Thermal attenuation noise of optical power from a 420nm light source in hot 85,87Rb vapor.

Photo of the setup

The Idea

The project mainly uses an experiment which was build up during my master thesis which will be finished in a few weeks. The experiment aims to do doppler free absorption spectroscopy in the 6P manifold. This is possible due to the recent advancements in GaN diode laser technology[1-3], for which the 2014 Nobel price was awarded[4] and allows for a compact laser at 420.3 nm in a Littrow external cavity diode laser design (ECDL). This is beneficial for us since the ECDL inhibits a very low linewidth (<150 kHz) and therefore does not perturb our modulated deviations. The modulation of perturbations is made via a hot gas cell with a natural mix of Rubidium inside it. Natural abundances of Rubidium is subdivided in only to isotopes[5]:

Isotope Abundance
87Rb 28.487(11) %
85Rb 71.513(11) %

Those two have very similar atomic transitions although their hyperfine structure splitting is very different caused by different nuclear spins[6]. So one can use the gas cell

Gas Cell

which is heated from two ceramic facet heaters as well as multiple heating wires around its core. The cell is capable of producing up to 200°C. Also the inside and outside is strongly shielded against magnetic fields and isolated against heat loss.

The cell will serve as the power attenuation inside the setup. There are multiple options to drive the laser through it with a resonant frequency, or non resonant, or with different temperatures of polarizations.

Setup

As seen the light passes the cell two times in crossed polarizations and will then be detected by a amplified photodiode.

The guess now is that due to deflection, gas diffusion/movement and spurious reflections/diffractions a gaussian formed power attenuation will be modulated onto the laser beam. This should be able to be registered with the photodiode.

Proposed evaluation

In the project description it was proposed to invert the assumed gaussian distributed data to a uniform distribution through the means of inverting the box mueller transform[7]. But it turned out, the transformation is neither bijective nor fully invertable to different solution branches. So it was necessary to find a way of inverting the data. It turned out the solution is well known and easy to find[8]. One can just apply the cumulated distribution function with the estimated parameters of the distribution. This is an easy to do evaluation and served as a reliable method.

First measurements

Electrical Noise

The first measurement was just made on the amplified, electrical noise of the photodiode. It was set to a gain of 20 dB and the voltages where recorded. While it initially looked good the eye

Electrical Noise Gaussian

and even produced data which passed all statistical tests but one (in a monobit rounding evaluation) it was later found to be unreliable. This was due to the found discretization of the ADC on the electronics board which makes discrete 300 nV steps.

ADC gaps

Real laser measurements

The first laser measurements where found to be a bit shaky. This is caused by the laser stabilization which prefers a stable frequency with modulation of the diode current.

Laser power measurements

Nevertheless the small deviations are encoded in a much higher frequency in the data. Therefore a Fouriertransformation was made and as seen, the lower pseudo frequency parts where truncated and the result was transformed back.

Laser power fourier transformed histogram

This yielded a nice distribution. However, it was found that the best matching Gaussian distribution (red) does not match the histogram very well. This holds for a Lorentz distribution too. But it turned out, that the data follows a Voigt distribution which is a convolution of the latter mentioned distributions. This makes sense and could have been thought of already in the project description rather than just assuming a gaussian one. This hints to homogeneous and inhomogeneous broadening processes like pressure and doppler broadening respectively[9, 10].

Laser power Voigt fit

Applying the CDF of the Voigt distribution then yields the uniform distributed data which can be tested again.

Laser power random test results

Sadly the data does not passes the monobit test and in turn also not the cumulative sum tests. The compression test is also not passed as well as in the electric noise measurements. One could try the better evaluation method from the electrical noise evaluation but there where not enough datapoints to do that since the Fouriertransform truncated a lot of it.

Conclusions

In total this project has to be seen as a negative result in its current shape. It created random numbers but their quality was not that great compared to other methods. One could increase the quality with more measurements as well as other evaluation methods but this was not subject of this project. I suspect the correlations of successive measurements where just to strong and in turn pulled down the random number quality. However, the project showed that it is possible to create random numbers out of the power attenuation of a laser beam in hot Rubidium vapor. The numbers are from low quality but due to their quantum nature, can be used as a nice high entropy source for seeds or key creation.

References

  1. Nakamura, S., Mukai, T. & Senoh, M. High-power GaN pn junction blue-lightemitting diodes. Japanese Journal of Applied Physics 30, L1998 (1991).

  2. Nakamura, S., Mukai, T. & Senoh, M. Candela-class high-brightness InGaN/AlGaN double-heterostructure blue-light-emitting diodes. Applied Physics Letters 64, 1687{1689 (1994).

  3. Akasaki, I. & Amano, H. Breakthroughs in improving crystal quality of GaN and invention of the p{n junction blue-light-emitting diode. Japanese journal of applied physics 45, 9001 (2006).

  4. Nakamura, S. Nobel Lecture: Background story of the invention of efficient blue InGaN light emitting diodes. Reviews of Modern Physics 87, 1139 (2015).

  5. Lide, D. R. CRC handbook of chemistry and physics: a ready-reference book of chemical and physical data (CRC press, 1995).

  6. Steck, D. A. Rubidium 87 D line data 2001.

  7. Scott, D. W. Box Muller transformation. Wiley Interdisciplinary Reviews: Computational Statistics 3,177 179. issn: 1939-0068 (2011).

  8. “Harry49” math.stackexchange https://math.stackexchange.com/a/2344086/373704 (2017).

  9. Demtröder, W. Laserspektroskopie: Grundlagen und Techniken (Springer-Verlag, 2007).

  10. Demtröder, W. Laserspektroskopie 2: Experimentelle Techniken (Springer-Verlag, 2013).