Nonreciprocal Quantum Batteries

• Nonreciprocal quantum batteries are charger–battery systems with engineered couplings that favor directional energy flow while suppressing backflow.
• Techniques like reservoir engineering, non-Hermitian interference, and chiral waveguide couplings yield enhancements up to fourfold in energy storage and up to 34–55-fold in extractable work.
• Advanced models demonstrate that optimized network topologies and nonlinear mechanisms enable scalable, robust, and steady-state quantum energy storage.

Searching arXiv for papers on nonreciprocal quantum batteries and closely related architectures. Searching for “nonreciprocal quantum battery”, “chiral quantum batteries”, and related waveguide/cavity implementations. Nonreciprocal quantum batteries are charger–battery systems in which the effective coupling allows energy flow predominantly from charger to battery, with suppression or elimination of backflow. In the recent literature this directionality is realized through reservoir engineering, non-Hermitian interference, loss-engineered auxiliary cavities, chiral waveguide couplings, and phase-tunable waveguide-mediated interactions, rather than through a direct symmetric charger–battery Hamiltonian alone. Representative bosonic implementations report a fourfold increase in battery energy compared to conventional charger-battery systems, steady-state regimes in which the battery stores about four times more energy than remains in the charger, and chiral platforms exhibiting a 34-fold increase in energy capacity together with a 55-fold boost in extractable work (Ahmadi et al., 2024, Lin et al., 8 Dec 2025, Liu et al., 26 Mar 2026).

1. Foundational notion and minimal bosonic formulation

The canonical nonreciprocal quantum-battery construction uses two bosonic modes: a charger $a$ and a battery $b$, both modeled as harmonic oscillators and both coupled to local baths, with an additional shared reservoir engineered to mediate dissipative cross-coupling. In the laboratory-frame formulation,

$$H = \omega_a a^\dagger a + \omega_b b^\dagger b + (J a^\dagger b + J^* b^\dagger a) + \mathcal{E}\left(e^{i\omega_L t} a + e^{-i\omega_L t} a^\dagger\right),$$

while the open dynamics is governed by

$$\dot{\rho} = -i[H,\rho] + \sum_{i=a,b}\kappa_i \mathcal{L}_i[\rho] + \Gamma \mathcal{L}_z[\rho], \qquad z=p_a a + p_b b,$$

with $\Gamma_i=\Gamma |p_i|^2$, $\Lambda_i=\kappa_i+\Gamma_i$, and $\mu=-p_b p_a^*$ (Ahmadi et al., 2024).

The operational encoding of nonreciprocity is the cancellation of the battery backaction on the charger. This is achieved by imposing

$J = -i\mu \frac{\Gamma}{2},$

so that the charger equation becomes independent of the battery, whereas the battery remains driven by the charger. In this regime the dynamics is cascaded: charger $\to$ battery, but not battery $\to$ charger. Under resonant driving, the nonreciprocal steady-state battery energy is

$b$0

the charger energy is

$b$1

and the ratio

$b$2

defines a dissipative cooperativity. When $b$3, the battery holds more energy than the charger in steady state (Ahmadi et al., 2024).

This minimal model established the central conceptual shift in the field. In reciprocal charger–battery dimers, the energy oscillates back and forth and charging performance is sensitive to timing. In the nonreciprocal regime, by contrast, the battery energy grows monotonically to a stationary value, remains effective even in overdamped coupling regimes, and does not require precise temporal control over evolution parameters. In the symmetric case, the stationary enhancement over the reciprocal model approaches a factor of four (Ahmadi et al., 2024).

