We study the ultimate quantum limit of rotation sensing with a few strongly interacting bosons confined in a quasi-one-dimensional ring trap with two weak links. It is demonstrated that a self-consistent many-body solution of the problem is required to correctly predict the ultimate sensitivity of this strongly correlated many-body gyroscope to rotation. For both small rotation velocities and small particle numbers, the many-body quantum Fisher information becomes maximal for large interaction couplings, showing the potential of strongly interacting miniaturized many-body sensors to precisely estimate slow rotations with high spatial resolution.
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We study the ultimate quantum limit of rotation sensing with a few strongly interacting bosons confined in a quasi-one-dimensional ring trap with two weak links. It is demonstrated that a self-consistent many-body solution of the problem is required to correctly predict the ultimate sensitivity of this strongly correlated many-body gyroscope to rotation. For both small rotation velocities and small particle numbers, the many-body quantum Fisher information becomes maximal for large interaction couplings, showing the potential of strongly interacting miniaturized many-body sensors to precisely estimate slow rotations with high spatial resolution.
Atom interferometers provide exquisite measurements of the properties of noninertial frames. While atomic interactions are typically detrimental to good sensing, efforts to harness entanglement to improve sensitivity remain tantalizing. Here we explore the role of interactions in an analogy between atomic gyroscopes and SQUIDs, motivated by recent experiments realizing ring-shaped traps for ultracold atoms. We explore the one-dimensional limit of these ring systems with a moving weak barrier, such as that provided by a blue-detuned laser beam. In this limit, we employ Luttinger liquid theory and find an analogy with the superconducting phase-slip qubit, in which the topological charge associated with persistent currents can be put into superposition. In particular, we find that strongly interacting atoms in such a system could be used for precision rotation sensing. We compare the performance of this new sensor to an equivalent noninteracting atom interferometer, and find improvements in sensitivity and bandwidth beyond the atomic shot-noise limit.
We introduce a scheme to generate NOON states of few-body bosonic vortices and demonstrate their application as high-precision rotation sensors. Our approach is based on cold atoms in a weakly anisotropic two-dimensional harmonic trap, where the single-particle p orbitals define an effective two-mode Bose-Hubbard model with vortex modes (px±ipy) carrying opposite circulation. In the self-trapping regime, we show that the NOON manifold becomes spectrally isolated, and collective tunneling processes give rise to highly entangled vortex NOON states. However, these states emerge on prohibitively long timescales. To overcome this limitation, we develop two complementary acceleration strategies: geodesic counterdiabatic driving for small particle numbers, and resonance- and chaos-assisted tunneling in the semiclassical regime at larger particle numbers. Both approaches enable the generation of NOON states on experimentally relevant timescales while preserving near-unit fidelities. Finally, we quantify the metrological advantage of vortex NOON states by introducing an interferometric protocol that exploits their intrinsic sensitivity to rotation, enabling the detection of infinitesimal external rotations at the Heisenberg limit. Our work opens the door to rotation sensors based on atomic NOON states, generically realizable in bosonic Josephson junctions with vortex-type orbitals.
The quantum Fisher information of a quantum state with respect to a certain parameter quantifies the sensitivity of the quantum state to changes in that parameter. Maximizing the quantum Fisher information is essential for achieving the optimal estimation precision of quantum sensors. A typical quantum sensor involves a qubit(e.g. a spin-1/2) probe undergoing an unknown rotation, here the unknown rotation angle is the parameter to be estimated. A well known limitation is that if the rotation axis is unknown, the maximal quantum Fisher information is impossible to attain. This limitation has been lifted recently by leveraging entanglement between the probe qubit and an ancilla qubit. Namely, through measurement of the ancilla after the axis is revealed, one can prepare the probe that is optimal for any unknown rotation axis. This proposal, however, works only for a spin-1/2. Considering large spin probes can achieve a larger quantum Fisher information, offering enhanced metrological advantage, we here utilize the entanglement between a large spin probe and an ancilla to achieve optimal quantum Fisher information for estimating the rotation angle, without prior knowledge of the rotation axis. Different from the previous spin-1/2 case, achieving the optimal precision with large spins generally requires post-selection, resulting in a success probability dependent on the dimension of the Hilbert space. Furthermore, we extend the encoding state from the maximally entangled case to general entangled states, showing that optimal metrology can still be achieved with a certain success probability.
