Ultranarrow resonance due to coherent population oscillations in a \ensuremath{\Lambda}-type atomic system

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Ultranarrow resonance due to coherent population oscillations in a Λ-type atomic system

T. Lauprêtre, S. Kumar, P. Berger, R. Faoro, R. Ghosh, F. Bretenaker, and F. Goldfarb

Phys. Rev. A 85, 051805(R) – Published 24 May 2012

Abstract

It is well known that ultranarrow electromagnetically induced transparency (EIT) resonances can be observed in atomic gases at room temperature. We report here the experimental observation of another type of ultranarrow resonance, as narrow as the EIT ones, in a $Λ$ system selected by light polarization in metastable $^{4}$ He at room temperature. It is shown to be due to coherent population oscillations in an open two-level system (TLS). For perpendicular linearly polarized coupling and probe beams, this system can be considered as two coupled open TLSs, in which the ground-state populations exhibit antiphase oscillations. We also predict theoretically that in the case of two parallel polarizations, the system would behave like a closed TLS, and the narrow resonance associated with these oscillations would disappear.

Received 18 January 2012

DOI:https://doi.org/10.1103/PhysRevA.85.051805

Authors & Affiliations

T. Lauprêtre¹, S. Kumar², P. Berger^1,3, R. Faoro¹, R. Ghosh², F. Bretenaker¹, and F. Goldfarb^1,*

¹Laboratoire Aimé Cotton, CNRS–Université Paris Sud 11, 91405 Orsay Cedex, France
²School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
³Thales Research and Technology, Campus Polytechnique, 91767 Palaiseau Cedex, France

^*fabienne.goldfarb@u-psud.fr

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Vol. 85, Iss. 5 — May 2012

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Figure 1
(a),(b) Relevant level schemes in the case of excitation by orthogonal circular ( $σ ⊥ σ$ ) and linear ( $lin ⊥ lin$ ) polarizations. $Ω_{P}$ ( $Ω_{C}$ ) and $ω_{P}$ ( $ω_{C}$ ): Rabi and optical frequencies of the probe (coupling) beam. $δ = ω_{C} - ω_{P}$ . (c) Experimental setup. AO: acousto-optic modulator. PBS, polarizing beam-splitter; PD, photodetector.Reuse & Permissions
Figure 2
Experimental results with (green) and without (black) a 15 mG magnetic field, which shifts the $m = \pm 1$ Zeeman sublevels by $\pm Δ_{Z}$ , recorded with (a) circular polarizations and (b) linear polarizations. Two EIT peaks appear for $δ = \pm 2 Δ_{Z}$ , but the central resonance at $δ = 0$ does not correspond to any Raman resonance.Reuse & Permissions
Figure 3
(a) Experiment: evolution of the resonance width versus average coupling intensity for the standard EIT resonance (squares) and for the central resonance in the $lin ⊥ lin$ configuration (circle). Open (filled) symbols correspond to measurements performed in the absence (presence) of a magnetic field gradient. (b) Theory: simulated probe transmission spectra in the $lin ⊥ lin$ configuration for two values of the Raman coherence decay rate, $Γ_{R} / 2 π = 3 kHz$ (continuous blue), corresponding to the experimental values marked by the open symbols in (a), and $Γ_{R} / 2 π = 12 kHz$ (dashed purple). The transit decay rate is kept fixed at $Γ_{t} / 2 π = 2 kHz$ .Reuse & Permissions
Figure 4
Simulations of the transmission of an open TLS in the case of (a) $Γ_{e} / 2 π = Γ_{0} / 2 π = 1.6 MHz > Γ_{g} / 2 π = Γ_{t} / 2 π = 2 kHz$ and (b) $Γ_{e} = Γ_{t} ≪ Γ_{g} = Γ_{0} / 2$ . Continuous blue: simulations with the Floquet expansion of the complete density matrix. Dashed purple: simple rate equation model analysis. Inset: open TLS. $Γ_{coh}$ is the optical coherence relaxation rate. (c),(d) Evolutions of the oscillating parts $Δ N_{e} = (N_{1 e} e^{- i δ t} + c . c .)$ and $Δ N_{g} = (N_{1 g} e^{- i δ t} + c . c .)$ of the excited (continuous purple) and ground (dashed blue) -state populations versus $δ$ at a fixed time $t = 0.25 ms$ . (c) Same parameters as (a). (d) Same parameters as (b).Reuse & Permissions
Figure 5
(a) Simulated probe transmission spectrum in a $Λ$ system in the $lin ⊥ lin$ (continuous blue) and $lin ∥ lin$ (dashed purple) configurations. (b) Evolutions versus $δ$ of the oscillating parts $Δ N_{e} = (N_{1 e} e^{- i δ t} + c . c .)$ of the excited state (continuous purple), and $Δ N_{g 1} = (N_{1 g 1} e^{- i δ t} + c . c .)$ (dashed blue) and $Δ N_{g 2} = (N_{1 g 2} e^{- i δ t} + c . c .)$ (dotted green) of the two ground states, at a fixed time $t$ in the $lin ⊥ lin$ configuration. (c),(d) Evolutions versus $δ$ of the oscillating part $Δ N_{e}$ of the excited state (continuous purple) and of the sum $Δ N_{g 1} + Δ N_{g 2}$ of the oscillating parts of the two ground-state populations (dashed blue), in the $lin ∥ lin$ configuration.Reuse & Permissions

Physical Review A

covering atomic, molecular, and optical physics and quantum information

Ultranarrow resonance due to coherent population oscillations in a Λ-type atomic system

T. Lauprêtre, S. Kumar, P. Berger, R. Faoro, R. Ghosh, F. Bretenaker, and F. Goldfarb

Phys. Rev. A 85, 051805(R) – Published 24 May 2012

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Physical Review A

covering atomic, molecular, and optical physics and quantum information

Ultranarrow resonance due to coherent population oscillations in a Λ-type atomic system

T. Lauprêtre, S. Kumar, P. Berger, R. Faoro, R. Ghosh, F. Bretenaker, and F. Goldfarb

Phys. Rev. A 85, 051805(R) – Published 24 May 2012

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