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Despite almost a century's worth of study, it is still unclear how general relativity (GR) and quantum theory (QT) should be unified into a consistent theory. The conventional approach is to retain the foundational principles of QT, such as the superposition principle, and modify GR. This is referred to as 'quantizing gravity', resulting in a theory of 'quantum gravity'. The opposite approach is 'gravitizing QT' where we attempt to keep the principles of GR, such as the equivalence principle, and consider how this leads to modifications of QT. What we are most lacking in understanding which route to take, if either, is experimental guidance. Here we consider using a Bose-Einstein condensate (BEC) to search for clues. In particular, we study how a single BEC in a superposition of two locations could test a gravitizing QT proposal where wavefunction collapse emerges from a unified theory as an objective process, resolving the measurement problem of QT. Such a modification to QT due to general relativistic principles is testable near the Planck mass scale, which is much closer to experiments than the Planck length scale where quantum, general relativistic effects are traditionally anticipated in quantum gravity theories. Furthermore, experimental tests of this proposal should be simpler to perform than recently suggested experiments that would test the quantizing gravity approach in the Newtonian gravity limit by searching for entanglement between two massive systems that are both in a superposition of two locations.

We propose an experiment based on a Bose–Einstein condensate interferometer for strongly constraining fifth-force models. Additional scalar fields from modified gravity or higher dimensional theories may account for dark energy and the accelerating expansion of the Universe. These theories have led to proposed screening mechanisms to fit within the tight experimental bounds on fifth-force searches. We show that our proposed experiment would greatly improve the existing constraints on these screening models by many orders of magnitude.

A description of the dynamical response of uniformly trapped Bose-Einstein condensates (BECs) to oscillating external gravitational fields is developed, with the inclusion of damping. Two different effects that can lead to the creation of phonons in the BEC are identified; direct driving and parametric driving. Additionally, the oscillating gravitational field couples phonon modes, which can lead to the transition of excitations between modes. The special case of the gravitational field of a small, oscillating sphere located closely to the BEC is considered. It is shown that measurement of the effects may be possible for oscillating source masses down to the milligram scale, with a signal to noise ratio of the order of 10. To this end, noise terms and variations of experimental parameters are discussed and generic experimental parameters are given for specific atom species. The results of this article suggest the utility of BECs as sensors for the gravitational field of very small oscillating objects which may help pave the way towards gravity experiments with masses in the quantum regime.

The effect of gravity and proper acceleration on the frequency spectrum of an optical resonator-both rigid or deformable-is considered in the framework of general relativity. The optical resonator is modeled either as a rod of matter connecting two mirrors or as a dielectric rod whose ends function as mirrors. Explicit expressions for the frequency spectrum are derived for the case that it is only perturbed slightly and variations are slow enough to avoid any elastic resonances of the rod. For a deformable resonator, the perturbation of the frequency spectrum depends on the speed of sound in the rod supporting the mirrors. A connection is found to a relativistic concept of rigidity when the speed of sound approaches the speed of light. In contrast, the corresponding result for the assumption of Born rigidity is recovered when the speed of sound becomes infinite. The results presented in this article can be used as the basis for the description of optical and opto-mechanical systems in a curved spacetime. We apply our results to the examples of a uniformly accelerating resonator and an optical resonator in the gravitational field of a small moving sphere. To exemplify the applicability of our approach beyond the framework of linearized gravity, we consider the fictitious situation of an optical resonator falling into a black hole.

We propose an experiment based on a Bose-Einstein condensate interferometer for strongly constraining fifth-force models. Additional scalar fields from modified gravity or higher dimensional theories may account for dark energy and the accelerating expansion of the Universe. These theories have led to proposed screening mechanisms to fit within the tight experimental bounds on fifth-force searches. We show that our proposed experiment would greatly improve the existing constraints on these screening models by many orders of magnitude.

The current interest in laboratory detection of entanglement mediated by gravity was sparked by an information--theoretic argument: entanglement mediated by a local field certifies that the field is not classical. Previous derivations of the effect modelled gravity as instantaneous; here we derive it from linearised quantum general relativity while keeping Lorentz invariance explicit, using the path integral formalism. In this framework, entanglement is clearly mediated by a quantum feature of the field. We also point out the possibility of observing retarded entanglement, which cannot be explained by an instantaneous interaction. This is a difficult experiment for gravity, but is plausible for the analogous electromagnetic case.

