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Nanomechanical oscillators are at the heart of ultrasensitive detectors of force, mass and motion. As these detectors progress to even better sensitivity, they will encounter measurement limits imposed by the laws of quantum mechanics. For example, if the imprecision of a measurement of an oscillators position is pushed below the standard quantum limit (SQL), quantum mechanics demands that the motion of the oscillator be perturbed by an amount larger than the SQL. Minimizing this quantum backaction noise and nonfundamental, or technical, noise requires an information efficient measurement. Here we integrate a microwave cavity optomechanical system and a nearly noiseless amplifier into an interferometer to achieve an imprecision below the SQL. As the microwave interferometer is naturally operated at cryogenic temperatures, the thermal motion of the oscillator is minimized, yielding an excellent force detector with a sensitivity of 0.51 aN/rt(Hz). In addition, the demonstrated efficient measurement is a critical step towards entangling mechanical oscillators with other quantum systems.
We demonstrate a transducer of nanomechanical motion based on cavity enhanced optical near-fields capable of achieving a shot-noise limited imprecision more than 10 dB below the standard quantum limit (SQL). Residual background due to fundamental the
Under ideal conditions, quantum metrology promises a precision gain over classical techniques scaling quadratically with the number of probe particles. At the same time, no-go results have shown that generic, uncorrelated noise limits the quantum adv
Parameter estimation is of fundamental importance in areas from atomic spectroscopy and atomic clocks to gravitational wave detection. Entangled probes provide a significant precision gain over classical strategies in the absence of noise. However, r
We analyze methods to go beyond the standard quantum limit for a class of atomic interferometers, where the quantity of interest is the difference of phase shifts obtained by two independent atomic ensembles. An example is given by an atomic Sagnac i
Mechanical transduction of torque has been key to probing a number of physical phenomena, such as gravity, the angular momentum of light, the Casimir effect, magnetism, and quantum oscillations. Following similar trends as mass and force sensing, mec