Optical simulations of gravitational effects in the Newton–Schrödinger system

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Abstract

Some predictions of Einstein’s theory of general relativity (GR) still elude observation, hence analogous systems, such as optical set-ups, have been suggested as platforms for emulating GR phenomena. GR is inherently nonlinear: for example, the curvature of space is induced by masses whose dynamics is also affected by the curved space they themselves induce. But, thus far all GR emulation experiments with optical systems have reproduced only linear dynamics. Here, we study gravitational effects with optical wavepackets under a long-range nonlocal thermal nonlinearity. This system is mathematically equivalent to the Newton–Schrödinger model proposed to describe the gravitational self-interaction of quantum wavepackets. We emulate gravitational phenomena by creating interactions between a wavepacket and the gravitational potential of a massive star, observing gravitational lensing, tidal forces and gravitational redshift and blueshift. These wavepackets interact in the curved space they themselves induce, exhibiting complex nonlinear dynamics arising from the interplay between diffraction, interference and the emulated gravitational effects.

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Figure 1: Experimental settings and results.
Figure 2: Simulations and experiments showing the trajectories of the beam accelerating away from the ‘star’ and the deformation of its structure, unravelling the effect of tidal forces.
Figure 3: Using the inhomogeneous geodesic equation to model the trajectories of the beam accelerating away from the ‘star’ and the tidal forces acting on it.
Figure 4: Experimental observations of redshift and blueshift.

References

  1. 1

    Einstein, A. Die Grundlage der allgemeinen Relativitätstheorie. Ann. Phys. 354, 769–822 (1916).

    Article  Google Scholar 

  2. 2

    Unruh, W. G. Experimental black-hole evaporation? Phys. Rev. Lett. 46, 1351–1353 (1981).

    ADS  Article  Google Scholar 

  3. 3

    Lahav, O. et al. Realization of a sonic black hole analog in a Bose–Einstein condensate. Phys. Rev. Lett. 105, 240401 (2010).

    ADS  Article  Google Scholar 

  4. 4

    Weinfurtner, S., Tedford, E. W., Penrice, M. C. J., Unruh, W. G. & Lawrence, G. A. Measurement of stimulated Hawking emission in an analogue system. Phys. Rev. Lett. 106, 021302 (2011).

    ADS  Article  Google Scholar 

  5. 5

    Leonhardt, U. & Piwnicki, P. Optics of nonuniformly moving media. Phys. Rev. A 60, 4301–4312 (1999).

    ADS  Article  Google Scholar 

  6. 6

    Leonhardt, U. & Piwnicki, P. Relativistic effects of light in moving media with extremely low group velocity. Phys. Rev. Lett. 84, 822–825 (2000).

    ADS  Article  Google Scholar 

  7. 7

    Smolyaninov, I. I. Surface plasmon toy model of a rotating black hole. New J. Phys. 5, 147 (2003).

    ADS  Article  Google Scholar 

  8. 8

    Philbin, T. G. et al. Fiber-optical analog of the event horizon. Science 319, 1367–1370 (2008).

    ADS  Article  Google Scholar 

  9. 9

    Narimanov, E. E. & Kildishev, A. V. Optical black hole: Broadband omnidirectional light absorber. Appl. Phys. Lett. 95, 041106 (2009).

    ADS  Article  Google Scholar 

  10. 10

    Genov, D. A., Zhang, S. & Zhang, X. Mimicking celestial mechanics in metamaterials. Nature Phys. 5, 687–692 (2009).

    ADS  Article  Google Scholar 

  11. 11

    Sheng, C., Liu, H., Wang, Y., Zhu, S. N. & Genov, D. A. Trapping light by mimicking gravitational lensing. Nature Photon. 7, 902–906 (2013).

    ADS  Article  Google Scholar 

  12. 12

    Batz, S. & Peschel, U. Linear and nonlinear optics in curved space. Phys. Rev. A 78, 043821 (2008).

    ADS  Article  Google Scholar 

  13. 13

    Schultheiss, V. H. et al. Optics in curved space. Phys. Rev. Lett. 105, 143901 (2010).

    ADS  Article  Google Scholar 

  14. 14

    Bekenstein, R., Nemirovsky, J., Kaminer, I. & Segev, M. Shape-preserving accelerating electromagnetic wave packets in curved space. Phys. Rev. X 4, 011038 (2014).

