Correlated decoherence in a common environment activated by relative motion

Abstract: We study two spatially separated boundary subsystems coupled to a common structured environment under relative motion in a Gaussian open-system framework. By integrating out the environment, we obtain an influence functional governed by a dressed environmental correlator evaluated at the boundary positions, which encodes both coherent mediation and correlated fluctuations. Relative motion opens a correlated decoherence channel through Doppler-shifted spectral overlap of the boundary excitations, leading to a kinematic threshold at $v>2u_φ$. Below threshold, the dominant resonant contribution to the off-diagonal noise kernel is absent and the environment acts predominantly as a coherent mediator at leading resonant order. Above threshold, a resonant shell opens and the same environment supports a finite cross-noise channel, producing irreversible correlated decoherence. In the reduced dynamics, coherent coupling is governed by the retarded component of the dressed correlator, while the decoherence rate is controlled by its Hadamard component. These results establish a direct connection between motion-induced excitation production and correlated decoherence in open quantum systems, and point to experimentally accessible signatures in superconducting--phononic platforms through excess correlated dephasing.

• The paper demonstrates a velocity threshold (v > 2uₚ) where Doppler-shifted spectral overlap activates irreversible cross-decoherence between quantum subsystems.
• It employs a quadratic Gaussian field theory and closed-time-path formalism to separate coherent mediation from noise-driven decoherence effects.
• Experimental projections indicate that superconducting circuits and ultracold atoms can emulate and measure motion-induced correlated decoherence signatures.

Correlated Decoherence Activated by Relative Motion in a Common Environment

Model and Theoretical Framework

The investigated system consists of two spatially separated boundary subsystems (realized as parallel planar interfaces, labeled $A$ and $B$) immersed in a common, structured bosonic environment. Plate $A$ moves at constant velocity $v$ along the $x$-direction; Plate $B$ remains static. The inter-plate region is filled with a charged bosonic medium, effectively serving as a shared quantum bath coupled to both boundary modes, $\phi_A$ and $\phi_B$ (Figure 1).

Figure 1: Schematic representation—plate $A$ moves at velocity $v$, plate $B$0 is fixed, and the inter-plate medium (with amplitude fluctuation mode $B$1) acts as a common environment.

The system is modeled by a quadratic (Gaussian) field theory; the boundaries support real scalar surface excitations characterized by a propagation velocity $B$2 and effective mass $B$3. The cavity medium is described by a charged complex scalar field coupled to an Abelian $B$4 gauge field. At low energies, the boundary coupling is dominated by the density response (amplitude fluctuation) of the medium.

Tracing out the environmental degrees of freedom yields a nonlocal (in time and space) influence kernel for the reduced boundary system, decomposed into retarded (coherent mediation) and noise (correlated decoherence) components. Both local and cross-terms in the kernel arise due to the common environment.

Kinematic Threshold for Motion-Activated Cross-Decoherence

A central finding is the emergence of a velocity-controlled kinematic threshold for correlated decoherence. Relative motion modifies the spectra of the boundary modes via Doppler shifts—plate $B$5's spectral response experiences the shift $B$6—resulting in the possibility of resonance between excitations on the two plates only if their Doppler-shifted spectral domains overlap. This overlap is realized when

$B$7

where $B$8 is the surface excitation velocity.

Figure 2: Illustration of the velocity-controlled opening of the correlated decoherence channel, with threshold at $B$9.

For $A$0, there is no spectral overlap between the relevant modes (see Figure 3) and thus the dominant resonant, cross-environmental decoherence channel remains closed. When $A$1 exceeds $A$2, a finite region in momentum space allows for simultaneous excitation in both boundaries with environmental mediation, activating an irreversible cross-decoherence process.

Figure 3: Schematic of the boundary mode spectra. For $A$3 (dashed), Doppler-shifted and stationary branches do not intersect; for $A$4 (solid), a resonance shell opens.

Numerically, the leading resonant contribution to the imaginary part of the cross-environmental influence functional is strictly zero for $A$5 and shows a sharp onset at the threshold (see Figure 4).

Figure 4: Resonant contribution to the in-out excitation production ($A$6) as a function of velocity, with abrupt onset at $A$7.

