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Quantum rotation sensing with a four-site integrable model

Joel Bacellar Neves

Published Jan 1, 2026• 0 citations

Abstract

In this work, we present a four-site integrable model that describes the interaction and tunneling of ultracold dipolar bosons trapped in a rotating, tetrahedral site arrangement. The model is derived from an extension of the Bose-Hubbard model in a rotating frame where the interaction and tunneling parameters have been appropriately selected to produce four independent and conserved quantities, establishing integrability. Two of these conserved quantities – related to the two nonzero circulation modes found in the system – are used to derive an effective Hamiltonian dynamically equivalent to the system for large interactions, allowing for the analytical prediction of its quantum dynamics. By analyzing the site population dynamics in this large interaction regime, we find that rotation induces population imbalance in a manner akin to the Sagnac effect. This is exploited to design a simple rotation sensing protocol capable of estimating reference frame rotation through population imbalance measurements. We calculate the sensitivity of the proposed protocol and demonstrate it has a scaling advantage due to a nontrivial manifestation of the system’s nonlinearity, enabled by integrability. The findings presented here open further investigations into the effects of rotation in multi-site integrable models, highlighting their great potential for modeling quantum devices and quantum sensors.

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Detection based on quantum principles such as entanglement has the capacity to achieve finessed levels of sensitivity, bringing transformative impacts to applications. In this study, we propose a rotation sensor using ultra-cold dipolar atoms trapped in a four-well configuration. The design, based on a simple population imbalance measurement to quantify rotation, profits from the property of superintegrability. The implementation of the measurement protocol achieves rotation-detection sensitivity beyond the Heisenberg limit. Our results spotlight superintegrability opportunities for advancing the field of quantum sensing.

Following a novel experimental arrangement which can rotate a two-dimensional optical lattice at frequencies up to several kilohertz we discuss the ground state of the two-dimensional Bose-Hubbard Hamiltonian, relevant for rotating gaseous Bose-Einstein condensates, by employing U(1) quantum rotor approach and the topologically constrained path integral.Ultracold atoms in such a rotating lattice can be used for the direct quantum simulation of strongly correlated systems under large effective magnetic fields.We derive an effective quantum action for the Bose-Hubbard model, which enables a non-perturbative treatment of the zero-temperature phase transition in the rotating frame.We calculate the ground-state phase diagram, analytically deriving maximum repulsive energy for several rational values of the frustration rotation parameter f = 0, 1/2, 1/3, 1/4, and 1/6 for the square and triangular lattice.Performed calculations revealed strong non-monotonical dependence of the critical ratio of the kinetic energy to the repulsive on-site energy, that separates the global coherent from the insulating state, on topology of the lattice.

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A quantum device for measuring two-body interactions, scalar magnetic fields and rotations is proposed using a Bose–Einstein condensate (BEC) in a ring trap. We consider an imbalanced superposition of orbital angular momentum modes with opposite winding numbers for which a rotating minimal atomic density line appears. We derive an analytical model relating the angular frequency of the minimal density line rotation to the strength of the nonlinear atom–atom interactions and the difference between the populations of the counter-propagating modes. Additionally, we propose a full experimental protocol based on direct fluorescence imaging of the BEC that allows to measure all the quantities involved in the analytical model and use the system for sensing purposes.

We study the dynamics of vortices in a Bose-Einstein condensate within a rotating four-site lattice, which can be effectively described by a multimode model. Such a vortex dynamics develops along the low-density paths that separate the sites, and it is ruled by the phase differences between them. Hence, by appropriately selecting the initial conditions for on-site populations and phase differences, one can access distinct types of evolutions. We show that, by choosing equal populations in alternate sites, one can construct two-mode model Hamiltonians, which allows us to model a large variety of associated vortex orbits. In particular, one can select the type of trajectory of the vortex and predict the creation and annihilation of vortex-antivortex pairs near the trap center. Estimates for the periods of closed vortex orbits and for the times that the vortices spend inside the lattice when dealing with open orbits, are obtained in terms of the two-mode models parameters and the rotation frequency only. We believe that the present study establishes a suitable platform to engineer different vortex dynamics.