Gravity-induced interference and continuous quantum measurements

Kenneth C. Littrell, Brendan E. Allman, S. A. Werner

S. Werner, Helmut Kaiser, M. Arif +1 more

Jeeva S. Anandan

Abel Camacho, Astrophysikalisches Inst. Potsdam (Germany)

A very interesting quantum mechanical effect is the emergence of gravity-induced interference, which has already been detected. This effect also shows us that gravity is at the quantum level not a purely geometric effect, the mass of the employed particles appears explicitly in the interference expression. In this work we will generalize some previous results. It will be shown that the introduction of a second order approximation in the propagator of a particle, immersed in the Earth's gravitational field, and whose coordinates are being continuously monitored, allows us to include, in the corresponding complex oscillator, a frequency which now depends on the geometry of the source of the gravitational field, a fact that is absent in the case of a homogeneous field. Using this propagator we will analyze the interference pattern of two particle beams whose coordinates are being continuously monitored. We will compare our results against the case of a homogeneous field, and also against the measurement outputs of the Colella, Overhauser, and Werner experiment, and find that the difference in the dependence upon the geometry of the source of the gravitational field could render detectable differences in their respective measurement outputs. (orig.)

Vivishek Sudhir

Yubao Liu, Wenjie Zhong, Yanbei Chen +1 more

The evolution of quantum states influenced by semiclassical gravity is distinct from that in quantum gravity theory due to the presence of a state-dependent gravitational potential. This state-dependent potential introduces nonlinearity into the state evolution, of which the theory is named the Schr\"odinger-Newton (SN) theory. The formalism for understanding the continuous quantum measurement process on the quantum state in the context of semiclassical gravity theory has been previously discussed using the Schr\"odinger picture in Paper I [Semiclassical gravity phenomenology under the causal-conditional quantum measurement prescription, Phys. Rev. D 107, 024004 (2023).]. In this work, an equivalent formalism using the Heisenberg picture is developed and applied to the analysis of two optomechanical experiment protocols that targeted testing the quantum nature of gravity. This Heisenberg picture formalism of the SN theory has the advantage of helping the investigation of the covariance matrices of the outgoing light fields in these protocols and further the entanglement features. We found that the classical gravity between the quantum trajectories of two mirrors under continuous quantum measurement in the SN theory can induce an apparent entanglement of the outgoing light field (though there is no quantum entanglement of the mirrors), which could serve as a false alarm for those experiments designed for probing the quantum gravity induced entanglement.