Quantum sensing with ultracold simulators in lattice and ensemble systems: a review

TL;DR

The review surveys quantum sensing with ultracold simulators in both lattice and ensemble platforms, unifying the Fisher information framework with practical sensing protocols. It describes interferometric and criticality-based encoding, highlighting how entanglement, squeezing, and many-body phenomena yield precision beyond the standard quantum limit and toward the Heisenberg bound. The work catalogs ensemble approaches (spin ensembles, light-matter interfaces, BECs) and lattice models (Fermi-Hubbard, Bose-Hubbard, spin chains, topological and non-Hermitian systems), emphasizing metrological resources such as spin squeezing, criticality, and topological localization. It also discusses operator-based Fisher information as a bridge between theory and experiment, and outlines challenges and future directions for realizing scalable, robust quantum sensors with ultracold atoms and quantum simulators in AMO platforms.

Abstract

Sensing of parameters is an important aspect in all disciplines, with applications ranging from fundamental science to medicine. Quantum sensing and metrology is an emerging field that lies at the cross-roads of quantum physics, quantum technology, and the discipline in which the parameter estimation is to be performed. While miniaturization of devices often requires quantum mechanics to be utilized for understanding and planning of a parameter estimation, quantum-enhanced sensing is also possible that uses paradigmatic quantum characteristics like quantum coherence and quantum entanglement to go beyond the so-called standard quantum limit. The current review hopes to bring together the concepts related to quantum sensing as realized in ensemble systems, like spin ensembles, light-matter systems, and Bose-Einstein condensates, and lattice systems, like those which can be modeled by the Bose- and Fermi-Hubbard models, and quantum spin models.

Figures (7)

• Figure 1: Scaling of sensitivity with system size of Dicke states.The sensitivity of phase estimation $(\Delta\varphi)^2$ in an interferometric protocol with encoding on twin multimode states (TMS) is obtained using the Dicke model in superradiant phase and with parity measurements. Therefore, the Heisenberg limit is achievable here (black squares - twin multi-mode Dicke states), which reduces to the shot noise limit in presence of errors, which is anharmonic cavities (upward red triangles corresponds to $U/N=10$, while downward yellow triangles corresponds to $U/N = 10^3$) in this case. The figure is taken from Ref. Paulisch2019.
• Figure 2: Gravimeter based on Bose-Einstein Condensate. (a) Schematic depicting the activation of spin-collisions dynamics (green arrows) between atoms by dressing the transition $|1,0\rangle \leftrightarrow |2,0\rangle$ with mw pulses leading to the generation of two-mode squeezed vacuum state, transfer of $|1,0\rangle$ to $|2,0\rangle$ using mw (light gray arrows) and rf pulse induced transfer from $|1,\pm1\rangle$ to $|1,0\rangle$ (dark gray arrows). (b) Spin noise tomography of the input state of the interferometer is presented. The normalized population in $|2,0\rangle$ and the corresponding variances are presented against the scanned mw phase $\varphi$ in the top and bottom graphs respectively, with the inset focusing on the around the minimum that represents the optimal squeezing angle $\varphi_\text{opt}$. (c) Schematic depiction of the whole sequence of operation for the gravimeter. The dashed line indicate $|1,0\rangle$ and solid line $|2,0\rangle$. The Raman (R) pulses are depicted in red. In the bottom figure, the bloch sphere is depicted with $|2,0\rangle$ and $|1,0\rangle$ being the north and south pole respectively. The squeezed input state is rotated into the phase-squeezed direction (i) and the phase $\varphi_\text{sig}$ that is to be sensed is encoded in (ii)-(iv), which is finally estimated by measuring population imbalance in (v). The figure is taken from Ref. Cassens2025.
• Figure 3: Criticality enhanced sensing in Fermionic and Non-hermitian spin systems. (a) The topological phase diagram of the one-dimensional Kitaev model (given by Eq. \ref{['eq:kitaev']}) is presented with $\mu = \mu_c = 2$ being the gapless critical line (depicted with red) separating the topologically trivial phase (depicted with green) from the topological phase (depicted with blue) with winding number $w=+1$. The multi-parameter QFI, $G= (\text{Tr}[\mathbb{F}^{-1}])^{-1}$ ($\mathbb{F}$ being the QFI-matrix for multi-parameter estimation) of a point $C$ at the critical line with $\delta\Delta\rightarrow 0$ has super-HL scaling. In the inset, the system-size scaling of the QFI-s corresponding to estimating $\mu$, $\Delta$ and both simultaneously, which are given by $\mathcal{F}_{\mu\mu}$, $\mathcal{F}_{\Delta\Delta}$ and $G$ respectively for $\mu = \mu_c = 2$ and $\Delta = 10^{-7}$. (b) Non-Hermitian XY model with $KSEA$ interactions $K$ and non-Hermitian anisotropy $\gamma$ have rotation time $\mathcal{RT}$-symmetry. It can be mapped to Eq. \ref{['eq:kitaev']} with $\mu=2h$ and $H_\Delta$ extended to $H_{\gamma,K}=\sum_j i(\gamma-K)c_j^\dagger c_{j+1}^\dagger+i(\gamma+K)c_j c_{j+1}$. For the gapless critical line at $h=1$ (marked by red), the broken phase is separated from the unbroken phase by exceptional points (marked by green) shown for fixed $K$. The ground states shows super-HL scaling for sensing magnetic field $h$, as $\gamma-K\to 0$, showing advantage via competition between Hermitian and non-Hermitian interactions. Figures (a) and (b) are adapted from Ref. Mondal2024 and agarwal2025 respectively.
• Figure 4: Parameter estimation for an initial Fock state under a periodic drive.(a) The time evolution of the QFI, $\mathcal{F}^{(M)}$, for a Fock state as the initial state is shown here. The results are presented for total lattice sites $M = 2$ (blue), $3$ (red), and $4$ (orange). Here, $\mathcal{F}^{(M)}$ is scaled by $T^2$, and the peak value is defined as $\mathcal{F}^{(M)}_{\text{max}} = \max\left\{\frac{\mathcal{F}^{(M)}}{T^2}\right\}.$ The inset displays the unscaled QFI, which exhibits an oscillatory behavior as a function of time $T$. (b) The growth of the normalized peak QFI, $\mathcal{F}^{(M)}_{\text{max}} / \mathcal{F}^{(2)}_{\text{max}}$, shows a quadratic dependence on the system size $M$ in the limit $M \gg 1$. The inset illustrates that the $\tau$, the time at which $\mathcal{F}^{(M)}_{\text{max}}$ reaches its maximum value, increases linearly with $M$. The figure is taken from Ref. Pelayo2023.
• Figure 5: Thermometry in BH model. The false-color plot shows the variation of entropy per particle, $S/Nk_{B}$, as a function of the interaction parameter $u = U/J$ and the dimensionless temperature $T_J = k_B T / J$ for the 3D Bose-Hubbard model. The open circles represent values of $T_J$ extracted using momentum-space density, $\rho(k)$, thermometry. The white dotted line indicates an isentropic trajectory corresponding to $S/N = 0.8k_B$, while the black dotted line marks the critical temperature at unit filling. This figure is taken from Ref. Carcy2021.