Four-wave mixing in potassium vapor with off-resonant double lambda system

D. Arsenović, M. M. Ćurčić, B. Zlatković, A. J. Krmpot, I. S. Radojicić, T. Khalifa and B. M. Jelenković

Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia

Studying four-wave mixing (FWM) in alkali vapor is of the essential value for generating new states of light [1], important for probing quantum properties of light and for quantum information [2]. We studied theoretically and experimentally FWM in hot potassium vapor by co-propagating pump and probe, using off-resonant double Λ interaction scheme. Experimental setup that we used was presented in [3]. We compared theoretical and experimental results obtained for a wide range of parameters important for efficiency of FWM.

Experimental setup Double Λ interaction scheme

Model is semi-classical treatment of FWM. It is one with compete numerical calculation, without perturbation theories and approximation!

Total electric field that atoms experience: 𝑬 = 𝒆𝑖𝐸𝑖(+)

𝑒−𝑖𝜔𝑡+𝑖𝒌𝑖𝒓𝑖=𝑑,𝑝,𝑐 + 𝑐. 𝑐.

The Hamiltonian for atomic system: 𝐻 = 𝐻 0 +𝐻 𝑖𝑛𝑡 = ℏ𝜔𝑖 𝑖 𝑖 − 𝒅 ∙ 𝑬 𝒓, 𝑡 .4𝑖=1

Bloch equations for density matrix elements, for describing atomic dynamics:

𝜌 = −𝑖

ℏ𝐻 , 𝜌 + 𝑆𝐸 + 𝑅 .

Propagation of all three beams through K vapor, along the z direction, is described by: 𝜕

𝜕𝑧+

1

𝑐

𝜕

𝜕𝑡𝐸𝑑(+)

= 𝑖𝑘𝑁

2ℰ0 𝑑 𝜌 (42) + 𝜌 (31)

𝜕

𝜕𝑧+

1

𝑐

𝜕

𝜕𝑡𝐸𝑝(+)

= 𝑖𝑘𝑁

2ℰ0 𝑑𝜌 (32)

𝜕

𝜕𝑧+

1

𝑐

𝜕

𝜕𝑡𝐸𝑐

+ = 𝑖𝑘𝑁

2ℰ0 𝑑𝜌 (41)

Comparing between theory and experiment (cont.)

REFERENCES [1] C. F. McCormick et al., Phys Rev A 78, 043816 (2008). [2] C. Shu et al., Nat Comm. 7, 12783 (2016) DOI: 10.1038/ncomms12783. [3] B. Zlatkovicet al., Las Phys Lett 13, 015205 (2015).

Email:marijac@ipb.ac.rs

Acknowledgments: Authors acknowledge financial help from grants III45016 and OI131038 of the Ministry of education, science and technological development.

References:

Acknowledgments:

Ω =2𝑑𝐸0

+

ℎ , 𝐸 = 𝐸0 cos 𝜔𝑡 = 𝐸0

+𝑒−𝑖𝜔𝑡 + 𝐸0

−𝑒𝑖𝜔𝑡

𝐸0+

=𝐸02= 𝜂𝐼 2 , 𝜂 = 376.73 Ω,

d = 1.74 ∙ 10−29 𝐶𝑚

𝑔𝑎𝑖𝑛 = 𝐼𝑏𝑒ℎ𝑖𝑛𝑑 𝑡ℎ𝑒 𝑐𝑒𝑙𝑙

𝐼𝑖𝑛𝑝𝑢𝑡 𝑝𝑟𝑜𝑏𝑒

Theory : dependence on angle

conjugate

conjugate

optimum phase matching

conjugate

probe

probe

conjugate

Obtained gain - up to 536!!!

Exp: dependence on angle Dependence on probe power

Dependence on one-photon detuning

Dependence on two-photon detuning

- Good agreement between experimental results and theory predictions.

- Strong phase insensitive amplifier for Δ around 1 GHz and N~5.5 ∙ 1012 𝑐𝑚−3

- Resonances shift from zero, depending on the pump detuning and angle. .

(a) 𝑁 = 2 ∙ 1012 𝑐𝑚−3 b) 𝑁 = 2 ∙ 1011 𝑐𝑚−3 Ω𝑑= 1.95 𝐺𝐻𝑧, Ω𝑝 = 22.5 𝑀𝐻𝑧, 𝛿 = −10 𝑀𝐻𝑧, Δ = 1 𝐺𝐻𝑧

𝑁 = 5.5 ∙ 1012 𝑐𝑚−3 130𝑜𝐶 ,𝛿 = −3.7 𝑀𝐻𝑧, Δ = 1 𝐺𝐻𝑧,

𝑃𝑝𝑢𝑚𝑝 = 370 𝑚𝑊, 𝑃𝑝𝑟𝑜𝑏𝑒 = 25 𝜇𝑊.

(a) Ω𝑑= 1.95 𝐺𝐻𝑧, (b) 𝑃𝑝𝑢𝑚𝑝 = 370 𝑚𝑊,

Ω𝑝= 22.5 𝑀𝐻𝑧 𝑃𝑝𝑟𝑜𝑏𝑒 = 25 𝜇𝑊,

𝑁 = 1 ∙ 1012 𝑐𝑚−3, T = 130𝑜𝐶, Δ = 960 𝑀𝐻𝑧, 𝛿 = −3.7 𝑀𝐻𝑧.

(a) 𝛿 = −4.5 𝑀𝐻𝑧, (b) 𝛿 = −7.7 𝑀𝐻𝑧, Ω𝑑 = 1.95 𝐺𝐻𝑧, Ω𝑝 = 22.5 𝑀𝐻𝑧. 𝑁 = 1 ∙ 1012𝑐𝑚−3, (c) 𝛿 = 0.3 𝑀𝐻𝑧, (d) 𝛿 = −7.7 𝑀𝐻𝑧, 𝑃𝑝𝑢𝑚𝑝 = 370 𝑚𝑊, 𝑃𝑝𝑟𝑜𝑏𝑒 = 25 𝜇𝑊.

𝑁 = 5.5 ∙ 1012.

𝜃 = 5.5 𝑚𝑟𝑎𝑑

𝜃 = 5.5 𝑚𝑟𝑎𝑑

(a) Δ = 1 𝐺𝐻𝑧, (b) Δ = 1.35 𝐺𝐻𝑧, Ω𝑑 = 1.95 𝐺𝐻𝑧, Ω𝑝 = 22.5 𝑀𝐻𝑧, 𝑁 = 1 ∙ 1012𝑐𝑚−3, (c) Δ = 1 𝐺𝐻𝑧, (d) Δ = 1.35 𝐺𝐻𝑧 𝑃𝑝𝑢𝑚𝑝 = 370 𝑚𝑊, 𝑃𝑝𝑟𝑜𝑏𝑒 = 25 𝜇𝑊,

𝑁 = 5.5 ∙ 1012.