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Detection of space-time perturbations with quantum-enhanced metrology

Quiñones Valles, A Diego

Published Sep 29, 2017• 0 citations

Abstract

We present a new model of atomic decoherence by space-time perturbations. We propose that decoherence will arise as a result of two possible effects that gravitational fluctuations will have on the atom. One is that the nucleus will be displaced relative to the valence electron, which will be perceived as a sudden change in the electric potential. This will result in the wave function of the atom being partially projected into lower energy levels. The other is that the strain in space will change the local electric field as felt by the electron. This interaction will either induce a change in the angular momentum of the atom or a small shift in the transition of the energy levels, presenting two different experimental approaches for the detection of the effect. We calculate how the decoherence is related to the internal degrees of freedom of the atoms, obtaining that the effect will be more prominent for atoms initially in a highly excited state (Rydberg atoms). By applying the nuclear displacement model for the scatter- ing of neutral particles, we suggest that it could be potentially useful for the detection of weakly-interacting particles, like possible candi- dates of Dark Matter. The overall effect of gravitational waves for the strained-space model was calculated to be several orders of magnitude higher than for the nuclear displacement model, allowing for detection in different ranges of frequencies. We analyze how different quantum states are affected according to the proposed model, calculating that the information from the measurement of correlated atoms will be significantly higher. The optimal quantum state that minimizes the uncertainty of the measurement is described for an arbitrary number of atoms, giving a relation that follows closely the Heisenberg limit.

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We present a new model of atomic decoherence by space-time perturbations. We propose that decoherence will arise as a result of two possible effects that gravitational fluctuations will have on the atom. One is that the nucleus will be displaced relative to the valence electron, which will be perceived as a sudden change in the electric potential. This will result in the wave function of the atom being partially projected into lower energy levels. The other is that the strain in space will change the local electric field as felt by the electron. This interaction will either induce a change in the angular momentum of the atom or a small shift in the transition of the energy levels, presenting two different experimental approaches for the detection of the effect. We calculate how the decoherence is related to the internal degrees of freedom of the atoms, obtaining that the effect will be more prominent for atoms initially in a highly excited state (Rydberg atoms). By applying the nuclear displacement model for the scatter- ing of neutral particles, we suggest that it could be potentially useful for the detection of weakly-interacting particles, like possible candi- dates of Dark Matter. The overall effect of gravitational waves for the strained-space model was calculated to be several orders of magnitude higher than for the nuclear displacement model, allowing for detection in different ranges of frequencies. We analyze how different quantum states are affected according to the proposed model, calculating that the information from the measurement of correlated atoms will be significantly higher. The optimal quantum state that minimizes the uncertainty of the measurement is described for an arbitrary number of atoms, giving a relation that follows closely the Heisenberg limit.

A new heuristic model of interaction of an atomic system with a gravitational wave (GW) is proposed. In it, the GW alters the local electromagnetic field of the atomic nucleus, as perceived by the electron, changing the state of the system. The spectral decomposition of the wave function is calculated, from which the energy is obtained. The results suggest a shift in the difference of the atomic energy levels, which will induce a small detuning to a resonant transition. The detuning increases with the quantum numbers of the levels, making the effect more prominent for Rydberg states. We performed calculations on the Rabi oscillations of atomic transitions, estimating how they would vary as a result of the proposed effect.

We describe a new mechanism of decoherence in excited atoms that arise from particle scattering by the atomic nucleus. It is based on the idea that the scattering will produce a sudden displacement of the nucleus which will be perceived by the electron of the atom as an instant shift in the electrostatic potential. This will leave the atom’s wavefunction partially projected into lower-energy states which will lead to the decoherence of the atomic state. The decoherence is calculated to increase with the excitation of the atom, making observations of the effect easier in Rydberg atoms. We estimate the order of the decoherence for photons and massive particles scattering, analyzing several commonly presented scenarios. By maximizing the order of the effect it can be used for detection of weakly-interacting particles, like those which may be the constituents of Dark Matter, through applying very precise atomic spectroscopy.

Abstract A new heuristic model of interaction of an atomic system with a gravitational wave (GW) is proposed. In it, the GW alters the local electromagnetic field of the atomic nucleus, as perceived by the electron, changing the state of the system. The spectral decomposition of the wave function is calculated, from which the energy is obtained. The results suggest a shift in the difference of the atomic energy levels, which will induce a small detuning to a resonant transition. The detuning increases with the quantum numbers of the levels, making the effect more prominent for Rydberg states. We performed calculations on the Rabi oscillations of atomic transitions, estimating how they would vary as a result of the proposed effect.

We describe a new mechanism of decoherence in excited atoms as a result of thermal particles scattering by the atomic nucleus. It is based on the idea that a single scattering will produce a sudden displacement of the nucleus, which will be perceived by the electron in the atom as an instant shift in the electrostatic potential. This will leave the atom’s wave-function partially projected into lower-energy states, which will lead to decoherence of the atomic state. The decoherence is calculated to increase with the excitation of the atom, making observation of the effect easier in Rydberg atoms. We estimate the order of the decoherence for photons and massive particles scattering, analyzing several commonly presented scenarios. Our scheme can be applied to the detection of weakly-interacting particles, like those which may be the constituents of Dark Matter, the interaction of which was calculated to have a more prominent effect that the background radiation.

One of the biggest problems faced by those attempting to combine quantum theory and general relativity is the experimental inaccessibility of the unification scale. In this paper, we show how incoherent conformal waves in the gravitational field, which may be produced by quantum mechanical zero–point fluctuations, interact with the wave packets of massive particles. The result of this interaction is to produce decoherence within the wave packets which could be accessible in experiments at the atomic scale.Using a simple nonlinear model for the coherence properties of the gravitational field, we derive an equation for the evolution of the density matrix of such a wave packet. Following the primary state diffusion programme, the most promising source of space–time fluctuations for experimental detection is these zero–point energy fluctuations. According to our model, the absence of intrinsic irremovable decoherence in matter interferometry experiments puts bounds on some of the parameters of quantum gravity theories. Current experiments give λ >18, where λtPlanck is an effective cut–off for the validity of low–energy quantum gravity theories.