We show that an alkali atom with a tripod electronic structure can yield rich electromagnetically induced transparency phenomena even at room temperature. In particular we introduce doubledouble electromagnetically induced transparency wherein signal and probe fields each have two transparency windows. Their group velocities can be matched in either the first or second pair of transparency windows. Moreover signal and probe fields can each experience coherent gain in the second transparency windows. We explain using a semi-classical-dressed-picture to connect the tripod electronic structure to a double-Λ scheme.PACS numbers: 42.50. Gy, 42.50.Ex Electromagnetically induced transparency (EIT) exploits interfering electronic transitions in a medium to eliminate absorption and dramatically modify dispersion over a narrow frequency band with applications including slow light, reduced self-focusing and defocusing [1], and quantum memory [2]. Microscopically, a threelevel Λ electronic structure suffices to explain EIT. Double EIT (DEIT) extends EIT to creating two simultaneous transparency windows, one for a "signal" and the other for a "probe" field, with the aid of a third "coupling" field [3][4][5][6][7]. DEIT is valuable for coherent control and enabling long-lived nonlinear interactions between weak fields, which could enable deterministic all-optical two-qubit gates for quantum computing.Whereas the Λ scheme suffices to explain EIT, DEIT requires at least four levels. The tripod (⋔) scheme [3], which has one upper and three lower levels as shown in Fig 1(a), is one such four-level scheme. This scheme can be reframed in the semi-classical-dressed-picture [8,9] shown in Fig. 1(b), which has two lower (|1 and |3 ) and two upper (|± ) levels after eliminating the strong coupling (c) field.This semi-classical-dressed model of the ⋔ scheme corresponds effectively to a double Λ system, and double Λ schemes have been studied experimentally [10]. With our semi-classical-dressed analogy, we show that this ⋔ electronic structure exhibits rich hitherto-unnoticed EIT phenomena, namely what we now call double DEIT (DDEIT). Our DDEIT phenomenon has the property that both the signal and the probe fields can each have two EIT windows given the right parameter choices.One particular aspect of our system, namely the second EIT window for the probe, has been predicted [11] and observed experimentally [7,12], but this previously observed effect corresponds only to one aspect of our system, namely a double window for the probe and not to our full DDEIT for both signal and probe fields. Moreover, these new second EIT windows for each of the sig- nal and probe fields exhibit coherent gain, which has not previously been expected. We now reprise the dynamics of the driven ⋔ atom [3]. For ≡ 1 andσ ı := |ı |, the free Hamiltonian isĤ 0 = 4 ı=1 ω ı σ ıı . For ω ı := ω ı − ω , the ⋔ atom is driven by a probe field with frequency ω p = ω 41 − δ p , a coupling field with frequency ω c = ω 42 − δ c , and a signal field with frequency ω s...
For Doppler-broadened media operating under double-double electromagnetically induced transparency (EIT) conditions, we devise a scheme to control and reduce the probe-field group velocity at the center of the second transparency window. We derive numerical and approximate analytical solutions for the width of EIT windows and for the group velocities of the probe field at the two distinct transparency windows, and we show that the group velocities of the probe field can be lowered by judiciously choosing the physical parameters of the system. Our modeling enables us to identify three signal-field strength regimes (with a signal-field strength always higher than the probe-field strength), quantified by the Rabi frequency, for slowing the probe field. These three regimes correspond to a weak signal field, with the probe-field group velocity and transparency window width both smaller for the second window compared to the first window, a medium-strength signal field, with a probe-field group velocity smaller in the second window than in the first window but with larger transparency-window width for the second window, and the strong signal field, with both group velocity and transparency window width larger for the second window. Our scheme exploits the fact that the second transparency window is sensitive to a temperature-controlled signal-field nonlinearity, whereas the first transparency window is insensitive to this nonlinearity.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.