Single-quantum system

Plakhotnik T, Walser D, Pirotta M, Renn A and Wild U P 1996 Nonlinear spectroscopy on a single quantum system two-photon absorption of a single molecule Science 271 1703-5... 

Figure. 4. A single quantum system emitted by the monoparticle source is split into two at the beamsplitter. When the detector is triggered, the observer sees the light.

We start out by determining the rate at which a single quantum system can emit photons. This will put us into a position to estimate the orders of magnitude of signal and background we may expect. To this end, we approximate the manifold of electronic states of the quantum systems3 by just two effective states, which for example could be the highest... 

Fig. 1. Single-quantum system approximated by a system of three levels with occupation probabilities pi interconnected by transition rates kij. A third level is taken into account in order to accommodate transitions to triplet or other dark states.

B. Hecht, Nano-optics with single quantum systems, Proc. R. Soc. Lond. A 362, 881 (2004). 

Averaging over all different possible stochastic behaviors in SMS yields the master equation used in ensemble spectroscopy, but the averaged master equation does not determine the dynamics of the (pure) states of individual molecules. Certain attempts have been made to derive a proper theory of individual behavior of single quantum systems, but a rigorous interpretation is still lacking. 

Some interesting behavior in single-molecule spectroscopy involves the stochastic migration of lines. Usual statistical quantum theory describes only mean values or dispersions of observables, but not the actual fluctuations in the dynamics of single quantum systems. In an individual formalism of quantum mechanics, such fluctuations are of great importance. 

A Single Quantum System Evolution, Prediction, Observation... 

For the unequivocal demonstration of the real QZE, it seems indispensable to address a single quantum system. Let us examine in more detail how incomplete information from an ensemble disqualifies an attempted proof. 

Turning now to the nanosecond time regime (lower half of Fig. 11), the emitted photons from a single molecule can provide still more useful information. On the time scale of the excited state lifetime, the statistics of photon emission from a single quantum system are expected [84] to show photon antibunching, which means that the photons space themselves out in time , that is, the probability for two photons to arrive at the detector at the same time is small. This is a uniquely quantvun-mechanical effect, which was first observed for Na atoms in a low-density beam [85]. Antibunching is fundamentally measured by computing the second-order correlation of the electric field (r) (whieh is simply the normalized form of the intensity-... 

One experiment that is now possible would be to use the emission from a single molecule as a light source of sub-nm dimensions for near-field optical microscopy [97]. Of course, this would involve the technical difficulty of placement of the single emitting molecule at the end of a pulled fiber tip or pipette. In all cases, improvements in SNR would be expected to open up a new level of nanoscopic detail and possibly new applications. Because this field is relatively new, the possibilities are only limited at present by the imagination and the persistence of the experimenter and the continuing scientific interest in the properties of single quantum systems in solids. 

Panels Al and Bl in Fig. 9.15 show confocal images of the Nb-doped rutile Ti02 (110) surface under the conditions of without (A) and with alizarin (B), respectively. Most of the hot spots in the confocal image (without the tip) in Fig. 9.15A1 show as donut-shape features, and only a small number of them show as circular or ellipsoidal-shaped spots. Such different diffraction limited fluorescence excitation patterns can only be observed when single quantum systems are raster scanned through the field distribution of a tightly focused radially polarized laser beam. Since the excitation rate is proportional to the square of the projection of the transition dipole moment onto the electric field. 

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