Transcript 21 April 2004 - Physics and Astronomy

SUPERLUMINALITY:
Breaking the Universal Speed Limit
Quantum Optics
Brian Winey
Department of Physics and Astronomy
University of Rochester
21 April 2004
1
SUPERLUMINALITY
Quantum Optics
Department of Physics and Astronomy, University of Rochester

People


Advisor: John Howell
Authors of several papers
21 April 2004
2
SUPERLUMINALITY
Quantum Optics
Department of Physics and Astronomy, University of Rochester

Overview





Review of Pulse Propagation
Pulse Propagation in Dispersive Media
Description of Fast Light
Experimental Demonstrations
Information Theory and Special Relativity
21 April 2004
3
SUPERLUMINALITY
4
Quantum Optics
Department of Physics and Astronomy, University of Rochester
Plane Waves:
Phase
E( z , t )  Ae
i ( kz t )
 c. c
  kz  t
t
Phase Velocity
z  c
vp 
 
t k n
21 April 2004
E
z
SUPERLUMINALITY
5
Quantum Optics
Department of Physics and Astronomy, University of Rochester
A “Bunch” of plane waves
Pulse
E
t
E
z
Group Velocity

c
c
vg 


k   
ng
dn 
n   d 
 
21 April 2004
z
SUPERLUMINALITY
6
Quantum Optics
Department of Physics and Astronomy, University of Rochester
Possible Group Velocities
Since
with
c
vg 
ng
dn 

ng  n  


d
  

ng  1  vg  c
Slow Light
ng  1  vg  c or vg  0
21 April 2004
Fast Light
Boyd et. al.
Wang et.al.
Gauthier et.al.
SUPERLUMINALITY
Quantum Optics
Department of Physics and Astronomy, University of Rochester

Some questions:



21 April 2004
What is the physical meaning of fast light?
What is the physical meaning of a negative group
velocity?
What would fast light look like?
7
SUPERLUMINALITY
Quantum Optics
Department of Physics and Astronomy, University of Rochester
A guess by Gauthier and Stenner:
But, electromagnetic wave propagation in media is a complicated topic…
21 April 2004
8
SUPERLUMINALITY
Quantum Optics
Department of Physics and Astronomy, University of Rochester

How would one produce fast light pulses?
Super Duper
Superluminal Pulse
Machine
TURBO
21 April 2004
9
SUPERLUMINALITY
10
Quantum Optics
Department of Physics and Astronomy, University of Rochester

Regions of Anomalous Dispersion Between Two Gain
Peaks

Anomalous Dispersion: when n   0



Index of Refraction (n)
Re  ( )
n  1
2
Susceptibility

N e2 
1
 ( ) 
 0    t  i 2 
For two gain peaks:
N e2 
1
1
 ( ) 


 0    t1  i 2   t2  i
21 April 2004


2 
But there’s the
imaginary part of
the story…
SUPERLUMINALITY
Quantum Optics
Department of Physics and Astronomy, University of Rochester

Absorption Coefficient of Media is determined by Im χ


4
Im  ( )
c
Im χ and Re χ are related by the Kramers-Kronig Thm.
 Im  ( )
Re  ( )  P 
d
2
2
0

 
  Re  ( )
2
Im  ( )  
P
d
2
2
0  

2
21 April 2004

11
SUPERLUMINALITY
Quantum Optics
Department of Physics and Astronomy, University of Rochester

Due to the relationship of Im χ and Re χ, in regions of
anomalous dispersion there is optical gain instead of
absorption.
n   0   (Re  ( ))   0
 (Re  ( ))   0   (Im  ( ))   0, by K - K Thm
 (Im  ( ))   0   ( )  0
 ( )  0  Gain instead of absorption

But the situation is slightly more complicated: we want
two gain peaks.
21 April 2004
12
SUPERLUMINALITY
Quantum Optics
Department of Physics and Astronomy, University of Rochester

How does one “find” two gain peaks?
Gain Peak 1
Gain Peak 2
“As we round the corner, the famous
Swiss Gain Peaks will come into view.”
21 April 2004
13
SUPERLUMINALITY
14
Quantum Optics
Department of Physics and Astronomy, University of Rochester

Achieve a gain doublet using stimulated Raman
scattering with a bichromatic pump field
Classifieds:
SRP: Lonely probe field photon seeks
excited atoms willing to return to their
ground states. Prefers photon of same
frequency.
Wang et. al.
21 April 2004
SUPERLUMINALITY
Quantum Optics
Department of Physics and Astronomy, University of Rochester