Architecture	Nonreciprocal mechanism	Representative outcome
Shared-reservoir bosonic dimer	Coherent–dissipative interference	Fourfold increase in battery energy (Ahmadi et al., 2024)
Bad-cavity non-Hermitian dimer	Adiabatically eliminated lossy auxiliary mode	$b$4 on resonance (Lin et al., 8 Dec 2025)
Loss-induced three-cavity scheme	Direct/indirect interference via engineered auxiliary loss	$b$5 for selected parameters (Zafar et al., 12 May 2026)
Chiral magnonic waveguide battery	$b$6 from spin–momentum locking	34-fold energy and 55-fold ergotropy enhancement (Liu et al., 26 Mar 2026)

2. Reservoir engineering and non-Hermitian directional charging

A more explicit non-Hermitian implementation introduces a charger cavity $b$7, a battery cavity $b$8, and a strongly damped auxiliary “bad cavity” $b$9. In the rotating frame, the full Hamiltonian reads

$$H = \omega_a a^\dagger a + \omega_b b^\dagger b + (J a^\dagger b + J^* b^\dagger a) + \mathcal{E}\left(e^{i\omega_L t} a + e^{-i\omega_L t} a^\dagger\right),$$0

with strong-damping conditions

$$H = \omega_a a^\dagger a + \omega_b b^\dagger b + (J a^\dagger b + J^* b^\dagger a) + \mathcal{E}\left(e^{i\omega_L t} a + e^{-i\omega_L t} a^\dagger\right),$$1

Adiabatic elimination of $$H = \omega_a a^\dagger a + \omega_b b^\dagger b + (J a^\dagger b + J^* b^\dagger a) + \mathcal{E}\left(e^{i\omega_L t} a + e^{-i\omega_L t} a^\dagger\right),$$2 yields an effective two-mode non-Hermitian Hamiltonian with coherent couplings $$H = \omega_a a^\dagger a + \omega_b b^\dagger b + (J a^\dagger b + J^* b^\dagger a) + \mathcal{E}\left(e^{i\omega_L t} a + e^{-i\omega_L t} a^\dagger\right),$$3, dissipative coupling $$H = \omega_a a^\dagger a + \omega_b b^\dagger b + (J a^\dagger b + J^* b^\dagger a) + \mathcal{E}\left(e^{i\omega_L t} a + e^{-i\omega_L t} a^\dagger\right),$$4, and renormalized linewidths $$H = \omega_a a^\dagger a + \omega_b b^\dagger b + (J a^\dagger b + J^* b^\dagger a) + \mathcal{E}\left(e^{i\omega_L t} a + e^{-i\omega_L t} a^\dagger\right),$$5 (Lin et al., 8 Dec 2025).

The directional regime arises when one off-diagonal channel is cancelled by destructive interference: $$H = \omega_a a^\dagger a + \omega_b b^\dagger b + (J a^\dagger b + J^* b^\dagger a) + \mathcal{E}\left(e^{i\omega_L t} a + e^{-i\omega_L t} a^\dagger\right),$$6 Then the first-moment equation for the charger decouples from the battery, while the battery still depends on the charger. The resulting effective coupling matrix is triangular, and the directionality is explicit at the level of energy flow: energy can be pumped from the drive into $$H = \omega_a a^\dagger a + \omega_b b^\dagger b + (J a^\dagger b + J^* b^\dagger a) + \mathcal{E}\left(e^{i\omega_L t} a + e^{-i\omega_L t} a^\dagger\right),$$7, then from $$H = \omega_a a^\dagger a + \omega_b b^\dagger b + (J a^\dagger b + J^* b^\dagger a) + \mathcal{E}\left(e^{i\omega_L t} a + e^{-i\omega_L t} a^\dagger\right),$$8 to $$H = \omega_a a^\dagger a + \omega_b b^\dagger b + (J a^\dagger b + J^* b^\dagger a) + \mathcal{E}\left(e^{i\omega_L t} a + e^{-i\omega_L t} a^\dagger\right),$$9, but not from $$\dot{\rho} = -i[H,\rho] + \sum_{i=a,b}\kappa_i \mathcal{L}_i[\rho] + \Gamma \mathcal{L}_z[\rho], \qquad z=p_a a + p_b b,$$0 back into $$\dot{\rho} = -i[H,\rho] + \sum_{i=a,b}\kappa_i \mathcal{L}_i[\rho] + \Gamma \mathcal{L}_z[\rho], \qquad z=p_a a + p_b b,$$1 (Lin et al., 8 Dec 2025).

