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arXiv:2506.06173 · Physical Review A

Tilt-induced localization in interacting Bose-Einstein condensates for quantum sensing

Argha Debnath, Mariusz Gajda, Debraj Rakshit

Published Mar 23, 2026• 0 citations
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Abstract

We investigate localization transitions in interacting Bose-Einstein condensates (BECs) confined in tilted optical lattices, focusing on both the continuum limit accessed via shallow lattice depths and the tight-binding limit realized in the deep lattice regime. Utilizing the Gross-Pitaevskii equation (GPE) and the many-body Bose-Hubbard model, we analyze the scaling behavior of localization indicators, such as the root mean square width and fidelity susceptibility, as a function of the applied tilt. Our results reveal clear signatures of a localization-delocalization transition driven by the linear potential, with scaling properties that characterize criticality even in the presence of interactions within the GPE description. Despite the single-mode nature of the condensate wavefunction, we demonstrate that it can effectively probe quantum criticality. Building on this, we propose the use of interacting BECs in tilted lattices as a platform for quantum critical sensing, where the condensate wavefunction serves both as a sensitive probe of localization and a practical resource for quantum-enhanced metrology. This approach opens new avenues for precision gradient sensing based on localization phenomena in bosonic systems.

DOI
10.1103/rmvy-35tj

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We investigate localization transitions in interacting Bose-Einstein condensates (BECs) confined in tilted optical lattices, focusing on both the continuum limit accessed via shallow lattice depths and the tight-binding limit realized in the deep lattice regime. Utilizing the Gross-Pitaevskii equation (GPE) and the many-body Bose-Hubbard model, we analyze the scaling behavior of localization indicators, such as the root mean square width and fidelity susceptibility, as a function of the applied tilt. Our results reveal clear signatures of a localization-delocalization transition driven by the linear potential, with scaling properties that characterize criticality even in the presence of interactions within the GPE description. Despite the single-mode nature of the condensate wavefunction, we demonstrate that it can effectively probe quantum criticality. Building on this, we propose the use of interacting BECs in tilted lattices as a platform for quantum critical sensing, where the condensate wavefunction serves both as a sensitive probe of localization and a practical resource for quantum-enhanced metrology. This approach opens new avenues for precision gradient sensing based on localization phenomena in bosonic systems.
We study nonequilibrium signatures of tilt-induced localization in a one-dimensional Bose-Einstein condensate loaded in a shallow optical lattice. The tilt strength acts as a control parameter for the localization-delocalization crossover. We also consider the effects of repulsive interactions, which tend to delocalize the condensate. We first characterize localized and delocalized regimes through sudden quenches of the interaction strength and the external tilt. The resulting dynamics is analyzed using the survival probability and its power spectral density. Localized condensates exhibit strong memory retention, pronounced revivals, regular dynamics and a narrow spectral response, whereas delocalized condensates show suppressed recurrences, irregular dynamics and a broader distribution of spectral weight over many frequencies. We then investigate finite-rate ramps of the tilt strength across the localization threshold. Using the localization length and the Bogoliubov excitation gap, we extract the relevant critical exponents and perform Kibble-Zurek scaling analysis in the driven dynamics. Our results establish quench response and finite-rate scaling as complementary dynamical probes of localization in interacting Bose gases, with direct relevance to cold-atom experiments in tilted optical lattices.
