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arXiv:2308.08340 · Physical Review Letters

Detecting a Long-Lived False Vacuum with Quantum Quenches

Gianluca Lagnese, Federica Maria Surace, Siddhardh C. Morampudi, Frank A. Wilczek

Published Dec 12, 2024• 21 citations
arXivHTMLPDF

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 timescales 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.

DOI
10.1103/physrevlett.133.240402

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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 timescales 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.
False vacuum decay describes the relaxation of a metastable state through the nucleation and growth of bubbles of the stable phase. Despite describing a broad variety of phenomena across different fields, the quantum version of the nucleation theory has little experimental or numerical support. Testing its predictions is particularly important in two or more spatial dimensions, where bubble nucleation acquires its true geometrical nature. Here, we study false vacuum decay in the quantum Ising model in two dimensions. Through tree tensor network simulations we extract the decay rate, the effective interface tension and the critical bubble size. We compare them to new semi-classical field theory calculations, and find excellent agreement. These results provide numerical evidence that the critical-bubble picture survives in an interacting quantum spin system in 2+1 dimensions.
Microscopic Dynamics of False Vacuum Decay in the 2+12+12+1D Quantum Ising Model
False vacuum decay, which is understood to happen through bubble nucleation, is a prominent phenomenon relevant to elementary particle physics and early-universe cosmology. Understanding its microscopic dynamics in higher spatial dimensions is currently a major challenge and research thrust. Recent advances in numerical techniques allow for the extraction of related signatures in tractable systems in two spatial dimensions over intermediate timescales. Here, we focus on the 2+12+12+1D quantum Ising model, where a longitudinal field is used to energetically separate the two Z2\mathbb{Z}_2Z2​ symmetry-broken ferromagnetic ground states, turning them into a ``true'' and ``false'' vacuum. Using tree tensor networks, we simulate the microscopic dynamics of a spin-down domain in a spin-up background after a homogeneous quench, with parameters chosen so that the domain corresponds to a bubble of the true vacuum in a false-vacuum background. Our study identifies how the ultimate fate of the bubble -- indefinite expansion or collapse -- depends on its geometrical features and on the microscopic parameters of the Ising Hamiltonian. We further provide a realistic quantum-simulation scheme, aimed at probing bubble dynamics on atomic Rydberg arrays.
Abstract The quantum decay of a relativistic scalar field from a metastable state (‘false vacuum decay’) is a fundamental idea in quantum field theory and cosmology. This occurs via local formation of bubbles of true vacuum with their subsequent rapid expansion. It can be considered as a relativistic analog of a first-order phase transition in condensed matter. Here we expand upon our recent proposal (Fialko O et al 2015 Europhys. Lett. 110 56001 ) for an experimental test of false vacuum decay using an ultra-cold spinor Bose gas. A false vacuum for the relative phase of two spin components, serving as the unstable scalar field, is generated by means of a modulated linear coupling of the spin components. We analyze the system theoretically using the functional integral approach and show that various microscopic degrees of freedom in the system, albeit leading to dissipation in the relative phase sector, will not hamper the observation of the false vacuum decay in the laboratory. This is well supported by numerical simulations demonstrating the spontaneous formation of true vacuum bubbles on millisecond time-scales in two-component 7 Li or 41 K bosonic condensates in one-dimensional traps of ∼ 100 μ m size.
In quantum field theory (QFT), the "vacuum" is not just empty space but the lowest-energy state of a quantum field. If the energy landscape has multiple local minima, the local ground states are the false vacuum (FV) which can tunnel towards the global ground state (true vacuum, TV). This process exhibits signature akin to classical supercooled gas transitions and many-body tunneling in discrete quantum systems. Here, we study the FV decay and bubble nucleation in a Rydberg atom ring. The 1/r61/r^61/r6 van-der-Waals interactions and individual-site addressability allow us to explore physics beyond the standard Ising model. We observe that the FV decay rate decreases exponentially with the inverse of the symmetry-breaking field, directly mirroring QFT predictions. Moreover, we demonstrate that even minor deviations from the ideal metastable state can cause a stark departure from this universal scaling law. Extending beyond short-time decay dynamics, we also examine resonant bubble nucleation, a feature distinctive to systems with discrete energy spectra. Our findings and methods open avenues for future studies of many-body tunneling in higher dimensions or more complex geometries.
The false vacuum decay has been a central theme in physics for half a century with applications to cosmology and to the theory of fundamental interactions. This fascinating phenomenon is even more intriguing when combined with the confinement of elementary particles. Due to the astronomical timescales involved, the research has so far focused on theoretical aspects of this decay. The purpose of this Letter is to show that the false vacuum decay is accessible to current optical experiments as quantum analog simulators of spin chains with confinement of the elementary excitations, which mimic the high energy phenomenology but in one spatial dimension. We study the nonequilibrium dynamics of the false vacuum in a quantum Ising chain and in an XXZ ladder. The false vacuum is the metastable state that arises in the ferromagnetic phase of the model when the symmetry is explicitly broken by a longitudinal field. This state decays through the formation of ``bubbles'' of true vacuum. Using infinite volume time evolving block decimation (iTEBD) simulations, we are able to study the real-time evolution in the thermodynamic limit and measure the decay rate of local observables. We find that the numerical results agree with the theoretical prediction that the decay rate is exponentially small in the inverse of the longitudinal field.
False vacuum decay-the transition from a metastable quantum state to a true vacuum state-plays an important role in quantum field theory and non-equilibrium phenomena such as phase transitions and dynamical metastability. The non-perturbative nature of false vacuum decay and the limited experimental access to this process make it challenging to study, leaving several open questions regarding how true vacuum bubbles form, move and interact. Here we observe quantized bubble formation in real time, a key feature of false vacuum decay dynamics, using a quantum annealer with 5,564 superconducting flux qubits. We develop an effective model that captures both initial bubble creation and subsequent interactions, and remains accurate under dissipation. The annealer reveals coherent scaling laws in the driven many-body dynamics for more than 1,000 intrinsic qubit time units. This work provides a method for investigating false vacuum dynamics of large quantum systems in quantum annealers.