Optimal position detection of a dipolar scatterer in a focused field

Abstract

We theoretically analyze the problem of detecting the position of a classical dipolar scatterer in a strongly focused optical field. We suggest an optimal measurement scheme and show that it resolves the scatterer's position in three dimensions at the Heisenberg limit of the imprecision-backaction product. We apply our formalism to levitated-optomechanics experiments and show that backscattering detection provides sufficient information to feedback-cool the particle's motion along the optical axis to a phonon occupancy below unity under realistic experimental conditions. arXiv:1907.12838v1 [physics.optics]

Quantum motional state tomography with nonquadratic potentials and neural networks

“…We emphasize, however, that the method is very general since a neural network allows to optimally adapt the quantum state tomography to any given physical scenario in an experiment by using training examples from the particular situation. For the case of levitated nanoparticles, ground-state cooling is closely approached [28][29][30][31][46][47][48][49][50][51][52][53] and hence the development of quantum tomography schemes is not only important but timely. At the same time, implementing nonquadratic potentials is also a fantastic tool to prepare non-Gaussian states.…”

“…Let us now introduce the overall procedure: We propose to train the neural network on simulated data and then use the trained network to deduce the initial quantum state from experimentally measured trajectories u 1 (t ) and u 2 (t ). Experimentally, these trajectories could be obtained by repeatedly repreparing a particle in the same initial state and then evolving it (in the absence of measurements) up to a time t 1 when the position is measured, for instance, via optical position detection [28,29]. Averaging over the many repetitions, this reveals the expectation value and variance of the position at this time t 1 .…”

Quantum control of a nanoparticle optically levitated in cryogenic free space

“…The detection of the particle's motion relies on the fact that its position is predominantly encoded in the phase of the light scattered back into the trapping lens [44]. This backscattered field is directed by an optical circulator to the detection setup, where 90% (10%) of the signal is sent to a homodyne (heterodyne) receiver.…”

Testing the foundation of quantum physics in space via Interferometric and non-interferometric experiments with mesoscopic nanoparticles

“…The trapping is then removed and the nanosphere remains in free-fall for a time t after which its position is measured. Achieving a high position resolution is possible by, for example, combining a coarse-grained standard optical detection on a CMOS chip with a highresolution backscattering detection scheme 84 , which could eventually provide a position accuracy on the order of ε = 10 −12 m at a typical bandwidth of 100 kHz, by controlling the measurement back-action 85 . By repeating such a procedure N times, one can reconstruct the position spread σ 2 and thus quantify the effects of the non-unitary dynamics through Eq.…”