Vacuum Coherence in Quantum Systems

• Vacuum coherence is the emergence of quantum coherence from vacuum field fluctuations, enabling effects such as spontaneous emission interference, population trapping, and nonlocal correlations.
• Advanced techniques like squeezed vacuum engineering and boundary modifications actively control decoherence by altering decay channels and extending coherence times.
• Experimental realizations in systems from quantum optics to many-body dynamics demonstrate how vacuum coherence enables precise manipulation and measurement, offering new tools for quantum information processing.

Vacuum coherence refers to the emergence, manipulation, and consequences of quantum coherence originating from interactions with the electromagnetic vacuum or broader quantum vacuum fields. This phenomenon, distinct from coherence induced by external fields, is centrally involved in processes such as spontaneous emission interference, population trapping in various quantum systems, control of decay rates, and nonlocal correlations in relativistic quantum field settings. Vacuum coherence mechanisms extend across atomic, molecular, solid-state, high-energy, and macroscopic quantum platforms.

1. Mechanisms of Vacuum-Induced Coherence (VIC) in Multilevel Systems

Vacuum-induced coherence (VIC) typically arises when two or more excited states share nonorthogonal transition dipole moments and decay via indistinguishable vacuum channels to a common lower state. The essential condition is nonorthogonality of the dipole matrix elements—if $\mathcal{D}_1$ and $\mathcal{D}_2$ denote transition dipoles between two excited ro-vibrational levels and the ground continuum, then their overlap underpins the nonvanishing cross damping term in the evolution equations. For ultracold photoassociation in molecules (Das et al., 2011), the model Hamiltonian splits into coherent and incoherent parts: $\mathcal{H} = \mathcal{H}_c + \mathcal{H}_{inc}$ where $\mathcal{H}_c$ governs laser-driven transitions and $\mathcal{H}_{inc}$ captures vacuum-induced spontaneous emission. Under Wigner–Weisskopf and Markovian approximations, the equations of motion for excited state amplitudes become: $$\dot{a}_1 = -(\mathcal{G}_1 + i\delta_{12}) a_1 - \mathcal{G}_{12} a_2, \qquad \dot{a}_2 = -\mathcal{G}_2 a_2 - \mathcal{G}_{21} a_1$$ with $$\mathcal{G}_{12} \sim \langle \phi_1 |\mathcal{D}_1|E'\rangle \langle E'|\mathcal{D}_2|\phi_2\rangle$$, rendering coherence between $\phi_1$ and $\phi_2$ after spontaneous decay, even if initial populations are incoherent.

Closely related phenomena are observed in quantum dot pairs (Sitek et al., 2012), cavity QED (Vafafard et al., 2017), and molecular fluorescence (Crispin et al., 2018) where vacuum correlations between spontaneous emission channels generate long-lived dark states, coherent trapping, and phase-sensitive emission spectra.

2. Control and Suppression of Decoherence via Vacuum Engineering

Quantum coherence in atomic and artificial systems is fundamentally limited by vacuum fluctuations—the source of radiative decay and dephasing. However, “squeezed vacuum” environments, engineered via parametric amplifiers, redistribute quantum noise between conjugate quadratures (Murch et al., 2013). For a two-level system coupled to such a reservoir, the Gardiner–Bloch equations predict modified decay rates: $$\langle \dot{\sigma}_x \rangle = -\gamma (N-M+\tfrac{1}{2}) \langle \sigma_x \rangle, \quad \langle \dot{\sigma}_y \rangle = -\gamma (N+M+\tfrac{1}{2}) \langle \sigma_y \rangle$$ where $N, M$ are squeezing parameters. In the squeezed quadrature, coherence times can exceed the fundamental vacuum limit, with experiments observing $T_2>2T_1$.

Control over decoherence via boundary engineering is also possible: a reflecting boundary modifies the spatial modes of vacuum electromagnetic fields, suppressing decoherence for transversely polarized atoms located close to the mirror (Liu et al., 2015). The decoherence rate becomes $[1 - f(\omega_0,z_0)]\gamma_0$, with $f$ approaching unity near the boundary, leading to “freezing” of coherence.

In quantum tunneling through squeezed vacuum (Bhattacharya et al., 2014), coherence preservation is achieved via quantum Zeno dynamics or by tuning the squeezing phase and detuning such that $\mathrm{Im}(M)=0$, eliminating reservoir-induced dephasing: $T_C \propto \frac{1}{\mathrm{Im} M}$

3. Nonlocal Vacuum Coherence and Harvesting in Quantum Fields

Vacuum coherence extends to nonlocal phenomena in quantum field theory, where particle detectors harvest coherence from vacuum correlations (Wang et al., 2023). For Unruh–DeWitt detectors weakly coupled to a massless scalar field, the reduced density matrix includes off-diagonal elements $C$ and $X$ capturing nonlocal coherence. The $\ell_1$-norm of coherence,

$C_{l_1}(\rho_{AB}) = 2|C| + 2|X|$

demonstrates robustness of nonlocal coherence to detector separation, with “harvesting-achievable separation range” exceeding that of entanglement.