Under effective resonance, $$\dot{\rho} = -i[H,\rho] + \sum_{i=a,b}\kappa_i \mathcal{L}_i[\rho] + \Gamma \mathcal{L}_z[\rho], \qquad z=p_a a + p_b b,$$2, the long-time energies are

$$\dot{\rho} = -i[H,\rho] + \sum_{i=a,b}\kappa_i \mathcal{L}_i[\rho] + \Gamma \mathcal{L}_z[\rho], \qquad z=p_a a + p_b b,$$3

and

$$\dot{\rho} = -i[H,\rho] + \sum_{i=a,b}\kappa_i \mathcal{L}_i[\rho] + \Gamma \mathcal{L}_z[\rho], \qquad z=p_a a + p_b b,$$4

For the symmetric case $$\dot{\rho} = -i[H,\rho] + \sum_{i=a,b}\kappa_i \mathcal{L}_i[\rho] + \Gamma \mathcal{L}_z[\rho], \qquad z=p_a a + p_b b,$$5 and $$\dot{\rho} = -i[H,\rho] + \sum_{i=a,b}\kappa_i \mathcal{L}_i[\rho] + \Gamma \mathcal{L}_z[\rho], \qquad z=p_a a + p_b b,$$6, the ratio becomes

$$\dot{\rho} = -i[H,\rho] + \sum_{i=a,b}\kappa_i \mathcal{L}_i[\rho] + \Gamma \mathcal{L}_z[\rho], \qquad z=p_a a + p_b b,$$7

so the battery stores about four times more energy than remains in the charger on resonance. The same study shows that the instantaneous power reaches $$\dot{\rho} = -i[H,\rho] + \sum_{i=a,b}\kappa_i \mathcal{L}_i[\rho] + \Gamma \mathcal{L}_z[\rho], \qquad z=p_a a + p_b b,$$8 at $$\dot{\rho} = -i[H,\rho] + \sum_{i=a,b}\kappa_i \mathcal{L}_i[\rho] + \Gamma \mathcal{L}_z[\rho], \qquad z=p_a a + p_b b,$$9 under resonance, decreases slightly to $\Gamma_i=\Gamma |p_i|^2$0 for $\Gamma_i=\Gamma |p_i|^2$1, and falls drastically to $\Gamma_i=\Gamma |p_i|^2$2 for $\Gamma_i=\Gamma |p_i|^2$3, with strong oscillations in time (Lin et al., 8 Dec 2025).

This non-Hermitian framework also introduces exceptional-point operation as a partially nonreciprocal regime. There both off-diagonal channels remain nonzero, but the dynamical matrix is tuned to an exceptional point. The paper reports that, in comparison to the fully nonreciprocal scheme, the battery operating at the exceptional point exhibits greater resilience to parameter fluctuations, especially under finite detuning and damping asymmetry (Lin et al., 8 Dec 2025).

3. Loss-induced interference and fully remote waveguide charging

A distinct route dispenses with a shared bath between charger and battery and instead uses local loss in an auxiliary cavity to induce directional interference. In the three-cavity optical model, the charger cavity $\Gamma_i=\Gamma |p_i|^2$4 is directly driven, the battery cavity $\Gamma_i=\Gamma |p_i|^2$5 stores energy, and an auxiliary cavity $\Gamma_i=\Gamma |p_i|^2$6 with tunable loss $\Gamma_i=\Gamma |p_i|^2$7 mediates an indirect transmission path. The Hamiltonian contains direct coherent coupling $\Gamma_i=\Gamma |p_i|^2$8 between charger and battery, plus coherent couplings $\Gamma_i=\Gamma |p_i|^2$9 and $\Lambda_i=\kappa_i+\Gamma_i$0 to the lossy auxiliary cavity (Zafar et al., 12 May 2026).

