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Quantum Galileo's experiments and mass estimation in a gravitational field

Luigi Seveso, Valerio Peri, Matteo G. A. Paris

Published Mar 31, 2016• 1 citation
OpenAlex

Abstract

We address the problem of estimating the mass of a (quantum) particle interacting with a classical gravitational field. In particular, we analyze in details the ultimate bounds to precision imposed by quantum mechanics and study the effects of gravity in a variety of settings. Our results show that the presence of a gravitational field generally leads to a precision gain, which can be significant in a regime half-way between the quantum and classical domains. We also address quantum enhancement to precision, i.e. the advantages coming from taking into account the quantum nature of the probe particle, and show that non-classicality is indeed a relevant resource for mass estimation. In particular, we suggest schemes for mass-sensing measurements using quantum probes and show that upon employing non-classical states like quantum coherent superpositions one may improve precisions by orders of magnitude. In addition, we discuss the compatibility of the weak equivalence principle (WEP) within the quantum regime using as a guide the notion of Fisher Information. We find that the information on the probe's mass that can be extracted through position measurements is unchanged by turning on a uniform gravitational field. This conclusion is somehow at variance with certain views expressed in the literature that the WEP cannot hold in the quantum regime. In fact, our results show that in an information-theoretic framework, no clash occurs between quantum mechanics and the WEP.

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We address the problem of estimating the mass of a (quantum) particle interacting with a classical gravitational field. In particular, we analyze in details the ultimate bounds to precision imposed by quantum mechanics and study the effects of gravity in a variety of settings. Our results show that the presence of a gravitational field generally leads to a precision gain, which can be significant in a regime half-way between the quantum and classical domains. We also address quantum enhancement to precision, i.e. the advantages coming from taking into account the quantum nature of the probe particle, and show that non-classicality is indeed a relevant resource for mass estimation. In particular, we suggest schemes for mass-sensing measurements using quantum probes and show that upon employing non-classical states like quantum coherent superpositions one may improve precisions by orders of magnitude. In addition, we discuss the compatibility of the weak equivalence principle (WEP) within the quantum regime using as a guide the notion of Fisher Information. We find that the information on the probe's mass that can be extracted through position measurements is unchanged by turning on a uniform gravitational field. This conclusion is somehow at variance with certain views expressed in the literature that the WEP cannot hold in the quantum regime. In fact, our results show that in an information-theoretic framework, no clash occurs between quantum mechanics and the WEP.
We address the problem of estimating the mass of a quantum particle in a gravitational field and seek the ultimate bounds to precision of quantum-limited detection schemes. In particular, we study the effect of the field on the achievable sensitivity and address the question of whether quantumness of the probe state may provide a precision enhancement. The ultimate bounds to precision are quantified in terms of the corresponding Quantum Fisher Information. Our results show that states with no classical limit perform better than semiclassical ones and that a non-trivial interplay exists between the external field and the statistical model. More intense fields generally lead to a better precision, with the exception of position measurements in the case of freely-falling systems.
Abstract We address the problem of estimating the mass of a quantum particle in a gravitational field and seek the ultimate bounds to precision of quantum-limited detection schemes. In particular, we study the effect of the field on the achievable sensitivity and address the question of whether quantumness of the probe state may provide a precision enhancement. The ultimate bounds to precision are quantified in terms of the corresponding quantum Fisher information. Our results show that states with no classical limit perform better than semiclassical ones and that a non-trivial interplay exists between the external field and the statistical model. More intense fields generally lead to a better precision, with the exception of position measurements in the case of freely-falling systems.
We investigate the use of quantum probes to accurately determine the strength of the local gravitational field on Earth. Our findings show that delocalized probes generally outperform localized ones, with the precision enhancement scaling quadratically with the separation between the two wavefunction components. This advantage persists under realistic position measurements, where performance are degraded by less than one order of magnitude with respect to the ultimate bound. We also discuss the influence of Earth’s surface, demonstrating that its effect can be neglected until shortly before the particle hits the floor. Finally, we address the joint estimation of the gravitational acceleration g and the probe mass m , proving that the excess estimation noise arising from their inherent incompatibility is negligible.
We show that a single spatially superposed 'source' mass acting on a 'probe' matter wavepacket can reveal the quantum nature of the gravitational field. For this we use a specific state preparation and measurement of the superposed source mass, including a postselection, which altogether results in a repulsive gravitational force on the probe particle. A classical gravitational field can never lead to repulsion, as the effect requires quantum interference of two distinct states of gravity. The eventual observation of such an effect would be a violation of Einstein's theory of general relativity, where gravity is always attractive. We also present a calculation in the Heisenberg picture under the formalism of weak values that illustrates how repulsion is achieved. Finally, we estimate the range of parameters (masses and the spatio-temporal extent of interference) for which the experiment is feasible.
We address the precision of the estimation procedures for the minimum length arising from gravitational theories. In particular, we provide bounds on precision and assess the use of quantum probes to enhance the estimation performance. At first, we review the concept of minimum length and how it induces a perturbative term appearing in the Hamiltonian of any quantum system, which itself is proportional to a parameter depending on the minimum length. We then systematically study the effects of this perturbation on different state preparations and for several one-dimensional systems, and evaluate the quantum Fisher information in order to find the ultimate bounds to precision. Eventually, we investigate the role of dimensionality by analyzing the use of two-dimensional square well and harmonic oscillator systems to probe the minimal length. Our results show that quantum probes are convenient resources, providing potential enhancement in precision. Additionally, our results provide a set of guidelines to design future experiments to detect the minimum length.
Abstract We review the dynamics of a bouncing ball, both from the classical and the quantum points of view, studying the role of its inertial and gravitational masses. We analyze the behavior of quantum particles of different masses, embedded in a uniform gravitational field. We show that the bouncing ball is a useful didactic example to show that the coupling between rest mass and gravity cannot be avoided at the quantum level and that the equivalence principle must be reformulated in quantum mechanics. Galileo’s experiment of falling bodies can be still satisfied if one considers only the average quantum values of observables.