Direct Observations of Quantum Jumps

In quantum mechanics the probability (t) of finding an atomic system at the time t in the quantum state 1 is described by time-dependent wave functions. If one wants to find out whether a system is with certainty = 1] in 

Laser-spectroscopic experiments with single ions confined in a trap have proved that such information can be obtained. The original idea was proposed by Dehmelt [14.83] and has since been realized by several groups [14.84-14.86]. It is based on the coupling of an intense allowed transition with a weak dipole-forbidden transition via a common level. For the example of the Ba ion (Fig. 14.27) the metastable 5 D5/2 level with a spontaneous lifetime of r = (32 5) s can serve as a shelf state. Assume that the Ba ion is cooled by the pump laser at X = 493.4 nm and the population leaking by fluorescence into the 5 D3/2 level is pumped back into the 6 Pi/2 level by the second laser at A = 649.7 nm. If the pump transition is saturated, the fluorescence rate is about 10 photons per second with the lifetime r(6 Pi/2) = 8 ns. 

If the metastable 5 Ds/2 level is populated (this can be reached, for example, by exciting the 6 P3/2 level with a weak laser at X = 455nm, which decays by fluorescence into the 5 D5/2 level, or even without any further laser by a nonresonant Raman transition induced by the cooling laser), the ion is, on the average, for r(5 D5/2) = 32 s not in its ground state 6 Si/2 and therefore cannot absorb the pump radiation at A = 493 nm. The fluorescence rate becomes zero but jumps to its value of 10 photons/s as soon as the 5 D5/2 level returns by emission of a photon at A = 1.762 p.m back into the 6 Si/2 level. 

The allowed transition 6 Si/2 — 6 Pi/2 serves as an amplifying detector for a single quantum jump on the dipole-forbidden transition 5 Ds/2 6 Si/2 

Similar observations of quantum jumps have been made for Hg+ ions confined in a Penning trap [14.86]. 

Laser-spectroscopic experiments with single ions confined in a trap have proved that such information can be obtained. The original idea was proposed by Dehmelt [14.63] and has meanwhile been realized by several groups [14.64-66]. It is based on the coupling of an intense allowed transition with a weak dipole-forbidden transition via a common level. For the example of the Ba+ ion (Fig. 14.21) the metastable level with a 

Of fundamental interest are measurements of the photon statistics in a three-level system, which can be performed by observing the statistics of quantum jumps. While the durations Atj of the on-phases or off-phases show an exponential distribution, the probability P(m) of quantum jumps per second exhibits a Poisson distribution (Fig. 14.23). In a two-level system the situation is different. Here, a second fluorescence photon can be emitted after a first emission only, when the upper state has been reexcited by absorption of a photon. The distribution P(AT) of the time intervals AT between successive emission of fluorescence photons shows a sub-Poisson distribution which tends to zero for AT 0 photon antibunching) because 

In quantum mechanics the probability Viit) of finding an atomic system at the time t in the quantum state 11) is described by time-dependent wave functions. If one wants to find out whether a system is with certainty [Pi(r) = 1] in a well-defined quantum state 1 one has to perform a measurement that, however, changes this state of the system. Many controversial opinions have been published on whether it is possible to perform experiments with a single atom in such a way that its initial state and a possible transition to a well-defined final state can be unambiguously determined. 

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Basche, T., Kummer, S. and Brauchle, C. Direct spectroscopic observation of quantum jumps of a single molecule, Nature, 373 (1995), 132-134... 

The time distribution of the fluorescence photons emitted by a single dye molecule reflects its intra- and intermolecular dynamics. One example are the quantum jumps just discussed which lead to stochastic fluctuations of the fluorescence emission caused by singlet-triplet quantum transitions. This effect, however, can only be observed directly in a simple fluorescence counting experiment when a system with suitable photophysical transition rates is available. By recording the fluorescence intensity autocorrelation function, i.e. by measuring the correlation between fluorescence photons at different instants of time, a more versatile and powerful technique is available which allows the determination of dynamical processes of a single molecule from nanoseconds up to hundreds of seconds. It is important to mention that any reliable measurement with this technique requires the dynamics of the system to be stationary for the recording time of the correlation function. 

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