Spacetime-Curvature Quench Analysis

• Spacetime-curvature quench is a rapid, localized change in geometric curvature that directly impacts quantum coherence and system evolution.
• It is characterized by nonadiabatic shifts in Riemann tensor components and analyzed via Bogoliubov transforms linking pre- and post-quench field modes.
• Experimental protocols employ ultra-rapid detectors and quantum simulators like Bose–Einstein condensates to measure curvature-induced decoherence and mode mixtures.

A spacetime-curvature quench is a protocol or physical process in which the spacetime curvature—typically encoded through specific components of the Riemann tensor or associated geometric invariants—undergoes a sudden or engineered change, with direct, measurable impacts on quantum, thermodynamic, or field-theoretic observables. This concept is foundational to a range of scenarios, from quantum coherence loss in composite systems propagating in curved backgrounds to the design of dynamical analogues in laboratory quantum simulators. Rigorous treatments universally express the effects of a spacetime-curvature quench in terms of geometric data (e.g., $R_{0i0j}$) and provide operational protocols to detect or exploit such quenches across quantum gravity, cosmology, condensed matter, and quantum information.

1. Mathematical Structure and Physical Definition

The defining feature of a spacetime-curvature quench is a rapid, spatially and/or temporally localized variation in the geometric curvature of spacetime, not to be confused with more general parameter quenches in Hamiltonians. In precise terms, the quench is associated with a nonadiabatic temporal change in components of the Riemann tensor, Ricci scalar, or metric modulations coupling directly to the system of interest. The generalized effect is captured covariantly in Fermi normal coordinates: in the Hamiltonian of a localized system, curvature enters via terms like $\frac12\,R_{0i0j}\,x^i x^j$ (Singh et al., 2023, Basso et al., 2024). In a field-theoretic context, the propagation or matching of mode functions across a curvature-quench hypersurface can be analyzed with Bogoliubov transforms, fully characterized by the change in geometric data.

2. Quantum Systems and Curvature-Driven Decoherence

For a composite quantum system with internal degrees of freedom, a spacetime-curvature quench produces genuine decoherence—even in a locally inertial frame—by coupling the internal energy to tidal components of the background Riemann tensor (Singh et al., 2023). If the system is prepared in a spatial superposition of two localized packets, the reduced density matrix for the center of mass acquires off-diagonal elements whose visibility decays:

$$V(t) = \left| \left\langle e^{-i H_{\rm int} \Delta\Theta/\hbar} \right\rangle_{\rho_{\rm int}} \right|, \qquad \Delta\Theta = \int_0^t [\Theta_2(t') - \Theta_1(t')]\,dt'$$

with

$$\Theta = \frac12 R_{0i0j} x^i x^j \;+\; \text{(kinematic terms)}$$

leading to a decoherence timescale

$$t_{\rm dec} \sim \frac{\hbar}{\Delta E} \;\left| R_{0i0j}\Delta x^i\Delta x^j\right|^{-1/2}$$

where $\Delta E$ is the internal energy spread and $\Delta x^i$ the superposition size (Singh et al., 2023).

This decoherence, termed curvature-quench decoherence (Editor's term), is distinct from environmental or acceleration-induced mechanisms: the kinematic time-dilation contribution ($a_i x^i$) vanishes in inertial frames, but the tidal curvature persists and cannot be gauged away. The effect is universal and covariant, directly connecting quantum coherence decay to the intrinsic curvature.

3. Quantum Fields, Entanglement, and Analogue Simulators

Curvature quenches in quantum field theories are realized by piecewise or continuously modulated metrics, often across a matching surface or via a time-dependent scale factor. Examples include $(1+1)$-dimensional Minkowski-to-Rindler transitions through a curvature bridge, engineered as analogues in cold atom platforms or optical systems (Louko, 2018, Lopez-Raven et al., 8 Jun 2025). The procedure typically involves:

• Pre-quench: Field modes and vacuum defined with respect to a baseline spacetime (e.g., Minkowski).
• Post-quench: Propagation in a distinct, nontrivial curved metric (e.g., Rindler, de Sitter, or FLRW), with mode expansion and Bogoliubov transformation relating initial and final bases.
• Physical observables (e.g., detector excitation probabilities, entanglement measures) are then directly sensitive to the induced curvature profile and the associated energy/mode-mixing.

In quantum simulators such as 2D Bose–Einstein condensates, a spacetime-curvature quench is implemented by rapidly modulating the scale factor $a(t)$ via control of the s-wave scattering length and trap geometry. The resulting dynamics of the phononic field—real and momentum space density correlations, particle production rates—quantitatively match analytical predictions for quantum fields in curved spacetimes, including metrics with nontrivial spatial or temporal curvature (Viermann et al., 2022).