We analyze the scaling of quantum Fisher information with the number of system particles in the limit of large number of particles, as a function of the number of parties interacting with each other, for encoding Hamiltonians having arbitrary-body interactions. We find that estimation of coupling strength of such arbitrary-body encoding Hamiltonians provide a super-Heisenberg scaling that increases monotonically with an increase in the number of interacting particles, in the limit of large number of system particles. Moreover, we also find that the optimal probes corresponding to Hamiltonians that contain even-body interaction terms, may be entangled, but certainly not so in all bipartitions, and particularly, it is possible to attain optimal precision using asymmetric probes. Thereby we find a complementarity in the requirement of asymmetry and genuine entanglement in optimal probes for estimating strength of odd- and even-body interactions respectively. Additionally, we provide an upper bound on the number of parties up to which one can always obtain an asymmetric product state that gives the best metrological precision for even-body interactions. En route, we find the quantum Fisher information in closed form for two- and three-body interactions for arbitrary number of parties. We also provide an analysis of the case when the Hamiltonian contains local fields and up to k-body interaction terms, where the strength of interaction gradually decreases with an increase in the number of parties interacting with each other. Interestingly, we find a similar dichotomy in the nature of the optimal probe in this case as well. Further, we identify conditions on the local component of the Hamiltonian, for which this dichotomy is still shown to exist for two- and three-body encoding Hamiltonians with arbitrary local dimensions.
Quantum sensing utilizes the quantum resources of well-controlled quantum systems to measure small signals with high sensitivity, and has great potential in both fundamental science and concrete applications. Interacting quantum systems have attracted increasing interest in the field of precise measurements, owing to their potential to generate quantum-correlated states and exhibit rich many-body dynamics. These features provide a novel avenue for exploiting quantum resources in sensing applications. Although previous studies have shown that using such systems can improve sensitivity, they mainly focused on measuring individual physical quantities. In experiment, the challenge of using interacting quantum systems to achieve high-precision measurements of multiple physical parameters simultaneously has not been explored to a large extent. In this study, we demonstrate a first realisation of interaction-based multiparameter sensing by using strongly interacting nuclear spins under ultra-low magnetic field conditions. We find that, as the interaction strength among nuclear spins becomes significantly larger than their Larmor frequencies, a different regime emerges where the strongly interacting spins can be simultaneously sensitive to all components of a multidimensional field, such as a three-dimensional magnetic field. Moreover, we observe that the strong interactions between nuclear spins can increase their quantum coherence times to as long as several seconds, thereby improving measurement precision. Our sensor successfully achieves precision measurement of three-dimensional vector magnetic fields with a field sensitivity reaching the order of 10–11 T and an angular resolution as high as 0.2 rad. Importantly, this approach eliminates the need for external reference fields, thereby avoiding calibration errors and technical noise commonly encountered in traditional magnetometry. Experimentally optimized protocol further enhances the sensitivity of the interacting spin-based sensor by up to five orders of magnitude compared with non-interacting or classical schemes. These results demonstrate the enormous potential of interacting spin systems as a powerful platform for high-precision multi-parameter quantum sensing. The techniques developed here pave the way for a new generation of quantum sensors that use intrinsic spin interactions to exceed the traditional sensitivity limits, presenting a promising route toward ultra-sensitive, calibration-free magnetometry in complex environments.
Quantum Fisher information (QFI) determines the ultimate precision of a quantum sensor after optimization over all allowed measurements, but it does not quantify how difficult the optimal readout is to implement. We introduce a moment Fisher hierarchy FM(k), which measures the fraction of QFI accessible to collective spin moments up to degree k, together with a readout-complexity scale k90 defined by the minimum degree required to recover 90% of the QFI. Applying this framework to a nonlinear collective-spin sensor, we show that many-body dynamics can preserve large QFI while transferring the optimal readout into high-rank SU(2) tensor sectors inaccessible to low-order collective observables. For system sizes up to N=100, first moments access only ∼10−2 of the available QFI, while the degree required to recover 90% of it grows to k90≃28. A rank-resolved analysis of the symmetric logarithmic derivative (SLD) under weak damping shows that the nonlinear protocol pushes the optimal readout toward the highest available tensor ranks while strongly depleting its low-rank weight. These results identify nonlinear tangent-space shear as the mechanism behind a finite-size readout-complexity bottleneck in many-body quantum metrology.