Environmental Kernel Structure and Decoherence Functional

The influence functional, expressed in closed-time-path (CTP) formalism, yields both retarded and Hadamard (noise) kernels. The off-diagonal elements (cross noise) are directly tied to the spectral properties of the environment evaluated between the plates, encoded in the Hadamard kernel component

$A$8

where $A$9 is the symmetrized correlator of the dressed environmental amplitude fluctuation mode.

Figure 5: Frequency-resolved retarded (top) and noise (bottom) cross-kernels below and above threshold $v$0. Coherent mediation persists throughout, but noise is suppressed below threshold.

The cross-noise kernel is highly suppressed below threshold, but above $v$1, it becomes nonzero with support determined by Doppler-shifted resonance. This leads to pronounced suppression of off-diagonal components of the boundary reduced density matrix, quantified via a coherence factor

$v$2

with the decay functional $v$3 scaling with the cross-noise kernel and the system-environment coupling.

Parameter Dependence and Experimental Projections

Finite velocity $v$4 is the primary control for activating correlated decoherence. The threshold for channel opening, $v$5, is purely kinematic—independent of separation $v$6, chemical potential $v$7, or other bath parameters. Above threshold, the magnitude of cross-decoherence is shaped by the strengths of coupling, environmental spectral weight, and screening, as well as plate separation (which introduces exponential attenuation due to finite environmental correlation length).

Figure 6: Velocity dependence of the cross-decoherence rate, $v$8, comparing several linewidths. The threshold is sharpened in the narrow-width limit.

Figure 7: Density plot of resonant cross-decoherence rate vs. velocity and separation. Rate decays exponentially with $v$9 and shows sharp threshold in $x$0.

Figure 8: Cross-decoherence rate as a function of $x$1, for different screening values. Increased screening suppresses correlation length and decoherence.

Figure 9: Velocity-dependence of resonant cross-decoherence rate for multiple chemical potentials $x$2, demonstrating nonmonotonic dependence driven by combined enhancements in coupling and screening effects.

Figure 10: Peak resonant cross-decoherence rate as a function of $x$3, illustrating maximization at intermediate $x$4 due to competing system-environment coupling and screening-induced spatial attenuation.

Diverse parameter regimes relevant for ultracold atoms, superconducting circuits, graphene, and plasmonic nanostructures map onto the same dimensionless velocity threshold $x$5 (see Figure 11).

Figure 11: Normalized resonant cross-decoherence rate, $x$6, vs. $x$7 across experimental platforms. Universal threshold reflects kinematic origin.

Superconducting circuits with phononic waveguides enable direct emulation of the setup, leveraging synthetic motion (e.g., traveling-wave modulation) to sweep $x$8 and detect the onset of excess correlated dephasing via joint echo or Ramsey visibility measurements. In ultracold gases, the finding connects to critical velocities for heating and dissipation. In nanophotonic contexts, the results imply sharp onset of nonreciprocal energy transfer or quantum friction.

Implications and Future Outlook

This work introduces a unifying framework showing that the onset of correlated decoherence in spatially separated quantum systems can be tightly controlled by kinematic (Doppler) spectral matching. Below threshold, the common environment mediates predominantly coherent interactions without leading-order irreversible decoherence; above threshold, a resonant cross-noise channel opens, causing rapid loss of coherence between the boundaries. The theoretical connection between in-out excitation rates and the CTP noise functional elucidates the physical mechanism and guides design principles for quantum devices where correlated bath effects are strategically engineered or suppressed.

Extensions to non-Gaussian environments, inclusion of strong-coupling or non-Markovian effects, and generalization to multipartite or extended systems could unlock richer regimes of motion-induced decoherence control. Experimentally, synthetic implementations in circuit QED, nanomechanics, or engineered cold-atom arrays are directly accessible, with thresholded decoherence or noise cross-correlations serving as benchmarks for the framework.

Conclusion

This study establishes a kinematic, velocity-activated threshold for correlated decoherence between spatially separated quantum subsystems sharing a structured environment. The activation occurs only for $x$9, corresponding to the opening of a Doppler-induced spectral overlap. The identification of this sharp onset and its mapping onto experimentally detectable signatures support its broad significance for quantum information processing, decoherence suppression strategies, and the control of environment-induced correlations in complex quantum devices.

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Reference: "Correlated decoherence in a common environment activated by relative motion" (2604.10109)