  Coherence time is an important resource to generate enhancement in quantum
metrology. In this work, based on continuous-variable models, we propose a new
design of the signal-probe Hamiltonian which generates an exponential
enhancement of measurement sensitivity. The key idea is to include into the
system an ancilla that does not couple directly to the signal. An immediate
benefit of such design is one can expand quantum Fisher information(QFI) into a
power series in time, making it possible to achieve a higher-order time scaling
in QFI. Specifically, one can design the interaction for a qubit-oscillator
Ramsey interferometer to achieve a quartic time scaling, based on which, one
can further design a chain of coupled harmonic oscillators to achieve an
exponential time scaling in QFI. Our results show that linear scaling in both
time and the number of coupling terms is sufficient to obtain exponential
enhancement. Such exponential advantage is closely related to the
characteristic commutation relations of quadratures.