The ability to create and manipulate strongly correlated quantum many-body states is of central importance to the study of collective phenomena in several condensed-matter systems. In the last decades, a great amount of work has been focused on ultracold atoms in optical lattices, which provide a flexible platform to simulate peculiar phases of matter both for fermionic and bosonic particles. The recent experimental demonstration of Bose-Einstein condensation (BEC) of light in dye-filled microcavities has opened the intriguing possibility to build photonic simulators of solid-state systems, with potential advantages over their atomic counterpart. A distinctive feature of photon BEC is the thermo-optical nature of the effective photon-photon interaction, which is intrinsically nonlocal and can thus induce interactions of arbitrary range. This offers the opportunity to systematically study the collective behavior of many-body systems with tunable interaction range. In this paper, we theoretically study the effect of nonlocal interactions in photon BEC. We first present numerical results of BEC in a double-well potential, and then extend our analysis to a short one-dimensional lattice with open boundaries. By resorting to a numerical procedure inspired by the Newton-Raphson method, we simulate the time-independent Gross-Pitaevskii equation and provide evidence of surface localization induced by nonlocality, where the condensate density is localized at the boundaries of the potential. Our work paves the way toward the realization of synthetic matter with photons, where the interplay between long-range interactions and low dimensionality can lead to the emergence of unexplored nontrivial collective phenomena.
Bose–Einstein condensation represents a quintessential manifestation of quantum mechanics at macroscopic scales, where a dilute gas of bosonic atoms undergoes a phase transition to form a coherent matter wave. This study presents a comprehensive theoretical investigation of collective excitations and critical phenomena in interacting Bose–Einstein condensates (BECs). Beginning with the Gross–Pitaevskii equation , we develop the Bogoliubov theory of excitations yielding the spectrum , where is the free-particle energy and characterizes contact interactions. The spectrum reveals phonon behavior at low momenta with sound velocity , transitioning to free-particle dispersion at momenta exceeding the inverse healing length . Collective modes in harmonically trapped condensates are analyzed in the Thomas–Fermi regime, yielding breathing mode frequency and quadrupole frequency . Damping mechanisms including Landau damping ( ) and Beliaev damping ( ) are characterized. The Lee–Huang–Yang correction extends the equation of state beyond mean field. Critical phenomena near are analyzed within the 3D XY universality class, with critical exponents , , and the interaction-induced shift with . All predictions show excellent agreement with experimental measurements on ultracold atomic gases.
We investigate the disorder-induced localization transition in Bose-Einstein condensates for the Anderson and Aubry-Andr\'e models in the noninteracting limit using exact diagonalization. We show that, in addition to the standard superfluid fraction, other tools such as the entanglement and fidelity can provide clear signatures of the transition. Interestingly, the fidelity exhibits good sensitivity even for small lattices. Effects of the system size on these quantities are analyzed in detail, including the determination of a finite-size-scaling law for the critical disorder strength in the case of the Anderson model.
We study the tunneling decay of a Bose-Einstein condensate from tilted optical lattices within the mean-field approximation. We introduce a method to calculate ground and excited resonance eigenstates of the Gross-Pitaevskii equation, based on a grid relaxation procedure with complex absorbing potentials. This algorithm works efficiently in a wide range of parameters where established methods fail. It allows us to study the effects of the nonlinearity in detail in the regime of resonant tunneling, where the decay rate is enhanced by resonant coupling to excited unstable states.
We study the expansion of repulsively interacting Bose-Einstein condensates (BECs) in shallow one-dimensional potentials. We show for these systems that the onset of wave chaos in the Gross-Pitaevskii equation (GPE), that is, the onset of exponential separation in Hilbert space of two nearby condensate wave functions, can be used as an indication for the onset of depletion of the BEC and the occupation of excited modes within a many-body description. Comparison between the multiconfigurational time-dependent Hartree for bosons method and the GPE reveals a close correspondence between the many-body effect of depletion and the mean-field effect of wave chaos for a wide range of single-particle external potentials. In the regime of wave chaos the GPE fails to account for the fine-scale quantum fluctuations because many-body effects beyond the validity of the GPE are non-negligible. Surprisingly, despite the failure of the GPE to account for the depletion, coarse-grained expectation values of the single-particle density such as the overall width of the atomic cloud agree very well with the many-body simulations. The time-dependent depletion of the condensate could be investigated experimentally, for example, via decay of coherence of the expanding atom cloud.