Table-top nanodiamond interferometer enabling quantum gravity tests

Abstract

Unifying quantum theory and general relativity is the holy grail of contemporary physics. Nonetheless, the lack of experimental evidence driving this process led to a plethora of mathematical models with a substantial impossibility of discriminating among them or even establishing if gravity really needs to be quantized or if, vice versa, quantum mechanics must be "gravitized" at some scale. Recently, it has been proposed that the observation of the generation of entanglement by gravitational interaction, could represent a breakthrough demonstrating the quantum nature of gravity. A few experimental proposals have been advanced in this sense, but the extreme technological requirements (e.g., the need for free-falling gravitationally-interacting masses in a quantum superposition state) make their implementation still far ahead. Here we present a feasibility study for a table-top nanodiamond-based interferometer eventually enabling easier and less resource-demanding quantum gravity tests. With respect to the aforementioned proposals, by relying on quantum superpositions of steady massive (mesoscopic) objects our interferometer may allow exploiting just small-range electromagnetic fields (much easier to implement and control) and, at the same time, the re-utilization of the massive quantum probes exploited, inevitably lost in free-falling interferometric schemes.

Figures (11)

• Figure 1: The proposed experiment relies on two single-NV-centre nanodiamonds (trapped along $y$ and $z$ by a gravito-magnetic potential, but free along $x$) both in a spatially-delocalized superposition. The distance mismatch between the superposition components of the two NDs should allow the gravitational potential to entangle the NDs, an impossible task for local operations and classical communication.
• Figure 2: One-period motion along $x$ of the $S_x=+1$ (orange curve) and $S_x=-1$ (blue curve) components of a 250 nm diameter ND in a magnetic field gradient $B'=10^3$ T/m as a function of the bias magnetic field $B_0$.
• Figure 3: Plots (a-c): Phase space diagram of the ND superposition components, in absence of DD and for two different $\omega_{DD}$ values. In plots (b) and (c), red, green-dashed and orange curves, respectively: dynamics generated by $H_x^{(\uparrow)}$, $H_x^{(\downarrow)}$ and $H_x^{(DD)}$ for $S_x=+1$. Blue, azure-dashed and purple curves, respectively: dynamics generated by $H_x^{(\uparrow)}$, $H_x^{(\downarrow)}$ and $H_x^{(DD)}$ for $S_x=-1$. See Appendix for further details.
• Figure 4: Step-by-step scheme of the ND-based experiment unveiling quantum features in gravity: a) two single-NV-centre NDs are confined in the same trap along $y$ and $z$, leaving $x$ unconstrained; b) a magnetic gradient $B'=dB/dx$ is generated, putting both NDs in a spatially-delocalized superposition; c) $B'$ is switched off, leaving the two superpositions freely-evolving by gravitational interaction; d) $B'$ is turned on again, to recombine both spatial superpositions; e) $B'$ is finally turned off, and a correlated measurement of the two NV-centres is performed to detect gravity-induced entanglement.
• Figure 5: Yellow surface: time needed to complete the entire experimental protocol of Fig. \ref{['exp']} and entangle the two NDs by accumulating a gravity-induced phase $\Delta\phi=0.01\pi$ in the (c) step, as a function of the NDs mass $m$ and the magnetic field gradient $B'$, considering the NDs initially put at the minimum distance $d_{min}$ of Eq. \ref{['dmin']}, allowing to keep the Casimir-Polder potential one order of magnitude below the gravitational one. Red surface: time needed to complete the same protocol and achieve a gravity-induced phase $\Delta\phi=0.01\pi$ in the ND bipartite state considering also the progressive phase accumulation achieved in the (b) and (d) steps of the protocol, as a function of the NDs mass $m$ and the magnetic field gradient $B'$ and considering NDs initially put at the same minimum distance $d_{min}$.