Volume 8 Issue 10 - May 22, 2009
Observation of Retardation Effect via Current Noise
Yueh-Nan Chen

Department of Physics, College of Sciences, National Cheng Kung University

Appl. Phys. Lett. 93, 132101 (September, 2008)

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The article is selected as the cover story of the Sep.29 2008 issue of Applied Physics Letters.

The question on the speed of light had long been an important issue for both scientists and philosophers. Kepler and Descartes thought that the speed of light is infinite, while Galileo thought its speed is finite. Of course, we now all know that the speed of light is roughly equal to 3×108 m/s. But, in experiment, how the light speed is measured? The first attempt was made by Galileo in 1635. He and his assistant each carried a lamp and climbed two hills with the separation of 1 km. There, they performed the first measurement on the speed of light. From the modern knowledge, of course, this experiment failed. However, it at least tells us that the light travels with an extremely high speed. Few decades later, Roemer (Denmark physicist, 1644~1710), who adopted the observation method in astronomy, proved that the speed of light is finite. By observing the motions of Jupiter and its satellite, the speed of light Roemer measured was 2.1×108 m/s. Later on, many scientists kept measuring the speed of light with the methods in astronomy, and the measurement results are gradually close to 3×108 m/s. Without using the astronomy methods, the first experiment, which was set on the “earth surface”, for the speed of light was performed by Fizeau (French physicist) in 1849. A gear wheel and reflecting mirror, separated by a distance of 8.633km, were used to give the measurement results: 3.18×108 m/s. In 1920, a mirror with eight faces was used to replace the gear wheel by Michelson (American physicist, 1852~1931). After hundreds of measurements, the speed of light was given by 2.99796×108 m/s. One thing worth mention is that, similar to Galileo’s experiment, the light source and eight-face-mirror were placed separately on two hills in Michelson’s experiment. 

Due to rapid developments of optical technology, the research of atomic and molecular physics has become increasingly important in the past two decades, especially after the successful demonstrations of Bose-Einstein Condensation (BEC) in atomic systems. From the development quantum physics, people already knew that the electrons of an atom actually circle around the nuclei. The energy levels of the electrons are quantized. If an electron is relaxed from a higher level to lower one, a photon is emitted to preserve the energy conservation. In the end of last century, physicists were able to trap single ion and measured its spontaneous emission with single photon detector. With the advance of technology, physicists at Innsbruck last year demonstrated a fancy experiment of trapping single ion in front of a mirror [Phys. Rev. Lett. 98, 183003 (2007)]. The laser pulses are shined on the ion to excite the electron as shown in Fig. 1. When the electron is relaxed to the lower state, the emitted photon may have the chance to go left first, such that it can be reflected by the mirror. In this case, the additional optical path is 2L, and the detector on the right-hand side can obtain the interference pattern of photons. If the distance between the atom and mirror is large enough, one would expect to observe the “retardation” effect of the reflected photons.
Fig 1: Schematic view of trapping a single Barium ion [From F. Dubin, D. Rotter, M. Mukherjee, C. Russo, J. Eschner, and R. Blatt, Phys. Rev. Lett. 98, 183003 (2007).].

Motivated by this experiment, we started to think that is it possible to see the retardation effect in solid state system? The first candidate is the so called “Self-Assembled Quantum Dots”. If an InAs QD is excited by a laser pulse, it’s possible to create an exciton and then emit a photon. The exciton is just like the two-level atom in atomic physics. The energy of the spontaneous emission photon is around 1.3 ~ 1.5 eV. However, the direction of the spontaneous emission is random. To enhance the retardation effect, we propose to embed two quantum dots inside a one-dimensional cavity made by photonic crystal (Fig. 2) so that the emitted photon is restricted in one dimension. In our proposal, the retardation effect not only comes from the reflecting mirror, but also from the presence of another dot.
Fig 2: Schematic view of embedding two quantum dots inside a one-dimensional waveguide made by photonic crystal.

The question now is how to read the signal of retardation? Fortunately, due to the advance of nano-technology, it is now possible to embed quantum dots inside a p-i-n structure, such that the electron and hole can be injected separately from opposite sides and then emit a photon. This allows one to examine the exciton dynamics in a QD via electrical currents. Recently, the interest in measurements of shot noise in quantum transport has risen owing to the possibility of extracting valuable information not available in conventional dc transport experiments. The definition of the shot noise is

, where I(t) is the current through the device. If the electrons in a conductor are uncorrelated, the zero-frequency noise is:. Therefore, it is conventionally to define the Fano factor as

where is the average current. For the value of F=1, it has the characteristic of Poissonian noise. In quantum systems, however, the electrons are usually quantum correlated, and the Fano factor is usual below unity. It is the called, sub-Poissonian noise. On the other hand, if F is larger than unity, it is super-Poissonian noise.

Therefore, in our work, we thus suggest that by embedding quantum dot p-i-n junction inside the photonic crystal waveguide [Fig. 3 (a)], one can detect the retardation effect from the noise spectrums [SID(ω)]. As shown in Fig. 3 (b), the black line shows the results with the consideration of retardation, while the green line represents the results without retardation. From our theoretical predictions, we indeed find that there are some “peaks” in the noise spectrums. This could be a feature to tell whether there is retardation effect in the system. Hopefully, the solid state physicists in the near future can really measure the retardation effect as the atomic physicists have demonstrated.   
Fig 3: (a) Schematic view of quantum dot p-i-n junction inside the waveguide. (b) Current-noise spectrums of the system with(black line)/without(green line) the consideration of retardation.

【Cover Image on Applied Physics Letters】
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