Generation of Entanglement from Mechanical Rotation

Many phenomena and fundamental predictions, ranging from Hawking radiation to the early evolution of the Universe rely on the interplay between quantum mechanics and gravity or more generally, quantum mechanics in curved spacetimes. However, our understanding is hindered by the lack of experiments that actually allow us to probe quantum mechanics in curved spacetime in a repeatable and accessible way. Here we propose an experimental scheme for a photon that is prepared in a path superposition state across two rotating Sagnac interferometers that have different diameters and thus represent a superposition of two different spacetimes. We predict the generation of genuine entanglement even at low rotation frequencies and show how these effects could be observed even due to the Earth’s rotation. These predictions provide an accessible platform in which to study the role of the underlying spacetime in the generation of entanglement.

Figure 1

Scheme for generating path-polarization entanglement from mechanical rotation. (a) The scheme consists of a single photon source, polarizing beam splitters (PBSs), and half-wave plates (HWPs) denoted by $\lambda /2$. We consider fiber loops with radii $r_b\sim 0.5\mathrm{m}$, $r_a\sim r_b/2$ (with total length $l\sim 2\pi r_b{N}_b$ with winding number $N_b=10$) and a photon wavelength 800 nm. The experimental setup is placed on a platform which can be set in rotation with frequency $\mathrm{\Omega }$. The green and purple arrows indicate the paths $a$, $b$, while the polarization is denoted by $H$, $V$. We start with a separable path-polarization photon $|{\psi }_{\text{initial}}⟩$; depending on the frequency of rotation $\mathrm{\Omega }$ the final photon $|{\psi }_{\text{final}}⟩$ can remain separable or becomes entangled. We can generate a maximally entangled Bell state by tuning the frequency of the platform to ${\mathrm{\Omega }}_{\text{Bell}}=\pi c^2/(2\omega \mathcal{A})$, where $\omega$ is the mean photon frequency, and $\mathcal{A}=\mathrm{\Delta }rl$ is the effective area of the interferometer ($\mathrm{\Delta }r=r_b-r_a$ is the difference of the radii, and $l$ is the path length assumed to be equal for the $a$, $b$ paths). (b) The detector $B_j$ measures the Bell state ${\psi }_j$ ($j=1,\dots ,4$). The first PBS is rotated by $\pi /4$, and the quarter-wave plates (QWPs) are denoted by $\lambda /4$ (with the fast axis oriented at $\pi /4$ which transforms circular polarization to linear polarization). (c) The detector $B1$ ($B2$) measures the maximally entangled Bell state ${\psi }_1({\psi }_2)$ at frequency ${\mathrm{\Omega }}_{\text{Bell}}(3{\mathrm{\Omega }}_{\text{Bell}})$, where the concurrence achieves the maximum possible value $C=1$. We find ${\mathrm{\Omega }}_{\text{Bell}}\sim 2\pi \times 1.2\mathrm{Hz}$, which can be readily achieved with similar photonic setups [14]. (d) Universal unitary gate for single-photon two-qubit states which can be used for tomographic reconstruction or implementing entanglement witnesses. The two beam splitters (BSs) together with the mirrors form a Mach-Zehnder interferometer, and $V_j(j=1,R,L,2)$ denotes an optical element composed of a HWP, two enclosing QWPs, and a phase shifter. (e) Optimal entanglement witnesses ${\mathcal{W}}_1$ (${\mathcal{W}}_2$) for the maximally entangled Bell state ${\psi }_1({\psi }_2)$ as a function of rotation frequency. Entanglement is witnessed when ${\mathcal{W}}_j<0$ ($j=1$, 2).