    Google Scholar 

  15. 15

    Gorbach, A. V. & Skryabin, D. V. Light trapping in gravity-like potentials and expansion of supercontinuum spectra in photonic-crystal fibres. Nature Photon. 1, 653–657 (2007).

    ADS  Article  Google Scholar 

  16. 16

    Batz, S. & Peschel, U. Solitons in curved space of constant curvature. Phys. Rev. A 81, 053806 (2010).

    ADS  Article  Google Scholar 

  17. 17

    Smolyaninov, I. I. Analog of gravitational force in hyperbolic metamaterials. Phys. Rev. A 88, 033843 (2013).

    ADS  Article  Google Scholar 

  18. 18

    Engheta, N. & Ziolkowski, R. W. Metamaterials: Physics and Engineering Explorations (John Wiley, 2006).

    Google Scholar 

  19. 19

    Shalaev, V. M. Optical negative-index metamaterials. Nature Photon. 1, 41–48 (2007).

    ADS  Article  Google Scholar 

  20. 20

    Weinberg, S. Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (John Wiley, 1972).

    Google Scholar 

  21. 21

    Jacobson, T. Thermodynamics of spacetime: The Einstein equation of state. Phys. Rev. Lett. 75, 1260–1263 (1995).

    ADS  MathSciNet  Article  Google Scholar 

  22. 22

    Zee, A. Einstein Gravity in a Nutshell (Princeton Univ. Press, 2013).

    Google Scholar 

  23. 23

    Dabby, F. W. & Whinnery, J. R. Thermal self focusing of lasers beams in lead glasses. Appl. Phys. Lett. 13, 284–286 (1968).

    ADS  Article  Google Scholar 

  24. 24

    Rotschild, C., Cohen, O., Manela, O., Segev, M. & Carmon, T. Solitons in nonlinear media with an infinite range of nonlocality: First observation of coherent elliptic solitons and of vortex-ring solitons. Phys. Rev. Lett. 95, 213904 (2005).

    ADS  Article  Google Scholar 

  25. 25

    Rotschild, C., Alfassi, B., Cohen, O. & Segev, M. Long-range interactions between optical solitons. Nature Phys. 2, 769–774 (2006).

    ADS  Article  Google Scholar 

  26. 26

    Pertsch, T., Dannberg, P., Elflein, W., Bräuer, A. & Lederer, F. Optical Bloch oscillations in temperature tuned waveguide arrays. Phys. Rev. Lett. 83, 4752–4755 (1999).

    ADS  Article  Google Scholar 

  27. 27

    Schwartz, T., Bartal, G., Fishman, S. & Segev, M. Transport and Anderson localization in disordered two-dimensional photonic lattices. Nature 446, 52–55 (2007).

    ADS  Article  Google Scholar 

  28. 28

    Lahini, Y. et al. Anderson localization and nonlinearity in one-dimensional disordered photonic lattices. Phys. Rev. Lett. 100, 013906 (2008).

    ADS  Article  Google Scholar 

  29. 29

    Plotnik, Y. et al. Experimental observation of optical bound states in the continuum. Phys. Rev. Lett. 107, 183901 (2011).

    ADS  Article  Google Scholar 

  30. 30

    Rechtsman, M. C. et al. Photonic Floquet topological insulators. Nature 496, 196–200 (2013).

    ADS  Article  Google Scholar 

  31. 31

    Penrose, R. On gravity’s role in quantum state reduction. Gen. Relativ. Gravit. 28, 581–600 (1996).

    ADS  MathSciNet  Article  Google Scholar 

  32. 32

    Moroz, I. M., Penrose, R. & Tod, P. Spherically-symmetric solutions of the Schrödinger–Newton equations. Class. Quantum Gravity 15, 2733–2742 (1998).

    ADS  Article  Google Scholar 

  33. 33

    Tod, P. & Moroz, I. M. An analytical approach to the Schrödinger–Newton equations. Nonlinearity 12, 201–216 (1999).

    ADS  MathSciNet  Article  Google Scholar 

  34. 34

    Page, D. N. Classical and quantum decay of oscillations: Oscillating self-gravitating real scalar field solitons. Phys. Rev. D 70, 023002 (2004).

