Dennis Rätzel - Sensing of Weak Gravitational Effects

Sensing of Weak Gravitational Effects

High precision sensors for gravity and inertial effects can be employed for exciting applications in fundamental research such as: precision measurements of Newton’s constant G (the least precisely known fundamental constant), searches for short range modifications of gravity (e.g. related to dark energy), tests of the equivalence principle, and the detection of gravitational waves and other general relativistic gravity effects such as the gravitational attraction due to light and ultra-relativistic particle beams. With new and improved quantum sensors, new categories of effects may become accessible, for example, quantum properties of the gravitational field. The application and further development of quantum sensors for gravity and relativity is one of my main research interests.

Oscillating gravitational fields

My research has focused especially on oscillating gravitational fields that appear in many dynamical situations, for example, when masses move in front of a detector or in gravitational wave physics. The advantage of an oscillating signal for the detection is the increased sensitivity that may be achieved by making use of the knowledge of the gravitational signal's frequency (if that is available).

For example, with collaborators from Vienna and Nottingham, I have investigated how an oscillating gravitational field affects the quasiparticles in a Bose-Einstein Condensate (BEC) [1], a phase of ultra-cold atomic gases (more on BECs can be found here). In principle, the effect on the quasiparticles can be used for measuring gravitational signals, although the precision is strongly limited due to omnipresent decoherence effects [2].

A particularly promising type of sensors for oscillating gravitational fields are optomechanical sensors consisting of a mechanical oscillator interacting with light that can be operated in the quantum regime due to the high level of control over light achievable. More details about the technology and the corresponding research field can be found here. With a group of collaborators, we have investigated the fundamental limit of sensing oscillating gravitational fields with optomechanical systems in the non-linear regime [3]. In particular, we have found that resonant modulations of system paramters (e.g. parametric driving) can be of great advantage.

Gravitational field of light and ultra-relativistic matter

The gravitational field of pulses of light and ultra-relativistic matter is an extremely weak signal even for the strongest laser pulses or the proton bunches at the Large Hadron Collider (LHC). Therefore, although predicted by General Relativity the effect has not been measured so far. Indeed, the smallest gravitational acceleration that has been measured in the lab to date is five orders of magnitude larger than the gravitational field of the LHC's proton bunches.

In [4], Felix Spengler, Daniel Braun and I discuss the necessary sensing abilities of detectors to detect the effect focussing on three types of sensors based on mechanical oscillators. At least for the proton bunches in the LHC, detection could be possible with near future technology combining many detectors along the LHC ring. This would correspond to the first direkt measurement of the gravitational attraction due to kinetic energy as for ultra-relativistic particles, the kinetic energy is much larger than the energy corresponding to the rest mass and dominates the gravitational field.

The gravitational field of light and ultra-relativistic matter has many more faszinating properties. For example, in another article with Daniel Braun and Fabienne Schneiter [5], we have shown that circular polarization of a focused light beam leads to frame dragging and gravitational spin-spin coupling of light. In principle, these effects may be tested with laser interferometric techniques, however, not in the near future.

Dark Energy

With Sofia Qvarfort and Stephen Stopyra, I have investigated to which extend optomechanical systems can be used to constrain cosmological models that try to explain the accelerated expansion of the universe - also associated with the term "dark energy" - by postulating non-linear dynamical scalar fields [6].

In particular, we focused on Chameleon fields that bear that name because their effects are strongly suppressed in high-mass-density environments like the solar system, while they are un-suppressed in low-density environments like the intergalactic voids. Chameleon fields would lead to modifications of Newton's law of gravity at short distances which could be tested, for example, in a vacuum chamber (due to the low mass density environment). In our article, we derived the expressions for the Chameleon force affecting the mechanical oscillator, which depends on its shape and density and we obtained fundamental bounds on the sensitivity of quantum optomechanical systems for these modifications.

One can also raise the question if the accelerated rate of the cosmological expansion can be measured in solar system experiments directly. Felix Spengler, Alessio Belenchia, Daniel Braun and I considered laser signals between satellites and optical resonators as sensors for this task [7] and found that state-of-the-art technology is far from providing the necessary sensitivity. Therefore, astrophysical observations and indirect tests of dark energy theories remain the most viable approaches to learn about the origin of the accelerated expansion of the universe.

