Session Q05: Precision Measurements of Gravity

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Quantum technologies are rapidly expanding the observable horizon of gravitational-wave astrophysics. The Advanced Laser Interferometer Gravitational-wave Observatory (LIGO) consists of twin quantum-limited, 4-km, Michelson laser interferometers, configured to detect the gravitational radiation from cataclysmic cosmic events such as the merger of black holes and neutron star binaries. At LIGO, we have recently commissioned large-scale quantum upgrades to detect gravitational waves with interferometric precision exceeding the standard quantum limit (SQL). This advance is possible with our introduction of a high-finesse, long-baseline filter cavity for frequency-dependent squeezed light injection – a substantial upgrade from our initial year-long observing run with broadband squeezing. The filter cavity rotates the quadrature squeezing angle at low frequencies to evade opto-mechanical backaction, and enable broadband quantum noise reduction for sub-SQL gravitational-wave detection in our upcoming astrophysical observing run. We will present on recent quantum upgrades to the Advanced LIGO detectors, and showcase the profound impact of quantum enhancement on gravitational-wave astrophysics.   

High Power, Phase Stabilized, Frequency Agile Laser System for Gravitational Wave and Dark Matter Detection Using Atom Interferometry (MAGIS-100)

MAGIS-100 is a 100-meter atom interferometer currently being built at Fermilab which will leverage modern atom optics techniques to search for oscillations in fundamental constants and time-dependent, equivalence-principle-violating forces which are key signatures of several ultra-light dark matter candidates. In addition, the interferometer can test the coherence limits of spatially separated wave packets and will also serve as a prototype gravitational wave detector in the frequency band between the peak sensitivities of LIGO and LISA. Generation and precise control of meter-separated quantum atomic superpositions within the interferometer requires an agile laser system able to rapidly shift the optical frequency up to a rate of 100 GHz/s while maintaining a phase lock to our static frequency comb. To meet the power requirement of the experiment, two lasers coherently locked must be robust to these rapid frequency shifts. Furthermore, the laser spatial mode is cleaned through fiber coupling and long free space propagation in vacuum. Frequency noise introduced by the fiber is suppressed with a custom FNC method that enables noise cancellation for a pulsed laser beam passing through the fiber.   

Towards Gravity Tests at Sub-Micron Scale With Levitated Nanoparticles

Nano- and micron-sized dielectric objects trapped with optical tweezers in a cryogenic extremely-high-vacuum (CEHV) environment open doors to new precision tests of the standard model [1]. Thanks to decoupling by levitation, low environmental noise combined with active center-of-mass laser cooling [2] quantum shot-noise limited force measurements are in reach. Of particular interest is the search for deviations from the inverse-square-law of gravity [3]. 

I will report on our optical trap in a new CEHV vibration-stabilized vacuum chamber, combined with a lithographically fabricated source mass for gravity measurements at a sub-micron scale. The progress of the experiment, together with expected statistical and systematic uncertainties using simulations and current experimental data, will be presented. 

[1] D. C. Moore and A. A. Geraci, (2021),  Searching for new physics using optically levitated sensors. Quantum Sci. Tecnol. 6.

[2] L. Magrini, P. Rosenzweig, C. Bach, A. Deutschmann-Olek, S. Hofer, S. Hong, N. Kiesel, A. Kugi and M. Aspelmeyer, (2021),  Real-time optimal quantum control of mechanical motion at room temperature. Nature, 595. 373–377

[3] Murata J. and Tanaka S., (2015), A review of short-range gravity experiments in the LHC era. Class. Quant. Grav., 32. 033001   

Towards Matter-Wave Interferometry with Optically Levitated Nanospheres

Demonstration of matter-wave interference with optically levitated nanospheres has the potential

to extend the current limit on matter-wave interference by three to four orders of magnitude.

This would provide pathways towards the realization of gravity-induced entanglement experiments

as well as tests of decoherence and wave function collapse models. Towards this end, I report

progress on the construction of a cryogenic and extremely high vacuum (EHV) experiment suitable

for laser-cooling and optical levitation of dielectric nanospheres. To preserve a coherence time

of approximately 200ms, experimental challenges such as near motional ground state cooling,

pressures below 10-13mbar, internal temperatures below 100K, and relative position stability on

the order of tens of nanometers must be overcome. This apparatus additionally allows for precision

measurements of short-range forces to test Newtonian gravity at sub-micron scales, the Casimir-

Polder force, matter neutrality, and other fundamental forces.   

Suspended animation - testing Newtonian gravity at the micron scale

An active experimental front in the modern study of Gravity is testing the (Newtonian) law of gravitation at the 1 μm – 100 μm length scale. Electromagnetic forces are several orders of magnitude stronger than gravity, and pose a formidable challenge in any experiment aiming to measure the latter. This work describes results from a platform based on optically trapped neutral microspheres that probes deviations from Newtonian gravity. In addition to modest improvements to a previous iteration of the experimental apparatus, we present a novel technique that allows further suppression of electromagnetic backgrounds. This technique, which relies an optomechanical force sensor, provides a complementary technique to previous searches that have largely relied on variations of mechanical springs.   

Progress toward tests of gravity and quantum mechanics using atom interferometry with Strontium

Following recent developments in light-pulse atom interferometry (AI) [1], the ability to perform sufficiently sensitive measurements of gravitational effects have opened a window into exploring novel fundamental physics. For example, investigation of the gravitational forces at the 0.1-1 meter distance scale using AI [2] has the potential to reveal violations of the gravitational inverse square law, study the gravitational Aharonov-Bohm effect, and test theories of gravity-induced quantum decoherence; these research topics are the focus of the atomic fountain (AF) described in this work.