The nonreciprocity originates from interference between two transmission channels: the direct path $\Lambda_i=\kappa_i+\Gamma_i$1 and the indirect path $\Lambda_i=\kappa_i+\Gamma_i$2, with the complex susceptibility of the lossy auxiliary cavity introducing the additional phase needed to produce constructive interference in one direction and destructive interference in the other. The steady-state battery and charger energies, for resonance and equal couplings $\Lambda_i=\kappa_i+\Gamma_i$3, are

$\Lambda_i=\kappa_i+\Gamma_i$4

$\Lambda_i=\kappa_i+\Gamma_i$5

so that the energy-transfer gain is

$\Lambda_i=\kappa_i+\Gamma_i$6

For $\Lambda_i=\kappa_i+\Gamma_i$7, reciprocity is recovered and $\Lambda_i=\kappa_i+\Gamma_i$8. For selected parameters in Fig. 2, $\Lambda_i=\kappa_i+\Gamma_i$9, and in the strong-coupling regime the nonreciprocal battery stores up to $\mu=-p_b p_a^*$0 times more energy than the bipartite reciprocal case (Zafar et al., 12 May 2026).

A second remote architecture removes even the direct local interaction and relies solely on engineered waveguide-mediated interference. In this waveguide-QED construction, a driven charger and a remote battery are coupled only via a one-dimensional waveguide. After eliminating the waveguide, the effective dynamics contains a coherent exchange $\mu=-p_b p_a^*$1, collective decay $\mu=-p_b p_a^*$2, and directional couplings

$\mu=-p_b p_a^*$3

The nonreciprocal condition is $\mu=-p_b p_a^*$4, which yields cascaded-like unidirectional charging. The nonreciprocal ratio is

$\mu=-p_b p_a^*$5

and, for linear driving in steady state,

$\mu=-p_b p_a^*$6

The relative storage ratio is

$\mu=-p_b p_a^*$7

The central result is that nonreciprocity and storage efficiency can be independently engineered. Among four configurations, the giant-small-emitter mirror-terminated geometry simultaneously achieves perfect nonreciprocity and battery-dominated storage, while both giant-small-emitter configurations exhibit distance-insensitive directionality (Guo et al., 21 May 2026).

4. Nonlinear bosonic mechanisms and two-photon nonreciprocal charging

Nonreciprocal quantum batteries intersect with a broader bosonic program in which strong nonlinearities reorganize the accessible charging pathways. A particularly transparent example is the nonlinear bosonic battery with Hamiltonian

$\mu=-p_b p_a^*$8

where one quantum of the charger is resonant with $\mu=-p_b p_a^*$9 quanta of the battery. For $J = -i\mu \frac{\Gamma}{2},$0, the dynamics is confined to the two-state subspace $J = -i\mu \frac{\Gamma}{2},$1, and under equal-variance comparison with the linear model the charging time becomes

$J = -i\mu \frac{\Gamma}{2},$2

with full charging

$J = -i\mu \frac{\Gamma}{2},$3

and power

$J = -i\mu \frac{\Gamma}{2},$4

The classical counterpart of the nonlinear Hamiltonian shows no charging at all for $J = -i\mu \frac{\Gamma}{2},$5. However, the model is reciprocal: the interaction is symmetric and energy can flow back and forth, so the directional behavior is only protocol-level, obtained by switching off the interaction at the first maximum. The paper therefore treats nonlinear bosonic conversion as a coherent core that could be embedded in explicitly nonreciprocal architectures such as cascaded cavities or chiral waveguides (Andolina et al., 2024).

