Jaynes–Cummings theory out of the box

Abstract

We report new results in neoclassical quantum optics by applying the central theme of the Jaynes–Cummings paper of 1963. This theme, which Jaynes and Cummings emphasized in several ways, is the key role that must be assigned to radiative back reaction in quantum radiation dynamics. Its consequences are well known in subjects related to cavity quantum electrodynamics, and its influence on optical pulse evolution theory is equally strong. Here we provide a new solitonic extension of the radiation reaction theme to short-pulse broad-bandwidth propagation theory. We report a single formula encapsulating a three-pulse scenario in which the stable imprint of signal-pulse coherence, placed in an atomic medium at a predictable location by an initial pulse pair, is subsequently transferred by a third pulse to a different location. This is analysed by reference to our new analytic solution of the nonlinearly coupled density matrix equations that incorporate the radiation reaction fields obtained from the Maxwell equations for the pulses in the atomic medium.

Multipulse storage and manipulation via solitonic solutions

“…This is the same result as the one obtained when superimposing a type 1 and a type 2 first order solution except that the sign of the displacement is inverted, and so the imprint is moved to the right. This has already been shown in [24,25].…”

“…Here, we wrote the Darboux parameter as λ a = i/τ a , with τ a ∈ R which makes it easier to associate it to a physical quantity, namely, the duration of the pulses. Two possible solutions arising from this have already been thoroughly studied by Groves, Clader and Eberly [24] so we will just summarize the results that we will need. Table 1 contains all the elements of the involution M a for the three first order solutions that are going to be considered.…”

“…Other studies have been carried out for the case of ultra-cold atoms, where one can neglect the effects of Doppler broadening and homogeneous relaxation. Given these assumptions, Groves et al deduced a second order solution that led to an alternative scheme for storage and manipulation of light [24]. Complementary numerical simulations [25] showed the relevance of this procedure even under the effects of the ever-present spontaneous emission.…”

Vector-soliton storage and three-pulse-area theorem

“…5. Additionally, as long as the signal pulse is only stored in one channel, we can displace the imprint and retrieve it (if we consider a finite medium) by the results already obtained for a Λ system [25,26]. It is also interesting to note that, together with the displacement of the imprint, the intensity of the control pulses is inverted (see Fig.…”

“…Recent research has shown how the interaction of broadband pulses with matter opens the door to high-speed switching. In this framework, it has been shown that storage, manipulation and retrieval of a signal pulse in a Λ system is possible [25] even in non-idealized conditions [26] and how the methodology presented there can be extended to accommodate the storage of multiple pulses and added control of the information stored [27]. A generalized two-pulse area was shown to play a role [28]:…”