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Physical Review A

Non-Markoffian effects in Josephson radiation

Subir K. Bose, David T. Ng

Published Apr 1, 1976• 3 citations
Publisher

Abstract

Non-Markoffian effects in the Josephson-radiation linewidth are investigated by using the projection-operator formalism of Mori. The memory function as well as the frequency are calculated in perturbation theory. We develop formal expressions for these to order ${\ensuremath{\lambda}}^{4}$, $\ensuremath{\lambda}$ being a perturbation parameter, and discuss the simpler results valid to order ${\ensuremath{\lambda}}^{2}$.

DOI
10.1103/physreva.13.1548

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Non-Markoffian effects in the Josephson-radiation linewidth are investigated by using the projection-operator formalism of Mori. The memory function as well as the frequency are calculated in perturbation theory. We develop formal expressions for these to order \ensuremathλ4{\ensuremath{\lambda}}^{4}\ensuremathλ4, \ensuremathλ\ensuremath{\lambda}\ensuremathλ being a perturbation parameter, and discuss the simpler results valid to order \ensuremathλ2{\ensuremath{\lambda}}^{2}\ensuremathλ2.
In this chapter, we present a theory of the laser based on the Heisenberg–Langevin approach. This is a different, but completely equivalent approach to the density operator approach discussed in the previous chapter. In general, the density operator approach is better suited to study the photon statistics of the radiation field whereas the Heisenberg–Langevin approach has certain calculational advantages in the determination of phase diffusion coefficients, and consequently laser linewidth. In Section 12.1, a simple approach to determine laser linewidth based on a linear theory is presented. This analysis is especially interesting and useful in that it includes atomic memory effects, something that is difficult to do within a density matrix theory. In Sections 12.2–12.4, we consider the complete nonlinear theory of the laser and rederive all the important quantities related to the quantum statistical properties of the radiation field. A simple Langevin treatment of the laser linewidth including atomic memory effects† The full nonlinear quantum theory of the laser discussed in the previous chapter yields most of the interesting quantum statistical properties of the radiation field. In many problems of interest, however, we do not need such an elaborate treatment. For example, as we saw in the previous chapter, the natural linewidth of the laser can be determined from a linearized theory of the laser. That is, the full nonlinear theory serves to determine the amplitude of the field but the phase fluctuations about this operating point are described by a linear theory.
We develop a theory of quantum beats in molecular fluorescence taking into account collision effects (such as pure dephasing due to elastic collision) without invoking the Markoff approximation. Model calculations of the time dependent fluorescence from molecules with two excited levels are performed in order to see how the non-Markoffian character in the collision process exerts influence upon the quantum beat pattern. It is suggested that if the pure dephasing between the excited states is a Markoffian ‘‘the degree of modulation of the beats’’ decreases exponentially with time; if it is in the static limit the degree of modulation of the beats decreases as a Gaussian function (the non-Markoffian behavior in the quantum beats). A given case can be classified as either Markoffian or non-Markoffian, depending on the relative magnitudes of the collision duration time τc, the beat frequency ω, and the coupling strength v which is characteristic of the pure dephasing process. The Markoff approximation holds only if the condition ω<v<1/τc is satisfied; the non-Markoffian behavior appears in the quantum beat pattern when ω>v, even if v2τ2c<1 .