    ADS  Article  Google Scholar 

  35. 35

    Guzmán, F. S. & Ureña-López, L. A. Evolution of the Schrödinger–Newton system for a self-gravitating scalar field. Phys. Rev. D 69, 124033 (2004).

    ADS  Article  Google Scholar 

  36. 36

    Diósi, L. Notes on certain Newton gravity mechanisms of wavefunction localization and decoherence. J. Phys. A 40, 2989–2995 (2007).

    ADS  MathSciNet  Article  Google Scholar 

  37. 37

    Giulini, D. & Großardt, A. Centre-of-mass motion in multi-particle Schrödinger–Newton dynamics. New J. Phys. 16, 075005 (2014).

    ADS  MathSciNet  Article  Google Scholar 

  38. 38

    Bahrami, M., Großardt, A., Donadi, S. & Bassi, A. The Schrödinger–Newton equation and its foundations. New J. Phys. 16, 115007 (2014).

    ADS  MathSciNet  Article  Google Scholar 

  39. 39

    Diósi, L. Gravitation and quantum-mechanical localization of macro-objects. Phys. Lett. A 105, 199–202 (1984).

    ADS  Article  Google Scholar 

  40. 40

    Einstein, A. Time, space, and gravitation. Science 51, 8–10 (1920).

    ADS  Article  Google Scholar 

  41. 41

    Carlip, S. Is quantum gravity necessary? Class. Quantum Gravity 25, 154010 (2008).

    ADS  MathSciNet  Article  Google Scholar 

  42. 42

    Berry, M. V. & Balazs, N. L. Nonspreading wave packets. Am. J. Phys. 47, 264–267 (1979).

    ADS  Article  Google Scholar 

  43. 43

    Siviloglou, G. A. & Christodoulides, D. N. Accelerating finite energy Airy beams. Opt. Lett. 32, 979–981 (2007).

    ADS  Article  Google Scholar 

  44. 44

    Siviloglou, G. A., Broky, J., Dogariu, A. & Christodoulides, D. N. Observation of accelerating Airy beams. Phys. Rev. Lett. 99, 213901 (2007).

    ADS  Article  Google Scholar 

  45. 45

    Baumgartl, J., Mazilu, M. & Dholakia, K. Optically mediated particle clearing using Airy wavepackets. Nature Photon. 2, 675–678 (2008).

    ADS  Article  Google Scholar 

  46. 46

    Polynkin, P., Kolesik, M., Moloney, J. V., Siviloglou, G. A. & Christodoulides, D. N. Curved plasma channel generation using ultraintense airy beams. Science 324, 229–232 (2009).

    ADS  Article  Google Scholar 

  47. 47

    Schley, R. et al. Loss-proof self-accelerating beams and their use in non-paraxial manipulation of particles’ trajectories. Nature Commun. 5, 5189 (2014).

    Article  Google Scholar 

  48. 48

    Kaminer, I., Nemirovsky, J., Rechtsman, M., Bekenstein, R. & Segev, M. Self-accelerating Dirac particles and prolonging the lifetime of relativistic fermions. Nature Phys. 11, 261–267 (2015).

    ADS  Article  Google Scholar 

  49. 49

    Bekenstein, R. & Segev, M. Self-accelerating optical beams in highly nonlocal nonlinear media. Opt. Express 19, 23706 (2011).

    ADS  Article  Google Scholar 

  50. 50

    Alfassi, B., Rotschild, C., Manela, O., Segev, M. & Christodoulides, D. N. Boundary force effects exerted on solitons in highly nonlinear media. Opt. Lett. 32, 154–156 (2007).

    ADS  Article  Google Scholar 

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Acknowledgements

We thank A. Ori for valuable discussions that considerably contributed to our work, and A. Arie and I. Dolev for letting us use their phase masks for generating the accelerating beams. R. Bekenstein gratefully acknowledges the support of the Adams Fellowship Program of the Israel Academy of Sciences and Humanities, and a fellowship from the Israel Ministry of Science and Technology. This research was also supported by the ICore Excellence centre ‘Circle of Light’ and the Binational USA-Israel Science Foundation BSF.

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Correspondence to Rivka Bekenstein.

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Bekenstein, R., Schley, R., Mutzafi, M. et al. Optical simulations of gravitational effects in the Newton–Schrödinger system. Nature Phys 11, 872–878 (2015). https://doi.org/10.1038/nphys3451

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