Optical bistability and multistability via quantum interference in an Er3+-doped optical fiber
Highlights
► The bistable behaviors in the scheme are controlled by both the coherent and incoherent fields. ► Optical multistability is realized in this system, which will have more advantages than the OB in some applications where more than two states are needed. ► Four kinds of convenient ways to obtaining the transition from OB to OM or vice versa are showed in this scheme.
Introduction
Over the last few years, quantum optical phenomena based on quantum coherence and interference have attracted a lot of attention of many researchers in the quantum optics [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16]. One of the interesting quantum optical phenomena, the optical bistability (OB) in multilevel atoms confined in an optical ring cavity, has been the subject of many recent studies [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34] because of its potential wide applications in all-optical switches, memories, transistors, and logic circuits [35], [36], [37]. These studies show that one can control the bistable threshold intensity and the hysteresis loop via different approaches such as the field-induced transparency [23], the phase fluctuation [24], [25], the squeezed state field [26], [27], [28], the spontaneously generated coherence [29], [30], [31], [32], the atomic cooperation parameter [33], the intensity of the microwave field [34], and so on.
On the other hand, the optical multistability (OM) confined in an optical cavity has also been extensively studied in the multilevel atomic systems in recent years. For instance, Xiao groups [20] reported an experimental scheme in a three-level rubidium atomic system, and they found that the observed multistability is very sensitive to the induced atomic coherence in the system and can evolve from a normal bistable behavior with the change of the coupling field as well as the atomic number density. Quite recently, Li et al. [33] analyzed a theoretical scheme in a generic N-type atomic system driven by a degenerate probe field and a coherent coupling field, they showed that the hybrid multistability can be observed under the appropriate detuning. Of course, the other schemes for realizing the optical multistability are also subsequently studied [38], [39].
In this paper, we investigate the optical bistability and multistability in a four-level Er3+ ionic system in an Er3+-doped ZrF4–BaF2–LaF3–AlF3–NaF optical fiber inside a unidirectional ring cavity. The optical bistability in solid-state media confined in an optical cavity has been studied by Xiao groups [40] and Li [41] quite recently, however, the optical multistability can not be realized in their solid-state systems to our best knowledge, which motivate us to carry out the current work. Our work and the system are based on the Refs. [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [38], [39], [40], [41], [42], but our scheme is very different from those works. First, the bistable behavior in our scheme is realized by the coherent and incoherent fields, which is very different from some conventional schemes that the bistable behavior is just induced by the coherent field, and the optical bistability and multistability can be manipulated efficiently via both coherent and incoherent fields. Second, we have realized optical multistability in this optical fiber system, which will have more advantages than the OB in some applications where more than two states are needed. Third, we show four kinds of convenient ways to obtaining the transition from OB to OM or vice versa, which make our scheme much more practical than the other counterparts. Our paper is organized as follows: in Section 2, we present the theoretical model and establish the corresponding equations. Our numerical results and physical analysis are shown in Section 3. In Section 4, some simple conclusions are given.
Section snippets
The model and the dynamic equations
We consider a four-level Er3+ ionic system in an Er3+-doped ZrF4–BaF2–LaF3–AlF3–NaF optical fiber as shown in Fig. 1 (see Ref. [42]). The experimental system for this scheme can be realized by the Er3+ ion with , , , and behaving the , , , and state labels, respectively. The states , , and comprise a light amplification subsystem, while the states , , and form a usual EIT subsystem. The transition is mediated by a coherent
Numerical results and physical analysis
Now we give some numerical studies for the steady state of the output intensity versus the input intensity under various parametric conditions, as shown in Fig. 2, Fig. 3, Fig. 4, Fig. 5, Fig. 6. In the following numerical calculations, all the parameters will be scaled by , and it is reasonable that we can choose the decay rates as , , , , and based on Refs. [42], [44], all of which will not be given again in Fig. 2, Fig. 3, Fig. 4, Fig. 5, Fig. 6.
In
Conclusions
To sum up, we have investigated a new scheme for realizing the optical bistability and multistability behavior in an Er3+-doped ZrF4–BaF2–LaF3–AlF3–NaF optical fiber inside an optical ring cavity. A four-level physical model is presented to explain the observed OB and OM phenomena. By manipulating the absorption and nonlinear optical properties of this optical system via the quantum interference induced by the coherent field, the optical multistability can evolve from a normal bistable behavior
Acknowledgments
The author thanks Professor Benli Yu for his help and encouragement. The author also acknowledges helpful advice and comments from the referees.
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