An explicit nonreciprocal realization of nonlinear charging is provided by the two-photon-driven bosonic battery. The charger is pumped by

$J = -i\mu \frac{\Gamma}{2},$6

and the reduced dynamics includes local damping, coherent charger–battery coupling, and a collective dissipator

$J = -i\mu \frac{\Gamma}{2},$7

The unidirectional condition is again

$J = -i\mu \frac{\Gamma}{2},$8

which suppresses battery $J = -i\mu \frac{\Gamma}{2},$9 charger backflow. The dynamics admits a stable steady state only when

$\to$0

Within this regime, increasing the two-photon drive enhances both stored energy and ergotropy, and for $\to$1 the two-photon scheme yields larger stored energy and ergotropy than the single-photon case. The trade-off is that stronger two-photon driving prolongs equilibration time, and the relative conversion-efficiency ratio

$\to$2

remains below unity in the explored regimes, so the single-photon scheme can be more efficient in ergotropy per unit charger energy even when the two-photon scheme has higher absolute capacity and ergotropy (Xu et al., 15 Nov 2025).

This juxtaposition clarifies a frequent misconception. Nonlinearity does not, by itself, guarantee nonreciprocity: the reciprocal nonlinear model remains symmetric in its Hamiltonian exchange. Conversely, nonreciprocity does not, by itself, guarantee maximal extractable work: in the two-photon model, performance depends on how squeezing-generated second moments are converted into ergotropy and on how the equilibration threshold constrains the drive (Andolina et al., 2024, Xu et al., 15 Nov 2025).

5. Chiral and biophotomimetic nonreciprocal batteries

Chiral waveguide QED provides a microscopic realization of nonreciprocity through direction-dependent system–continuum couplings. In the magnonic battery, two yttrium iron garnet spheres are embedded in a rectangular metallic microwave waveguide operated in the fundamental $\to$3 mode. The left sphere serves as the charger, the right sphere as the battery, and the chiral magnon–photon interaction leads to distinct right- and left-propagating decay rates

$\to$4

The chirality parameter is

$\to$5

with $\to$6 reciprocal and $\to$7 fully chiral. The effective coherent couplings are

$\to$8

and the collective dissipators are built from

$\to$9

For realistic parameters, the fully chiral case yields a 34-fold increase in energy capacity and a 55-fold boost in extractable work compared to the achiral counterpart, while the work efficiency approaches $\to$0. The ergotropy enhancement is maximal at constructive-interference distances

$\to$1

and minimal at

$\to$2

showing that nonreciprocity determines how much energy arrives, whereas coherent interference determines how much of that energy remains useful as work (Liu et al., 26 Mar 2026).

A structurally different notion of nonreciprocity appears in the biophotomimetic battery inspired by bacterial light-harvesting complexes. There the effective battery is a five-level system

$\to$3

where $\to$4 is a bright superradiant state, $\to$5 is a dark subradiant state, $\to$6 is an intermediate storage state, and $\to$7 is a discharge state coupled to a unimodal cavity. The bright and dark rates are extracted from an effective non-Hermitian ring–center Hamiltonian with eigenvalues $\to$8,

$\to$9

so geometry directly shapes the open-system kinetics. The charging bath acts only on $b$00, while the cavity acts only on $b$01, producing a directional energy funnel from bath to storage manifold to work mode. Numerically, $b$02 at all times, $b$03 can be reduced to $b$04 at large $b$05, ergotropy peaks around $b$06, work around $b$07, flux around $b$08, and power around $b$09. The study also reports that ergotropy exceeds capacity and approaches it linearly with increasing system size, with an optimal small-size regime that disappears under strong coupling (Kalita et al., 16 Mar 2026).

These two platforms use very different microscopic resources—spin–momentum locking in one case, bright/dark-state geometry in the other—but they converge on the same systems-level lesson: nonreciprocal charging is not only about suppressing backflow; it is also about shaping the coherence structure of the stored energy so that extractable work remains large (Liu et al., 26 Mar 2026, Kalita et al., 16 Mar 2026).

6. Network topology, scaling laws, and transport engineering

Nonreciprocity becomes especially consequential in multi-battery networks, where the central question is no longer only how much energy can be stored, but how energy propagates across connected battery nodes. One proposal constructs non-Hermitian Aharonov–Bohm triangles from direct coherent links and indirect links through lossy intermediate modes. In cascaded chains,

$b$10

nonreciprocity yields terminal-battery energy

$b$11

and in the weak interaction regime $b$12, the gain over the reciprocal chain obeys

$b$13

with maximal asymptote

$b$14

The same architecture yields identical asymptotic enhancement in maximal charging power,

$b$15

while the parallel configuration gives size-independent gains of $b$16 in energy and power relative to reciprocal case I (Zhao et al., 28 Mar 2025).

