Spontaneous lifetimes

If in atoms a transition /) ) can be selected, which represents a true two level system (i.e., the fluorescence from A ) terminates only in /)), the atom may be excited many times while it flies through the laser beam. At a spontaneous lifetime r and a travel time T through the laser beam, a maximum of n = Tl 2x) excitation-fluorescence cycles can be achieved (photon burst). With T — 10 s and r = 10 s... 

Here the following problem arises the molecules excited by laser Li into level /c) travel during their spontaneous lifetime of t = 10 ns at around thermal velocities of about v = 5 x 10" m/s only a distance of cl = 5 pm before they decay into lower levels. The second laser L2 must therefore be focused in a similar way as Li and its focus must overlap that of Li within a few microns. 

The different sensitive techniques of Doppler-limited laser spectroscopy discussed in the previous sections supplement each other in an ideal way. In the visible and ultraviolet range, where electronic states of atoms or molecules are excited by absorption of laser photons, excitation spectroscopy is generally the most suitable technique, particularly at low molecular densities. Because of the short spontaneous lifetimes of most excited electronic states E, the quantum efficiency tjk reaches... 

For a collinear arrangement of the two laser beams k A 2 the Doppler shift becomes very small for k — A 2 A i, and the width of the OODR signal S o)2) is only determined by the sum of the level widths of the initial and final levels, while the width of the upper level 2) does not enter into the signal width. If the two levels 1) and m) are, for example, vibrational-rotational levels in the electronic ground state of a molecule, their spontaneous lifetimes are very long (even infinite for homonuclear diatomics ) and the level widths are only determined by the transit time of the molecule through the laser beams. In such cases, the linewidth of the OODR signal may become smaller than the natural linewidth of the optical transitions 11 2) (Sect. 9.4). 

According to (6.55-6.58) the effective lifetime is determined by the inverse sum of all deactivation processes of the excited level fc). In order to obtain the spontaneous lifetime tspont = 1/A one has to measure teftip, l) at different pressures p and different laser intensities 7l, and extrapolate the results towards p 0 and /l 0. The influence of induced emission is a definite drawback of the phase-shift method. It can be eliminated if (p is measured at different intensities /l with the extrapolation... 

Loss-less propagation through media. This means the energy of the pulse is preserved. There is no spontaneous emission, because the Rabi frequency 2r is large compared to the inverse spontaneous lifetime of the atoms 2r... 

The experimental techniques for the investigation of inelastic collisions involving molecules in their electronic ground state generally differ from those discussed in Sect. 8.2. The reasons are the long spontaneous lifetimes of ground-state levels and the lower detection sensitivity for infrared radiation compared to those for the visible or UV spectrum. Although infrared fluorescence detection has been used, most of the methods are based on absorption measurements and double-resonance techniques. 

Example 9.3 When an atom passes with a thermal velocity v = 500 m/s through a laser beam with 2 mm diameter, the transit time is T = 4 ps. For a spontaneous lifetime Xk = 10 s the atom can undergo q <(TI2)lxk= 400 absorption-emission cycles during its transit time. 

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 [1230] and has since been realized by several groups [1231-1233]. 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. 9.46) the metastable 5 T>5/2 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 A. = 493.4 nm and the population leaking by fluorescence into the 5 1)3/2 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 T>5/2 level is populated (this can be reached,... 

When the upper level /) has the spontaneous lifetime Zf = 1/k/ part of the excited molecules decay before they reach the second zone, and the transition amplitude becomes... 

It turns out that the spontaneous lifetime of the Rydberg levels is shortened if the cavity is tuned into resonance with the frequency a>o of the atomic transition n) n — 1). liis prolonged if no cavity mode matches coq [1297]. This effect, which had been predicted by quantum electrodynamics, can intuitively be understood as follows in the resonant case, that part of the thermal radiation field that is in the resonant cavity mode can contribute to stimulated emission in the transition n) n — 1), resulting in a shortening of the lifetime (Sect. 6.3). For the... 

If molecules are excited into an upper level with the spontaneous lifetime t = 1 /y by a light pulse ending at r = 0, the time-resolved fluorescence amplitude is given by... 

It is well-known that the spontaneous lifetime of an excited atom is proportional to the density of modes of the electromagnetic field p(u) ) about the atomic transition frequency u . Specifically, the Weiss-kopf-Wigner spontaneous lifetime is given by 125]... 

This shows that, everything else being kept constant, the spontaneous lifetime is reduced in proportion to the initial population inversion. 

SF applications. Since no mirrors, with of course limited transparency, are needed for SF, it is in principle the most efficient process to produce very narrow pulses of coherent light. In the frequency range where mirrors are difficult to produce it could be the only way to obtain coherent sources such would be the case for X-rays and y-rays. However the drawback is that the spontaneous lifetime of individual atoms becomes very short due to its dependence and this is probably the most important cause of dephasing. 

After the time Zi = 1/A/ the population density Ni has decreased to 1/e of its initial value at r = 0. The time Zi represents the mean spontaneous lifetime of the level / as can be seen immediately from the definition of the mean time... 

An optically excited sodium atom Na(3F) with a spontaneous lifetime r(3F) = 16ns is placed in a cell filled with lOmbar nitrogen gas at a temperature of T = 400K. Calculate the effective lifetime Teff (3F) if the quenching cross section for Na(3F)-N2 collisions is = 4 x 10 cm. ... 

In many experiments in laser spectroscopy, the interaction time of molecules with the radiation field is small compared with the spontaneous lifetimes of excited levels. Particularly for transitions between rotational-vibrational levels of molecules with spontaneous lifetimes in the millisecond range, the transit time T = df v of molecules with a mean thermal velocity v passing through a laser beam of diameter d may be smaller than the spontaneous lifetime by several orders of magnitude. 

An excited atom with spontaneous lifetime r suffers quenching collisions. Show that the line profile stays Lorentzian and doubles its linewidth if the mean time between two collisions is 7c = t. Calculate the pressure of N2 molecules at T = 400K for which 7c = r for collisions Na -fN2 with the quenching cross section = 4 x 10 cm. ... 

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