# Interplay of Gravity and Quantum Mechanical Superpositions

Lead Research Organisation:
University College London

Department Name: Physics and Astronomy

### Abstract

The two most fundamental and well-verified theories of physics are General Relativity,

which describes gravity, and Quantum Mechanics, which describes the other three

fundamental forces known to us. A consistent quantum mechanical theory of gravity still

eludes us. The unification of quantum mechanics and gravity has been a greatly desired

prospect for some time. With the unification of quantum mechanics and special relativity

being achieved with Quantum Field Theory, it has been seen as inevitable for General

Relativity to also be, at some level, quantum in nature. To determine if this is the case

numerous tests have been proposed -- however no definitive answers have been

found. With this in mind this project will seek, among other things, to help answer whether

gravity, at least in its low energy limit, is fundamentally quantum in nature.

Some have started to question whether gravity is fundamentally a quantum entity, raising

the possibility of whether it could be a classical field/background happily co-existing with

quantum mechanics. Perhaps the most striking arena where we will suffer if gravity is

indeed classical is to predict the gravitational field when matter in peculiarly quantum

states, say in highly delocalized superpositions, acts as the source of gravity. To this end,

the broad aim of this project will be to design experiments which couple quantum

superpositions of states of mesosocpic objects to gravity, or use them as sources of gravity

and through that infer about the quantum nature of gravity. We will also investigate the

potential of these experiments to enable both precision accelerometry and gravimetry and

to enable the determination of gravitational force law and Newton's constant over short

distances.

The current project will seek to

(i) Extend the above gravitational accelerometry proposals for superpositions of

squeezed states and other engineered non-classical quantum states so as to

optimize the precision of measurements for a given investment of energy.

(ii) Extend the above proposals up to the macroscopic boundary of the mesoscopic

regime to explore the boundary between the quantum regime and gravity. In

particular, the extrapolation from nano-meter radii beads to micro-meter radii

beads, which can serve as the origin of measurable gravitational fields, will be

examined. For this purpose, a new way to split the spatial position through

inhomogeneous electric fields coupling to spin states through crystal

anisotropies, will be used.

(iii) A theoretical calculation of the decoherence of a superposition of distinct

energy-momentum states of a system in one region of space due to the presence

and fluctuations of other surrounding systems that couple gravitationally to it

will be made.

(iv) By bringing a probe mass in proximity to another mass in a highly non-classical

state, we are going to investigate the precisions to which the Newton's Constant

G, and potential corrections to Newton's law for short distances, stemming, for

example from extra dimensions, could be determined.

(v) Expand these investigations to two interferometer systems in order to include

bipartite entanglement to further explore how gravity addresses a highly

quantum, massive system. We will consider the interactions of two masses in

highly non-Gaussian states (prepared by methodologies founded earlier in the

project) to generate some form of 'loophole free' tests for the quantum nature

of gravity.

which describes gravity, and Quantum Mechanics, which describes the other three

fundamental forces known to us. A consistent quantum mechanical theory of gravity still

eludes us. The unification of quantum mechanics and gravity has been a greatly desired

prospect for some time. With the unification of quantum mechanics and special relativity

being achieved with Quantum Field Theory, it has been seen as inevitable for General

Relativity to also be, at some level, quantum in nature. To determine if this is the case

numerous tests have been proposed -- however no definitive answers have been

found. With this in mind this project will seek, among other things, to help answer whether

gravity, at least in its low energy limit, is fundamentally quantum in nature.

Some have started to question whether gravity is fundamentally a quantum entity, raising

the possibility of whether it could be a classical field/background happily co-existing with

quantum mechanics. Perhaps the most striking arena where we will suffer if gravity is

indeed classical is to predict the gravitational field when matter in peculiarly quantum

states, say in highly delocalized superpositions, acts as the source of gravity. To this end,

the broad aim of this project will be to design experiments which couple quantum

superpositions of states of mesosocpic objects to gravity, or use them as sources of gravity

and through that infer about the quantum nature of gravity. We will also investigate the

potential of these experiments to enable both precision accelerometry and gravimetry and

to enable the determination of gravitational force law and Newton's constant over short

distances.

The current project will seek to

(i) Extend the above gravitational accelerometry proposals for superpositions of

squeezed states and other engineered non-classical quantum states so as to

optimize the precision of measurements for a given investment of energy.

(ii) Extend the above proposals up to the macroscopic boundary of the mesoscopic

regime to explore the boundary between the quantum regime and gravity. In

particular, the extrapolation from nano-meter radii beads to micro-meter radii

beads, which can serve as the origin of measurable gravitational fields, will be

examined. For this purpose, a new way to split the spatial position through

inhomogeneous electric fields coupling to spin states through crystal

anisotropies, will be used.

(iii) A theoretical calculation of the decoherence of a superposition of distinct

energy-momentum states of a system in one region of space due to the presence

and fluctuations of other surrounding systems that couple gravitationally to it

will be made.

(iv) By bringing a probe mass in proximity to another mass in a highly non-classical

state, we are going to investigate the precisions to which the Newton's Constant

G, and potential corrections to Newton's law for short distances, stemming, for

example from extra dimensions, could be determined.

(v) Expand these investigations to two interferometer systems in order to include

bipartite entanglement to further explore how gravity addresses a highly

quantum, massive system. We will consider the interactions of two masses in

highly non-Gaussian states (prepared by methodologies founded earlier in the

project) to generate some form of 'loophole free' tests for the quantum nature

of gravity.

### Organisations

### Publications

Marshman R
(2020)

*Mesoscopic interference for metric and curvature & gravitational wave detection*in New Journal of Physics
Marshman R
(2020)

*Locality and entanglement in table-top testing of the quantum nature of linearized gravity*in Physical Review A
Van De Kamp T
(2020)

*Quantum gravity witness via entanglement of masses: Casimir screening*in Physical Review A### Studentship Projects

Project Reference | Relationship | Related To | Start | End | Student Name |
---|---|---|---|---|---|

EP/N509577/1 | 30/09/2016 | 24/03/2022 | |||

1930690 | Studentship | EP/N509577/1 | 30/09/2017 | 23/09/2021 | Ryan Marshman |

Description | We have achieved three primary objectives: 1 Explored which gravitational signals can be detected using large mass interferometry (LMI). Specifically how employing large masses in spatial superpositions can yield unique advantages over other methods of detecting gravitational waves. This can be seen with such a device being sensitive to lower frequency ranges while also beingany orders of magnitude smaller. 2 considered in detail the underlying mechanisms for two spatially superposed masses to become entangled and in particular identified all underlying assumptions and conditions for witnessing the quantum nature of linearized gravity. 3 considered the likely method of creating such large mass interferometers using a stern Gerlach like device including discussions with experimentalists to determine the most feasible implementation and to identify as many likely issues as possible, including the limiting effect of induced diamagnetism in such devices. |

Exploitation Route | This work has layed the groundwork for how large mass interferometry (LMI) can serve to measure both classical and quantum mechanical aspects of gravity. We have not yet however explored all possible uses for such devices, nor have we settled on a clearly optimal implementation of LMI. Further work should follow both these paths as well as seek to actually implement such a device in the laboratory. |

Sectors | Aerospace Defence and Marine Education Environment Other |

URL | http://www.scientificamerican.com/article/tiny-gravitational-wave-detector-could-search-anywhere-in-the-sky/ |