Quantum properties of the gravitational field

To decide the question how and if our theories of gravity and quantum mechanics fit together, empirical evidence is necessary. One possible source of such evidence may be laboratory experiments with gravitationally interacting masses in the quantum regime [8,9]. A range of theories that postulate “classical” properties of gravity may be excluded based on such experiments.

In [10], Doug Plato, Chuanqi Wan and I have investigated the fundamental limitations to perform tests of quantum properties of the gravitational field with quantum optomechanical systems. We have found that, in particular, the environmental noise on the mechanical oscillators imposes very strong constraints which will need many years of research to be overcome.

Gravitational Waves

Quantum optomechanical systems or other highly precise small-scale force sensors may be also used for gravitational wave detection. Indeed, there are several proposals of this type around [11,12]. In an article with Ivette Fuentes [13], I have proposed to test such small-scale detectors by employing moving masses to generate gravitational fields that resemble the tidal forces induced by gravitational waves.

[1] Rätzel D., Howl R., Lindkvist J., Fuentes I., "Dynamical response of Bose-Einstein condensates to oscillating gravitational fields" New J. Phys. 20 073044 (2018), doi.org/10.1088/1367-2630/aad272; Preprint arxiv.org/abs/1804.11122

[2] Rätzel D., Schützhold R. “Decay of quantum sensitivity due to three-body loss in Bose-Einstein condensates” Phys. Rev. A 103, 063321 (2021), doi.org/10.1103/PhysRevA.103.063321; Preprint arxiv.org/abs/2101.05312

[3] Qvarfort S., Plato A.D.K., Bruschi D.E., Schneiter F., Braun D., Serafini A., Rätzel D., “Optimal estimation of time-dependent gravitational fields with quantum optomechanical systems”, Physical Review Research 3.1 (2021): 013159 doi.org/10.1103/PhysRevResearch.3.013159; Preprint arxiv.org/abs/2008.06507

[4] Spengler F., Rätzel D., Braun D. “Perspectives of measuring gravitational effects of laser light and particle beams” New Journal of Physics 24.5 (2022): 053021, https://doi.org/10.1088/1367-2630/ac5372; Preprint: arxiv.org/abs/2104.09209

[5] Schneiter F., Rätzel D., Braun D., "Rotation of polarization in the gravitational field of a laser beam—Faraday effect and optical activity", Classical and Quantum Gravity 36 (20), 205007 (2019), doi.org/10.1088/1361-6382/ab3523; Preprint arxiv.org/abs/1812.04505

[6] Qvarfort S., Rätzel D., Stopyra S. “Constraining modified gravity with quantum optomechanics” New Journal of Physics 24.3 (2022): 033009, doi.org/10.1088/1367-2630/ac3e1b; Preprint: arxiv.org/abs/2108.00742

[7] Spengler F., Belenchia A., Rätzel D., Braun D., “Influence of cosmological expansion in local experiments”, Classical and Quantum Gravity 39.5 (2022): 055005, https://doi.org/10.1088/1361-6382/ac4954; Preprint: arxiv.org/abs/2109.03280

[8] Bose S., et al. "Spin entanglement witness for quantum gravity" PRL, 119(24), 240401 (2017) https://doi.org/10.1103/PhysRevLett.119.240401

[9] Marletto C., Vedral V. Gravitationally induced entanglement between two massive particles is sufficient evidence of quantum effects in gravity. PRL, 119(24), 240402 (2017). https://doi.org/10.1103/PhysRevLett.119.240402

[10] Plato A.D.K., Rätzel D., Wan C. “Enhanced Gravitational Entanglement in Modulated Optomechanics” Preprint: arxiv.org/abs/2209.12656

[11] Sabín C., Bruschi D. E., Ahmadi M., Fuentes, I. (2014). Phonon creation by gravitational waves. New Journal of Physics, 16(8), 085003. https://doi.org/10.1088/1361-6382/ab3523

[12] Singh, S., De Lorenzo, L. A., Pikovski, I., & Schwab, K. C. (2017). Detecting continuous gravitational waves with superfluid 4He. New Journal of Physics, 19(7), 073023. 10.1088/1367-2630/aa78cb

[13] Rätzel D., Ivette F. "Testing small scale gravitational wave detectors with dynamical mass distributions." Journal of Physics Communications 3.2 (2019): 025009, doi.org/10.1088/2399-6528/aaff1f; Preprint arxiv.org/abs/1709.08099

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