Quantum sensing of a weak drive signal in cascaded quantum van der Pol oscillators

We have constructed a quantum sensing system composed of two quantum van der Pol (vdP) oscillators. Coherent and dissipative couplings are combined to establish a generic nonreciprocal coupling between the two vdP subsystems. A weak driving signal to be measured is applied to an oscillator (probe system) and then transferred via non-reciprocal coupling to another oscillator (measurement system) that is easier to measure. This allows for the acquisition of information about the driving strength of the signal being measured. For the classic cascaded dual vdP oscillators, complete non-reciprocal coupling yields a much higher susceptibility than a single classical vdP oscillator alone. For the quantum vdP system, the sensitivity generally does not diverge at the zero driving force point. When only dissipative coupling and two-particle loss are present, the system will have a dark mode at the zero driving force point, which enables the measurement precision to ultimately reach the Heisenberg limit in the time domain. Enhancing incoherent driving can effectively resist dissipation and thereby improve measurement precision. Moreover, in the strong incoherent driving regime, the improvement factor of non-reciprocal coupling over reciprocal coupling in terms of measurement precision tends to infinity as the two-particle loss rate of the measurement system approaches zero.