We demonstrate real-time displacement measurement using spectrally resolved Hong–Ou–Mandel (HOM) interference that saturates the quantum Cram´er-Rao bound. Unlike conventional HOM-based methods, our approach does not require the displacement to be confined within the HOM dip width, typically a few tens of microns. By analyzing the periodicity of spectral interference fringes, we can maintain sensitivity at the quantum limit over displacement ranges extending to hundreds of microns. In principle, the measurable range can be extended up to the coherence length of the pump laser, limited only by the spectral resolution of the detector. We further demonstrate that real-time displacement tracking is feasible with current technology, establishing this technique as a practical and powerful tool for quantum-enhanced sensing and metrology.
Optomechanical systems have been proven to be very useful for precision sensing of a variety of forces and effects. In this work, we propose an opto-magno-mechanical setup for spatial displacement sensing where one mirror of the optical cavity is levitated in vacuum via diamagnetic forces in an inhomogenous magnetic field produced by two layers of permanent magnets. We show that the optomechanical system can sense small changes in separation between the magnet layers, as the mechanical frequency of the levitated mirror shifts with changing magnet layer separation
d. We use Quantum Fisher Information (QFI) as a figure of merit of the displacement sensing precision, and study the fundamental precision bound that can be reached in our setup. Nonlinear interaction inherently present in the optomechanical Hamiltonian improves the precision, and we show that in the case of a pure state of the optical cavity, one can achieve extremely small displacement sensing precision of
Δd∼36×10−21m. Further, we incorporate decoherence into our system to study the effect of leaking photons from the optical cavity on the QFI.
Quantum noises impose limits on both backaction cooling and displacement measurements in macroscopic resonators. Here, we demonstrate that for dissipative optomechanical systems in the deeply unresolved sideband regime, squeezed-vacuum engineering of Fano interference enables broadband, tunable suppression of backaction noise and complete evasion of backaction heating, along with destructive noise correlations in the measurement spectrum. This leads to ground-state cooling over a cavity-linewidth scale for both blue- and red-detuned drives, as well as substandard quantum limit position sensitivity both at and away from mechanical resonance. Our Letter establishes squeezed-reservoir engineering as a powerful platform for exploring nonclassical correlations, quantum sensing, and information processing via noise-interference control.
Quantum-enhanced displacement sensing with bosonic systems is typically formulated assuming that the oscillator is cooled close to its ground state before nonclassical probe preparation. We investigate whether such near-ground-state initialization is necessary, or whether sensitive probes can instead be generated directly from thermal states. We analyze hot quantum probes produced by squeezing, number-raising, and Schrödinger-cat-state generation applied to thermal inputs. We identify two distinct mechanisms by which thermal mixedness can remain compatible with enhanced displacement sensitivity. First, projecting a mixed probe onto a definite parity sector removes the usual thermal suppression of the displacement quantum Fisher information, which can then increase with initial thermal occupation. Second, coherent superpositions of opposite displacements can retain sensitivity through coherence between their displaced components, even when the underlying state is mixed. We use these two mechanisms to classify hot-state protocols according to whether their sensitivity comes from parity selection, coherence between displaced components, or both. Finally, we formulate an experimentally relevant optimization problem comparing initial cooling with direct hot-state preparation under realistic decoherence and show that complete cooling is not universally optimal. Our results establish hot-state engineering as a route to quantum-enhanced bosonic displacement sensing without mandatory ground-state initialization.