Casimir Forces and Gravitation at short range

Project goal

The aim of this project is to study short range interactions using atom interferometry techniques. This experiment will allow realizing precise measurements of gravity at short distance, searching for possible deviations to Newtonian gravity. Such deviations are made possible by new gravitational-type interactions with range on the order of the micrometer, as considered by various unification theories. The measurement of such interactions appears as a promising way for the observation of the first experimental signals of new physics beyond the standard model.

The FORCA-G project will set constraints (or discover new physics) on the interactions at short distance, focusing its investigation in the micrometer range. A simple phenomenological model describes a potential new interaction as a modification of the Newtonian potential with a Yukawa type term

where U_N is the Newtonian potential, and α and λ are the amplitude and the range of the new interaction. The goal of the project is to improve the sensitivity on α for ranges from 100 nm to 10 μm, and a precise measurement (and cancellation) of the Casimir-Polder potential between an atom and a surface. This last effect, which constitutes the dominant limitation for the measurement of new interactions, deserves precise study for itself: it is the most accessible manifestation of quantum field fluctuations in the macroscopic world.

Physical system

As a first step we demonstrated the realisation of a trapped atom interferometer in a 1D vertical lattice far from any surface.The principle of the experiment relies on the proposal by P. Wolf et al, Phys Rev A 75, 063608 (2007). Our system consists in laser-cooled ⁸⁷Rb atoms trapped in the fondamental band of a 1D vertical optical lattice. The Bloch frequency of this system is defined by the potential energy difference between two adjacent lattice sites :ν_B = m_ag λ_l/2h where λ_l is the lattice wavelength, m_a is the atomic mass, g the earth gravity acceleration and h is the Planck constant. The eigenstates |W_m> of this system are called Wannier-Stark states (WS) and form a ladder of localised states separated in energy by the Bloch frequency. They are indexed by the quantum number m defining the lattice site where the center of the spatial wavefunction is located.

Transitions between neighbouring Wannier Stark states

Principle of the interferometer

We use counterpropagating Raman transitions between the two hyperfine states |g>=|5²S_1/2,F=1,m_F=0> and |e>=|5²S_1/2,F=2,m_F=0> to drive transitions between WS states: |g,W_m> -> |e,W_m+Δ_m> separated by a number &Delta_m of lattice sites at Raman frequencies: ν_R =ν_HFS +/-Δ_m x ν_B where ν_HFS is the hyperfine frequency.

Raman spectroscopy of Wannier-Stark states

Raman spectrum of the transition probability bewteen |g> and |e> as a function of the Raman frequency ν_R. The peaks separated by the Bloch frequency are the signature of a displacement of the atoms between the lattice sites (ν_B = 569 Hz).

We perform a Ramsey type interferometer on a transition between two different lattice sites to measure the Bloch frequency. Using a symmetrized interferometer configuration, we have demonstrated a state of the art relative sensitivity in the measurement of the Bloch frequency of about 1.8x10^-6 at 1s [A. Hilico et al Phys. Rev. A91, 053616 (2015)]. Such a result would give a measurement of the Casimir Polder force with a statistical uncertainty of 1 part in 10³ for a measurement time of a few minutes only, provided that the interferometer is done with a single lattice site, at a distance of a few micrometers from the lattice retroreflecting mirror.

Ramsey fringes

Ramsey fringes on the Δ_m = - 3 transition
for a free evolution time of T = 150 ms
The contrast of the fringes is 60%.

A long coherence time, recent results

We recently installed a crossed optical dipole trap in order to increase the number of atoms per well from a few to up to about one thousand thanks to evaporative cooling. Working with much denser and smaller atomic cloud allowed reducing coupling and phase inhomogeneities in the interferometer.

In the optical dipole trap, at densities of few 10¹² at/cm³, we observe a non monotonic evolution of the contrast of the symmetrized interferometers, which is unexpected. We understand this phenomenon as a subtle competition between the spin-echo technique and an exchange-interaction driven spin self-rephasing mechanism based on the identical spin rotation effect (ISRE). In trapped atomic clocks, ISRE, originating from particle indistinguishability, can enhance the clock’s coherence via the so-called spin self-rephasing mechanism, up to several tens of seconds! [Deutsch et al PRL 105, 020401 (2010)].Together with the spin-echo technique, it leads to complex spin dynamics as we first showed in [Solaro et al. Phys. Rev. Lett. 117, 163003 (2016)].

Contrast evolution

Evolution of the contrast as a function of the density for standard and symmetrized Ramsey interferometers

Impact of atomic interactions

In our interferometer scheme with atoms trapped in the lattice, the two partial wavepackets associated to the two internal states do not perfectly overlap and ISRE is found to be weaker. We are currently studying the dependence of SSR with this overlap. Our first Ramsey spectroscopy results show large and unexpected density-dependent shifts on the Bloch frequency that need theoretical frameworks going beyond simple mean-field treatment.models.

At ultracold temperatures, the atom-atom interactions are governed by a pure s-wave quantum scattering and quantum statistics play an important role. This has motivated for instance the development of atomic clocks and matter-wave sensors based on fermionic atoms: as the Pauli principle forbids two identical fermions to collide, interaction shifts are expected to be suppressed. However, the absence of such collisional shifts strongly rely on atom indistinguishability and hence on the probing field. Indeed, slight amplitude or phase inhomogeneities of the probe fields make fermions distinguishable and lead to novel collisional shifts [Campbell et al Science 324,360 (2009), Gibble PRL 103, 113202 (2009)].

