Trans-Planckian physics in Laboratory Black-Holes

Transcription

1 Trans-Planckian physics in Laboratory Black-Holes Benni Reznik Tel Aviv University Physics Colloquium, Saarland University, July 21, 2011.

2 Dark stars John Mitchell, (1783). Pierre-Simon Laplace (1796) is light affected by gravity?

3 Einstein s theory of General Relativity Riemannian structure of space time.

4 Karl Schwarzschild s solution

5 Singularity hidden by a horizon Eienstein:.singularities do not exist in reality cosmic censorship

6 Black-hole classical physics

7 Black-hole classical physics

8 Black-hole entropy?

9 Black-hole Thermodynamics

10 Black-hole Thermodynamics

11 Hawking Effect- 1 (intuitive picture)

12 Hawking effect -2 (Hawking s approach)

13 Hawking effect -3 (without a black hole!)

14 Hawking effect -3

15 Hawking effect -3

16 The trans-planckian puzzle! vacuum ¼ exp(t/4m)/m For M bh =M sun, T Hawking ¼ 10-7 K After t¼1 sec! vacuum ¼ while! Planck =(c/~)(g~/c 3 ) -1/2 ¼ The problem is that a naïve cutoff will kill the Hawking effect. Unruh, t Hooft, Susskind, Jacobson.

17 We need some sort of a non-trivial dynamical cutoff that involves new physics at the Planck scale! Clues from Laboratory analog systems?? Can we simulate and detect the Hawking radiation?!

18 Sonic fluid black-hole ( dumb-hole ) Unruh, PRL 1981.

19 1D Black holes Black hole Schwarzschild geometry. Seen by freely falling observer. Painleve -Gullstrand coordinates The observer crosses smoothly the horizon. Curved geometry describes a fluid with a changing velocity!

20 But all models need to confront the short distance problem

21 Cutoff in the fluid wavelength s of inter-ion scales are excluded. But short distance physics is here well known. Can be described by modified dispersion relation:

22 Mode conversion process Time runs backwards! Unruh, PRD 1996.

23 Discrete sonic BH with trapped ions B. Horstman, B. Reznik, S. Fagnocchi, J.I. Cirac, PRL (2010)

24 Ring Traps Waki et al., Nature (1992) Microfabricated traps (Ulm) Miniature toroidal mass spectrometers.

25 Propagation of phonon perturbations Schematic depiction of the pulse propagation on an ion ring.

26 Discrete sonic BH with trapped ions Phononic group velocity c(k) in the flat subsonic region as a function of k for full Coulomb interactions (blue dashed line) and nearest-neighbor interactions only (green straight line).

27 Ion trap Sonic horizon t Outgoing wave Sonic Horizon Incoming wave

28 Commoving frame Unruh s mechanism Bloch oscillation Lab. frame Fluid frame (note the moving horizon)

29 Measurement of Hawking radiation: correlations In-out EPR pairs are generated at the horizon, in laboratory black holes they can be in principle observable! Ballbinot et. al. (2008). Fast pairs inside bh HR

30 Correlations Nearest-neighbor interactions With long range Interactions.

31 Entanglement generation by the bh Entropy of entanglement Time evolution of Negativity

32 Experimental realization The emerging entanglement can be measured on two routes: measuring the covariance matrix through a measurement of correlation in the ion displacements Or by swapping the entanglement from the motional to the internal degrees of freedom of the ions: Retzker, J. I. Cirac, B. Reznik, PRL (2005). The basic mechanism in all proposals involves the coupling of the ion displacements to their internal levels with lasers:

33 Experimental parameters If the initial temperature is two orders of magnitude higher then Hawking temperature, cross correlations remain present and ground State cooling is not required!

34 Discussion There is a curious similarity between law and high energy physics structure that might be helpful when studying high energy effects within the laboratory low energy atomic models. Ideas from law energy physics systems might help to shed new light on problems in other fields. The Hawking or other gravity effects are possibly measurable/testable within the framework laboratory toy models.

35 Thank you! ISF