Signal and noise conversion in four-level quantum systems

Starting from the microscopic viewpoint, the dynamics of nuclear induction is derived by means of statistical methods. The only essential lack of generality lies in the assumption that the nuclei in the sample are independent of each other, so that the treatment does not account for features arising from spin-spin interaction. By considering the simultaneous action of an arbitrary external field and of the molecular surroundings upon a representative nucleus a system of linear differential equations of the first order is derived for the "distribution matrix." It is analogous to the classical Boltzmann equation for the distribution function and allows, upon integration, to determine the macroscopic average value of any spin function in its dependence upon time. This general result is particularly applied to the time dependence of the macroscopic nuclear polarization, and the conditions are investigated under which it satisfies the phenomenological differential equation originally proposed by one of the authors (F.B.). Besides the fact that this equation does not describe line structures caused by the interaction of neighboring spins its validity is found to be seriously restricted only for nuclei having a spin larger than unity and in cases where, in addition, quadrupole relaxation is essential. It demands in these cases that the molecular surroundings are isotropic, e.g., as in gaseous and liquid samples, and further, that their characteristic frequencies of interaction with the nuclei are large compared to the Larmor frequency so that there exists equality between the longitudinal and the transverse relaxation time.

The Dynamical Theory of Nuclear Induction

Microwave Solid‐state Masers

A discussion of the paramagnetic properties of Cr3+ in TiO2 is given with particular reference to its use in solid‐state masers. Energy level diagrams are included for magnetic fields in the (110), (1l0), (001), and (100) planes.

Chromium‐Doped Titania as a Maser Material

Quantum formalism adapted to radiation in a coherent field

It is well known that a three‐level system functions as a mixer for radiation at its three resonant frequencies. Here the topic is treated in detail by analogy to a three terminal‐pair circuit element, one pair for each frequency. To one pair, fixed power is applied from a local oscillator, or ``pump.'' Attention is then centered on the other two pairs to determine their small‐signal response and transfer characteristics. A slight generalization of the impedance concept takes account of the frequency changes and allows the results to be expressed as self‐impedance at each terminal pair, and a transfer impedance between pairs. The damping effect of molecular surroundings is taken into account. The three‐level maser is a special case in which the terminal pair for the idle frequency is open, and the self‐impedance at the signal terminals has a negative resistive part.Quantization of the radiation field is included by expressing quantum uncertainties in the same form as classical noise, i.e., correlation fun...

Signal and noise conversion in four-level quantum systems

References

The Dynamical Theory of Nuclear Induction

Microwave Solid‐state Masers

Chromium‐Doped Titania as a Maser Material

Quantum formalism adapted to radiation in a coherent field

Heterodyne Properties of a Three‐Level Quantum System

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