Gravitational Quantum Optics
Gravitational Quantum Optics
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For nearly a century there has been tension between the known laws of physics. The classical theory of General Relativity describes all macroscopic gravitational phenomena, while Quantum Field Theory is the basis for the description of matter at the microscopic scale. Yet, to date, there has been no consensus on how, or even if, they can fit together. A conclusive final answer can only be provided by empirical evidence. Gravitational Quantum Optics comprises research at the interface of gravity and quantum physics in the low energy regime (i.e. far below the Planck scale) searching for novel effects that may be tested in experiments.
Quantum Optics in Curved Spacetime Backgrounds
Quantum Optics in Curved Spacetime Backgrounds
Most quantum optical experiments related to gravity can be described by fixed gravitational background, that is, the gravitational effect of the involved quantum systems can be neglected, the curved spacetime background is merely the stage on which quantum physics happens.
Optical Resonators
Optical Resonators
Laser light is an ingredient in almost all quantum optics experiments. Due to its high coherence and brightness, it provides a great frequency reference and control over other quantum systems such as atoms. Hence, as a pre-requisite for quantum optics in curved spacetime, one needs corresponding models to describe laser light and its generation. An important ingredient of lasers and other elements of quantum optical setups are optical resonators the most simple version of which is a Fabry-Pérot cavity consisting of two mirrors that set the boundaries for the light field.
In [1], collaborators from Vienna and Tübingen and I have investigated the frequency spectrum of optical resonators in curved spacetime. In particular, we considered the situation of the two mirrors at the ends of the optical resonator being connected by a rod of a given material that deforms under spacetime curvature and acceleration. Our expressions contain the effect of deformations on the same footing as that of gravitational frequency shift, where the frequency of light depends on the potential level of the receiver with respect to the emitter.
Optical resonators are also often an important element of optomechanical systems, where the physical length of an optical resonator becomes a mechanical degree of freedom that the light couples to. Due to the great control over light achieved in the lab, quantum optomechanical systems can be operated in the quantum regime. In particular, they are promising sensors for forces and gravitational acceleration. More details on optomechanical system can be found here and on sensing of weak gravitational effects here.
Light Clocks
Light Clocks
The optical resonator in a curved spacetime also provides the basis for a model of a quantum clock that is consistent with both general relativity and quantum mechanics.
In [2], Tupac Bravo, Ivette Fuentes and I studied such a quantum light clock in the gravitational field of the earth. This type of research becomes particularly interesting with the increasing precision of optical atomic clocks, where the gravitational frequency shift can be measured on the length scale of millimeters [3,4]. This is a scale over which the wave functions of the clock atoms can be extended and their quantum properties become relevant. In particular, the concept of proper time which is of fundamental importance in general relativity is not anymore a property of the whole quantum system.
Optical Fibers
Optical Fibers
In many quantum optical experiments, light does not propagate in free space, but in optical fibers. Here again, the direct effect of gravity and acceleration on the light propagating in the fiber has to be combined with the effect of curved spacetime on the fiber. As one can expect, the former effect is much larger than the latter as the fiber is easily deformed due to gravity and acceleration. Felix Spengler, Alessio Belenchia, Daniel Braun and I looked into such setup for the case of non-linear optical fibers which give rise to optical solitons, that is, light pulses that do not disperse [5]. In particular, we have derived a simplified set of field equations describing the solitons in a fiber in curved spacetime from Maxwell's equations and determined how velocity and shape of solitons are affected by gravity.
Quantum Liquids
Quantum Liquids
Analyzing the quantum properties of massive matter systems in quantum optical experiments in gravitational fields is also a very active and versatile field of research. In particular, cold atoms are used in matter wave optics for the measurement of gravitational acceleration [6] and spacetime curvature [7] with high precision. If many atoms are combined in a cloud and cooled to very low temperatures, they can form quantum liquids, like superfluid Helium or a Bose-Einstein condensate (BEC) with fascinating properties (more can be found here).
Tupac Bravo, Ivette Fuentes and I, investigated the effect of gravitational fields on the quasiparticles of sound in a BEC [8,9] which can be used, in principle, to infer parameters of the gravitational field. Details on sensing of weak gravitational effects with BECs can be found here.
Entanglement
Entanglement
An important element of quantum physics is the concept of entanglement, correlations between quantum systems that are much stronger than those that could be achieved in systems consistently described by classical physics. Due to this property, entanglement is famously used in tests of quantum mechanics. To understand the interplay of gravity and quantum mechanics, it is then interesting to study gravitational effects on entanglement. In particular, gravitational time dilation can lead to entanglement dynamics, where entanglement is swapped between different degrees of freedom of quantum systems [10,11] which can lead to detrimental effects in quantum optics experiments and quantum communication.
Roy Barzel, Mustafa Gündoğan, Markus Krutzik, Claus Lämmerzahl and I have investiged the effect of gravitational red shift in interferometry with entangled photons [12]. We have found that the effect may be witnessed by storing the photons in quantum memories at different potential levels in the Earth's gravitational field.
Gravitationally Interacting Quantum Systems
Gravitationally Interacting Quantum Systems
When precision of experiments is increased, at some point, also the gravitational field of quantum systems will become important. Besides practical experiments in the future, describing the gravitational field of quantum systems can be used for Gedankenexperiments and to obtain fundamental insights into the interface of the two theories general relativity and quantum mechanics.