Tripartite coherence in three detectors is maximized in an equilateral triangle geometry: $C_{l_1}(\rho_{ABC}) = 6|C| + 6|X|$ and exhibits monogamy, i.e. total tripartite coherence is completely bipartite in nature: $$C_{l_1}(\rho_{AB}) + C_{l_1}(\rho_{AC}) + C_{l_1}(\rho_{BC}) = C_{l_1}(\rho_{ABC})$$

4. Vacuum Coherence in Superconducting and QCD Environments

Vacuum coherence is also crucial in systems described by gauge theories and macroscopic quantum states. In the dual superconductor scenario for the QCD vacuum (Cea et al., 2014, Cea et al., 2013, Cea et al., 2014), coherence length $\xi$ and penetration depth $\lambda$ are extracted from the transverse profile of the chromoelectric flux tube: $$E_l(x_t) = \frac{\phi}{2\pi} \frac{\mu^2}{\alpha} \frac{K_0\big(\sqrt{\mu^2 x_t^2 + \alpha^2}\big)}{K_1(\alpha)}$$ with $\mu = 1/\lambda$ and $1/\alpha = \lambda/\xi_v$, fitting lattice QCD correlators. The Ginzburg–Landau parameter

$$\kappa = \lambda/\xi = \frac{\sqrt{2}}{\alpha}\sqrt{1 - [K_0(\alpha)/K_1(\alpha)]^2}$$

characterizes the type-I (chromoelectric flux tubes merge) or type-II (flux tube repulsion) nature of vacuum coherence structure.

5. Experimental Manifestations, Probes, and Technological Applications

Vacuum coherence manifests in diverse quantum optical experiments:

• In SPDC biphoton interferometry, induced coherence arises when two crystals share the same vacuum idler mode, yielding high-visibility interference in the signal channel. Opening a third, uncorrelated idler channel degrades single-photon interference but restores biphoton coherence in coincidence counting (Heuer et al., 2014). Complementarity between fringe visibility ($V$) and which-path information ($K$) is strictly observed: $V^2 + K^2 \leq 1$.
• In molecular systems, VIC enhances magneto-optical rotation (MOR), with the MOR angle $\Theta$ directly linked to the difference in refractive indices arising from interference among decay channels. Maximized MOR (up to $180^\circ$) and ultra-sensitive magnetometry are attainable (Kumar et al., 2015).
• Population trapping in excited doublets is achieved via delayed pulse sequences and chirping, decoupling the states and allowing VIC to robustly generate mixed, trapped-state manifolds even in the presence of large decay (Kumawat et al., 2017).
• Control over fluorescence spectra is realized via phase-sensitive interference between decay channels in a four-level atom; the dressed-state formalism reveals VIC-dependent enhancement and suppression of spectral peaks (Crispin et al., 2018).
• In strong-field-ionized molecules, tunnel ionization builds lasting quantum coherence exploited for tunable, narrow-band coherent DUV/VUV source generation via resonant four-wave mixing, with polarization and wavelength switching enabled by pump field control (Wan et al., 2020).
• In macroscopic quantum systems, e.g., levitated nano-oscillators, second-order coherence analysis isolates pure energy decoherence by analyzing the zero-frequency peak in the squared displacement power spectral density, yielding robust, absolute pressure sensing over eight orders of magnitude (Liu et al., 10 Apr 2024).

6. Vacuum Coherence in Many-Body and False Vacuum Dynamics

Recent work elucidates vacuum coherence in the context of metastable many-body systems and false vacuum decay (Ge et al., 4 Sep 2025). In the transverse- and longitudinal-field Ising model near specific resonance conditions ($h \approx 2J/n$), conventional exponential decay is replaced by coherent two-state oscillations: $$e^{-iHt}|\Omega\rangle \simeq e^{-i\nu_g t}\left[\cos(\tfrac{\omega t}{2})|\Omega\rangle - i\sin(\tfrac{\omega t}{2})|S_n\rangle \right]$$ where $|\Omega\rangle$ is the initial false vacuum state and $|S_n\rangle$ a symmetric resonant bubble state. Superradiant-like enhancement of the oscillation frequency, scaling as $\sqrt{L}$, is observed: $\omega \approx 2\kappa(h)\sqrt{L}g^3$ Bubble size blockade and long-range interactions isolate the coherent subspace, making coherence mechanisms robust beyond perturbative and finite-size limits.

7. Context, Unifying Principles, and Outlook

Vacuum coherence mechanisms constitute a fundamental thread connecting disparate quantum systems—from molecular, atomic, and solid-state platforms to high-energy, many-body, and macroscopic quantum environments. The underlying principle is that quantum interference, activated by the structure and correlations of the vacuum field, can reshape evolution, create decoherence-free subspaces, enable long-range quantum memory, and offer precision tools for metrology and quantum information processing.

Open research directions include harvesting vacuum coherence in relativistic quantum fields, reservoir engineering for enhanced coherence times, topological manipulations of vacuum structure, and exploiting collective many-body effects for quantum simulation. The interplay between geometric, field-theoretic, and engineered environmental structures continues to provide a rich context for the paper and application of vacuum coherence phenomena.