4. Thermodynamic and Fluctuation Perspectives

The dynamical interplay between curvature quenches and quantum thermodynamic behavior is formalized in generalized fluctuation theorems. Employing a two-point measurement protocol on a localized quantum system traversing a curved background, the distribution of work performed during a metric quench satisfies a Crooks-type detailed fluctuation theorem:

$\frac{P_F(W)}{P_B(-W)} = e^{\beta(W-\Delta F)}$

where $\beta$ is inverse temperature, and the local Hamiltonians $H_{\rm int}(\tau)$ carry explicit curvature dependence through Fermi normal coordinates (Basso et al., 2024). Specifically, in an expanding FLRW universe, the curvature-driven term $-(m/2)(\ddot a/a)x^2$ in the oscillator Hamiltonian acts as an external quench, producing level transitions, entropy generation, and a unidirectional arrow of time. Notably, the entropy production is observer-dependent, encoding the relativity of simultaneity and local time readouts.

5. Holographic and Emergent-Gravity Instances

In holographic contexts, a spacetime-curvature quench typically corresponds to a Vaidya-type geometry: the injection of energy (e.g., null-dust shell) abruptly modifies the bulk curvature, leading to nontrivial evolution of boundary observables such as subregion complexity. The AdS curvature scalar remains constant, but the Kretschmann invariant acquires a jump proportional to the shell mass and radial position (Chen et al., 2018). The extremal surfaces governing complexity and entropy exhibit discontinuities or phase transitions (swallowtails) precisely at the quench-induced curvature transition. This behavior is mirrored in matrix models with emergent $(1+1)$-geometry, where instantaneous shifts in coupling inject regions of constant positive or negative curvature (dS$_2$/AdS$_2$), and the corresponding spacelike singularity boundaries exemplify curvature quenches that regularize or cap geometric invariants (Das et al., 2019).

6. Operational Protocols and Experimental Realization

Several operational strategies exist for detecting or exploiting spacetime-curvature quenches:

• Ultra-rapid Unruh–DeWitt (UDW) detector protocols: By delta-coupling spatially extended detectors to a field, and varying their shape, excitation probabilities become linearly sensitive to all local components of Ricci and Riemann tensors, linkable through the Hadamard expansion of the Wightman function (Perche et al., 2022).
• Entanglement harvesting with detector pairs in quenched spacetimes: Detector correlators and extracted quantum correlations display measurable deviations (e.g., enhancement during a propagating curvature/energy pulse), precisely tracking the local geometric pulse generated by the quench (Lopez-Raven et al., 8 Jun 2025).
• Quantum simulation: In BECs, curvature quenches are implemented via rapid or controlled ramps of $a_s(t)$ (via Feshbach resonances), with direct readout through density–density correlations, Sakharov oscillations, and extracted pair production spectra (Viermann et al., 2022).
• Decoherence interferometry: Interferometric visibility loss in superposed composite systems acts as a direct probe of background curvature, requiring high sensitivity to millisecond-scale decoherence for near-Earth or neutron-star-scale curvatures (Singh et al., 2023).

7. Limiting Curvature and Geometric Bounds

A fundamental geometric interpretation of a spacetime-curvature quench arises from maximal acceleration frameworks. Imposing a universal upper bound on the proper acceleration, $a_{\rm max}$, enforces pointwise upper limits on Riemann tensor components and curvature invariants:

$$|R_{0k0k}| \leq a_{\rm max}\,, \qquad R_{\mu\nu\rho\sigma} R^{\mu\nu\rho\sigma} \leq C a_{\rm max}^2$$

for an appropriate constant $C$. Such a principle naturally quenches (caps) the attainable curvature, providing a geometric mechanism for singularity avoidance in gravitational theories (Torromé, 2019).

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References:

• (Singh et al., 2023) Decoherence due to Spacetime Curvature
• (Basso et al., 2024) Quantum fluctuation theorem in a curved spacetime
• (Viermann et al., 2022) Quantum field simulator for dynamics in curved spacetime
• (Lopez-Raven et al., 8 Jun 2025) Quenched entanglement harvesting
• (Chen et al., 2018) Holographic subregion complexity under a thermal quench
• (Louko, 2018) Thermality from a Rindler quench
• (Das et al., 2019) Quantum Quench in $c=1$ Matrix Model and Emergent Space-times
• (Torromé, 2019) Maximal acceleration geometries and spacetime curvature bounds
• (Perche et al., 2022) Spacetime curvature from ultra rapid measurements of quantum fields
• (Belkovich et al., 17 Nov 2025) Global quenches and correlator dynamics in de Sitter space