Population-Dominated Ergotropy in a Capacitively Coupled Double-Quantum-Dot Battery under 1/f Charge Noise

Abstract: We investigate extractable work storage in a capacitively coupled double quantum dot (DQD) quantum battery (QB) subjected to experimentally motivated detuning charge noise. The battery is modeled as two interacting charge qubits with an Ising-type capacitive coupling and is charged by resonant microwave modulation of the tunnel coupling channel. Detuning fluctuations are introduced as classical stochastic processes generated from a band-limited 1/f noise spectrum. For each noise realization, the evolution remains unitary, whereas decoherence and loss of contrast emerge after ensemble averaging. We analyze the total ergotropy, its population and coherent contributions, the energy basis populations, a passive ordering violation diagnostic, and the Jensen-Shannon coherence of the noise-averaged state. The results show that resonant tunnel coupling driving selects a dominant E0 <-> E3 population transfer channel in the interacting DQD spectrum. The dominant extractable work is stored in non-passive population distributions, in agreement with recent population ordering interpretations of ergotropy in QBs, while coherence accompanies and supports the resonant transfer as a transient dynamical resource. Detuning noise reduces the energy basis coherence amplitude and also weakens the population transfer pathway responsible for the dominant population ergotropy. This framework provides a noise-aware description of semiconductor QB charging based on extractable work rather than on injected energy alone.

• The paper demonstrates that ergotropy in capacitively coupled DQD quantum batteries is mainly due to non-passive population distributions rather than coherence.
• It employs resonant microwave modulation to selectively drive E0↔E3 transitions using experimentally relevant parameters from Si/SiGe DQDs.
• It shows that 1/f detuning noise critically degrades charging dynamics by suppressing population ordering, reducing the battery's extractable work.

Ergotropy Dynamics in Capacitively Coupled Double-Quantum-Dot Batteries Under 1/f Charge Noise

System Architecture and Noise Model

The study investigates a two-qubit quantum battery (QB) architecture realized by capacitively coupled double quantum dots (DQDs), each operating in the charge qubit regime. The static battery Hamiltonian comprises local detuning ($\epsilon_{0,i}$), tunnel splitting ($\Delta_{0,i}$), and a capacitive Ising-type coupling ($J$) representing the interaction. Static parameters are derived from experimentally relevant Si/SiGe DQDs: $\Delta_{0,1}/h=8.4$ GHz, $\Delta_{0,2}/h=6.6$ GHz, and $J/h=15.3$ GHz at the symmetric detuning sweet spot ($\epsilon_{0,1} = \epsilon_{0,2} = 0$).

The external environment is modeled by band-limited $1/f$ stochastic detuning fluctuations, dominant in Si/SiGe platforms, with a spectral amplitude $c_\epsilon$ and frequency cutoffs $(\omega_l, \omega_h)$. For each noise realization, detuning enters longitudinally as $\Delta_{0,i}$0, affecting both the resonance condition and dynamical channel. Ensemble averaging over many stochastic traces captures the realistic decoherence and loss of contrast.

Figure 1: The static coupled DQD energy spectrum and noise-averaged charging dynamics reveal dominant $\Delta_{0,i}$1 population transfer and coherence generation, degraded under detuning charge noise.

Resonant Charging and Channel Selection

Charging occurs via resonant microwave modulation of the tunnel couplings, transverse in the localized charge basis. The drive frequency is tuned to $\Delta_{0,i}$2 GHz, directly addressing the highest-lowest energy transition. This choice enables selective population transfer and superposition generation, with the charging branch predominantly governed by the $\Delta_{0,i}$3 channel.

Dynamic evolution shows oscillatory population exchange between $\Delta_{0,i}$4, with intermediate levels ($\Delta_{0,i}$5, $\Delta_{0,i}$6) weakly involved during the first charging branch. The system thus acts as an effectively two-level QB embedded in a four-level manifold. Jensen–Shannon quantum coherence ($\Delta_{0,i}$7) remains finite, serving as a quantitative measure of dynamical superposition in the energy basis.

