Autler-Townes effect in a strongly driven electromagnetically induced transparency resonance

Lijun Yang, Lianshui Zhang, Xiaoli Li, Li Han, Guangsheng Fu, Neil B. Manson, Dieter Suter, and Changjiang Wei

Phys. Rev. A 72, 053801 – Published 1 November 2005

Abstract

In this paper we study the nonlinear behavior of an electromagnetically induced transparency (EIT) resonance subject to a coherent driving field. The EIT is associated with a $Λ$ three-level system where two hyperfine levels within an electronic ground state are coupled to a common excited state level by a coupling field and a probe field. In addition there is an radio-frequency (rf) field driving a hyperfine transition within the ground state. The paper contrasts two different situations. In one case the rf-driven transition shares a common level with the probed transition and in the second case it shares a common level with the coupled transition. In both cases the EIT resonance is split into a doublet and the characteristics of the EIT doublet are determined by the strength and frequency of the rf-driving field. The doublet splitting originates from the rf-field induced dynamic Stark effect and has close analogy with the Autler-Townes effect observed in three-level pump-probe spectroscopy study. The situation changes when the rf field is strong and the two cases are very different. One is analogous to two $Λ$ three-level systems with EIT resonance associated with each. The other corresponds to a doubly driven three-level system with rf-field-induced electromagnetically induced absorption resonance. The two situations are modeled using numerical solutions of the relevant equation of motion of density matrix. In addition a physical account of their behaviors is given in terms of a dressed state picture.

Received 13 June 2005

DOI:https://doi.org/10.1103/PhysRevA.72.053801

Authors & Affiliations

Lijun Yang¹, Lianshui Zhang^1,*, Xiaoli Li¹, Li Han¹, Guangsheng Fu¹, Neil B. Manson², Dieter Suter³, and Changjiang Wei^1,2

¹College of Physical Science and Technology, Hebei University, Baoding 071002, China
²Laser Physics Center, The Australian National University, Canberra, ACT 0200, Australia
³Fachbereich Physik, University of Dortmund, 44221 Dortmund, Germany

^*Corresponding author: ZhangLS@mail.hbu.edu.cn

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 72, Iss. 5 — November 2005

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Energy level scheme for case (a) and (b). In the bare state picture, a coupling laser (frequency $ω_{c}$ and Rabi frequency $Ω_{c}$ ) interacts with the $∣ 3 ⟩ \to ∣ 4 ⟩$ transition and a probe laser (frequency $ω_{p}$ and Rabi frequency $Ω_{p}$ ) interacts with the $∣ 1 ⟩ \to ∣ 4 ⟩$ transition, forming a $Λ$ three-level system and giving rise to an EIT resonance. An rf field (frequency $ω_{rf}$ and Rabi frequency $Ω_{rf}$ ) drives a hyperfine transition and splits the EIT resonance. Two situations are considered: (a) the rf-driven transition shares a common level with the probed transition and (b) the rf-driven transition shares a common level with the coupled transition. In the dressed state picture, the EIT double splitting occurs due to the fact that there are two occasions where the coupling and probe laser satisfy a two-photon resonance condition and give rise to two EIT resonances.Reuse & Permissions
Figure 2
Absorption of the probe laser. Curve (i) gives a normal absorption spectrum when both coupling field and rf field are absent $(Ω_{c} = Ω_{r f} = 0)$ . Curve (ii) shows an EIT resonance when a coupling field is applied resonantly with the $∣ 3 ⟩ \to ∣ 4 ⟩$ transition $(Ω_{c} = 0.2)$ . Curve (iii) shows splitting of an EIT resonance when both coupling field and rf field are applied $(Ω_{c} = Ω_{r f} = 0.2)$ . In case (a) the rf field is resonant with the $∣ 1 ⟩ \to ∣ 2 ⟩$ transition and in case (b) the rf field is resonant with the $∣ 2 ⟩ \to ∣ 3 ⟩$ transition. The probe detuning has been normalized to $W_{4}$ .Reuse & Permissions
Figure 3
Absorption of the probe laser showing a linear EIT splitting as a function of rf field Rabi frequency. The rf field is resonant with the $∣ 1 ⟩ \to ∣ 2 ⟩$ transition for case (a) and with the $∣ 2 ⟩ \to ∣ 3 ⟩$ transition for case (b). The coupling field is resonant with the $∣ 3 ⟩ \to ∣ 4 ⟩$ transition and has a Rabi frequency $Ω_{c} = 0.2$ . The probe detuning and rf Rabi frequency have been normalized to $W_{4}$ .Reuse & Permissions
Figure 4
Absorption of the probe laser showing EIT splitting as a function of rf field detuning for case (a) and (b). The coupling field is resonant with the $∣ 3 ⟩ \to ∣ 4 ⟩$ transition and has a Rabi frequency $Ω_{c} = 0.2$ . The rf field has a Rabi frequency $Ω_{rf} = 0.2$ . The probe detuning and rf detuning have been normalized to $W_{4}$ .Reuse & Permissions
Figure 5
Absorption of the probe laser for the situation where the rf field Rabi frequency is comparable to or larger than the optical linewidth. The rf field is resonant with the $∣ 1 ⟩ \to ∣ 2 ⟩$ transition for case (a) and with the $∣ 2 ⟩ \to ∣ 3 ⟩$ transition for case (b). The coupling field is resonant with the $∣ 3 ⟩ \to ∣ 4 ⟩$ transition and has a Rabi frequency $Ω_{c} = 0.2$ . The probe detuning and rf Rabi frequency have been normalized to $W_{4}$ .Reuse & Permissions
Figure 6
Absorption of the probe laser for the situation where both coupling field and rf field Rabi frequencies are comparable to or larger than the optical linewidth. The rf field is resonant with the $∣ 1 ⟩ \to ∣ 2 ⟩$ transition for case (a) and with the $∣ 2 ⟩ \to ∣ 3 ⟩$ transition for case (b). The coupling field is resonant with the $∣ 3 ⟩ \to ∣ 4 ⟩$ transition and has the Rabi frequency $Ω_{c} = 4$ . The probe detuning and rf Rabi frequency have been normalized to $W_{4}$ .Reuse & Permissions

Physical Review A

covering atomic, molecular, and optical physics and quantum information