Massive spatial qubits: Testing macroscopic nonclassicality and Casimir entanglement

An open challenge in physics is to expand the frontiers of the validity of quantum mechanics by evidencing nonclassicality of the center of mass state of a macroscopic object. Yet another equally important task is to evidence the essential nonclassicality of the interactions which act between macroscopic objects. Here we introduce a new tool to meet these challenges: massive spatial qubits. In particular, we show that if two distinct localized states of a mass are used as the $|0\rangle$ and $|1\rangle$ states of a qubit, then we can measure this encoded spatial qubit with a high fidelity in the ${\sigma }_x,{\sigma }_y$, and ${\sigma }_z$ bases simply by measuring its position after different duration of free evolution. This technique can be used reveal the irreducible nonclassicality of the spin and center of mass entangled state of a nanocrystal implying macrocontextuality. Further, in the context of Casimir interaction, this offers a powerful method to create and certify non-Gaussian entanglement between two neutral nano-objects. The entanglement such produced provides an empirical demonstration of the Casimir interaction being inherently quantum.

Figure 1

Spatial detection for ${\sigma }_x,{\sigma }_y$ measurements: a pair of detectors (color: orange) located at phase angle $\theta =0,\theta =\pi$ perform ${\sigma }_x$ measurement. The detectors (color: purple) at $\theta =\pi /2,\theta =-\pi /2$ perform ${\sigma }_y$ measurement.

Figure 2

Detection scheme for the entanglement of spin and center of mass of a Stern-Gerlach state: A spin bearing nano-object is measured to be in a set of zones of size $\delta x$, where the size is set by the strength and duration of lasers scattered from the object, which serves to measure the spatial qubit. Within each spatial zone a suitable method is used to measure the spin in different bases, for example, by rotating the spin states by microwave pulses followed by fluorescence of certain states under excitation by a laser of appropriate frequency.

Figure 3

Application in witnessing Casimir-induced entanglement: Two masses, each prepared in a superposition of two states, act as two qubits $\frac{1}{\sqrt{2}}{\left(\right|0\rangle }_1+{|1\rangle }_1)\otimes \frac{1}{\sqrt{2}}{\left(\right|0\rangle }_2+{|1\rangle }_2)$. The system freely propagates and undergoes mutual interactions for a time $\tau$. This interaction induces entanglement which can be witnessed from correlations of spatial qubit Pauli measurements. For example, in the figure, ${\sigma }_x, {\sigma }_y$ measurements on test mass 1 and ${\sigma }_z$ measurements on test mass 2 are depicted. Casimir interaction induced by virtual photons as quantum mediators is shown [79].