Control of the optical multistability in a three-level ladder-type quantum well system

doi:10.1016/j.optcom.2009.09.013

Optics Communications

Volume 282, Issue 24, 15 December 2009, Pages 4745-4748

https://doi.org/10.1016/j.optcom.2009.09.013 Get rights and content

Abstract

We theoretically investigated a hybrid absorptive–dispersive optical multistability (OM) behavior in a three-level ladder-type quantum well system inside a unidirectional ring cavity. We find that the frequency detuning of the control field and the electronic cooperation parameter as well as the total decay rates can affect the optical multistability behavior dramatically, which can be used to manipulate efficiently the threshold intensity and the hysteresis loop. The effect of the intensity of the control field on the OM is also studied. Our study is much more practical than its atomic counterpart due to its flexible design and the wide adjustable parameters. Thus it may provide some new possibilities for technological applications in optoelectronics and solid-state quantum information science.

Introduction

In the past few decades, a great deal of quantum optical phenomena based on coherence and quantum interference have attracted a lot of attention of many researchers in the quantum coherent media [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [33]. One of the interesting phenomena, the optical bistability (OB) in multilevel atoms confined in an optical cavity [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], has been the subject of many recent studies because of its potential wide applications in all-optical switches, memories, transistors, and logic circuits [25], [26], [27]. The studies show that one can control the bistable threshold intensity and the hysteresis loop via different approaches such as the field-induced transparency [14], the spontaneously generated coherence [20], [21], [22], [23], [24], the phase fluctuation [15], [16], the squeezed state field [17], [18], [19], the atomic cooperation parameter [24], the finite pump laserline width [21], the intensity of the microwave field [22] and so on.

On the other hand, the optical multistability (OM) has also been extensively studied in the multilevel atomic system involving interactions between nonlinear media and two different optical cavity field modes [28], [29], [30], [31]. In the earlier studies, Kitano et al. [28] proposed a scheme for optical tristability under the limiting condition of large atomic detuning with no saturation in a three-level $\land$ -type atomic system, then the scheme was experimentally achieved by Cecchi et al. [29]. By including saturation in the dispersive limit, Savage et al. [30] showed that the asymmetric state becomes unstable and gives rise to self-oscillations and a different kind of optical turbulence. Later on, Arecchi et al. [31] reported that not only the tristability but also higher-order bistability can be achieved by including the effect of ground-state coherence. Very recently, some new schemes for optical multistability in multilevel atoms confined in an optical cavity have been studied theoretically [24] and experimentally [13]. It has been shown that the possibility of obtaining optical multistability in the multilevel atomic systems can be realized via the spontaneously generated coherence [20], [22], via the strength or the frequency detuning of the coupling field [21], [24], via the atomic number density [13], or via the sideband [16], etc.

It should be worth pointing out that a great deal of nonlinear quantum optical phenomena based on the quantum interference and coherence are also been extensively studied in the semiconductor quantum wells (SQWs) in recent years [34], [35], [36], [37], [38], [39], [40], [41], [42], [43], [44], [45], [46], [47], such as gain without inversion [34], [35], [36], electromagnetically induced transparency [37], [38], [39], [40], [46], optical bistability [41], [42], Kerr nonlinearity [43], optical soliton [44], four-wave mixing [45]. The reason for this is mainly the phenomena in the SQWs have many potentially important applications in optoelectronics and solid-state quantum information science. Otherwise, the devices based on inter-subband transitions in the SQWs have many inherent advantages that the atomic systems do not have, such as the large electric dipole moments due to the small effective electron mass, the great flexibilities in devices design by choosing the materials and structure dimensions, the high nonlinear optical coefficients, and the transition energies and the dipoles as well as the symmetries can also be engineered as desired [42].

In this work, we investigate a hybrid absorptive–dispersive optical multistability behavior in a three-level ladder-type quantum well system inside a unidirectional ring cavity. The optical bistability has been studied by Joshi and Xiao [41] and Li [42] quite recently, however, the optical multistability can not be realized in their quantum well systems, which motivate us to carry out the current work. Our study and the system based on the Refs. [41], [42], [47], but our work are drastically different from those works. First and foremost is that we are interested in showing the controllability of the hybrid absorptive–dispersive optical multistability behavior via the different parameters. Second, an important advantage of our scheme is that we have realized optical multistability in our quantum well system. It is well known that the OM also plays a crucial role in nonlinear quantum optics, which will have more advantages than the OB in some applications where more than two states are needed. 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 three-level ladder-type quantum well system with three levels as shown in Fig. 1 (see Refs. [41], [47]). Two laser fields $\tilde{E} = 1 / 2 (E_{c} e^{- i ω_{c} t} + E_{p} e^{- i ω_{p} t} + c . c .)$ are mediated, of which E_c is a control laser field and serves as coherent driving with Rabi frequencies $Ω_{c 1} = μ_{12} E_{c} / ℏ and Ω_{c 2} = μ_{23} E_{c} / ℏ$ , and E_p a weak field and is used as a probe field with Rabi frequencies $Ω_{p 1} = μ_{12} E_{p} / ℏ and Ω_{p 2} = μ_{23} E_{p} / ℏ$ . Following the method described in the Ref. [33], the Hamiltonian of the system is given by $(ℏ = 1)$ : $H = H_{c} + H_{p}$

Numerical results

Now we give some numerical studies under the steady-state conditions, as shown in Fig. 2, Fig. 3, Fig. 4, Fig. 5. In the following numerical calculations, we choose the also parameters to be dimensionless units by scaling $γ = 1 meV$ and let $δ = 0$ . In addition, we assume that all subbands have the same effective mass and the electron–electron effects have very small influence on our results, and the choices of the parameters are based on some results from Refs. [40], [41], [42], [46]. The choice of

Conclusion

To sum up, we theoretically investigated a hybrid absorptive–dispersive optical multistability behavior in a three-level ladder-type quantum well system inside a unidirectional ring cavity. We find that the frequency detuning of the control field and the electronic cooperation parameter as well as the total decay rates can affect the optical multistability behavior dramatically, which can be used to manipulate efficiently the threshold intensity and the hysteresis loop. The effect of the

Acknowledgements

The author thank Prof. Hong-Yi Fan and Prof. Ai-Xi Chen for their support.

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Control of the optical multistability in a three-level ladder-type quantum well system

Abstract

Introduction

Section snippets

The model and the dynamic equations

Numerical results

Conclusion

Acknowledgements

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