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Register a new userObserving the fate of the false vacuum with a quantum laboratory
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We design and implement a quantum laboratory to experimentally observe and study dynamical processes of quantum field theories. Our approach encodes the field theory as an Ising model, which is then solved by a quantum annealer. As a proof-of-concept, we encode a scalar field theory and measure the probability for it to tunnel from the false to the true vacuum for various tunnelling times, vacuum displacements and potential profiles. The results are in accord with those predicted theoretically, showing that a quantum annealer is a genuine quantum system that can be used as a quantum laboratory. This is the first time it has been possible to experimentally measure instanton processes in a freely chosen quantum field theory. This novel and flexible method to study the dynamics of quantum systems can be applied to any field theory of interest. Experimental measurements of the dynamical behaviour of field theories are independent of theoretical calculations and can be used to infer their properties without being limited by the availability of suitable perturbative or nonperturbative computational methods. In the near future, measurements in such a quantum laboratory could therefore be used to improve theoretical and computational methods conceptually and may enable the measurement and detailed study of previously unobserved quantum phenomena.
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Motivated by cosmological examples we study quantum field theoretical tunnelling from an initial state where the classical field, i.e. the vacuum expectation value of the field operator is spatially homogeneous but performing a time-dependent oscillation about a local minimum. In particular we estimate both analytically and numerically the exponential contribution to the tunnelling probability. We additionally show that after the tunnelling event, the classical field solution - the so-called bubble - mediating the phase transition can either grow or collapse. We present a simple analytical criterium to distinguish between the two behaviours.
Quantum decay of a relativistic scalar field from a false vacuum is a fundamental idea in quantum field theory. It is relevant to models of the early Universe, where the nucleation of bubbles gives rise to an inflationary universe and the creation of matter. Here we propose a laboratory test using an experimental model of 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 radio-frequency coupling of the spin components. Numerical simulations demonstrate the spontaneous formation of true vacuum bubbles with realistic parameters and time-scales.
Using the holographic correspondence as a tool, we study the dynamics of first-order phase transitions in strongly coupled gauge theories at finite temperature. Considering an evolution from the large to the small temperature phase, we compute the nucleation rate of bubbles of true vacuum in the metastable phase. For this purpose, we find the relevant configurations (bounces) interpolating between the vacua and we compute the related effective actions. We start by revisiting the compact Randall-Sundrum model at high temperature. Using holographic renormalization, we compute the kinetic term in the effective bounce action, that was missing in the literature. Then, we address the full problem within the top-down Witten-Sakai-Sugimoto model. It displays both a confinement/deconfinement and a chiral symmetry breaking/restoration phase transition which, depending on the model parameters, can happen at different critical temperatures. For the confinement/deconfinement case we perform the numerical analysis of an effective description of the transition and also provide analytic expressions using thick and thin wall approximations. For the chiral symmetry transition, we implement a variational approach that allows us to address the challenging non-linear problem stemming from the Dirac-Born-Infeld action.
We analyze properties of unstable vacuum states from the point of view of the quantum theory. In the literature one can find some suggestions that some of false (unstable) vacuum states may survive up to times when their survival probability has a non-exponential form. At asymptotically late times the survival probability as a function of time $t$ has an inverse power--like form. We show that at this time region the energy of the false vacuum states tends to the energy of the true vacuum state as $1/t^{2}$ for $t to infty$. This means that the energy density in the unstable vacuum state should have analogous properties and hence the cosmological constant $Lambda = Lambda (t)$ too. The conclusion is that $Lambda$ in the Universe with the unstable vacuum should have a form of the sum of the bare cosmological constant and of the term of a type $1/t^{2}$: $Lambda(t) equiv Lambda_{bare} + d/ t^{2}$ (where $Lambda_{bare}$ is the cosmological constant for the Universe with the true vacuum).
The Krylov-Fock expression of non-decay (or survival) probability, which allows to evaluate the deviations from the exponential decay law (nowadays well established experimentally), is more informative as it readily provides the distribution function for the lifetime as a random quantity. Guided by the well established formalism for describing nuclear alpha decay, we use this distribution function to figure out the mean value of lifetime and its fluctuation rate. This theoretical framework is of considerable interest inasmuch as it allows an experimental verification. Next, we apply the Krylov-Fock approach to the decay of a metastable state at a finite temperature in the framework of thermo-field dynamics. In contrast to the existing formalism, this approach shows the interference effect between the tunnelings from different metastable states as well as between the tunneling and the barrier hopping. This effect looks quite natural in the framework of consistent quantum mechanical description as a manifestation of the double-slit experiment. In the end we discuss the field theory applications of the results obtained.
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