Squeezing Mechanical Motion

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Heisenberg's uncertainty principle takes the form of a trade-off: It's always possible, at least in theory, to reduce the quantum uncertainty in a parameter of interest (a particle's position, say) at the expense of increasing the uncertainty of something else (its momentum). In optics, the trade-off gives rise to so-called squeezed states of light, which can be constructed, for example, with lower uncertainty in their amplitude and higher uncertainty in their phase. The ability to produce squeezed light has enabled optical measurements to be made with greater precision than would otherwise be possible. Now Caltech's Keith Schwab and collaborators have achieved the long-standing goal of similarly squeezing the motion of a micron-scale mechanical resonator.

In their device, shown here, the center-square capacitor and the spiral-wire inductor form an LC circuit with a resonant frequency of 6.2 GHz. Furthermore, the top plate of the capacitor is free to move, with a vibrational frequency of 3.6 MHz. A major obstacle to teasing out such a system's quantum character is that even at a chilly 10 mK, thermal fluctuations in the mechanical motion overwhelm quantum fluctuations by two orders of magnitude. Prior research has shown that driving the circuit at the difference between the two resonant frequencies can sap the mechanical resonator's energy and cool the resonator into the quantum regime. Schwab and company went a step further: They drove the circuit at the sum and difference frequencies simultaneously, thereby cooling and squeezing the motion at the same time. By analyzing the circuit's output frequency spectrum, they deduced that the positional uncertainty over part of the mechanical resonator's cycle was squeezed to 80% of the quantum zero-point level.