The behavior of indistinguishable quantum particles is governed by the spin-statistics theorem. Its best known consequence is probably the enforced antisymmetry of the wavefunction of fermions which in turn causes the Pauli exclusion principle: The probability amplitudes that lead to states where two or more fermions occupy the same state interfere destructively and thus no two fermions can occupy exactly the same state. Equally important, but less well known is the opposite effect: Indistinguishable bosons show a tendency to end up in the same state.
The simplest demonstration of this behavior arises for two identical particles arriving simultaneously at two different entry ports of a beam splitter. As depicted above, two bosons will always leave the beam splitter via the same exit port and two fermions will always leave the beam splitter via different exit ports. Turning that effect around allows us to draw conclusions about some particles of interest from their statistical properties. For example spontaneously emitted photons from a laser operated below threshold will show bunching behavior, while they will be emitted statistically independent of each other above the lasing threshold.
The prime quantities which determine whether particles are indistinguishable or not are the coherence volume and the coherence time. While coherence times can be pretty long for single atoms and the light emitted from them, they can be as short as a few picoseconds in semiconductor many body systems. This extremely short timescale poses a challenge for the identification of the statistical properties of light emitted from semiconductors.
The most common approach to determine the statistical properties of light by using two photo diodes and performing coincidence counting is not necessarily suitable for emission processes from semiconductors as the photo diode time resolution is usually on the order of a nanosecond, while the statistical properties are visible on a timescale of tens of picoseconsds. Therefore we developed a novel approach to correlation measurements based on a modified streak camera which enables us to perform correlation measurements with a time resolution of up to 2 picoseconds. A typical picture of more than 30 consecutive emission pulses from a semiconductor laser is shown in the figure below. The upper panel gives a typical integrated streak camera image allowing us to investigate the emission dynamics. The lower panel shows photon emission events during a single emission cycle. Each white dot corresponds to a photon detection event. The insets show several photon pair detection events. Keeping track off all of these events allows us to determine the statistical properties of the emitted light. Even time-resolved and higher-order studies are possible.
As a first demonstration of our ultrafast streak camera correlation technique, we were able to identify the lasing threshold of quantum dot and quantum well microcavity lasers by investigating the statistical properties of the emitted light. We could show that photons emitted below the lasing threshold have a tendency to clump together. Further, we could even show that this bunching tendency gets even stronger when more photons are involved.
Details can be found in the following publications.
"Higher-Order Photon Bunching in a Semiconductor Microcavity"
M. Aßmann, F. Veit, M. Bayer, M. van der Poel, and J.M. Hvam
SCIENCE 325 (5938), 297 (2009)
"Direct observation of correlations between individual photon emission events of a microcavity laser"
J. Wiersig, C. Gies, F. Jahnke, M. Aßmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Höfling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel
NATURE 460 , 245 (2009)
Another well known consequence of the bosonic tendency to occupy the same state is the possibility of Bose-Einstein condensation at low temperatures. The critical temperature below which Bose-Einstein condensation can occur is determined by the mass of the condensed particles. Lighter particles allow higher condensation temperatures. For so-called exciton-polaritons, hybrid, strongly coupled quasiparticles consisting of photons and semiconductor excitations, recently condensation has been demonstrated. Owing to their light mass, about four to five orders of magnitude smaller than electrons, these could even condense at room temperature. However, they do not achieve a steady state, but show a kind of dynamical condensation. Future work will be devoted to studies of polariton condensates in optically created potentials and potential applications for all-optical switching.
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Location & approach
The campus of TU Dortmund University is located close to interstate junction Dortmund West, where the Sauerlandlinie A 45 (Frankfurt-Dortmund) crosses the Ruhrschnellweg B 1 / A 40. The best interstate exit to take from A 45 is "Dortmund-Eichlinghofen" (closer to Campus Süd), and from B 1 / A 40 "Dortmund-Dorstfeld" (closer to Campus Nord). Signs for the university are located at both exits. Also, there is a new exit before you pass over the B 1-bridge leading into Dortmund.
To get from Campus Nord to Campus Süd by car, there is the connection via Vogelpothsweg/Baroper Straße. We recommend you leave your car on one of the parking lots at Campus Nord and use the H-Bahn (suspended monorail system), which conveniently connects the two campuses.
TU Dortmund University has its own train station ("Dortmund Universität"). From there, suburban trains (S-Bahn) leave for Dortmund main station ("Dortmund Hauptbahnhof") and Düsseldorf main station via the "Düsseldorf Airport Train Station" (take S-Bahn number 1, which leaves every 20 or 30 minutes). The university is easily reached from Bochum, Essen, Mülheim an der Ruhr and Duisburg.
You can also take the bus or subway train from Dortmund city to the university: From Dortmund main station, you can take any train bound for the Station "Stadtgarten", usually lines U41, U45, U 47 and U49. At "Stadtgarten" you switch trains and get on line U42 towards "Hombruch". Look out for the Station "An der Palmweide". From the bus stop just across the road, busses bound for TU Dortmund University leave every ten minutes (445, 447 and 462). Another option is to take the subway routes U41, U45, U47 and U49 from Dortmund main station to the stop "Dortmund Kampstraße". From there, take U43 or U44 to the stop "Dortmund Wittener Straße". Switch to bus line 447 and get off at "Dortmund Universität S".
The AirportExpress is a fast and convenient means of transport from Dortmund Airport (DTM) to Dortmund Central Station, taking you there in little more than 20 minutes. From Dortmund Central Station, you can continue to the university campus by interurban railway (S-Bahn). A larger range of international flight connections is offered at Düsseldorf Airport (DUS), which is about 60 kilometres away and can be directly reached by S-Bahn from the university station.
The H-Bahn is one of the hallmarks of TU Dortmund University. There are two stations on Campus Nord. One ("Dortmund Universität S") is directly located at the suburban train stop, which connects the university directly with the city of Dortmund and the rest of the Ruhr Area. Also from this station, there are connections to the "Technologiepark" and (via Campus Süd) Eichlinghofen. The other station is located at the dining hall at Campus Nord and offers a direct connection to Campus Süd every five minutes.
The facilities of TU Dortmund University are spread over two campuses, the larger Campus North and the smaller Campus South. Additionally, some areas of the university are located in the adjacent "Technologiepark".