Quantum state tomography of a mechanical oscillator

Quantum mechanics places strict limits on how precisely the two motional quadratures of an object can be simultaneously measured. To noiselessly reconstruct an unknown quantum state of motion, a single quadrature measurement can be repeated over all of phase space, and the density matrix describing the quantum state can be reconstructed via quantum state tomography. Here we demonstrate a pulsed measurement of the motion of a micromechanical oscillator embedded in a superconducting electromechanical circuit. The measurement can be tuned from a nearly quantum-limited simultaneous measurement of both quadratures, to a single quadrature measurement with added noise of -10 dB relative to vacuum fluctuations in one quadrature, resulting in a total measurement efficiency of 92% . The high efficiency measurement is used to accurately reconstruct the density matrix of a dissipatively squeezed mechanical oscillator (-3.3 dB relative to vacuum fluctuations), demonstrating that the measurement is suitable for tomography of arbitrary quantum states of the mechanical oscillator.