Noise-Induced Coherences in Quantum Systems

• Noise-induced coherences are off-diagonal density-matrix elements produced by stochastic environments that enable quantum interference and surprisingly prolonged coherence in open systems.
• They arise from non-orthogonal dipole alignments in multilevel systems and manifest as either transient oscillations or long-lived plateaus depending on the energy-splitting and decay rates.
• These coherences improve quantum heat engine performance, facilitate efficient energy transport, and offer insights for engineering decoherence-free subspaces in quantum networks.

Noise-induced coherences are off-diagonal density-matrix elements generated by stochastic environments, such as incoherent light or classical/quantum noise sources, that fundamentally lack the fixed phase reference of coherent (laser-drive) fields. This phenomenon arises from quantum-mechanical interference between indistinguishable transitions or transfer pathways in open quantum systems, enabling the formation and, in many cases, unexpectedly prolonged persistence of quantum coherences under conditions where classical intuition would predict rapid decoherence. Noise-induced coherence mechanisms span diverse settings, including molecular systems, coupled quantum oscillators, quantum heat engines, and engineered quantum networks.

1. Theoretical Origins and Formal Mechanisms

Noise-induced coherence appears in diverse platforms but is most fundamentally rooted in the evolution of the reduced density matrix of an open system coupled to thermal or stochastic baths. In the archetypal V-type system, incoherent light simultaneously excites two transitions from a common ground state $|g\rangle$ to excited states $|e_1\rangle$ and $|e_2\rangle$. Quantum interference between $g\to e_1$ and $g\to e_2$ pathways generates a coherence $\rho_{e_1e_2}$ proportional to the overlap of the transition dipoles, parameterized by $$p=(\mu_{g e_1}\cdot\mu_{g e_2})/(|\mu_{g e_1}||\mu_{g e_2}|)$$ (Tscherbul et al., 2014, Dodin et al., 2021, Dodin et al., 2015).

The non-secular terms in the master equation couple populations and coherences, leading to dynamics not captured by the secular Redfield or Pauli-rate-limited treatments. In the generic form: $$\begin{aligned} \frac{d}{dt}\rho_{e_1 e_2} & = -\Gamma_C\,\rho_{e_1e_2} - i \Delta\,\rho_{e_1e_2} + p\,f(\{\rho_{ij}\}) + \ldots \end{aligned}$$ where $\Gamma_C$ is the overall decoherence rate, $\Delta$ the level splitting, and $f$ encodes pumping from population terms (Tscherbul et al., 2014, Dodin et al., 2017). The essential ingredient for noise-induced coherence is the presence of non-orthogonal dipoles or, more generally, geometric constraints preventing all transition dipoles from being orthogonal—a generic situation in any multilevel system with four or more states (Dodin et al., 2023).

2. Dynamical Regimes and Analytical Structure

The time evolution and qualitative behavior of noise-induced coherences strongly depend on the system parameters, especially the ratio of energy splitting $\Delta$ to decay/broadening rates $\gamma$. Two primary regimes are established:

• Underdamped ($\Delta \gg \gamma$): Coherences oscillate at the frequency $\Delta$ and decay on the timescale $1/\gamma$, generating transient quantum beats (Tscherbul et al., 2014). These survive for modest times and are prominent in systems with well-separated levels.
• Overdamped ($\Delta \ll \gamma$): Coherences build up quickly to a value comparable to the populations and persist as long-lived quasi-stationary plateaus decaying on the slow timescale $$\tau_\text{long} \sim (2/\gamma)(\Delta/\gamma)^{-2}$$, potentially many orders of magnitude longer than the direct radiative lifetime as $\Delta\rightarrow 0$ (Tscherbul et al., 2014, Dodin et al., 2015).

Robustness against dephasing and additional loss channels depends on the relationship between $\gamma$, pure dephasing rates, and the system’s symmetry; the quasi-stationary plateau may persist until environmental decoherence rates become dominant (Tscherbul et al., 2014).

3. Noise-Induced Coherence in Complex and Multilevel Systems

In multilevel systems, such as molecular complexes or solid-state manifolds, geometric constraints guarantee the presence of noise-induced coherences. For four or more energy levels, it is generically impossible for all relevant dipole vectors to be pairwise orthogonal; consequently, one or more nonzero alignment parameters $p$ are inevitable and thus so are noise-induced coherences (Dodin et al., 2023).

A salient feature in these systems is coherence transfer: coherences generated in one manifold (e.g., excited states) can induce corresponding coherences in another manifold (e.g., ground states), driving genuine population oscillations even under purely incoherent excitation—a phenomenon forbidden in strictly secular treatments. The underlying mechanism is continually present in molecules, Rydberg-atom ladders, and artificial quantum networks (Dodin et al., 2023).

The table below summarizes typical systems and manifestations:

System	Mechanism	Observational Signature
V-type atom	Pumping-induced Fano coherence	Quantum beats or long-lived off-diagonals
Multilevel molecule	Geometric dipole overlap	Ground–excited coherence transfer, oscillating populations
Quantum heat engine	Fano interference in baths	Enhanced ergotropy, multiple ergotropy regimes
Coupled oscillators	Correlated dissipation	Noise-protected synchronization, entanglement

4. Quantum Thermodynamics and Information Transport

Noise-induced coherence has direct implications for quantum thermodynamics and energy transport. In quantum heat engines based on multi-level systems, steady-state coherences induced by baths can enhance extractable work (ergotropy), lead to multiple ergotropy intervals, and affect power-flux characteristics (Sarmah et al., 9 Apr 2024, Sarmah et al., 2023). The presence and magnitude of noise-induced coherences are tunable via bath-induced dipole alignment factors and can be inferred from full counting statistics of photon exchange fluctuations (Sarmah et al., 2023).

