Trans-Planckian physics in Laboratory Black-Holes

Benni Reznik Tel Aviv University

Physics Colloquium, Saarland University, July 21, 2011.

Dark stars

John Mitchell, (1783). Pierre-Simon Laplace (1796)

is light affected by gravity?

Einstein’s theory of General Relativity

Riemannian structure of space time.

Karl Schwarzschild’s solution

Singularity “hidden” by a horizon

Eienstein:….singularities do not exist in reality… “cosmic censorship”

Black-hole classical physics

Black-hole classical physics

Black-hole entropy?

Black-hole Thermodynamics

Black-hole Thermodynamics

Hawking Effect- 1 (intuitive picture)

Hawking effect -2 (Hawking’s approach)

Hawking effect -3 (without a black hole!)

Hawking effect -3

Hawking effect -3

The “trans-Planckian” puzzle

! vacuum ¼ exp(t/4M)/M

For Mbh=Msun, THawking ¼ 10-7 K After t¼1 sec → ! vacuum¼ 10 1000

while ! P lanck =(c/~)(G~/c3)-1/2¼ 10 44

Unruh, t’Hooft, Susskind, Jacobson.

The problem is that a naïve cutoff will kill the Hawking effect.

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 ?!

Sonic fluid black-hole (“dumb-hole”)

Unruh, PRL 1981.

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!

But all models need to confront the short distance problem…

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:

Mode “conversion” process

Unruh, PRD 1996.

Time runs backwards!

Discrete sonic BH with trapped ions

B. Horstman, B. Reznik, S. Fagnocchi, J.I. Cirac, PRL (2010)

Ring Traps

Waki et al., Nature (1992) Microfabricated traps (Ulm)

Miniature toroidal mass spectrometers.

Propagation of phonon perturbations

Schematic depiction of the pulse propagation on an ion ring.

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).

Ion trap Sonic horizon

t

Incoming wave

Outgoing wave

Sonic Horizon

Commoving frame

Unruh’s mechanism

“ Bloch oscillation”

Lab. frame Fluid frame (note the moving horizon)

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

Correlations

With long range Interactions.

Nearest-neighbor interactions

Entanglement generation by the bh

Entropy of entanglement Time evolution of Negativity

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:

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!

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.

Thank you!

ISF