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arXiv:2608.20311

Imaging the vacuum fluctuations of a quantum field

Yansheng Zhang, Feiyang Wang, Yi Jiang, Alexander C. Jenkins, Paul H. C. Wong, Christoph Eigen, Gehrig Carlse, Zoran Hadzibabic

cond-mat.quant-gasastro-ph.COhep-thphysics.atom-phquant-phSubmitted Aug 20, 2026• Announced Aug 21, 2026• 0 citations
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Abstract

Heisenberg uncertainties lead to inevitable fluctuations in the measurement outcomes for quantum-mechanical observables. For quantum fields, these uncertainties result in random spatial structures in snapshots of a field, even when the field is in its ground (vacuum) state. Such `vacuum fluctuations' are at the heart of a wide range of phenomena, from spontaneous decay processes to the Casimir force and Hawking radiation. Their existence is a key manifestation of the quantumness of the physical world, but usually it is only their consequences that are directly observed. Here, we directly observe spatial vacuum fluctuations of a bosonic quantum field. Our experiments are based on a homogeneous planar atomic Bose--Einstein condensate. The condensate comprises two coherently coupled interacting components (spin states), and the quantum field describes its spin degrees of freedom. In the regime where the interactions dominate over the coherent coupling, our system emulates a (massive relativistic) sine-Gordon field. Images of the field reveal simultaneous fluctuations on different length scales, with scale-dependent amplitudes consistent with theoretical predictions for a vacuum state. Observing such fluctuations in the sine-Gordon limit opens many possibilities for laboratory simulations of relativistic fields in regimes that are presently not theoretically tractable.

