Condition

1
Ellipsometry noise spectrum, suspension transfer
function measurement and closed-loop control of
the suspension system in the Q A experiment
Sheng-Jui Chen, Hsien-Hao Mei and Wei-Tou Ni
Alignment error signal spectrum

• Abstract

The Q A experiment, aiming at the detection of
vacuum birefringence predicted by quantum
electrodynamics, mainly consists of a suspended
3.5 m Fabry-Perot cavity, a rotating permanent
dipole magnet and an ellipsometer. The 2.3 T
magnet can rotate up to 10 rev-per-sec,
introducing an ellipticity signal at twice the
rotation frequency. The X-pendulum gives a good
isolation ratio for seismic noise above its main
resonant frequency, in our case 0.3 Hz. At
present, the ellipsometry noise decreases with
frequency, from 1?10-5 radHz-1/2 at 5 Hz, 2?10-6
radHz-1/2 at 20 Hz to 5?10-7 radHz-1/2 at 40
Hz. The shape of noise spectrum indicates
possible improvement when the movement between
the cavity mirrors is further reduced. From the
preliminary result of yaw motion alignment
control, it can be seen that some peaks due to
yaw motion of the cavity mirror was suppressed.
In this paper, we first give a schematic view of
the Q A experiment, and then present the
measurement of transfer function of the compound
X-pendulum-double pendulum suspension. A
closed-loop control was carried out to verify the
validity of the measured transfer function. The
ellipsometry noise spectra with and without yaw
alignment control and the newest improvement will
be presented.
Control parameters need to be optimized
A closed-loop control was carried out to verify
the validity of measured transfer functions

• Preliminary results

Open-loop
Closed-loop
The noise floor for ellipticity detection
decreases with frequency and reached 3?10-7
rad?Hz-0.5 at 75 Hz. The noise floor seems to
have a good correlation with the cavity mirrors
motion which can be seen more clearly in
measurements in which alignment control was
turned on. Some peaks were suppressed and noise
floor below 15 Hz was lowered. But for noise
above 15 Hz, the noise floor is higher than that
without alignment control. That is probably due
to the spurious alignment error signal coming
from common beam spot motion and higher-order
Gaussian mode.

• Vacuum Birefringence

4.05 µm ? 0.23 µm
Predicted by QED, vacuum is birefringent under
the influence of a strong magnetic field, for
B2.5 T
Sensitivity curve of ellipticity detection
(Alignment off)
Condition Air Pressure 1 atm Relative angle
between B and E 90 deg
15.48 µrad ? 4.4 µrad
And induced ellipticity
The noise density decreases with frequency

• Feedback control

6?10-6 rad?Hz-0.5
We use Pound-Drever-Hall technique for
longitudinal control, a 2-loop control including
laser frequency control and cavity length
control, and differential wave-front sensing
technique for alignment control
2?10-6 rad?Hz-0.5
5?10-7 rad?Hz-0.5
3?10-7 rad?Hz-0.5
Detection band

• Experiment setup

To be added, not yet implemented
Effect of alignment control
After passing through the optics necessary for
Pound-Drever-Hall error signal extraction, the
light is polarized by a high extinction-ratio
polarizer and sent into the Fabry-Perot cavity
with a 2.3 T rotating magnetic field in its
resonant path. After coming out from the CM2,
the polarization of the light becomes
elliptically polarized. Before analyzed by
another high extinction-ratio polarizer, this
ellipticity is transformed into polarization
rotation and modulated by a Faraday cell for
lock-in detection.
This result is limited by the laser frequency
noise

• Transfer function measurement of the double
  pendulum

Alignment off
In Q A experiment, the cavity mirrors are
suspended by the X-pendulum and a double pendulum
for seismic noise isolation. The X-pendulum,
designed and developed by TAMA laser-interferometr
ic gravitational wave detection team, has a
fundamental resonant frequency of 0.3 Hz in our
experiment and provides a good isolation ratio in
our detection band, 1020 Hz. The double
pendulum is used for active control of cavity
length, mainly for compensating the large
resonant displacement of the X-pendulum. For
this purpose, we measured the transfer functions
of double pendulum in two degrees of freedom
Preliminary result of alignment control

• Future works

• Add alignment-control to rest degrees of freedom
• ?Maintaining FP cavity at its optimum working
  point
• Stabilize laser frequency to an external fixed
  cavity (L17 cm, measured finesse45000)
• ?A better frequency standard for cavity length
  below 220 Hz
• Add a fiber as a simple mode cleaner
• ?Reducing alignment signal from higher-order
  Gaussian mode
• Goal sensitivity 5?10-8 rad?Hz-0.5 at 10Hz 20 Hz