In this talk, I will provide recent technical updates on the construction of a 2 meter baseline AF using ultracold Strontium (Sr). First, I will review the architecture of the laser system required to laser cool (1 mK) and trap the Sr atoms and perform AI using a two-photon Bragg transition at 461 nm. Second, I will review our progress on the installation of the ultrahigh vacuum system of the AF. Finally, I will present an example of how we plan to use micron-precision translation stages to measure gravity from well-characterized test source masses in the 100-1000 kg range.

[1] Kovachy et al. (2015). Nature 528, 530

[2] Asenbaum et al. (2017). Phys. Rev. Lett. 118, 183602   

Quantum Tunneling for Matter-wave Gravimetry

One promising candidate for high-precision gravimetry is atom interferometry. In contrast to light in optical interferometers, matter waves consisting of massive particles couple strongly to gravity, making them a tool suitable for gravimetry. In addition to gravity, the motion of atomic wave packets is manipulated by optical potentials that trap, guide or diffract the atoms. Contrary to classical waves, quantum physics allows for tunneling through forbidden regions and thus offers an additional tool to influence the atomic motion.

The combination of quantum tunneling and atom interferometers leads to gravimeters based on an analogue to optical Fabry-Pérot cavities [1]. In this contribution, we theoretically study the transmission spectrum of matter-wave Fabry-Pérot interferometers, present their sensitivity to accelerations and discuss their applicability to gravimetry. Similar to optical Fabry-Pérot cavities that act as monochromators, matter-wave devices introduce a velocity filtering, allowing to select specific momenta of the atomic wave packet. In addition to this effect, we study the preparation of a quantum gas inside the cavity and its asymmetry in tunneling, an effect that has no direct optical analogue.

[1] P. Schach, A. Friedrich, J. R. Williams, W. P. Schleich, and E. Giese, Tunneling gravimetry, EPJ Quantum Technology 9, 20 (2022)   

MAIUS - B: System status and mission goals

Dual-species atom interferometry is a promising tool to probe hypothetical models of fundamental physics which question the validity of the weak equivalence principle. The accuracy of atom interferometric measurements scales with the square of the time between the light pulses. Thus, the accuracy of current ground-based atom interferometers employing free falling atoms is ultimately limited by the size of the apparatus. To benefit from the full potential of atom interferometry, one of the long-term goals of the scientific community is to have a dual-species atom interferometer aboard a satellite which is in continuous free fall around the Earth.

The sounding rocket missions of the MAIUS program (Matterwave Interferometry under Microgravity) aim to demonstrate dual-species atom interferometry with Rb-87 and K-41 in space.

MAIUS-1 achieved the first generation of Bose-Einstein condensate (BEC) in space with Rb-87 atoms [1], followed by studies on shear interferometry [2]. The upcoming missions MAIUS-2 and -3 will focus on two-species BEC generation and their mixture dynamics as well as simultaneous interferometry based on Raman-Double diffraction. Together with other international efforts like the Cold Atom Lab on the International Space Station and the quantum gases lab on the Tiangong Spacestation, the sounding rocket experiments provide a complementory approach towards experiments with ultracold atoms in space.

This contribution presents the current status of the system and flight preparations. Emphasis is placed on the generation of BEC mixtures, magnetic atomic transport and Delta-Kick collimation on ground. The transfer of experimental sequences from gravity into microgravity is discussed which is a central part of the mission preparation. In line with this, a careful characterization of the system parameters is needed as well as their implementation in simulation tools.

[1] D. Becker, M. D. Lachmann, S. T. Seidel et al. Nature 562, 391-395 (2018)

[2] M. D. Lachmann, H. Ahlers, D. Becker et al. Nature Comm. 12, 1317 (2021)   

Using Feynman Diagrams to Analytically Compute Higher Order Quantum Corrections to Atom Interferometer Phase Shifts

In atom interferometry, the differential phase accumulated between two arms due to spatially varying gravitational fields is often analyzed under a semi-classical approximation that disregards the finite spatial extent of an atom's wavefunction. Deviations from this approximation have not yet been measured definitively, but as atom interferometers become more sensitive, higher order quantum corrections could potentially be observed. These measurements would offer insight into the connection between quantum mechanics and gravity and reveal a novel source of systematic error. We introduce a Feynman diagram based approach to analytically computing the phase shift in an atom interferometer which incorporates these higher-order quantum corrections. This approach can also be used to calculate phase shifts caused by spatially varying magnetic fields and optical potentials.   

Inference of gravitational field superposition from quantum measurements

Experiments are beginning to probe the interaction of quantum particles with gravitational fields beyond the uniform-field regime. In non-relativistic quantum mechanics, the gravitational field in such experiments can be written as a superposition state. We empirically demonstrate that alternative theories of gravity can avoid gravitational superposition states only by decoupling the gravitational field energy from the quantum particle's time evolution. Furthermore, such theories must specify a preferred quantum reference frame in which the equations of motion are valid. To the extent that these properties are theoretically implausible, recent experiments provide indirect evidence that gravity has quantum features. Proposed experiments with superposed gravitational sources would provide even stronger evidence that gravity is nonclassical.