Dynamic control of four-wave-mixing enhancement in coherently driven four-level atoms

Xue Yan, He Qiong-Yi, G. C. LaRocca, M. Artoni, Xu Ji-Hua, and Gao Jin-Yue

Phys. Rev. A 73, 013816 – Published 23 January 2006

Abstract

We analyze a four-wave mixing enhancement scheme based on a specific lifetime-broadened four-level atomic configuration. The enhancement can mainly be controlled through the time-dependent propagation dynamics of the applied pulse fields, but it is also found to depend on the sample density and spontaneous emission of the levels involved. A systematic analysis, that illustrates how the applied pulses dynamics, density, and spontaneous emission affect the mixing conversion efficiency, is carried out, anticipating substantially large efficiencies for realistic atomic parameters and short weak laser pulses.

Received 21 September 2005

DOI:https://doi.org/10.1103/PhysRevA.73.013816

Authors & Affiliations

Xue Yan^1,2, He Qiong-Yi^1,2, G. C. LaRocca^3,*, M. Artoni^4,5,†, Xu Ji-Hua³, and Gao Jin-Yue^1,2,‡

¹College of Physics, Jilin University, Changchun 130023, P. R. China
²Key Lab of CLAMS of Educational Ministry, Changchun 130023, P. R. China
³Scuola Normale Superiore and INFM, Pisa, Italy
⁴Department of Physics and Chemistry of Materials and LENS, Brescia University, Brescia, Italy
⁵European Laboratory for Non-Linear Spectroscopy, Sesto Fiorentino, Italy

^*Email address: larocca@sns.it
^†Email address: artoni@lens.unifi.it
^‡Corresponding author. Email address: jygao@mail.jlu.edu.cn

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Vol. 73, Iss. 1 — January 2006

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Images

Figure 1
Energy level diagram for a $Λ$ configuration where the common excited level is coupled to the two lower levels by two laser pulses with Rabi frequencies $Ω_{1}$ and $Ω_{2}$ . Pulse sequence leading to standard stirap (b) whereby population is transferred from ∣1⟩ to ∣2⟩ with 100% efficiency. A pulse sequence leading to a fractional stirap (c) where a pair of pulses with the same trailing edge generates maximum coherence between the two lower levels ∣1⟩ and ∣2⟩.Reuse & Permissions
Figure 2
Energy level diagram (a) for a lifetime-broadened four-level atomic system where, in the presence of two strong coupling laser pulses $Ω_{1}$ and $Ω_{2}$ , a weak probe laser pulse $Ω_{3}$ generates the signal field $Ω_{4}$ . Schematic time sequence (b) leading to efficient four-wave-mixing conversion, where $t_{0}$ is the delay between the coupling pulse $Ω_{2}$ and $Ω_{1}$ and $t_{1}$ is the time delay between the probe pulse $Ω_{3}$ and $Ω_{1}$ . Here $τ_{1}$ , $τ_{2}$ , and $τ_{3}$ denote the three sine-square pulses time durations.Reuse & Permissions
Figure 3
Scaled signal pulse shapes vs time $τ$ for different probe pulse input times $τ_{10}^{1} = 20 ns$ , $τ_{10}^{2} = 40 ns, \dots, τ_{10}^{4} = 80 ns$ shown in the abscissa. The probe has a fixed intensity $Ω_{30} = 0.1 MHz$ and a time duration $τ_{3} = 20 ns$ . The coupling beams parameters are $Ω_{10} = Ω_{20} = 10 MHz$ , $τ_{0} = 0$ and $τ_{1} = τ_{2} = 200 ns$ while the initial atomic parameters are $ρ_{11} (τ = ξ = 0) = 1$ , $ρ_{i j} (τ = ξ = 0) = 0$ , and ( $i \neq j$ or $i = j \neq 1$ ) with $Γ_{21} = Γ_{31} = 4 MHz$ , $Γ_{42} = Γ_{43} = 7 MHz$ , and an atomic density $N = 0.98 \times 10^{11} {cm}^{- 3}$ .Reuse & Permissions
Figure 4
Time evolution $(b, c)$ of the maximum four-wave mixing signal conversion efficiency $(η)$ for different coupling pulses delays $(τ_{0})$ . The probe pulse is kept at the delay optimal value $τ_{10} = τ - τ_{3} ∕ 2$ where $τ_{3} = 20 ns$ and $Ω_{30} = 0.1 MHz$ . The other parameters are the same as in Fig. 3. Temporal sequence $(a)$ used in $(b, c)$ and relevant probe (dot) and coupling (solid-dash) pulse shapes.Reuse & Permissions
Figure 5
Maximum mixing efficiency and atomic coherences $ρ_{12}, ρ_{13}, ρ_{23}$ vs time for coupling pulses whose mutual delay is (a) $τ_{0} = 0 ns$ , (b) $τ_{0} = 10 ns$ , (c) $τ_{0} = 100 ns$ , and (d) $τ_{0} = 120 ns$ . In (a) $ρ_{12}$ and $ρ_{13}$ overlap. The other parameters are the same as in Fig. 4.Reuse & Permissions
Figure 6
Maximum efficiency (a) vs the coupling pulse Rabi frequency $Ω_{10}$ and vs the relevant transition radiative decay $Γ_{21}$ when the probe-coupling pulses mutual delays are $τ_{0} = 100 ns$ and $τ_{10} = 140 ns$ . Thin lines guide the eye to the corresponding axes. The three lower levels populations and coherences around the region of coupling beam intensities leading to optimal conversion efficiency are instead shown in the inset. Maximum efficiency (b) vs the probe pulse Rabi frequency $Ω_{30}$ and relevant transition decay rate $Γ_{42}$ with the same pulse sequence as in (a). Signal efficiency $η$ (c) vs the sample atomic density $N$ . All other parameters are the same as in Fig. 4.Reuse & Permissions

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