In biological transport networks, environmental noise can assist excitation transfer by both generating and sustaining coherences among delocalized excitonic states. “Phonon antenna” effects—resonant matching between system splittings and environmental spectral densities—provide a route to long-lived coherence and optimized energy migration in, e.g., the Fenna–Matthews–Olson complex (Chin et al., 2012).

5. Noise-Induced Coherences Beyond Markovian Baths: Correlated Noise and Decoherence-Free Subspaces

Correlated and anticorrelated noise environments can both generate and protect quantum coherence and even entanglement. In coupled qubit or oscillator arrays, specific subspaces (e.g., symmetric or antisymmetric manifolds) can become decoherence-free under fully correlated (or anticorrelated) noise, leading to persistence of entanglement and long-time synchronization (Bittner et al., 2023, Bittner et al., 29 Oct 2024). In such cases, certain Bell states become immune to dephasing when local noise correlations are engineered, as directly observable via fidelity and purity measurements (Bittner et al., 2023).

In networks of indistinguishable particles or bosonic modes, collective noise can induce steady-state coherences in permutation-symmetric sectors that are robust to arbitrarily strong dephasing—a hallmark of decoherence-free subspaces emerging from the symmetry of noise coupling (Perez-Leija et al., 2017, Mogilevtsev et al., 2016).

6. Experimental Platforms and Observables

Noise-induced coherences have well-defined observable consequences:

• Fluorescence anisotropy/quantum beats: Angle- and polarization-resolved fluorescence from atoms or molecules subject to incoherent light can display oscillatory or stationary coherences, with clear differences between secular and non-secular master-equation predictions (Dodin et al., 2017, Dodin et al., 2021).
• Transient absorption: In multilevel systems, oscillations of population under transient incoherent excitation are direct signatures of noise-induced coherence (Dodin et al., 2023).
• Photon statistics: Nonequilibrium fluctuations in quantum heat engines encode the magnitude of noise-induced coherences and can be inferred via machine learning on photon-counting cumulants (Sarmah et al., 2023).
• Entanglement witnesses: Measurable increases in entanglement negativity and high-fidelity evolution in entangled qubit pairs under correlated noise distinguish noise-induced protection mechanisms (Bittner et al., 29 Oct 2024, Bittner et al., 2023).
• Induced-coherence interferometry: Heralded single-photon detection protocols remove the detrimental effect of thermal background, restoring visibility that would otherwise be washed out by incoherent noise (Theerthagiri et al., 5 Nov 2025).

7. Applications, Limitations, and Outlook

Noise-induced coherence is now recognized as not merely a theoretical anomaly but an experimentally validated effect with potential for engineered quantum control, energy-harvesting, and information processing. Practical exploitation requires nearly degenerate levels, non-orthogonal dipole transitions, and environmental decoherence slow compared to system decay. Controlled synthetic platforms—ranging from cold-atom ensembles and quantum dots to photonic networks—are increasingly used to probe and harness these effects (Tscherbul et al., 2014, Sarmah et al., 9 Apr 2024, Theerthagiri et al., 5 Nov 2025).

Challenges remain in scaling noise-induced coherence to macroscopic or room-temperature regimes, quantifying behavior in strongly non-Markovian environments, and connecting to functional roles in biological quantum processes. Nevertheless, the geometric inevitability of these coherences in realistic multilevel systems ensures their ubiquity and ongoing relevance for quantum science and technology (Dodin et al., 2023).

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Key Primary References

• Tscherbul & Brumer, "Long-lived quasi-stationary coherences in V-type system driven by incoherent light" (Tscherbul et al., 2014)
• Dodin, Tscherbul & Brumer, "Population Oscillations and Ubiquitous Coherences in multilevel quantum systems driven by incoherent radiation" (Dodin et al., 2023)
• Bittner, Tyagi, "Noise-induced synchronization in coupled quantum oscillators" (Bittner et al., 29 Oct 2024)
• Chew et al., "Noise induced coherent ergotropy of a quantum heat engine" (Sarmah et al., 9 Apr 2024)
• Vlaming et al., "Coherence and Decoherence in Biological Systems: Principles of Noise Assisted Transport and the Origin of Long-lived Coherences" (Chin et al., 2012)
• Bittner et al., "Correlated noise enhances coherence and fidelity in coupled qubits" (Bittner et al., 2023)
• Tscherbul & Brumer, "Secular vs. Non-secular Redfield Dynamics and Fano Coherences in Incoherent Excitation: An Experimental Proposal" (Dodin et al., 2017)
• Chenu et al., "Noise-Induced Coherence in Molecular Processes" (Dodin et al., 2021)
• Yuan et al., "Endurance of Quantum Coherence in Born-Markov Open Quantum Systems" (Perez-Leija et al., 2017)
• Mogilevtsev & Slepyan, "Diffusive lossless energy and coherence transfer by noisy coupling" (Mogilevtsev et al., 2016)
• Ghosh et al., "Learning coherences from nonequilibrium fluctuations in a quantum heat engine" (Sarmah et al., 2023)
• Barzanjeh et al., "Heralded Induced-Coherence Interferometry in a Noisy Environment" (Theerthagiri et al., 5 Nov 2025)