[Paper Review] Detecting a long lived false vacuum with quantum quenches

Gianluca Lagnese, Federica Maria Surace+2 more|arXiv (Cornell University)|Aug 16, 2023

Theoretical and Computational PhysicsPhysics and Astronomy3 citations

TL;DR

This paper demonstrates that quantum quenches in the tilted Ising model reveal distinct dynamical signatures in the spectral density that diagnose whether a system is in a true or long-lived false vacuum, even when decay times are astronomically long. The key finding is that subcritical bubble dynamics leave measurable, time-scale-specific imprints in the Fourier transform of the magnetization, enabling early detection of metastability without waiting for decay.

ABSTRACT

Distinguishing whether a system supports alternate low-energy (locally stable) states -- stable (true vacuum) versus metastable (false vacuum) -- by direct observation can be difficult when the lifetime of the state is very long but otherwise unknown. Here we demonstrate, in a tractable model system, that there are physical phenomena on much shorter time scales that can diagnose the difference. Specifically, we study the time evolution of the magnetization following a quench in the tilted quantum Ising model, and show that its magnitude spectrum is an effective diagnostic. Small transition bubbles are more common than large ones, and we see characteristic differences in the size dependence of bubble lifetimes even well below the critical size for false vacuum decay. We expect this sort of behavior to be generic in systems of this kind. We show such signatures persist in a continuum field theory. This also opens the possibility of similar signatures of the potential metastable false vacuum of our universe well before the beginning of a decay process to the true vacuum.

Motivation & Objective

• To address the challenge of experimentally distinguishing long-lived false vacua from true vacua when decay times are prohibitively long.
• To explore whether non-equilibrium quantum quench dynamics can reveal signatures of metastable states before actual decay occurs.
• To establish that spectral features in real-time evolution after a quench can diagnose the presence of a false vacuum.
• To generalize the method to continuum field theories and experimental platforms like Rydberg atom arrays.
• To investigate the role of subcritical, virtual bubbles in generating observable dynamical effects on accessible time scales.

Proposed method

• Perform a quantum quench in the transverse field Ising model with a tilted longitudinal field, suddenly changing the Hamiltonian parameter $ h_z $ across a first-order transition point.
• Initialize the system in a spin-polarized state ($\ket{\psi_\downarrow}$), then evolve it in imaginary time to prepare the ground state for $ h_z = 0 $, corresponding to a ferromagnetic phase with negative magnetization.
• Sudden real-time evolution is initiated from this state with $ h_z > 0 $ (true vacuum) or $ h_z < 0 $ (false vacuum), using the time-evolved Schrödinger equation.
• Compute the time evolution of the local magnetization $ \langle S_z(t) \rangle = \frac{1}{2N} \sum_i \langle \psi(t) | \sigma_i^z | \psi(t) \rangle $, and analyze its Fourier transform $ S_z(\omega) $ to extract spectral features.
• Use a fermionic representation via Jordan-Wigner transformation to map the spin model to a quadratic fermionic Hamiltonian, enabling analytical and numerical treatment of the spectral function.
• Analyze the spectral density for different bubble sizes and quench parameters, focusing on the size dependence of lifetimes and the emergence of distinct oscillatory modes.

Experimental results

Research questions

• RQ1 Can quantum quench dynamics reveal the presence of a long-lived false vacuum without waiting for actual decay?
• RQ2 Do subcritical, virtual bubbles—too small to grow—produce measurable dynamical signatures in the spectral response?
• RQ3 How do the spectral features of the magnetization time evolution differ between true and false vacuum initial states?
• RQ4 Can these signatures be generalized to continuum field theories and experimental platforms like ultracold atoms or trapped ions?
• RQ5 What is the role of bubble size and shape in determining the lifetime and spectral response in non-equilibrium dynamics?

Key findings

• The Fourier transform of the time-evolved magnetization reveals distinct oscillatory modes in the spectral density that clearly differentiate the true vacuum (with a single dominant peak) from the false vacuum (with multiple, size-dependent modes).
• Subcritical bubbles—those below the critical size for runaway expansion—still produce measurable, transient oscillations in the spectral function, with lifetimes that depend on their size in a characteristic way.
• The spectral response shows that small bubbles are more common than large ones, and their lifetimes exhibit a non-monotonic size dependence, even well below the critical size.
• These dynamical signatures persist in the continuum limit of the model, indicating that the mechanism is robust and not an artifact of lattice discretization.
• The method allows detection of false vacuum metastability on experimentally accessible time scales, far short of the false vacuum decay time.
• The approach is generalizable to other systems, including Rydberg atom arrays and quantum simulators, where such signatures could be probed in current experiments.