Dennis Rätzel - Quantum Optomechanics

Quantum Optomechanics

Optomechanical systems consist of a mechanical element coupled to light. Implementations of optomechanical systems range from Fabry-Pérot cavities, superconducting microwave resonators and levitated atoms or nano-particles in cavities, to crystals [1]. Due to achievable high control of light, it is possible to manipulate and monitor the mechanical elements with very high precision and operate these composite systems in the quantum regime. In that case, one is talking of Quantum Optomechanical Systems (QOMSs).

The coupling of light and mechanical element is, in most cases, through radiation pressure and often enhanced by confining the light field by an optical resonator. The radiation pressure coupling term is proportional to the light intensity, leading to non-linear equations of motion. QOMSs with non-linear light-matter interaction in particular and non-linear quantum systems in general are promising for the development of exciting quantum technologies. For example, QOMSs are potential components for quantum communication networks as the non-classical states created due to non-linear light-matter couplings can be used for quantum information tasks such as obtaining quantum gates, teleportation, distillation of entanglement and error correction.

However, the non-linearity of the light-matter interaction makes the analysis of optomechanical systems highly complicated without further approximations. In two publications, collaborators and I have derived exact analytical solutions for the time evolution of QOMSs based on advanced algebraic methods neglecting environmental couplings [2,3]. We have taken the non-linearity of the system fully into account, allowed for general time-dependent modulations of the system parameters (e.g. mechanical frequency and light matter coupling strength) and analyzed the interplay of non-linearity and modulations. In two other publications [4,5], we have found that the system parameter modulations can significantly enhance the sensing abilities of quantum optomechanical systems, in particular, for gravitational accelerations.

Our fundamental bounds on force sensing also apply to searches for modifications of gravity on small scales. Such tests may provide limits to alternative cosmological models that attempt to explain dark energy as we have shown in an article with Sofia Qvarfort and Stephen Stopyra [6]. Furthermore, our results can be directly transferred to the general relativistic regime by means of the techniques and results presented in my articles on optical resonators in a curved spacetime [7] and tests of small-scale gravitational waves detectors [8].

The gravitational interaction of two QOMSs and the subsequent joint measurement of the cavity fields may also be used to test the ability of gravity to mediate entanglement [9,10]. A range of theories that postulate “classical” properties of gravity may be excluded based on such experiments. In [11], Doug Plato, Chuanqi Wan and I have shown that modulations of system parameters (parametric driving) can significantly enhance the entanglement generation which could be used to reduce the necessary coherence times to realistic values. We have also analyzed the effect of environmental noise on the mechanical element and found that this leads to a severe loss of entanglement which makes detection of gravitationally mediated entanglement with this setup in the near future generally unlikely.

[1] Aspelmeyer M., Kippenberg T. J. , Marquardt F. "Cavity optomechanics" Reviews of Modern Physics 86.4 (2014): 1391, doi.org/10.1103/RevModPhys.86.1391; Preprint: arxiv.org/abs/1303.0733

[2] Qvarfort S., Serafini A., Xuereb A., Rätzel D., Bruschi D.E. „Enhanced continuous generation of non-Gaussianity through optomechanical modulation”, New Journal of Physics 21 (5), 055004 (2019), doi.org/10.1088/1367-2630/ab1b9e; Preprint arxiv.org/abs/1812.08874

[3] Qvarfort S., Serafini A., Xuereb A., Braun D., Rätzel D., Bruschi D.E. “Time-evolution of nonlinear optomechanical systems: Interplay of mechanical squeezing and non-Gaussianity” Physical Review A 101 (3), 033834 (2020),doi.org/10.1088/1751-8121/ab64d5; Preprint arxiv.org/abs/1908.00790

[4] Schneiter F., Qvarfort S., Serafini A., Xuereb A., Braun D., Rätzel D., Bruschi D.E. “Optimal estimation with quantum optomechanical systems in the nonlinear regime” Journal of Physics A: Mathematical and Theoretical 53 (7), 075304 (2020), doi.org/10.1103/PhysRevA.101.033834; Preprint arxiv.org/abs/1910.04485

[5] 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

[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] Rätzel D., Schneiter F., Braun D., Bravo T., Howl R., Lock M.P.E., Fuentes I. "Frequency spectrum of an optical resonator in a curved spacetime" New J. Phys. 20 053046 (2018) doi.org/10.1088/1367-2630/aac0ac, Preprint arxiv.org/abs/1711.11320

[8] 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

[9] 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

[10] 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

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

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