Atomic systems photon correlations

The generation of the pure TPE state is an example of mapping of a state of quantum correlated light onto an atomic system. The two-photon correlations... 

The two-photon correlations stored in the pure TPE state can be measured by detecting fluctuations of the fluorescence field emitted by the atomic system. Squeezing in the fluorescence field is proportional to the squeezing in the atomic dipole operators (squeezing in the atomic spins) which, on the other hand, can be found from the steady-state solutions for the density matrix elements. 

In a complete quantum theory of radiation several interesting phenomena regarding photon statistics are predicted. One such effect is photon anti-bunching for a two-level system. When an atom has just emitted a photon it cannot immediately radiate a second photon since it is in the lower state [4.17,18]. This behaviour is experimentally observed in photon correlation experiments. 

The origin of these effects has been debated. One possibility is the Peierls instability [57], which is discussed elsewhere in this book In a one-dimensional system with a half-filled band and electron-photon coupling, the total energy is decreased by relaxing the atomic positions so that the unit cell is doubled and a gap opens in the conduction band at the Brillouin zone boundary. However, this is again within an independent electron approximation, and electron correlations should not be neglected. They certainly are important in polyenes, and the fact that the lowest-lying excited state in polyenes is a totally symmetric (Ag) state instead of an antisymmetric (Bu) state, as expected from independent electron models, is a consequence... 

It is important to point out that even at 77 = 0 the observed value V = 0.942 0.006 is far from its ideal value of V = 0. One important source of error is the finite retrieval efficiency, which is limited by two factors. Due to the atomic memory decoherence rate 7C, the finite retrieval time Tr always results in a finite loss probability p 7c Tr. For the correlation measurements we use a relatively weak retrieve laser ( 2 mW) to reduce the number of background photons and to avoid APD dead-time effects. The resulting anti-Stokes pulse width is on the order of the measured decoherence time, so the atomic excitation decays before it is fully retrieved. Moreover, even as 7C —> 0 the retrieval efficiency is limited by the finite optical depth q of the ensemble, which yields an error scaling as p 1/ y/rj. The measured maximum retrieval efficiency at 77 = 0 corresponds to about 0.3. In addition to finite retrieval efficiency, many other factors reduce correlations, including losses in the detection system, background photons, APD afterpulsing effects, and imperfect spatial mode-matching. 

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-... 

In the case that a sufficient number of individual atoms and molecules participate in the photon-matter interaction, the medium undergoes macroscopic changes, which may be global or localized. Such changes can be measured using detectors sensitive to them, and one can deduce properties of the probed species from correlating the system response to the laser wavelength and photon flux density. 

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