Abstract
A nanoscale object evidenced in a non-classical state of its centre of mass will hugely extend the boundaries of quantum mechanics. To obtain a practical scheme for the same, we exploit a hitherto unexplored coupled system: an atom and a nanoparticle coupled by an optical field. We show how to control the center-of-mass of a large $\sim500$nm nanoparticle using the internal state of the atom so as to create, as well as detect, nonclassical motional states of the nanoparticle. Specifically, we consider a setup based on a silica nanoparticle coupled to a Cesium atom and discuss a protocol for preparing and verifying a Schr\"{o}dinger-cat state of the nanoparticle that does no require cooling to the motional ground state. We show that the existence of the superposition can be revealed using the Earth's gravitational field using a method that is insensitive to the most common sources of decoherence and works for any initial state of the nanoparticle.
Highlights
Quantum mechanics has been probed experimentally over a vast range of energies and scales
Possible approaches for nonclassical state preparation in levitated optomechanics are based on nonlinearities in the potential [10], as well as coupling to quantized fields along with possible usage of measurements [11,12,13,14,15,16]
We show that one can generate a small spatial superposition of the nanoparticle so that it is well protected from environmental decoherence, and yet such a small superposition can be revealed using the Earth’s gravitational field [19,27]
Summary
Quantum mechanics has been probed experimentally over a vast range of energies and scales. Possible approaches for nonclassical state preparation in levitated optomechanics are based on nonlinearities in the potential [10], as well as coupling to quantized fields along with possible usage of measurements [11,12,13,14,15,16] Difficulties of these approaches include small single-photon nonlinearities and/or detecting the effect of nonlinearities in the regime of small oscillations, where the motion is typically well described by a linear theory. A possible strategy is to cool the system to the ground state, i.e., | init = |↓ h|0 n, and to apply the procedure described by Monroe et al [22], which consists of π /2, π , and displacement pulses To make such a scheme work, one would, need additional optical fields to control the motional state of the nanoparticle. Creating a superposition of an arbitrary motional state (such as of a thermal state) still fully retains its coherent properties, and once the gravitational phase is transferred to the internal state it can be read out again using steps (8) and (9)
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