We introduce a quantum interferometric scheme that uses states that are sharp in frequency and delocalized in position. The states are frequency modes of a quantum field that is trapped at all times in a finite volume potential, such as a small box potential. This allows for significant miniaturization of interferometric devices. Since the modes are in contact at all times, it is possible to estimate physical parameters of global multi-mode channels. As an example, we introduce a three-mode scheme and calculate precision bounds in the estimation of parameters of two-mode Gaussian channels. This scheme can be implemented in several systems, including superconducting circuits, cavity-QED and cold atoms. We consider a concrete implementation using the ground state and two phononic modes of a trapped Bose-Einstein condensate. We apply this to show that frequency interferometry can improve the sensitivity of phononic gravitational waves detectors by several orders of magnitude, even in the case that squeezing is much smaller than assumed previously and that the system suffers from short phononic lifetimes. Other applications range from magnetometry, gravimetry and gradiometry to dark matter/energy searches.

This work investigates extensions to the Standard Model that are inspired by supersymmetric models with an E6 gauge group. The models are non-minimal supersymmetric theories which keep the Higgs mass stable against the quantum corrections from higher energy physics, but do not contain the mu-problem or little hierarchy problem of the Minimal Supersymmetric Standard Model (MSSM). Also, unlike conventional Grand Unified Theories, the E6 inspired models do not contain any doublet-triplet splitting and the Minimal E6 Supersymmetric Model (ME6SSM) only contains complete E6 multiplets at low energies. A particularly exciting feature of the ME6SSM is the prediction of gauge coupling unification at the Planck scale rather than the conventional GUT scale, hinting at a potential unification of the Standard Model forces with quantum gravity. If extended with a discrete non-Abelian family symmetry, the E6 inspired models can explain the masses and mixings of the quarks and leptons that are observed in particle experiments. These are not understood in the Standard Model since they are free parameters, creating a flavour problem for the theory. Extending the Standard Model or MSSM with a family symmetry oers an attractive resolution to the flavour problem, and the recent discovery of neutrino oscillations, which indicate a high-level of symmetry in the lepton mixings, has led to a renewed interest in these models. However, explaining why the Higgs mass is small is essential in these models since it sets the scale for the quark and lepton masses. This motivates the synthesis of a family symmetry with the E6 inspired supersymmetric models, which resolves a number of problems facing the Standard Model including the hierarchy problem and the avour problem. A particular success of the resulting models is their ability to suppress proton decay and favour changing neutral currents, from supersymmetry and extended Higgs sectors, using the same family symmetry that is responsible for a tri-bi-maximal mixing of leptons.

A promising route to testing quantum gravity in the laboratory is to look for gravitationally-induced entanglement (GIE) between two or more quantum matter systems. Proposals for such tests have principally used microsolid systems, with highly non-classical states, such as N00N states or highly-squeezed states. Here, we consider, for the first time, GIE between two atomic gas interferometers as a test of quantum gravity. We propose placing the two interferometers next to each other in parallel and looking for correlations in the number of atoms at the output ports as evidence of GIE and quantum gravity. GIE is possible without challenging macroscopic superposition states, such as N00N or Schr\"odinger cat states, and instead there can be just classical-like 'coherent' states of atoms. This requires the total mass of the atom interferometers to be on the Planck mass scale, and long integration times. However, with current state-of-the-art quantum squeezing in cold atoms, we argue that the mass scale can be reduced to approachable levels and detail how such a mass scale can be achieved in the near future.

Despite almost a century's worth of study, it is still unclear how general relativity (GR) and quantum theory (QT) should be unified into a consistent theory. The conventional approach is to retain the foundational principles of QT, such as the superposition principle, and modify GR. This is referred to as `quantizing gravity', resulting in a theory of `quantum gravity'. The opposite approach is `gravitizing QT' where we attempt to keep the principles of GR, such as the equivalence principle, and consider how this leads to modifications of QT. What we are most lacking in understanding which route to take, if either, is experimental guidance. Here we consider using a Bose-Einstein condensate (BEC) to search for clues. In particular, we study how a single BEC in a superposition of two locations could test a gravitizing QT proposal where wavefunction collapse emerges from a unified theory as an objective process, resolving the measurement problem of QT. Such a modification to QT due to general relativistic principles is testable near the Planck mass scale, which is much closer to experiments than the Planck length scale where quantum, general relativistic effects are traditionally anticipated in quantum gravity theories. Furthermore, experimental tests of this proposal should be simpler to perform than recently suggested experiments that would test the quantizing gravity approach in the Newtonian gravity limit by searching for entanglement between two massive systems that are both in a superposition of two locations.