Abstract
Because of the broken time-translation symmetry, in periodically driven vibrational systems fluctuations of different vibration components have different intensities. Fluctuations of one of the components are often squeezed, whereas fluctuations of the other component, which is shifted in phase by {\pi}/2, are increased. Squeezing is a multifaceted phenomenon; it attracts much attention from the perspective of high-precision measurements. Here we demonstrate a new and hitherto unappreciated side of squeezing: its direct manifestation in the spectra of driven vibrational systems. With a weakly damped nanomechanical resonator, we study the spectrum of thermal fluctuations of a resonantly driven nonlinear mode. In the attained sideband-resolved regime, we show that the asymmetry of the spectrum directly characterizes the squeezing. This opens a way to deduce squeezing of thermal fluctuations in strongly underdamped resonators, for which a direct determination by a standard homodyne measurement is impeded by frequency fluctuations. The experimental and theoretical results are in excellent agreement. We further extend the theory to also describe the spectral manifestation of squeezing of quantum fluctuations.
Highlights
When appropriately scaled, the coordinate and momentum of a vibrational system or their canonical conjugate linear combinations form two vibration components
The scaling is done in such a way that, classically, the components oscillate with equal amplitudes in an isolated system, whereas their phases differ by π=2
If the system is coupled to a thermal reservoir, the vibration components fluctuate with the same intensities, in the absence of driving
Summary
The coordinate and momentum of a vibrational system or their canonical conjugate linear combinations form two vibration components. The commonly employed method to detect squeezing is a homodyne measurement This technique has been used in all previous demonstrations of quantum or classical noise squeezing we are aware of, be it the case of a parametric amplifier or a Duffing resonator [1,9,10,11,14,15,16,17,18,19,20,21,22,23,24,25,26,29]. A nonequilibrium system does not have detailed balance and cannot be mapped onto a Brownian particle in a potential well Still, it can display an analog of a kinetic phase transition where the state populations are almost equal [30,38]. Our nanoresonator allows us to find the kinetic phase transition in a system lacking detailed balance and to quantitatively test a major aspect of the theory of fluctuations in such systems
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