Figure 2: Mechanical motional state preparation and full state reconstruction using optical pulsed quantum measurement.

The uppermost row shows the pulse protocols (pink - preparation, red - tomography). The two rows below show a subset of the measured probability distributions of the mechanical quadratures Pr(x,θ) and the reconstructed phase-space distributions W(X_M,P_M), respectively. The phase-space distributions were reconstructed using nine marginal angles up to θ·π/180=90° (with a larger number of bins used than that shown for the marginals). For our current measurement strength, that is, χ<1, all the mechanical motional states reconstructed here can be described classically. (a) In the first column, tomography and reconstruction of an initial mechanical thermal state driven by white noise up to a mode temperature of 1100 K is shown. The red dashedcircle has a radius equal to 2σ of the initial thermal distribution. (b) A single pulsed measurement reduces the mechanical position variance, but leaves the momentum distribution unchanged. (c) ‘Cooling-by-measurement’ performed with two pulses separated by one quarter of a mechanical period rapidly reduces the mechanical state’s entropy. The effective temperature of the mechanical state reconstructed here has been reduced to 16 K. (d) State reconstruction of a non-Gaussian mechanical state of motion generated by resonant sinusoidal drive. (e) The (one s.d.) width of the position distribution observed for states (a–c) with phase-space angle θ. The thermal state (red points) shows a position width approximately twice of that when at room temperature (dashed line). State (b) has a reduced position width for small phase-space angles (purple points). The position width of state (c) is reduced for all phase-space angles (blue points). The solid lines are theoretical fits obtained using Equation (2) generalized for all θ as well the two-pulse-preparation case. (f) Plot of the conditional mechanical width with pulse strength obtained using two pulses separated by 5° of mechanical evolution. The dashed line is a theoretical fit with a model using two units of optical quantum noise and finite mechanical evolution. The solid line is the inferred conditional mechanical width immediately after the preparation pulse. The vertical line indicates the pulse strength used for states (a–c). The error bars on (e) and (f) indicate a one s.d. uncertainty.