Non-Gaussian Quantum Charging: Fock-State Advantage

• Non-Gaussian quantum state charging is a method that uses photon-number (Fock) states to maximize energy transfer precision, power, and efficiency in quantum battery systems.
• It employs full counting statistics via two-point projective measurements to accurately quantify work, fluctuations, and signal-to-noise ratio, showing Fock states yield perfect excitation with zero variance.
• Sequential multi-qubit charging under the Tavis–Cummings model demonstrates superior performance over Gaussian chargers even in the presence of noise and detuning, highlighting practical advantages for quantum technologies.

Non-Gaussian quantum state charging refers to the use of genuinely quantum non-Gaussian states—primarily photon-number (Fock) states—for maximizing energy transfer precision, power, and efficiency in quantum battery systems, particularly under Jaynes–Cummings and Tavis–Cummings light–matter interaction models. This paradigm exploits full counting statistics (FCS) to rigorously characterize both average work and quantum fluctuations, demonstrating that non-Gaussian states outperform all Gaussian chargers (coherent, squeezed, or thermal states) across all relevant thermodynamic figures of merit—including signal-to-noise ratio, variance, and charging fidelity—under both single- and multi-qubit charging protocols (Rinaldi et al., 2024, Rinaldi et al., 17 Jan 2026).

1. Fundamental Model: Jaynes–Cummings Hamiltonian and Battery–Charger Architecture

The archetypal quantum battery–charger system models the battery as a two-level qubit and the charger as a single-mode bosonic field, typically an optical or microwave cavity. The interaction is governed by a number-conserving Jaynes–Cummings (JC) Hamiltonian under the rotating-wave approximation (RWA):

$$\hat{H} = \hbar\omega_{\text{qub}}\frac{1}{2}\hat{\sigma}_z + \hbar\omega_{\text{cav}}\hat{a}^\dagger\hat{a} + \hbar g(\hat{a}\hat{\sigma}^+ + \hat{a}^\dagger\hat{\sigma}^-)$$

where $\hat{a}, \hat{a}^\dagger$ are annihilation and creation operators for the cavity mode, $\hat{\sigma}_z$ is the Pauli-$z$ operator for the qubit, and $g$ is the coupling strength. The battery’s energy is associated with $$H_B=\hbar\omega_{\text{qub}}\frac{1}{2}\hat{\sigma}_z$$. The protocol analyzes scenarios both on perfect resonance ($\omega_{\text{qub}} = \omega_{\text{cav}}$) and under small detuning ($$\Delta\omega = \omega_{\text{qub}} - \omega_{\text{cav}}$$).

Generalization to $M$-qubit batteries employs the Tavis–Cummings Hamiltonian with parallel or sequential charging, using time-dependent controls for collisional charging protocols (Rinaldi et al., 17 Jan 2026). The charger is prepared in a non-Gaussian Fock state $|N\rangle$ or a Gaussian state (coherent $|\alpha\rangle$, squeezed vacuum $|0,r\rangle$, or phase-randomized mixtures) for comparative benchmarking.

2. Full Counting Statistics and Thermodynamic Observables

Charging protocols are quantitatively analyzed using full counting statistics (FCS) via two-point projective measurement (TPM) schemes. The stochastic work $W=E'-E$ is captured by its moment-generating function:

$$\chi(\lambda;\tau) = \text{Tr}\{\exp(i\lambda H_B) U(\tau) \exp(-i\lambda H_B) \rho(0) U^\dagger(\tau)\}$$

Cumulants are extracted by differentiation:

$$\langle W^n \rangle_c = (-i)^n \partial^n_\lambda \ln \chi(\lambda;\tau)\big|_{\lambda=0}$$

For average work, instantaneous power, and variance: \begin{align*} W(\tau) &= \text{Tr}[H_B\rho_B(\tau)] - \text{Tr}[H_B\rho_B(0)] \ P(\tau) &= W(\tau)/\tau \ \Delta W^2(\tau) &= \text{Tr}[H_B^2 \rho_B(\tau)] - [\text{Tr}(H_B\rho_B(\tau))]^2 \ \text{SNR}(\tau) &= W^2(\tau)/\Delta W^2(\tau) \end{align*} Here, $$\rho_B(\tau) = \text{Tr}_{\text{cav}}[U(\tau)(|g\rangle\langle g|\otimes\rho_{\text{cav}}(0))U^\dagger(\tau)]$$, and $U(\tau)$ is the JC time-evolution operator (Rinaldi et al., 2024).

