Optical analogues of the event horizon. Title. Friedrich König. New Frontiers in Physics

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1 Optical analogues of the event horizon Title Friedrich König New Frontiers in Physics 2014

2 St Andrews

3 Quantum effects in astrophysics?

4 Hawking radiation of black holes

5 Black holes and event horizons Nation et al., Rev. Mod. Phys. 84, (2012)

6 Hawking radiation: connections S. M. Hawking, Nature 248, 30 (1974) The Hawking effect connects the physics of everyday, the physics of the very large, and the very small!

7 Hawking radiation: problems

8 Contents Introduction to event horizons in analog systems Analogue horizons with water and light Waves encountering event horizons Generation of negative frequency waves in optics Summary and Outlook

9 Artificial event horizons: the black hole W. Unruh Illustration: Scientific American W. G. Unruh, Phys. Rev. Lett. 46, 1351 (1981) W. Schleich, M. Scully, Les Houches 1982, (1984)

10 Horizons in moving media Illustration: Peter Hoey, Science 319, 1321 (2008) Th. Philbin et al., Science 319, 1367 (2008)

11 Hydraulic jump Photo: Piotr Pieranski

12 Artificial event horizons in superfluid Helium-3 and Bose Einstein Condensates

13 Waves and Barriers Flow velocity: v -v D 1 > v 0 0 -v d v 0 B = 0 W. G. Unruh, Phys. Rev. Lett. 46, 1351 (1981) W. Schleich, M. Scully, Les Houches 1982, (1984) Wave velocity against flow (v 1 > c > v 0 ): -v 0 +c > 0 -v 1 +c < 0 v B = 0 -v 0 +c > 0 subluminal white hole horizon WH black hole horizon BH superluminal subluminal

14 Water waves Germain Rousseaux Rousseaux, G; Mathis, C; Maissa, P, et al. NEW JOURNAL OF PHYSICS 10, (2008)

15 Waves and Barriers Wave velocity in moving frame of water : c v 0 -v 1 +c < 0 v B = v 0 c white hole horizon WH black hole horizon BH Velocity profile: c 0 v 0 -v 1 +c<0 WH BH

16 Optical horizons in media at rest? Wave velocity in moving frame: optical pulse in Kerr medium v<v 0 v>v 0 v>v 0 v B = v 0 Velocity profile: WH BH v>v 0 0 v<v 0 Subluminal Superluminal Subluminal WH A pulse moves at velocity v 0 and locally modifies the refractive index (i.e. wave velocity) by the cross-kerr effect. BH

17 Optical event horizons Optical fibers Filamentation Philbin et. al. Science 319, 5868 (2008) Laval nozzle Belgiorno et al., PRL 105, (2010). Elazar et al. Phys. Rev. A 86, (2012)

18 Trapped pulse SF wavelength (a.u.) Conditions: Stationarity Stationarity: Soliton pulses in a 1-D fiber waveguide Filaments: F. Belgiorno et al., PRL 105, (2010). Negligible backaction: weak probe wave Nonstationary: Pulse trapping: N. Nishizawa et al., Opt. Lett. 27, 152 (2002) A. V. Gorbach et al., Nature Photonics 1, 653 (2007) S. Hill et al., Opt. Express 17, (2009) Trapped pulse: XFROG traces

19 Soliton formation Soliton Formation "runners«wave packet" * ultrashort pulses in optical fibers t 1 dispersion t 2 t 3 "soft mat" + nonlinearity Kerr-effekt z t 1 t 2 t 3 n = n(i) ( * Mollenauer) soliton z

20 Soliton formation Soliton Formation "runners«wave packet" * ultrashort pulses in optical fibers t 1 dispersion t 2 t 3 "soft mat" + nonlinearity Kerr-effekt z t 1 t 2 t 3 n = n(i) ( * Mollenauer) soliton z

21 Soliton formation Soliton Formation "runners«wave packet" * ultrashort pulses in optical fibers t 1 dispersion t 2 t 3 "soft mat" + nonlinearity Kerr-effekt z t 1 t 2 t 3 n = n(i) ( * Mollenauer) soliton z