A complementary network treatment frames the problem as architecture-dependent transport. In the nonreciprocal cascaded network, the optimal coupling obeys

$b$17

so

$b$18

in the large-$b$19 limit. In the nonreciprocal parallel network,

$b$20

so

$b$21

The reciprocal cascaded chain, by contrast, exhibits a parity-dependent spectral response: even $b$22 supports a zero-energy mode with large edge weight, whereas odd $b$23 does not, producing an odd–even transport effect absent in the nonreciprocal and parallel configurations. The same work further shows that thermal noise mainly increases passive energy, whereas squeezing enhances ergotropy and thus the useful fraction of stored energy (Liu et al., 24 Mar 2026).

These two lines of work address different aspects of scalability. One emphasizes gain factors in the weak-interaction regime; the other emphasizes optimal-coupling laws and topology-dependent transport. Together they establish that nonreciprocal battery networks must be designed at the architecture level: cascaded transport is limited by propagation distance, while parallel charging is limited by collective damping of the charger (Zhao et al., 28 Mar 2025, Liu et al., 24 Mar 2026).

7. Thermodynamic observables, implementation routes, and current limitations

The recent literature has broadened the set of performance metrics beyond stored energy. Standard bosonic models use

$b$24

and often define energy-transfer efficiency through ratios such as $b$25, $b$26, or $b$27. In Gaussian non-passive settings, the decisive quantity is ergotropy,

$b$28

with passive energy

$b$29

for the single-mode quadratic-driving battery, or, in the two-photon-driven bosonic model,

$b$30

These formulas make explicit that stored energy and useful work coincide only in restricted regimes, such as linearly driven coherent-state batteries at zero temperature (Guo et al., 21 May 2026, Xu et al., 15 Nov 2025).

Implementation proposals are correspondingly diverse. Superconducting circuits are a recurrent platform: the bad-cavity non-Hermitian battery reports typical parameters $b$31 MHz, $b$32 MHz, $b$33 MHz, $b$34 MHz, $b$35 MHz, and $b$36 MHz, consistent with $b$37 for full nonreciprocity (Lin et al., 8 Dec 2025). The loss-induced three-cavity scheme highlights microspherical optical cavities with a chromium-coated silica-nanofiber tip to tune the auxiliary loss rate, and also points to circuit QED as a feasible platform (Zafar et al., 12 May 2026). The nonlinear bosonic battery proposes a superconducting-circuit realization in which a Josephson junction mediates the effective interaction

$b$38

but also warns that the resonant term scales as $b$39, so high nonlinearity orders are realistic only for moderate $b$40, and non-resonant terms can spoil the ideal model for large $b$41 (Andolina et al., 2024). Chiral and waveguide-based batteries rely on platforms that can control propagation phases and spin–momentum locking, including YIG-waveguide magnonics and giant-emitter superconducting waveguide QED (Liu et al., 26 Mar 2026, Guo et al., 21 May 2026).

The principal limitations are now well delineated. Detuning strongly suppresses directional charging in reservoir-engineered non-Hermitian dimers. Markovian elimination of auxiliary reservoirs or waveguides remains a standing approximation in most models. Thermal noise generally increases passive energy rather than ergotropy. Strong coupling can enhance storage while degrading power output, as in the biophotomimetic battery. In nonlinear bosonic proposals, large-order processes are constrained by perturbative circuit parameters. These results suggest that the central open problem is no longer whether nonreciprocity can improve charging, but how to co-design directionality, coherence structure, and transport topology so that stored energy remains both large and extractable across realistic open-system networks (Lin et al., 8 Dec 2025, Kalita et al., 16 Mar 2026, Liu et al., 24 Mar 2026).