Tilt-Induced Localization in Interacting Bose-Einstein Condensates for Quantum Sensing

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.

Figures (5)

• Figure 1: Variation of density with three different relative Stark field strengths, $\tilde{V}=0.0002$ (red solid line), $\tilde{V}=0.02$ (brown circle), $\tilde{V}=0.2$ (green triangle up) for $g=0$. In (b) we showed variation of density for $\tilde{V}=0.02$ with $g$. Delocalization can be seen with the rise of interaction strength. Here, the plotted three different interaction strengths are, $g=0$ (yellow circle), $g=2$ (orange triangle up), $g=6$ (purple solid line). (c) and (d) are the log scale version of (a) and (b) respectively. We have taken $V=0.5$ and $L=50$.
• Figure 2: For $g=1$ (a) presents RMS width, $\zeta$ of the ground state against relative Stark field strength $\tilde{V}$ for different system sizes, $L=30$ (blue circle), $L=40$ (orange triangle up), $L=50$ (pink diamond), $L=70$ (green square) and $L=120$ (purple triangle down). (b) shows a collapse plot for the RMS width with the value of scaling exponent $\nu\sim 0.42$ and $\tilde{V}_c\sim 2.7\times 10^{-4}$. (c) Variation of critical Stark strength $\tilde{V}_c$ with interaction $g$. Green dashed line is added just to guide the eye of $\tilde{V}_c$'s incremental nature with increasing $g$.
• Figure 3: For $g=1$ (a) presents The QFI, $F_Q$ versus relative Stark field strength $\tilde{V}$ for different system sizes, $L=30$ (blue circle), $L=40$ (orange triangle up), $L=50$ (pink diamond), $L=70$ (green square) and $L=120$ (purple triangle down). (b) shows a collapse plot for the $F_Q$ with $(\beta, \nu, \tilde{V}_c)\sim(4.7,0.42, 2\times 10^{-4})$. (c) QFI (brown dots) as a function of $L$ for a fixed $\tilde{V}$. The dashed blue lines are fitting of the form $F_Q(\tilde{V}=10^{-5})\propto L^\beta$ with $\beta\sim4.73$. (d) we have plotted variation of $\beta$ with $g$.
• Figure 4: (a) Density profiles $n_i$ for different Stark potentials $h=0$ (red filled circle), 0.5 (green filled square), 1 (yellow filled diamond), 4 (light blue filled uptriangle) for $L=30$. (b) presents the QFI, $F_Q$ versus Stark field strength $h$ for different system sizes, $L=36$ (blue filled circle), $L=39$ (orange filled triangle up), $L=42$ (pink filled diamond), $L=45$ (green filled square) and $L=48$ (purple filled triangle down). (c) shows a collapse plot for the $F_Q$ with the value of scaling exponents $(\beta, \bar{\nu}, h_c)\sim(4.3, 0.71, 3\times 10^{-3})$. (d) Variation of $\beta$ with $U$. Each $\beta$ is obtained through fitting of the form $F_Q(h=10^{-3})\propto L^\beta$. For (a), (b) and (c) interaction strength is taken as $U=t=1$.
• Figure A1: Figure depicts the results with linear tilt. Figure (a) displays the variation of density with three different relative Stark field strengths, $\tilde{V}=0.0002$ (purple solid line), $\tilde{V}=0.02$ (yellow circle), $\tilde{V}=0.2$ (orange triangle up). Log scale counterpart of (a) is plotted in (b). (c) presents RMS width, $\zeta$ of the ground state against relative Stark field strength $\tilde{V}$ for different system sizes, $L=30$ (blue circle), $L=40$ (orange triangle up), $L=50$ (pink diamond), $L=70$ (green square) and $L=120$ (purple triangle down). (d) shows a collapse plot for with the value of scaling exponent $\nu\sim 0.42$ and $\tilde{V}_c\sim 2.7\times 10^{-4}$. (e) presents The QFI, $F_Q$ versus relative Stark field strength $\tilde{V}$ for different system sizes. (d) and (f) show collapse plots for the RMS width and $F_Q$ with $(\beta, \nu, \tilde{V}_c)\sim(4.7,0.42, 2\times 10^{-4})$, respectively.