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Nature Physics

False vacuum decay via bubble formation in ferromagnetic superfluids

Alessandro Zenesini, Anna Berti, Riccardo Cominotti, C. Rogora, Ian G. Moss, T. P. Billam, Iacopo Carusotto, Giacomo Lamporesi, Alessio Recati, G. Ferrari

Published Jan 22, 2024• 57 citations

Abstract

Abstract Metastability is ubiquitous in nature and is observed through the crossing of an energy barrier toward a configuration of lower energy as, for example, in chemical processes [1] or electron field ionization [2]. In classical many-body systems, metastability naturally emerges in the presence of a first-order phase transition and finds a prototypical example in supercooled vapour. In the last decades, the extension to quantum field theory and quantum many-body systems has attracted significant interest in the context of statistical physics [3, 4], protein folding [5, 6], and cosmology [7–9], where thermal and quantum fluctuations are expected to trigger the transition from the metastable state (false vacuum) to the ground state (real vacuum) via the probabilistic nucleation of spatially localized bubbles [10, 11]. However, the long-standing theoretical progress in estimating the relaxation rate of the metastable field via bubble nucleation has not yet found a counterpart in terms of experimental observations. Here we experimentally observe and characterize bubble nucleation in isolated and coherently-coupled atomic superfluids, and support our observations with numerical simulations. The agreement between our results and a novel analytic formula based on instanton theory confirms the quantum-field character of the observed decay, and promotes coherently-coupled atomic superfluids as emulators of out-of-equilibrium quantum field phenomena.

DOI: 10.1038/s41567-023-02345-4

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Abstract Metastability is ubiquitous in nature and is observed through the crossing of an energy barrier toward a configuration of lower energy as, for example, in chemical processes [1] or electron field ionization [2]. In classical many-body systems, metastability naturally emerges in the presence of a first-order phase transition and finds a prototypical example in supercooled vapour. In the last decades, the extension to quantum field theory and quantum many-body systems has attracted significant interest in the context of statistical physics [3, 4], protein folding [5, 6], and cosmology [7–9], where thermal and quantum fluctuations are expected to trigger the transition from the metastable state (false vacuum) to the ground state (real vacuum) via the probabilistic nucleation of spatially localized bubbles [10, 11]. However, the long-standing theoretical progress in estimating the relaxation rate of the metastable field via bubble nucleation has not yet found a counterpart in terms of experimental observations. Here we experimentally observe and characterize bubble nucleation in isolated and coherently-coupled atomic superfluids, and support our observations with numerical simulations. The agreement between our results and a novel analytic formula based on instanton theory confirms the quantum-field character of the observed decay, and promotes coherently-coupled atomic superfluids as emulators of out-of-equilibrium quantum field phenomena.

In quantum field theory, the decay of an extended metastable state into the real ground state is known as ``false vacuum decay'' and it takes place via the nucleation of spatially localized bubbles. Despite the large theoretical effort to estimate the nucleation rate, experimental observations were still missing. Here, we observe bubble nucleation in isolated and highly controllable superfluid atomic systems, and we find good agreement between our results, numerical simulations and instanton theory opening the way to the emulation of out-of-equilibrium quantum field phenomena in atomic systems.

Temperature plays a crucial role in metastable phenomena, not only by contributing to determine the state (phase) of a system, but also ruling the decay probability to more stable states. Such a situation is encountered in many different physical systems, ranging from chemical reactions to magnetic structures. The characteristic decay timescale is not always straightforward to estimate since it depends on the microscopic details of the system. A paradigmatic example in quantum field theories is the decay of the false vacuum, manifested via the nucleation of bubbles. In this Letter, we measure the temperature dependence of the timescale for the false vacuum decay mechanism in an ultracold atomic quantum spin mixture which exhibits ferromagnetic properties. Our results show that the false vacuum decay rate scales with temperature as predicted by the finite-temperature extension of the instanton theory, and confirm atomic systems as an ideal platform where to study out-of-equilibrium field theories.

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.

In this work, we theoretically investigate the false vacuum decay process in a ferromagnetic quantum spin-1/2 chain. We develop a many-body theory describing the nucleation and the coherent dynamics of true-vacuum bubbles that is analytically tractable and agrees with numerical matrix product state calculations in all parameter regimes up to intermediate times. This theory allows us to identify different regimes in the parameter space and unravel the underlying physical mechanisms, thus offering conceptual insight into the microscopic quantum dynamics of metastable states. In particular, analogies and differences with the cosmological false vacuum decay picture are highlighted and characterized in terms of experimentally observable quantities.

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/r^6

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.

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.