Comments
7 pages, 3 figures

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Heisenberg uncertainties lead to inevitable fluctuations in the measurement outcomes for quantum-mechanical observables. For quantum fields, these uncertainties result in random spatial structures in snapshots of a field, even when the field is in its ground (vacuum) state. Such `vacuum fluctuations' are at the heart of a wide range of phenomena, from spontaneous decay processes to the Casimir force and Hawking radiation. Their existence is a key manifestation of the quantumness of the physical world, but usually it is only their consequences that are directly observed. Here, we directly observe spatial vacuum fluctuations of a bosonic quantum field. Our experiments are based on a homogeneous planar atomic Bose--Einstein condensate. The condensate comprises two coherently coupled interacting components (spin states), and the quantum field describes its spin degrees of freedom. In the regime where the interactions dominate over the coherent coupling, our system emulates a (massive relativistic) sine-Gordon field. Images of the field reveal simultaneous fluctuations on different length scales, with scale-dependent amplitudes consistent with theoretical predictions for a vacuum state. Observing such fluctuations in the sine-Gordon limit opens many possibilities for laboratory simulations of relativistic fields in regimes that are presently not theoretically tractable.
Quantum fluctuations associated with the ground state of a system exist as a consequence of Heisenberg's uncertainty principle. These fluctuating fields manifest themselves indirectly through their influence on matter which has been extensively studied by considering e.g. the Casimir and Casimir-Polder force. More recently, these ground state fluctuations have been measured directly using nonlinear crystals by means of electro-optical sampling. Despite their common origin, these direct versus indirect evidence of ground-state fluctuations remain disjoint phenomena to date. Here we develop a theoretical framework for describing propagation of a quantized electric field through a nonlinear crystal, allowing for arbitrarily-shaped dispersive and absorptive environments. It can be used in different contexts, one of which is to forge the missing link between the different approaches to observing the quantum vacuum mentioned above. To demonstrate this we show that the change of the vacuum fluctuations induced by a macroscopic object can be directly observed using electro-optical sampling.
Quantum field theories provide fundamental models of complex interacting systems, from high-energy physics and cosmology to condensed matter. However, solving these models in non-perturbative and dynamical regimes is often challenging, particularly in more than one spatial dimension. Analog simulation using tunable synthetic quantum systems can both verify existing theoretical predictions and lead to new physical insights. Here, we realize analog simulation of massive relativistic quantum fields in 2+12+12+1 dimensions (two spatial dimensions and time), using two coherently coupled spin components in a uniform two-dimensional atomic Bose--Einstein condensate. Specifically, we encode the paradigmatic sine-Gordon model in the long-wavelength modes of the field describing the relative phase, φφφ, of the two components. In the perturbative regime, collective field excitations exhibit a relativistic dispersion with a tunable mass gap. We also observe explicitly non-perturbative phenomena, including the existence of topological domain walls across which φφφ rapidly winds by 2π2π2π. Our work opens possibilities for studies of cosmologically relevant phenomena including preheating, dynamics of topological defects, and relativistic false-vacuum decay.
This paper presents a physical theory of vacuum noise and decoherence within the framework of Relativistic Coherent Vacuum Gravity Theory (rCVGT). The work addresses the conceptual limitations of standard quantum field theory, where vacuum fluctuations are typically described in terms of operator uncertainties and decoherence is modeled through environmental entanglement without a direct physical description of vacuum dynamics. In rCVGT the vacuum is treated as a structured relativistic medium characterized by a coherence order parameter ψ(x), a coherence magnitude Q(x)=|ψ(x)|², a vacuum-flow four-field u^μ(x), and a physical time-rate field τ(x). Vacuum fluctuations are interpreted as dynamical perturbations of these fields around metastable equilibrium states. The theory provides a physical mechanism for vacuum noise and shows how decoherence can arise from irreversible amplification of coherence fluctuations through coupling to macroscopic systems. Within this framework, vacuum noise, decoherence, and the quantum-to-classical transition obtain a unified physical interpretation while preserving the empirical predictions of quantum mechanics. This work contributes to the ongoing development of rCVGT as a physically motivated extension of relativistic vacuum dynamics and provides a foundation for future theoretical and experimental investigations of vacuum structure and coherence phenomena.
It is shown that the vacuum state of weakly interacting quantum field theories can be described, in the Heisenberg picture, as a linear combination of randomly distributed incoherent paths that obey classical equations of motion with constrained initial conditions. We call such paths ``pseudoclassical'' paths and use them to define the dynamics of quantum fluctuations. Every physical observable is assigned a time-dependent value on each path in a way that respects the uncertainty principle, but in consequence, some of the standard algebraic relations between quantum observables are not necessarily satisfied by their time-dependent values on paths. We define ``collective observables'' which depend on a large number of independent degrees of freedom and show that the dynamics of their quantum fluctuations can be described in terms of unconstrained classical stochastic processes without reference to any additional external system or to an environment. Our analysis can be generalized to states other than the vacuum. Finally, we compare our formalism to the formalism of coherent states and highlight their differences.
Quantum field theory is the application of quantum physics to fields. It provides a theoretical framework widely used in particle physics and condensed matter physics. One of the most distinct features of quantum physics with respect to classical physics is entanglement or the existence of strong correlations between subsystems that can even be spacelike separated. In quantum fields, observables restricted to a region of space define a subsystem. While there are proofs on the existence of local observables that would allow a violation of Bell's inequalities in the vacuum states of quantum fields as well as some explicit but technically demanding schemes requiring an extreme fine-tuning of the interaction between the fields and detectors, an experimentally accessible entanglement witness for quantum fields is still missing. Here we introduce smeared field operators which allow reducing the vacuum to a system of two effective bosonic modes. The introduction of such collective observables is motivated by the fact that no physical probe has access to fields in single spatial (mathematical) points but rather smeared over finite volumes. We first give explicit collective observables whose correlations reveal vacuum entanglement in the Klein-Gordon field. We then show that the critical distance between the two regions of space above which two effective bosonic modes become separable is of the order of the Compton wavelength of the particle corresponding to the massive Klein-Gordon field.
Structured Quantum Noise (SQN) models environmental noise as a structured quantum process rather than as scalar attenuation alone. Previous work established the mathematical framework for SQN and demonstrated its implications for coherence redistribution and quantum decoherence. This paper addresses a different question: whether Quantum Field Theory (QFT) and vacuum fluctuations provide a physically motivated microscopic realization of the structured environments assumed by SQN. In QFT, the vacuum is the correlated ground state of quantum fields rather than an empty classical background, with measurable consequences including the Lamb shift, spontaneous emission, radiative corrections, and the Casimir effect. Building on this standard field-theoretic picture, we propose that vacuum fluctuations provide one possible microscopic realization of the structured environments assumed by the Structured Quantum Noise framework. In particular, interactions between a physical particle or qubit and one member of a virtual particle–antiparticle pair may transfer entanglement from the original virtual pair to a new entangled state involving the physical system, thereby providing one possible microscopic realization of the structured environment assumed by the Structured Quantum Noise framework. The paper does not modify the formalism of QFT, does not claim that all decoherence originates from vacuum fluctuations, and does not repeat the mathematical developments presented in earlier SQN papers. Its contribution is to establish the interpretive chain QFT → Vacuum Fluctuations → Structured Quantum Noise.