Abstract
Quantum optomechanics uses optical means to generate and manipulate quantum states of motion of mechanical resonators. This provides an intriguing platform for the study of fundamental physics and the development of novel quantum devices. Yet, the challenge of reconstructing and verifying the quantum state of mechanical systems has remained a major roadblock in the field. Here, we present a novel approach that allows for tomographic reconstruction of the quantum state of a mechanical system without the need for extremely high quality optical cavities. We show that, without relying on the usual state transfer presumption between light an mechanics, the full optomechanical Hamiltonian can be exploited to imprint mechanical tomograms on a strong optical coherent pulse, which can then be read out using well-established techniques. Furthermore, with only a small number of measurements, our method can be used to witness nonclassical features of mechanical systems without requiring full tomography. By relaxing the experimental requirements, our technique thus opens a feasible route towards verifying the quantum state of mechanical resonators and their nonclassical behaviour in a wide range of optomechanical systems.
Highlights
Optomechanics [1] where a mechanical oscillator interacts with an optical field via radiation pressure, is a promising direction of research for fundamental physics [2,3,4] and the development of novel weak-force sensors [5]
We further show that this condition is robust against noise and detection inefficiency, and describe an explicit experimental protocol which we show can be implemented with current technology in a variety of optomechanical systems
We have introduced a method that allows for the tomographic reconstruction of the phase space quasiprobability distributions of a mechanical resonator in a regime where the commonly used rotatingwave approximation does not hold
Summary
Optomechanics [1] where a mechanical oscillator interacts with an optical field via radiation pressure, is a promising direction of research for fundamental physics [2,3,4] and the development of novel weak-force sensors [5]. Most research to Continuous-variable quantum systems, such as optical fields or mechanical resonators, are best described using distribution functions over a quantum phase-space spanned by two quadratures of interest, such as position and momentum, or amplitude and phase. Of particular interest within this family is the Wigner function, corresponding to a value of s = 0, as the only distribution that faithfully represents the quantum state and, at the same time, correctly reproduces the marginal quadrature distributions. Another important case is the P-function, corresponding to s = 1, whose negativity is one of the main signatures of nonclassical behaviour [9]
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