In our setup based on bosonic 87Rb trapped in the lattice, the coherent control of the separation (or overlap) between the two partial wave-packets thanks to Raman transitions appears to be a powerfull tool to tune the atom-atom interactions and our experiment thus provides a very suitable instrument to probe them.

Short range forces measurements

When the Casimir-Polder is accurately modelled, the interferometer phase shift can be corrected from this effect, which then allows measuring the gravitational force between the atom and the surface, and realize a test of Newtonian gravity. For distances on the order of 10 micrometers, the Casimir-Polder potential can be corrected at the percent level, so that this effect can be rejected at a level comparable to the uncertainty in the measurement. The corrected measurement then reveals the presence of a new interaction, or at least allows for setting an upper bound on its amplitude. When getting closer to the surface, the Casimir-Polder force largely dominates the gravitational effects. It is then necessary to correct for this potential with a precision modern models can’t reach. It is nevertheless possible to get ride of this effect to a large extent by realizing a differential measurement with two different isotopes (⁸⁵Rb and ⁸⁷Rb), for which Casimir effects are nearly identical. We hope to increase significantly the quality of these tests for distances from 100 nm to 10 microns, by two to three orders of magnitude.

Mirrors under vacuum

Several mirrors have been installed in the vacuum chamber, on a movable support

To perform such measurements, we have installed mirrors under vacuum in a vacuum chamber placed above the chamber in which the ultra-cold atoms are produced. We now transport the atoms by means of a stationary wave in motion over the 30 cm that separates the dipole trap from the mirrors. We now make measurements of the interaction forces as a function of the distance between the atoms and the surface of one of the mirrors.

Measurement of the Casimir Polder force

We have optimized the sensitivity of our local force sensor near the surface, where new effects affect the measureme,t : loss of coherence due to stray light potentials, parasitic forces due to adsorbed atoms onto the surface ... We have reached an unprecedented stability for a local force measurement of 340 quectoNewton at 1s, averaging down to 4 qN. With this level of performance, we have successfully put into evidence the Casimir Polder force, despite its tiny amplitude.

Casimir Polder force measurements

Publications

 Yann Balland, Luc Absil, Franck Pereira dos Santos
"Quectonewton local force sensor"
Phys. Rev. Lett. 133, 113403 (2024)

 Luc Absil, Yann Balland, Franck Pereira dos Santos
"Long-range temperature-controlled transport of ultra-cold atoms with an accelerated lattice"
New J. Phys. 25, 073010 (2023)

 Alexis Bonnin, Cyrille Solaro, Xavier Alauze, Franck Pereira dos Santos
“Magic density in a self-rephasing ensemble of trapped ultracold atoms”
Phys. Rev. A 99, 023627 (2019)

 Xavier Alauze, Alexis Bonnin, Cyrille Solaro, Franck Pereira Dos Santos
“A trapped ultracold atom force sensor with a μm-scale spatial resolution”
New J. Phys. 20, 083014 (2018)

 C. Solaro, A. Bonnin, F. Combes, M. Lopez, X. Alauze, J.-N. Fuchs, F. Piéchon and F. Pereira Dos Santos
“Competition between Spin Echo and Spin Self-Rephasing
in a Trapped Atom Interferometer”
Phys. Rev. Lett. 117, 163003 (2016)
Copyright 2016 by the American Physical Society

 A. Hilico, C. Solaro, M. -K. Zhou, M. Lopez, and F. Pereira dos Santos
“Contrast decay in a trapped-atom interferometer”
Phys. Rev. A 91, 053616 (2015)
Copyright 2015 by the American Physical Society

 M-K. Zhou, B. Pelle, A. Hilico, F. Pereira dos Santos
"Atomic multiwave interferometer in an optical lattice"
Phys Rev A 88, 013604 (2013)
Copyright 2013 by the American Physical Society

 B. Pelle, A. Hilico, G. Tackmann, Q. Beaufils, F. Pereira dos Santos
"State labelling Wannier-Stark atomic interferometers"
Phys Rev A 87, 023601 (2013)

 G. Tackmann, B. Pelle, A. Hilico, Q. Beaufils, F. Pereira Dos Santos
"Raman laser spectroscopy of Wannier Stark states"
Phys. Rev. A 84, 063422 (2011)
Copyright 2011 by the American Physical Society

 R. Messina, S. Pelisson, M.-C. Angonin, and P. Wolf
"Atomic states in optical traps near a planar surface"
Physical Review A 83, 052111, (2011)
Copyright 2011 by the American Physical Society

 Q. Beaufils, G. Tackmann, X. Wang, B. Pelle, S. Pelisson, P. Wolf and F. Pereira dos Santos
"Laser controlled tunneling in a vertical optical lattice"
Physical Review Letters 106, 213002 (2011)
Copyright 2011 by the American Physical Society

 F. Pereira Dos Santos, P. Wolf, A. Landragin, M.-C. Angonin, P. Lemonde, S. Bize, And A. Clairon
"Measurement of short range forces using cold atoms"
Proceeding of the 7th International Symposium on Frequency Standards and Metrology, ed. by L. Maleki (World scientific) p44-52, (2009)