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24 Horizons in moving media: trajectories Soliton WH

25 Horizons in moving media: trajectories

26 Blue shifting at the white hole Th. Philbin, Ch. Kuklewicz, S. Robertson, S. Hill, F. König, U. Leonhardt Science 319, 5868, pp (2008) As part of supercontinuum: A. Efimov et al., Phys. Rev. Lett., 95,213902, (2005)

27 Conversion efficiency [10-6 ] Optical horizon physics Characteristic and efficient mode conversion can be observed Th. Philbin et al., Science 319, 1367 (2008) Fast waves can tunnel through the horizon Choudhary and Koenig, Opt. Expr. 20, 5538 (2012) Reflectvity R Frequency shift [THz] Light can be trapped and released behind horizons S. Hill et al., Opt. Express 17, (2009) Generation of waves with negative frequency E. Rubino et al., PRL 108, (2012) Generation of waves with negative frequency

28 Horizons and modes in the dispersion relation Transformation to the frame moving with the pulse: w IN w OUT k Res. radiation Negative res. radiation Input pulse k Relative wave vector: Moving frame frequency: Conservation of momentum in the lab frame Conservation of energy in the moving frame

29 Excitation of the RR mode in fibers RR Resonant radiation from solitons: Wai et. al. Optics Lett. 11, 464 (1986) Karpman, PRE, 47, 2073, (1993) Akhmediev and Karlsson, PRA, 51, 3 (1995) Tartara et. al. Appl. Phys. B, 77, 307 (2003) Skryabin et. al., Science, 301, 1705 (2003) Chang et al., Opt. Express 19, 6635 (2011) Degiorgio et. al., Opt. Expr. 12, 124 (2004)

30 Negative frequency? Negative frequencies are redundant!? Image: APS/Alan Stonebraker Hermitian annihilation / creation amplitudes

31 Negative frequency waves Time Time Space Space Soliton S. Weinfurtner et al., PRL (2011) Rousseaux, G., et al. New J. Phys. 10, (2008)

32 Experiments in fibers NRR RR E. Rubino et al., PRL 108, (2012)

33 NRR spectra L=2mm L=6mm L=10mm L=14mm J. McLenaghan and F. Koenig New J. Phys (2014)

34 NRR spectra ~2dB/mm J. McLenaghan and F. Koenig New J. Phys (2014)

35 Conclusion Optical pulses in fibers form analogue black and white hole horizons Characteristic and efficient mode conversion can be observed Negative frequencies are physical because we can couple positive and negative frequency modes to generate new waves Conversion between negative and positive frequencies leads to photon creation/ amplification First steps towards astrophysical particle creation in optical analogues

36 Applications of trapping and optical horizons Frequency conversion classical and quantum Frequency conjugation Dispersion management Ultrafast optical delay lines

37 Outlook: Mixing of amplitudes creates photon pairs, even from the quantum vacuum state. In astrophysics, the particle creation by mixing of positive and negative frequencies occurs: At the event horizon of black holes: Hawking effect (Hawking, Nature 248, 30 (1974)) In accelerated systems: Unruh effect (Unruh, Phys. Rev. D 14, 870 (1976)) Novel parametric amplifier Black hole Laser (S. Corley and T. Jacobson, PRD, 59:124011, 1999)

38 The horizon team Joseph Cousins University of St Andrews FK Joanna McLenaghan Maxime Jacquet Collaborators: Shalva Amiranashvili, Eleonora Rubino Francesco Belgiorno David Townsend Daniele Faccio Natalia Korolkova Niall Quinn Ulf Leonhardt WIAS Berlin Heriot-Watt, Edinburgh St. Andrews Weizmann Institute Former members: Susanne Kehr Tom Philbin Christopher Kuklewicz Steve Hill Amol Choudhary Scott Robertson Sven Rohr

39 Thank you! PhD projects available: