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arXiv:2512.13901

Quantum fields in a cold atomic simulator: relaxation and phase locking in tunnel-coupled 1D bosonic quasi-condensates

B. Fitos, G. Takács

cond-mat.quant-gashep-thquant-phSubmitted Dec 15, 2025• Announced Dec 17, 2025• 0 citations• Revised Sep 21, 2026 (v2)
v1 · Dec 15, 2025v2 · Sep 21, 2026
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Abstract

We consider a prime example of simulating interacting relativistic QFT with cold atoms: the realisation of the sine-Gordon model by tunnel-coupled quasi-1D Bose gases. While experiments have shown that it can realise the sine-Gordon model in equilibrium, studies of non-equilibrium dynamics have revealed phase-locking behaviour that contrasts with predictions from sine-Gordon field theory. Here, we examine a one-dimensional field-theoretic model of the system and find that the phase-locking behaviour can be understood in terms of the longitudinal harmonic trap, and that the additional degrees of freedom observed in the experiment do not appear to play a significant role. Therefore, the experimental setup provides a good simulator of the sine-Gordon quantum field theory, even out of equilibrium, if the inhomogeneous background induced by the trap is taken into account. Furthermore, our results support the idea that modifying the longitudinal trap to a box shape should result in agreement with standard sine-Gordon dynamics. The main remaining open issues are accounting for 3D corrections and modelling the effect of the boundaries.

Comments
17 pages, 9 figures. v2: added new discussion to clarify some points. Added references

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We consider a prime example of simulating interacting relativistic QFT with cold atoms: the realisation of the sine-Gordon model by tunnel-coupled quasi-1D Bose gases. While experiments have shown that it can realise the sine-Gordon model in equilibrium, studies of non-equilibrium dynamics have revealed phase-locking behaviour that contrasts with predictions from sine-Gordon field theory. Here, we examine a one-dimensional field-theoretic model of the system and find that the phase-locking behaviour can be understood in terms of the longitudinal harmonic trap, and that the additional degrees of freedom observed in the experiment do not appear to play a significant role. Therefore, the experimental setup provides a good simulator of the sine-Gordon quantum field theory, even out of equilibrium, if the inhomogeneous background induced by the trap is taken into account. Furthermore, our results support the idea that modifying the longitudinal trap to a box shape should result in agreement with standard sine-Gordon dynamics. The main remaining open issues are accounting for 3D corrections and modelling the effect of the boundaries.
We consider two weakly interacting quasi-1D condensates of cold bosonic atoms. It turns out that a time-dependent variation of the tunnel-coupling between those condensates is equivalent to the spatial expansion of a one-dimensional toy-Universe, with regard to the dynamics of the relative phase field. The dynamics of this field is governed by the quantum sine-Gordon equation. Thus, this analogy could be used to 'quantum simulate' the dynamics of a scalar, interacting quantum field on an expanding background. We discuss how to observe the 'freezing' of quantum fluctuations during an accelerating expansion in a possible experiment. We also analyze an experimental protocol to study the formation of sine-Gordon breathers in the relative phase field, seeded by quantum fluctuations.
We discuss the nonequilibrium time evolution of the phase field in the sine-Gordon model using two very different approaches: the truncated Wigner approximation and the truncated conformal space approach. We demonstrate that the two approaches agree for a period covering the first few oscillations, thereby giving a solid theoretical prediction in the framework of the sine-Gordon model, which is thought to describe the dynamics of two bosonic condensates in quasi-one-dimensional traps coupled via a Josephson tunneling term. We conclude, however, that the recently observed phase-locking behavior cannot be explained in terms of homogeneous sine-Gordon dynamics, which hints at the role of other degrees of freedom or inhomogeneity in the experimental system.
We consider a model of two tunnel-coupled one-dimensional Bose gases with hard-wall boundary conditions. Bosonizing the model and retaining only the most relevant interactions leads to a decoupled theory consisting of a quantum sine-Gordon model and a free boson, describing respectively the antisymmetric and symmetric combinations of the phase fields. We go beyond this description by retaining the perturbation with the next smallest scaling dimension. This perturbation carries conformal spin and couples the two sectors. We carry out a detailed investigation of the effects of this coupling on the non-equilibrium dynamics of the model. We focus in particular on the role played by spatial inhomogeneities in the initial state in a quantum quench setup.
The sine-Gordon model captures the low-energy effective dynamics of a wealth of one-dimensional quantum systems, stimulating the experimental efforts in building a versatile quantum simulator of this field theory and fueling the parallel development of new theoretical toolkits able to capture far-from-equilibrium settings. In this work, we analyze the realization of the sine-Gordon model from the interference pattern of two one-dimensional quasicondensates: we argue that the emergent field theory is well described by its classical limit, and we develop its large-scale description based on generalized hydrodynamics. We show how, despite the sine-Gordon model being an integrable field theory, trap-induced inhomogeneities cause instabilities of excitations and provide exact analytical results to capture this effect.
This thesis presents four theoretical studies on pairs of tunnel-coupled one-dimensional Bose gases. It first recapitulates how at low energies, the gases’ symmetric and antisymmetric combinations of density and phase are governed by two Tomonaga-Luttinger Liquids (TLL). Tunneling between the gases is believed to yield a quantum sine-Gordon model for the antisymmetric sector. The theoretical background and various applications of this model are summarized, before presenting the first new theoretical results. These show in detail how matter-wave interference measurements can access eigenvalues of the relative phase operator from the TLL, allowing to study the operator’s distribution functions and multi-point correlators. The derivation clarifies why this construction is limited to short expansion times and weak interactions and what modifications occur away from this limit. This leads to a new formula predicting longitudinal “density ripples”. The second half of the thesis was stimulated by recent and unexplained experimental results in the tunnel-coupled case, where density-phase oscillations were seen to rapidly damp out. The work first studies whether this can be explained within a translationally invariant sine-Gordon model. Treating this model in a self-consistent harmonic approximation leads to a negative conclusion. Second, the next leading perturbation due to the tunnel-coupling is investigated in a box geometry. Although this yields a non-negligible coupling between the (anti)symmetric sectors, the effects are not strong enough to explain the damping. Finally, a new low-energy theory is developed, which does not rely on the TLL and which allows to study the roles of both higher excited levels of the transverse potential and of a realistic longitudinal potential. Strong damping is observed as a result of the longitudinal potential, with a dependence on the particle number that is compatible with experimental results. This indicates that performing the experiments in a hard-wall box potential might eliminate the damping effects.
The sine-Gordon field theory emerges as the low-energy description in a wealth of quantum many-body systems. Recent efforts have been directed towards realizing quantum simulators of the model, by interfering two weakly coupled one-dimensional cold atomic gases. The weak interactions within the atomic clouds provide a sine-Gordon realization in the semiclassical regime. Furthermore, the intricate microscopic dynamics prevents a quantitative understanding of the effective sine-Gordon validity realm. In this work, we focus on a spin-ladder realization and observe the emergent sine-Gordon dynamics deep in the quantum regime. We use matrix-product state techniques to numerically characterize the low-energy sector of the system and compare it with the exact field-theory predictions. From this comparison, we obtain quantitative boundaries for the validity of the sine-Gordon description. We provide encompassing evidence for the emergent field theory by probing its rich spectrum and by observing the signatures of integrable dynamics in scattering events.