Quantum-mechanics-free subspaces in composite systems with incompatible energy spectra.

It is well established that quantum back action (QBA) can be reduced (or even completely canceled) in composite systems by engineering so-called quantum-mechanics-free subspaces (QMFSs) of commuting variables. An important ingredient in this approach is the negative-mass oscillator, a phenomenon that arises in, e.g., polarized spin ensembles and two-tone-driven optomechanical systems. Entanglement established between a system of interest and an auxiliary negative-mass reference system allows measurements of motion, fields and forces with, in principle, unlimited precision. To date, these principles have been developed theoretically and demonstrated experimentally for a number of composite systems. However, the utility of the concept has been limited by the dominating requirement of close proximity of the resonance frequencies of the system of interest and the negative-mass reference system, and by the need to embed the subsystems in a narrowband cavity, which could be problematic while at the same time achieving good overcoupling. Here we propose a general approach which overcomes these limitations by employing periodic modulation of the driving fields (e.g., two-tone driving) in combination with coherent or measurement-based anti-noise paths. This approach makes it possible to engineer a QMFS of two systems with vastly different spectra and with arbitrary signs of their masses, while dispensing with the need to embed the subsystems in a sideband-resolving cavity. We discuss the advantages of this novel approach for applications such as QBA evasion in gravitational wave detection, force sensing, and entanglement generation between disparate systems.