3. Impact of Non-Gaussian Fock-State Charging

Preparation of the charger in an exact Fock state $|N\rangle$ ($p_n=\delta_{n,N}$) enables closed-form analytic solutions for work and variance: \begin{align*} W_F(\tau) &= \hbar\omega_{\text{qub}} N \sin^2(g\sqrt{N}\tau) \ \Delta W^2_F(\tau) &= (\hbar\omega_{\text{qub}})^2 N \sin^2(g\sqrt{N}\tau)[1 - N \sin^2(g\sqrt{N}\tau)] \end{align*} The optimal interaction time $\tau_{\text{opt}} = \pi/(2g\sqrt{N})$ yields perfect qubit charging (fidelity $F=1$), zero fluctuation ($\Delta W^2 \to 0$), and infinite SNR.

By contrast, Gaussian state chargers (coherent and squeezed) never achieve perfect excitation, always yield finite fluctuations, and fail to match the Fock SNR at any time for fixed mean photon number. Table 1 summarizes the charger state performance metrics for $N$ photons (Rinaldi et al., 2024).

Charger State	Mean Work $W(\tau)$	Variance $\Delta W^2(\tau)$	SNR Peak Location
Fock $|N\rangle$	$\hbar\omega N\sin^2(g\sqrt{N}\tau)$	$(\hbar\omega)^2 N\sin^2(...)[1-N\sin^2(...)]$	$\tau_{\text{opt}}$
Coherent	$\hbar\omega N\sin^2(g\sqrt{N}\tau)$	$(\hbar\omega)^2[N\sin^2(...)+N\sin^4(...)]$	finite, nonzero
Squeezed	$\hbar\omega n̄\sin^2(g\sqrt{n̄}\tau)$	$$(\hbar\omega)^2[n̄\sin^2(...)+2n̄(n̄+1)\sin^4(...)]$$	finite, nonzero

Non-Gaussian Fock-state charging advantage persists under finite detuning, modest photon-number fluctuations, initial qubit admixture, and even in multi-qubit extension, provided preparation fidelity and cavity coherence remain high (Rinaldi et al., 17 Jan 2026).

4. Sequential versus Parallel Multi-Qubit Charging

The extension to multi-qubit charging (Tavis–Cummings model) reveals a qualitative distinction between sequential and parallel protocols. Sequential charging—where qubits interact one after another with the cavity—enables all $M=N$ qubits to reach perfect excitation ($F=1$) with suppressed fluctuations ($\text{Var}\to 0$), contingent upon precise tuning of each interaction time $\tau_j \propto 1/\sqrt{N_j}$. This regime manifests true “maximal-precision” charging, with the SNR diverging at optimal pins.

Parallel charging (simultaneous interaction of all qubits) or any protocol using Gaussian field states fails to reach zero variance, yielding only finite SNR, with fidelity degrading as $M$ increases. The mixed protocols further confirm the unique performance benefit conferred by genuine non-Gaussian resources in sequential schemes (Rinaldi et al., 17 Jan 2026).

5. Robustness and Practical Implementation Considerations

Fock-state quantum charging maintains its advantage over Gaussian-state chargers under several practical imperfections:

• Noise resilience: Advantage $D_{x,\langle n\rangle}$ (normalized average SNR difference) remains substantial (up to $\sim$150 for $\langle n\rangle=5$ photons) even for cavity preparation inefficiency ($p\simeq0.95$) and thermal photon numbers $n_{\text{th}}\simeq0.2$.
• Tolerance to detuning: The advantage persists for $\Delta \omega \leq 10^{-3}\omega_{\text{qub}}$.
• Robustness to qubit state impurities $q \leq 10^{-2}$.

Limitations include the need for Fock-state generation fidelity exceeding $\sim$90%, slow decoherence and cavity loss relative to optimal charging time $\tau_{\text{opt}}$, and validity of RWA at $g/\omega \lesssim 0.01$ (Rinaldi et al., 2024, Rinaldi et al., 17 Jan 2026). When these conditions are met, current circuit-QED and trapped-ion platforms can routinely prepare Fock states up to $N\sim5$–10, facilitating experimental demonstrations.

6. Extensions, Outlook, and Generalization

Recent work proposes extensions to time-dependent JC couplings, inclusion of counter-rotating terms (full quantum Rabi model), and non-trivial cavity mode engineering. These analyses confirm that while the absolute precision peak may be reduced under non-ideal controls, the non-Gaussian advantage endures as long as deviations from ideal conditions remain moderate. Sequential charging of qubit stacks using single-mode non-Gaussian fields is particularly promising for tasks demanding extremely high accuracy, such as quantum metrology and robust quantum information processing.

A plausible implication is the universality of non-Gaussian resource advantage for quantum energy transfer protocols, motivating further studies into scalable photon-number state generation, integration with error-suppressing quantum control, and optimization of charging protocols to mitigate practical imperfections (Rinaldi et al., 2024, Rinaldi et al., 17 Jan 2026).