Light and Particle Beams
Light and Particle Beams
General Relativity predicts that light gravitates and that the gravitational effect of ultra-relativistic massive particles such as the proton bunches in the Large Hadron Collider (LHC) at CERN on a non-relativistic accelerometer would be completely dominated by the particles' kinetic energy. More details about the gravitational field of these sources can be found here. The quantum properties of light can be well controlled in the lab, and therefore, light would serve as a versatile tool to study gravitational effects of quantum sources if the gravitational field of light would not be extremely weak even for the strongest light sources available. It is still interesting to investigate the gravitational interaction of light in quantum theory theoretically.
For example, Martin Wilkens, Ralf Menzel and I have analyzed the effect of polarization entanglement in gravitational photon-photon scattering [...] and found that it can enhance or increase the strength of the scattering depending on the symmetry of the state. This is an imprint of quantum interference in the scattering process that is however not unique for the gravitational interaction [13].
Chances are higher that the gravitational field of bunches of ultra-relativistic particle at the LHC can be detected with near future technology. If these particle beams could be brought into macroscopic quantum superposition states, for example, of their transverse position, they could be used to study the gravitational field of quantum source masses. A detailed discussion of this possibility is given in an article I wrote together with Felix Spengler and Daniel Braun [14].
Quantum Optomechanical Systems
Quantum Optomechanical Systems
The most realistic approach to study the gravitational interaction of quantum systems experimentally seems to employ mesoscopic massive objects in free fall [15,16] or as mechanical resonators [17,18].
Doug Plato, Chuanqi Wan and I studied the latter approach in our article [19] in the context of Quantum Optomechanical Sensors (QOMSs) (see details about this research field here). In particular, we have derived fundamental limitations to test the creation of entanglement between two gravitationally interacting QOMSs.
If this gravitationally mediated entanglement creation would be experimentally confirmed, some theories that postulate "classical" properties of gravity could be excluded, that is, one would obtain partial empirical evidence for the quantization of gravity. However, in realistic state-of-the-art experiments, mesoscopic masses are coupling by far too strongly to the environment which destroys the entanglement and many decades of engineering will be necessary to perform the proposed experiments successfully. From a fundamental perspective, it is still very interesting to investigate setups of gravitationally interacting massive quantum systems theoretically. For example, one can show that additionally assumptions about causality can be employed to make conclusions about the quantization of gravity [20,21].
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[2] Bravo T., Rätzel D., Fuentes I., "Gravitational time dilation in extended quantum systems: the case of light clocks in Schwarzschild spacetime" AVS Quantum Science 5 (1) (2023), 014401, doi.org/10.1116/5.0123228; Preprint: arxiv.org/abs/2204.07869
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[4] Zheng X. et al. "Differential clock comparisons with a multiplexed optical lattice clock" Nature 602, 425–430 (2022). https://doi.org/10.1038/s41586-021-04344-y
[5] Spengler F., Belenchia A., Rätzel D., Braun D., “Optical solitons in curved spacetime”, Preprint: arxiv.org/abs/2301.04986
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[8] Bravo T., Rätzel D., Fuentes I. "Phononic gravity gradiometry with Bose-Einstein condensates", Preprint: arxiv.org/abs/2001.10104
[9] 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
[10] Zych, M. et al. "General relativistic effects in quantum interference of photons" Classical and Quantum Gravity, 29(22), 224010 (2012), https://doi.org/10.1088/0264-9381/29/22/224010
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[12] Barzel R., Gündoğan M., Krutzik M., Rätzel D., Lämmerzahl C., “Gravitationally induced entanglement dynamics of photon pairs and quantum memories”, Preprint: arxiv.org/abs/2209.02099
[13] Rätzel D., Wilkens M., Menzel R. "The effect of entanglement in gravitational photon-photon scattering" EPL 115 (2016) 51002, doi.org/10.1209/0295-5075/115/51002; Preprint arxiv.org/abs/1511.01237
[14] 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
[15] Bose S., et al. "Spin entanglement witness for quantum gravity" PRL, 119(24), 240401 (2017) https://doi.org/10.1103/PhysRevLett.119.240401
[16] 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
[17] H. Miao, D. Martynov, H. Yang, and A. Datta, “Quantum correlations of light mediated by gravity” Phys. Rev. A, vol. 101, no. 6, p. 063804, Jun. 2020, doi/10.1103/PhysRevA.101.063804; Preprint: arxiv.org/abs/1901.05827
[18] A. Matsumura and K. Yamamoto, “Gravity-induced entanglement in optomechanical systems” Phys. Rev. D, vol. 102, no. 10, p. 106021, Nov. 2020, doi.org/10.1103/PhysRevD.102.106021; Preprint: arxiv.org/abs/2010.05161
[19] Plato A.D.K., Rätzel D., Wan C. “Enhanced Gravitational Entanglement in Modulated Optomechanics” Preprint: arxiv.org/abs/2209.12656
[20] Belenchia, A. et al. "Quantum superposition of massive objects and the quantization of gravity" Physical Review D, 98(12), 126009 (2018), https://doi.org/10.1103/PhysRevD.98.126009, Preprint: https://arxiv.org/abs/1807.07015
[21] Carney D. "Newton, entanglement, and the graviton" Physical Review D, 105(2), 024029 (2022) https://doi.org/10.1103/PhysRevD.105.024029, Preprint: https://arxiv.org/abs/2108.06320
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