Towards an experimental test of gravity-induced quantum state reduction

Abstract

Modern developments in condensed matter and cold atom physics have made the realization of macroscopic quantum states in the laboratory everyday practice. The ready availability of these states suggests the possibility of experimentally investigating different proposals for the mechanism of quantum state reduction. One such proposal is the hypothesis of Penrose and Diósi, according to which quantum state reduction is a manifestation of the incompatibilty of general relativity and the unitary time evolution of quantum physics. Dimensional analysis suggests that Schrödinger cat type states should collapse on measurable time-scales when masses and lengths of the order of bacterial scales are involved. We analyse this hypothesis in the context of the modern experimental realizations of macroscopic quantum states. First we consider ‘micromechanical’ quantum states, analysing the capacity of an atomic force microscopy based single spin detector to measure the gravitational state reduction, but we conclude that it seems impossible to suppress environmental decoherence to the required degree. We subsequently discuss ‘split’ cold atom condensates to find out that these are at present lacking the required mass-scale by many orders of magnitude. We then extend Penrose's analysis to superpositions of mass current carrying states, and we apply this to the flux quantum bits realized in superconducting circuits. We find that the flux qubits approach the scale where gravitational state reduction should become measurable, but bridging the few remaining orders of magnitude appears to be very difficult with present day technology.

Keywords:

• Bose condensation
• quantum mechanical calculation
• superconductors

Acknowledgements

We acknowledge stimulating discussions with R. Penrose, P.H. Kes, J. van den Brink, N.R. Cooper and J.C. Davis.