Collapse-induced orientational localization of rigid rotors [Invited]

Abstract

We show how the ro-translational motion of anisotropic particles is affected by the model of Continuous Spontaneous Localization (CSL), the most prominent hypothetical modification of the Schrödinger equation restoring realism on the macroscale. We derive the master equation describing collapse-induced spatio-orientational decoherence, and demonstrate how it leads to linear-and angular-momentum diffusion. Since the associated heating rates scale differently with the CSL parameters, the latter can be determined individually by measuring the random motion of a single levitated nanorotor.

Non-interferometric test of the continuous spontaneous localization model based on rotational optomechanics

“…[ˆ] can be Taylor expanded around the equilibrium position. The center of mass motion and the system's rotations can be decoupled from the internal dynamics and equation (3) reduces to [29]…”

“…which represents an extension of the master equation describing only the pure center of mass vibrations (the first of the two terms) to the roto-vibrational case; its general form for an arbitrary geometry of the system can be found in [29]. The explicit forms of the vibrational h ( ) V and rotations h ( ) R diffusion constants are reported in appendix A.…”

“…The CSL diffusion coefficients have been already computed in [14,15,29]. Given the mass density m ( ) r , they read…”

Probing macroscopic quantum superpositions with nanorotors

“…Here, τ gives the timescale on which the modification acts, m e is the electron mass, σ q is the width of the momentum-kick distribution, R W ( ) is the operator-valued rotation matrix, and q  ( ) is the Fourier transform of the mass density. This master equation is similar to that for rotational collapse dynamics in the model of continuous spontaneous localization [48]. For a homogeneous rod of mass M, length ℓ, and whose symmetry axis points into direction R m e z W = W ( ) ( ) , one obtains…”

“…The decay of the alignment signal when the rotor is exposed to an atomic beam or other controlled environments can be used for studying collisional decoherence and thermalization of quantum nanoscale rotors. Finally, objective collapse models could be tested by observing orientational quantum revivals that contradict the predicted loss of orientational coherence [48].…”