Noise-induced detuning shifts and fluctuations degrade both population transfer and coherence amplitude, manifesting as reduced oscillation contrast and suppressed $\Delta_{0,i}$8 upon ensemble averaging.

Ergotropy Decomposition and Population Ordering

Ergotropy ($\Delta_{0,i}$9), defined as the maximum extractable work via unitary operations with respect to $J$0, is decomposed into population ($J$1) and coherent ($J$2) contributions using energy-basis dephasing. The key finding is that, in this microwave-driven protocol, $J$3 is dominated by $J$4, with $J$5 comparatively minor.

Parametric analysis with coherence ($J$6) and $J$7-$J$8 population imbalance ($J$9) shows that passive ordering violations (diagnosed by the indicator $\Delta_{0,1}/h=8.4$0) occur before the stronger $\Delta_{0,1}/h=8.4$1 inversion. The onset of non-passivity in the diagonal energy-basis population distribution is the relevant threshold for positive population ergotropy, consistent with passivity theory.

Figure 2: Ergotropy channel decomposition highlights population-dominated storage and passive ordering violations, with noise reducing both total ergotropy and coherence.

Trajectories reveal that most extractable work is stored in non-passive populations, even as the drive generates transient coherence. This underscores the role of coherence as a dynamical resource supporting population redistribution, and not necessarily as the main repository of ergotropy in this protocol.

Noise-Induced Degradation: Channel Maps

Two-dimensional maps of ergotropy channels over time and $\Delta_{0,1}/h=8.4$2 visualize the degradation mechanism under $\Delta_{0,1}/h=8.4$3 detuning noise. Total ergotropy ($\Delta_{0,1}/h=8.4$4) and population ergotropy ($\Delta_{0,1}/h=8.4$5) show closely aligned structures, confirming the population-dominated character.

The region with large passive ordering violation ($\Delta_{0,1}/h=8.4$6) diminishes as detuning noise amplitude increases, signaling weakened population transfer pathways and reduced capacity to generate non-passive distributions. Coherent ergotropy ($\Delta_{0,1}/h=8.4$7) remains finite but subdominant throughout.

Figure 3: Channel-resolved ergotropy maps elucidate noise-induced suppression of passive ordering violation, driving loss of extractable work in the QB.

This establishes that detuning noise primarily impairs QB performance by disrupting the population transfer mechanisms underlying non-passive ordering, rather than simply by coherence decay. The physical origin is realization-dependent detuning shifts, which perturb selective resonant dynamics and reduce transfer efficiency.

Implications and Prospects

From a practical standpoint, the results imply that materials engineering to minimize detuning noise (e.g., using thin quantum wells [PaqueletWuetz2023]) will critically enhance QB robustness, not only by protecting energy basis coherence but more importantly by preserving population ordering pathways vital for ergotropy.

Theoretically, this population-centric ergotropy interpretation aligns with recent multichannel QB frameworks [Francica2020, Wang2026Ergotropy] and motivates the refinement of charging protocols that combine coherent driving with robust population transfer. It also suggests extensions—incorporation of relaxation, phonon interaction, correlated noise, or larger DQD arrays—to probe collective charge modes and scalable charging strategies.

Future directions include optimization of tunnel coupling drives for maximal population ergotropy with minimal detuning sensitivity and generalization of ergotropy channel analysis to multi-qubit and many-body QB systems.

Conclusion

The study presents a detailed stochastic Hamiltonian analysis of a capacitively coupled DQD quantum battery subjected to realistic $\Delta_{0,1}/h=8.4$8 detuning noise, with charging implemented via resonant tunnel coupling modulation. The extractable work is shown to be predominantly carried by non-passive population distributions in the energy eigenbasis, with coherence acting as a transient mediator. Detuning noise degrades battery performance chiefly by suppressing population ordering violations underlying ergotropy. This establishes a direct practical and theoretical connection between ergotropy-based battery metrics, charge qubit control protocols, and low-frequency noise physics in solid-state platforms.