Physics of quantum systems and the development of matter-wave quantum technology is at the peak of modern research.
In the Bose-Einstein Condensate (BEC) lab at the
Weizmann Institute of Science, rubidium atoms are brought to the
Bose-Einstein condensate (
) state.
This state predicted by Satyendra N. Bose and Albert
Einstein in the 1920 ’s enables the study of phenomena that occur at a very small scale.
To reach this new state, the atoms are brought to a very cold temperature of 170 nano Kelvin.
Cooling the atoms is achieved by pointing a very accurate
LASER from beam from all six directions to the center.
Hot atoms are moving, thus having their absorption line frequency shifted by the Doppler effect. This shift makes the hot atoms move in the opposite direction –resulting in them stopping – hence cooling.
The aim of the project is a feasibility test for using the
FxLMS algorithm as a control algorithm of the LASER output frequency.
Since surrounding noises cause vibrations of the LASER mechanical structure, which changes the output frequency, a compensation controller is used to reduce the error signal noise. The FxLMS algorithm is used as the control algorithm.
for
To achieve the high accuracy needed, a commercial
LASER diode is used together with an external cavity.
This external cavity is made using a diffraction grating and a piezoelectric actuator. The grating is a mirror that returns part of the beam back to the commercial laser’s internal cavity from a few centimetres distance, resulting in a very high accuracy laser beam.
The problem is that this scheme is sensitive to acoustic noise. Surrounding noise vibrates the mechanical structure holding the cavity components, thus causing the length of the cavity to change, generating changes in the output laser beam frequency.
External Cavity Beam Splitter
LASER
Rubidium Cell
LASER
Block diagram of the
DSP based controller.
The microphone that is located near the cavity, is receiving the acoustic noise, and the DSP is compensating for this noise, in real time.
Noise1 u
DF FIR d
DF FIR
SYSTEM1 x u e
LMS y
W
NOISE
DF FIR e y
SYSTEM
Piezo Out
Lock Signal
B
LACK f in
Simulated
System
3
4
1
2
1
2
3
4
LEFT (White)
RIGHT (Red)
NOISE
Controller
OUT (J4)
Simulation -
Output
Output Yn
3
4
IN (J5)
1 1
2 e 2 n error in
Noise In4
System In3
- Xn
Input
3
4
Piezo
Out
LEFT (White)
RIGHT (Red)
Measurements of the transfer function of the system and the transfer function of the noise reviled a very close to the theory picture :
This project is a feasibility proof of the implementation of the FxLMS algorithm as a noise reduction controller for an accurate laser output frequency.
Future work could implement this DSP algorithm in a real world system but, in our opinion, a faster DSP is needed.
Also faster analog to digital and digital to analog converters than the ones we used on the EZ-KIT demonstration board are required.
A faster DSP could also enable the use of sophisticated pattern recognition algorithms to enable automatic finding and locking on the desired absorption line of the laser’s output frequency detector.
A very fast DSP-based controller, enables real time compensation for the acoustic interference by changing the external cavity length. The DSP changes the voltage applied to the piezoelectric actuator according to the FxLMS adaptive filter algorithm.
n
n
n
n
n
S’(z) n
The controller’s job is to pick up the acoustic noise and compensate for this noise by changing the piezoelectric actuator's voltage. The S’(z) system is used to enable convergence of the adaptive filter despite the non-minimal phase system of the piezo.
Measured in reality
The simulated system output :
Expected from theory
Output Noise Input Noise
The FxLMS algorithm worked well and achieved significant Noise reduction.
The mean square error of the output signal was reduced by the DSP running the control algorithm
The FxLMS algorithm for noise cancellation is suitable for reducing the laser frequency output noise thus enhancing its stability and quality.
For more information on:
FxLMS Noise cancelling algorithm, Blackfin DSP implementation and more ideas for future projects.
Contact:
Moskovitch Moran & Fishelzon David
052-2725075 052-8735585
We would like to thank the BEC laboratory people who helped us with measurements on the real system
A special thanks to our instructor in the Advanced DSP
Lab, Mr. Alon Slapak who helped us find this algorithm and implement it.