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326                           Lasers

                                   12.12  Noise
                                   Why can masers be used as low noise amplifiers? Mainly, because their op-
                                   eration is not dependent on the motion of charge carriers, whose density and
                                   velocity are subject to fluctuations. So, we have managed to get rid of one
                                   source of noise, but we have now another kind of noise, namely that due to
                                   spontaneous emission.
                                     The amount of noise generated in an amplifier may be characterized by a
                                   parameter called ‘noise temperature’; a low noise temperature means a small
                                   amount of noise. For a maser it can be shown that under ideal conditions ∗
     ∗  Ideal conditions means high gain, no  this noise temperature is numerically equal to the negative temperature of the
     ohmic losses, and no reflections from a  emission mechanism. Hence, the aim is to have a low negative temperature,
     noisy load.
                                   that is, large population inversion.
                                     How can we achieve large population inversion? With reference to our
                                   three-level maser scheme, we have to do two things: (i) pump hard so that
                                   the population of levels 3 and 1 become roughly equal; (ii) keep the device at
                                                 †
     †  Low temperatures help incidentally in  a low temperature, so that the relative number of atoms is higher in level 1.
     reducing the ohmic losses as well.  Be careful, we are talking now of three different ‘temperatures’. The maser
                                   has to work at a low (ordinary) temperature to get a low negative (inversion)
                                   temperature, which happens to be equal to the noise temperature of the amp-
                                   lifier. Now what is the minimum noise temperature one can achieve? Can we
                                   approach the zero negative temperature and thus the zero noise temperature?
                                   We can certainly approach the zero negative temperature by cooling the amp-
                                   lifier towards 0 K. As the actual temperature approaches absolute zero, the
                                   ratio
                                                       number of atoms in level 1
                                                       number of atoms in level 2

                                   tends to infinity. Hence, after pumping, the negative temperature tends to zero.
                                   But spontaneous emission does not disappear, since it is proportional to the
                                   number of atoms in level 3. Thus, the noise temperature cannot reach zero.
                                     It turns out that, as the inversion temperature tends to zero, the noise
                                   temperature tends to the finite value of hν/k, where ν is the frequency of op-
                                                       9
                                   eration. When ν =5 × 10 Hz, the limiting noise temperature comes to about
                                   0.25 K. Experimental results on masers cooled to liquid helium temperatures
                                   are not far from this value. Noise temperatures around 2 K have actually been
                                   measured.
                                     All I have said so far about noise applies to lasers as well, though the nu-
                                   merical values will be radically different. For the argon laser mentioned before,
                                              14
                                   ν =6.6 × 10 Hz, giving T noise ∼ 30 000 K as the theoretically available
                                   minimum.

                                   12.13  Applications
                                   Finally I should like to say a few words about applications. What are lasers
                                   good for? Surprisingly, an answer to this question was not expected when the
                                   first lasers were put on the bench. It is true to say that never has so much
                                   effort been expended on a device with so little regard to its ultimate usefulness.
                                   Lasers were developed for their own sake.
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