[Paper Review] Electromagnetically induced transparency in systems with degenerate autoionizing levels in Λ-configuration

T. Bui Dinh, W. Leoński+2 more|ASEP|Jan 1, 2013

Quantum optics and atomic interactions29 references4 citations

TL;DR

This paper proposes a novel mechanism for generating additional electromagnetically induced transparency (EIT) windows in a Λ-type atomic system with two degenerate autoionizing (AI) levels coupled to a flat continuum. By introducing quantum interference between two AI channels, the model enables tunable control over the position, width, and depth of extra transparency windows via adjustable AI level parameters, offering a new route for multi-frequency slow light applications beyond conventional Zeeman-level schemes.

ABSTRACT

We discuss a Λ-like model of atomic levels involving two autoionizing (AI) states of the same energy. The system is irradiated by two external electromagnetic fields (strong -- driving and weak -- probing ones). For such a system containing degenerate AI levels we derive the analytical formula describing the medium susceptibility. We show that the presence of the second AI level lead to the additional electromagnetically induced transparency (EIT) window appearance. We show that the characteristic of this window can be manipulated by changes of the parameters describing the interactions of AI levels with other ones. This is a new mechanism which leads to additional transparency windows in EIT model, that differs from the mechanism, where a bigger number of Zeeman sublevels is taken into account.

Motivation & Objective

• To investigate how degenerate autoionizing (AI) levels in a Λ-configuration affect electromagnetically induced transparency (EIT) in the presence of strong and weak laser fields.
• To explore the role of quantum interference between two AI channels in generating additional EIT windows not present in single-AI-level systems.
• To derive an analytical expression for the medium susceptibility in a system with two degenerate AI levels and a flat continuum.
• To demonstrate that the characteristics of the additional EIT window—such as position, width, and depth—can be controlled by tuning parameters like AI level widths and asymmetry parameters.
• To extend the existing EIT model with single AI levels to include multiple AI levels, enabling new quantum interference effects and enhanced control over optical response.

Proposed method

• The model extends the Λ-configuration by introducing two degenerate autoionizing (AI) levels |a₁⟩ and |a₂⟩ with equal energy, both coupled to a common flat continuum |E⟩.
• The system is driven by a strong control field (frequency ωc) coupling |c⟩ to the AI levels and a weak probe field (frequency ωp) coupling |b⟩ to the AI levels.
• Theoretical analysis uses Fano diagonalization to transform the two AI levels and the continuum into a double Fano-structured continuum |E⟩, enabling treatment of the complex continuum structure.
• The medium susceptibility χ is analytically derived using the density matrix formalism under the rotating wave approximation and weak probe limit.
• The susceptibility is expressed as a function of detuning ω, AI level widths Γ₂₁, asymmetry parameters Qb and Qc, and coupling strengths ε₂, allowing quantitative analysis of transparency windows.
• Numerical simulations are performed to visualize the real and imaginary parts of χ across varying parameters, revealing the emergence and tunability of additional EIT windows.

Experimental results

Research questions

• RQ1 How does the presence of a second degenerate autoionizing level affect the formation of electromagnetically induced transparency (EIT) in a Λ-configuration system?
• RQ2 What role does quantum interference between two autoionization channels play in generating additional EIT windows?
• RQ3 Can the position, width, and depth of the additional EIT window be controlled by adjusting the parameters of the AI levels, such as their widths and asymmetry parameters?
• RQ4 How does the system's behavior change when the AI levels are degenerate versus non-degenerate, and what physical effects arise from this difference?
• RQ5 To what extent can the inclusion of multiple AI levels enable multi-frequency control of light propagation, such as slow light at multiple frequencies?

Key findings

• The presence of a second degenerate autoionizing level leads to the emergence of an additional EIT window in the transmission spectrum, which is absent in single-AI-level systems.
• The additional EIT window appears due to quantum interference between two distinct autoionization channels, a mechanism distinct from conventional EIT based on Zeeman sublevels.
• The width and position of the additional EIT window are tunable by adjusting the asymmetry parameters Qb and Qc associated with the probe and control fields.
• The depth of the EIT window is strongly dependent on the difference between the autoionization widths Γ₂₁ of the two AI levels; increasing this difference enhances the visibility and separation of the two transparency windows.
• When the two AI levels are identical in all parameters, the system behaves like a single effective AI level with an effective width and asymmetry, suppressing the additional window.
• Numerical results show that increasing Γ₂₁ from 0 to 0.4 (in units of Γ) leads to a pronounced splitting and broadening of the two transparency windows, confirming the controllability of the system's optical response.