Download AB poster4

Proposed experimental setup for testing
the electric Aharonov-Bohm effect
Günther Kassier1, Heinrich Schwoerer1, Justyna Fabianska2, and Thomas Feurer3
1Laser
Research Institute, Stellenbosch University, www.laser-research.co.za
2University of Bern,Sidlerstrasse 5, 3012 Bern, Switzerland
3Institute of Applied Physics, University of Bern, 3012 Bern, Switzerland
Introduction
Electric Aharonov Bohm (eAB) effect
In 1959, Aharonov and Bohm showed that electron waves experience a quantum phase shift
when exposed to electric/ magnetic potentials while being EXCLUDED from any
electromagnetic fields.1 → Aharonov-Bohm (AB) effects
1Aharonov,
Y. & Bohm, D. Phys. Rev. 115, 485–491 (1959).
1) Electron pulse coherently split and
directed through two metal tubes.
Voltage is off, no electric fields.
Electrostatic potential
3) Voltage switched off. Electron
interfere undisrupted by electric
fields, revealing eAB phase shift.
2) Voltage switched on. Coherently
split electron pulses are shielded
inside metal tubes. Phase shift only
due to eAB effect.
Magnetic vector potential
AB phase shift
Simple experiment in principle. However…
1) Electron wavelength typically very small (10 pm range)
2) Electron velocity high (107 m/s range)
No direct experimental evidence exists for electric AB
effect more than 50 years after its proposal!
eAB interference device needs to be small (µ
µm range) due to limitations in achievable coherence length. Voltage
and electron pulse timing with 1 ps accuracy required. Bringing all this together requires a CLEVER DESIGN!
Proposed Setup
eAB interference device
Pulsed electron source
Translation stage. Needed for setting temporal
overlap between THz pulse and electron pulse.
Compensates for temporal dispersion arising
from tuneable electron energy
Photo-field emitted
single electron pulse
train
800 nm oscillator
pulse train: ~100 fs,
1 nJ, 80 MHz
THz source. Consists of GaAs
THz antenna triggered by fs
laser. THz beam is focused to
mm size with spherical lens
and mirror. Possible to generate
10 µW avg power at 80 MHz,
resulting in peak THz fields of
order 103 V/m
fs oscillator. 80 MHz,
10 nJ, 100 fs
Field emission nanotip. Schottky barrier lowering by tip field strengths
in the GV/m range allow single photon triggering at 800 nm
Initial electron energy
spread = 1 eV
Nanotip emitter radius = 10 nm
1
,
,
≅
,
Photo-field emission gun
2∆
,
Tuneable voltage source
V = 1 kV ± 1%
~10
,
Transverse coherence length
> 1 µm for σx > 1 mm
e-beam, 107 e-/s
V
,
coherent e-beam, 104 e-/s
detector screen
electrostatic slit lens
Magnetic lens
2- ,
$
5-m
%
50
Fringe separation could be resolved
without microscope
~2 µm
Simulation assumptions:
1) Infinite width (1-dimensional wave
propagation
2) Perfectly conducting metal walls
3) Wave propagation in vacuum (no
dielectrics)
Tapered input to enhance coupling of
waveguide to THz pulse
-3
10 µm
Ein = 1 kV/m
⇒
-2
-1
The eAB effect would be proved if:
1) Interference fringe shift is in
0
accordance with
1 ) 2 $2
Waveguide is microstrip
transmission line
2 µm
' 10( )/
Proving the eAB effect
THz waveguide simulations
Isolating the eAB effect
!" ≅ 10
!
&
2!
vacuum chamber with magnetostatic and electromagnetic
shielding. Vacuum requirement < 10-8 mbar
1% electron energy bandwidth
allows the short longitudinal
coherence length of the
electrons. This is required to
exclude classical lag effects that
could obscure the eAB effect
≅
$
%
#
slit aperture
1 µm
Beam expansion to > 1 mm
within propagation distance
of a few cm possible
Interference fringes
eAB interference device
0
1
2
3
Electric field scale (a.u.)
Ein = 1 kV/m
2) No loss of interference
45
contrast for
3 ,
2
∆45
' 100
Summary and conclusion
If classical effects due to external
fields exist, there will be loss of
interference contrast for
sufficiently large observed phase
shift φ! Else not, since the AB effect
is dispersionless.
,
Δ
⇒
2
Δ
100 ⇒
Δ
2%
Dispersionless nature of eAB effect verifiable with a modest ±1%
relative energy bandwidth
This work is based upon research supported by the
South African Research Chair Initiative
of the Department of Science and Technology
and the National Research Foundation
Transverse electric field at waveguide
termination versus time. The peak electric field
of the input THz pulse (1 kV/m in this case) is
enhanced by an order of magnitude due to the
tapered input coupler structure. The pulse electric
field rises and completely decays in about 5 ps.
Transverse magnetic field at waveguide
termination versus time. The peak magnetic
field is relatively small as expected at a waveguide
termination. Inductive effects due to this field
result in negligible beam deflections.
Contact: [email protected]
A detailed experimental setup for proving
the electric Aharonov Bohm effect using
readily available technology has been
devised.
Approximate electromagnetic simulations
of the proposed eAB interference device
are very encouraging.