c) for different drive strengths $\Omega = 0.01$ and $\Omega = 0.02$. In (b) and (d), current correlation functions $C(\tau)$ for selected $\lambda$ values marked by crosses in $D-K$ plots in panels (a) and (c), respectively.