Mechanical oscillators operate in the degenerate parametric regime when their spring constant is modulated at twice the oscillator resonance frequency. In such regime, like in a child's swing, the response of the oscillator to an external excitation acting close to resonance is enhanced, and can easily reach a threshold marking the birth of self-oscillations (parametric resonance).
More precisely, the response is amplified if the motion is in phase with the parametric modulation (quadrature), and de-amplified if it is out of phase of 90 degree (orthogonal quadrature). As this phenomenon is active also for a stochastic excitation, the distribution of fluctuations in the phase plane is squeezed, that is its variance is reduced below its free-running value in the orthogonal quadrature. However, since the amplified quadrature evolves into self-oscillations for a parametric drive approaching the threshold, the corresponding reduction in the orthogonal quadrature is limited to -3 dB (0.5). This is a general feature of parametric squeezing that it has already been demonstrated for thermal oscillators, and is expected even for the quantum noise.
In this work [Physical Review Letters 112, 023601 (2014)], researchers from IMEM and INO, in collaboration with the Universities of Firenze and Trento, propose and apply an experimental scheme based on parametric feedback that, stabilizing the amplified quadrature without influencing the orthogonal one, allows to surpass the -3 dB barrier on noise reduction, with a best experimental result of -7.4 dB. In the experiment we use a micro-resonator as the end-mirror of an optical cavity, where the intensity of the reflected light changes proportionally to the position of the mirror. The parametric modulation is applied by changing the equivalent spring due to the light beam stored in the cavity, which adds to the mechanical spring to set the overall rigidity of the system. With this scheme it is possible to observe the squeezing in the motion of the orthogonal quadrature, and at the same time to control independently the motion in the amplified quadrature and to avoid the runaway feedback self-oscillation.
The technique is of particular interest because it keeps working even if used in a quantum context, and it is therefore potentially usable to operate on macroscopic systems close to their fundamental quantum state. In conclusion, this measurement strategy allows boosting the performance of a nonlinear squeezing effect known since the nineteenth century, extending the scope of its applications to the frontiers of modern physics.
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