Scanning the probe
field reveals the gain
experienced when
resonant with the two
pump fields
Wang et. al.
21 April 2004
15
SUPERLUMINALITY
Quantum Optics
Department of Physics and Astronomy, University of Rochester

A look at an experimental realization of a gain
doublet
Wang et. al.
21 April 2004
16
SUPERLUMINALITY
Quantum Optics
Department of Physics and Astronomy, University of Rochester

Results of Wang et.al.
21 April 2004
17
SUPERLUMINALITY
18
Quantum Optics
Department of Physics and Astronomy, University of Rochester

Why do we want two gain peaks?

Between the two turning points, there is a nearly constant region
of anomalous dispersion.

Having two
peaks also
increases the
frequency width
of our region of
interest.
Wang et. al.
21 April 2004
SUPERLUMINALITY
Quantum Optics
Department of Physics and Astronomy, University of Rochester

Information Theory and Special Relativity




L. Brillouin, Wave Propagation and Group Velocity
(Academic Press, New York, 1960).
R.W. Boyd and D. Gauthier, Progress in Optics 43,
ed. by E. Wolf (Elsevier,Amsterdam, 2002), Chap. 6.
L.J. Wang, A. Kuzmich and A. Dogariu, Nature
(London) 406, 277 (2000).
M. Stenner, D. Gauthier, and M. Neifeld, Nature
(London) 425, 695 (2003).
21 April 2004
19
SUPERLUMINALITY
Quantum Optics
Department of Physics and Astronomy, University of Rochester

Starting Point: What is information and how
fast can it travel?




Information: a non-analytical point of an
electromagnetic wave, Stenner et. al. and others.
Special Relativity: No wave can travel faster than c.
But, as shown, a pulse group velocity can exceed c.
Can a non-analytical point travel faster than c?
21 April 2004
20
SUPERLUMINALITY
Quantum Optics
Department of Physics and Astronomy, University of Rochester

21
Brillouin
Early Predictions:




Sommerfeld and Brillouin (1960) said that
speed of electron interactions govern the speed
of a wave front, a non-analytical point, such as
a square wave front.
Electrons can not interact faster than c.
Therefore, the wave front cannot travel faster
than c.
“Proved” through a long saddle point integration
method, that the wave front suffers extreme
distortion. Thus, loss of information.
21 April 2004
Sommerfeld
SUPERLUMINALITY
Quantum Optics
Department of Physics and Astronomy, University of Rochester

Garrett et al. (1970) proposed using Gausian
wave packets, instead of Brillouin and
Sommerfeld’s square waves.


Showed little distortion of wave front in regions of
anomalous dispersion
Failed to deal with the trouble of information
transfer
21 April 2004
22
SUPERLUMINALITY
Quantum Optics
Department of Physics and Astronomy, University of Rochester

Recently:



Stenner et.al., Wang et.al., and Chiao et.al. have all
tried to deal with information transfer and
superluminal signaling.
Use Non-analytical “signal” point
Optical response time of “signal” machine (EOM,etc)
21 April 2004
23
SUPERLUMINALITY
24
Quantum Optics
Department of Physics and Astronomy, University of Rochester

Results of Information Study by Stenner et.al.
Signal Propagation
Bit-Error-Rate (BER)
Stenner et.al.
21 April 2004
SUPERLUMINALITY
Quantum Optics
Department of Physics and Astronomy, University of Rochester

General consensus: quantum noise added to
the signal during pulse propagation saves our
dear friend causality.
Superluminality
But is this the end of the game….?
Garrison et.al.
21 April 2004
25
SUPERLUMINALITY
Quantum Optics
Department of Physics and Astronomy, University of Rochester

Conclusions:


Light Pulses have been shown to travel faster than
c in regions of anomalous dispersion
Causality is preserved in fast light experiments by
the introduction of quantum noise fluctuations in
photon number.
21 April 2004
26
SUPERLUMINALITY
27
Quantum Optics
Department of Physics and Astronomy, University of Rochester

Future Questions



Is there a limit to the speed of fast light? Singularity?
Are there better definitions of information that could
allow for superluminal signal propagation and low
BER?
Quantum noise seems like a weak solution to causal
paradoxes.
21 April 2004
SUPERLUMINALITY
Quantum Optics
Department of Physics and Astronomy, University of Rochester

Questions?
21 April 2004
28