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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.
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Good clocks are of importance both to fundamental physics and for applications in astronomy, metrology and global positioning systems. In a recent technological breakthrough, researchers at NIST have been able to achieve a stability of 1 part in $10^{18}$ using an Ytterbium clock. This naturally raises the question of whether there are fundamental limits to the stability of clocks. In this paper we point out that gravity and quantum mechanics set a fundamental limit on the stability of clocks. This limit comes from a combination of the uncertainty relation, the gravitational redshift and the relativistic time dilation effect. For example, a single ion hydrogen maser clock in a terrestrial gravitational field cannot achieve a stability better than one part in $10^{22}$. This observation has implications for laboratory experiments involving both gravity and quantum theory.
The nature of dark matter remains unknown to date; several candidate particles are being considered in a dynamically changing research landscape. Scalar field dark matter is a prominent option that is being explored with precision instruments such as atomic clocks and optical cavities. Here we report on the first direct search for scalar field dark matter utilising a gravitational-wave detector operating beyond the quantum shot-noise limit. We set new upper limits for the coupling constants of scalar field dark matter as a function of its mass by excluding the presence of signals that would be produced through the direct coupling of this dark matter to the beamsplitter of the GEO,600 interferometer. The new constraints improve upon bounds from previous direct searches by more than six orders of magnitude and are more stringent than limits obtained in tests of the equivalence principle by up to four orders of magnitude. Our work demonstrates that scalar field dark matter can be probed or constrained with direct searches using gravitational-wave detectors and highlights the potential of quantum-enhanced interferometry for dark matter detection.
Gravitational wave detectors (GWDs), which have brought about a new era in astronomy, have reached such a level of maturity that further improvement necessitates quantum-noise-evading techniques. Numerous proposals to this end have been discussed in the literature, e.g., invoking frequency-dependent squeezing or replacing the current Michelson interferometer topology by that of the quantum speedmeter. Recently, a proposal based on the linking of a standard interferometer to a negative-mass spin system via entangled light has offered an unintrusive and small-scale new approach to quantum noise evasion in GWDs [Phys. Rev. Lett. $mathbf{121}$, 031101 (2018)]. The solution proposed therein does not require modifications to the highly refined core optics of the present GWD design and, when compared to previous proposals, is less prone to losses and imperfections of the interferometer. In the present article, we refine this scheme to an extent that the requirements on the auxiliary spin system are feasible with state-of-the-art implementations. This is accomplished by matching the effective (rather than intrinsic) susceptibilities of the interferometer and spin system using the virtual rigidity concept, which, in terms of implementation, requires only suitable choices of the various homodyne, probe, and squeezing phases.
Spectra of molecular hydrogen (H$_2$) are employed to search for a possible proton-to-electron mass ratio ($mu$) dependence on gravity. The Lyman transitions of H$_2$, observed with the Hubble Space Telescope towards white dwarf stars that underwent a gravitational collapse, are compared to accurate laboratory spectra taking into account the high temperature conditions ($T sim 13,000$ K) of their photospheres. We derive sensitivity coefficients $K_i$ which define how the individual H$_2$ transitions shift due to $mu$-dependence. The spectrum of white dwarf star GD133 yields a $Deltamu/mu$ constraint of $(-2.7pm4.7_{rm stat}pm 0.2_{rm sys})times10^{-5}$ for a local environment of a gravitational potential $phisim10^4 phi_textrm{Earth}$, while that of G29$-$38 yields $Deltamu/mu=(-5.8pm3.8_{rm stat}pm 0.3_{rm sys})times10^{-5}$ for a potential of $2 times 10^4$ $phi_textrm{Earth}$.
The Hong-Ou-Mandel (HOM) effect is analyzed for photons in a modified Mach-Zehnder setup with two particles experiencing different gravitational potentials, which are later recombined using a beam-splitter. It is found that the HOM effect depends directly on the relativistic time dilation between the arms of the setup. This temporal dilation can be used to estimate the $gamma$ and $beta$ parameters of the parameterized post-Newtonian formalism. The uncertainty in the parameters $gamma$ and $beta$ are of the order $ 10^{-8}-10^{-12}$, depending on the quantum state employed.
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