Measuring gravity with milligram levitated masses

Gravity differs from all other known fundamental forces since it is best described as a curvature of spacetime. For that reason it remains resistant to unifications with quantum theory. Gravitational interaction is fundamentally weak and becomes prominent only at macroscopic scales. This means, we do not know what happens to gravity in the microscopic regime where quantum effects dominate, and whether quantum coherent effects of gravity become apparent. Levitated mechanical systems of mesoscopic size offer a probe of gravity, while still allowing quantum control over their motional state. This regime opens the possibility of table-top testing of quantum superposition and entanglement in gravitating systems. Here we show gravitational coupling between a levitated sub-millimeter scale magnetic particle inside a type-I superconducting trap and kg source masses, placed approximately half a meter away. Our results extend gravity measurements to low gravitational forces of attonewton and underline the importance of levitated mechanical sensors. Specifically, at a frequency of 26.7 Hz, a mass of 0.4 mg and showing Q-factors in excess of 10

^7

, we obtained a force noise of 0.5

fN\sqrt{Hz}

. We simultaneously detect the other 5 rotational and translational degrees of freedom.

Note:

13 pages, with 13 pages supplementary materials

References(43)

Figures(11)

[1]

The foundation of the general theory of relativity.

Albert Einstein

- Annalen Phys. 49 (1916) 7, 769-822,
- Annalen Phys. 14 (2005) 517-571,
- ,
- Annalen Phys. 354 (1916) 7, 769-822
•
DOI:
- 10.1002/andp.19163540702

[2]

0957 + 561 A, B - Twin quasistellar objects or gravitational lens

- Nature 279 (1979) 381-384
•
DOI:
- 10.1038/279381a0

[3]

Observation of Gravitational Waves from a Binary Black Hole Merger

LIGO Scientific and
Virgo

Collaborations

•

B.P. Abbott
(
- Caltech
)

et al.

- Phys.Rev.Lett. 116 (2016) 6, 061102
•
e-Print:
- 1602.03837
•
DOI:
- 10.1103/PhysRevLett.116.061102

[4]

Baloković, M., Barrett, J., Bintley, D., et al

K. Akiyama
,
A. Alberdi
,
W. Alef
,
K. Asada
,
R. Azulay

et al.

- Astrophys.J.Lett. 875 (2019) 4

[5]

MICROSCOPE Mission: First Results of a Space Test of the Equivalence Principle

Pierre Touboul
(
- Chatillon, ONERA
)
,
Gilles Métris
(
- Geoazur, Nice
)
,
Manuel Rodrigues
(
- Chatillon, ONERA
)
,
Yves André
(
- CNES, Toulouse
)
,
Quentin Baghi
(
- Geoazur, Nice
)

et al.

- Phys.Rev.Lett. 119 (2017) 23, 231101
•
e-Print:
- 1712.01176
•
DOI:
- 10.1103/PhysRevLett.119.231101

[6]

Gravity Probe B: Final Results of a Space Experiment to Test General Relativity

et al.

- Phys.Rev.Lett. 106 (2011) 221101
•
e-Print:
- 1105.3456
•
DOI:
- 10.1103/PhysRevLett.106.221101

[7]

Ye, J.: Resolving the gravitational redshift across a millimetre-scale atomic sample. Nature 602(7897), 420-424

T. Bothwell
,
C.J. Kennedy
,
A. Aeppli
,
D. Kedar
,
J.M. Robinson

et al.

[8]

Phase Shift in an Atom Interferometer due to Spacetime Curvature across its Wave Function

Peter Asenbaum
(
- Stanford U., Phys. Dept.
)
,
Chris Overstreet
(
- Stanford U., Phys. Dept.
)
,
Tim Kovachy
(
- Stanford U., Phys. Dept.
)
,
Daniel D. Brown
(
- Birmingham U.
)
,
Jason M. Hogan
(
- Stanford U., Phys. Dept.
)

et al.

- Phys.Rev.Lett. 118 (2017) 18, 183602
•
e-Print:
- 1610.03832
•
DOI:
- 10.1103/PhysRevLett.118.183602

[9]

Brukner, Č., Tino, G

G. Rosi
,
G. D'Amico
,
L. Cacciapuoti
,
F. Sorrentino
,
M. Prevedelli

et al.

- Nature Commun. 8 (2017) 15529

[10]

Atom-Interferometric Test of the Equivalence Principle at the $10^{-12}$ Level

- Phys.Rev.Lett. 125 (2020) 19, 191101
•
e-Print:
- 2005.11624
•
DOI:
- 10.1103/PhysRevLett.125.191101

[11]

: Precision measurement of the newtonian gravitational constant using cold atoms. Nature 510(7506), 518-521

G. Rosi
,
F. Sorrentino
,
L. Cacciapuoti
,
M. Prevedelli
,
G. Tino

[12]

Improved Determination of G Using Two Methods

- Phys.Rev.Lett. 111 (2013) 10, 101102
•
DOI:
- 10.1103/PhysRevLett.111.101102

[13]

Improved constraints on non-Newtonian forces at 10 microns

- Phys.Rev.D 78 (2008) 022002
•
e-Print:
- 0802.2350
•
DOI:
- 10.1103/PhysRevD.78.022002

[14]

Improvement for Testing the Gravitational Inverse-Square Law at the Submillimeter Range

Wen-Hai Tan
(
- Hua-Zhong U. Sci. Tech. and
- Hua-Zhong Normal U.
)
,
An-Bin Du
(
- Hua-Zhong U. Sci. Tech. and
- Hua-Zhong Normal U.
)
,
Wen-Can Dong
(
- Hua-Zhong U. Sci. Tech. and
- Hua-Zhong Normal U.
)
,
Shan-Qing Yang
(
)
,
Cheng-Gang Shao
(
- Hua-Zhong U. Sci. Tech. and
- Hua-Zhong Normal U.
)

et al.

- Phys.Rev.Lett. 124 (2020) 5, 051301
•
DOI:
- 10.1103/PhysRevLett.124.051301

[15]

Quantum theory of weak gravitational fields

Matvei Bronstein

- Gen.Rel.Grav. 44 (2012) 267-283
•
DOI:
- 10.1007/s10714-011-1285-4

[16]

: The role of gravitation in physics: report from thechapel hill conference. In: The Role of Gravitation in Physics: Report from theChapel Hill Conference (2011)