Soliton-train storage and retrieval in Λ-type three-level atom systems

Transcription

1 The 4th editi of the African school of physics fundamental physics N-linear Solit-train storage retrieval in Λ-type three-level atom systems Presented by Under the supervisi of Dr. Diké A. Moïse N-linear (LaRA University of Buea August, 2016 Solit-train storage retrieval in Λ-type three-level atom systems N-linear (LaRa 1

2 Nlinear Science (LaRA N-linear FIGURE: LaRAMaNS simulati lab (University of Buea, Camero) The Nlinear Science (LaRA, created in 2008, is the initiative of Dr. Alain M. Dike, Head of Physics Department, University of Buea. The main missi of the group is providing the Department of Physics of the University of Buea, with a formal frame for research in support of the existing postgraduate programme. Theoretical cdensed matter physics. Nlinear dynamics complex systems. Optics nlinear communicati. Material sciences. Solit-train storage retrieval in Λ-type three-level atom systems 2/16 N-linear (LaRa 2

3 Outline of the Presentati N-linear. The Atom-Cavity System. Intracavity Electromagnetically Induced Transparency : Formati of the dark state. single-phot. Cclusi Solit-train storage retrieval in Λ-type three-level atom systems N-linear (LaRa 3

4 N-linear Coherent light-matter interacti brings about novel applicatis due to coherence. Atomic coherence is the induced coherence between levels of a multi-level system when it interacts with coherent electromagnetic fields. Coherent preparati by laser light of the states of atoms can lead to interference in the amplitudes of optical transitis. Interference effects between excitati pathways modify the optical respse of the medium. Atomic coherence interference have been extended applied to many areas of optics. Quantum coherence interference in systems leads to interesting optical phenomena Examples being : coherent populati trapping (CPT), electromagnetically induced transparency (EIT), lasing without inversi (LWI), etc. Solit-train storage retrieval in Λ-type three-level atom systems N-linear (LaRa 4

5 N-linear Purpose of the investigati This work was stimulated by recent experiments in which electromagnetically induced transparency has been used to dramatically reduce the group velocity of light in vapours (L.V. Hau, et al. Nature 397, 594(1999)), etc. M. Fleischhauer et al.(opt. comm. 179, 395(2000)) used this idea to store retrieve the states of single phots in an optically dense ensemble of atoms inside a resator. Intracavity EIT technique (M.D. Lukin, et al. Opt. Lett. 23, 295(1998)) was used to store retrieve the travelling wave-packets. We use closely related ideas to investigate storage multiplexed time-entangled single-mode phot trains of optical pulses of finite entanglement period in an optically dense electromagnetically induced transparent medium. We anticipate the possibility of the high-fidelity memory for phot correlatis to new states of matter which have promises in applicatis in informati processing. Solit-train storage retrieval in Λ-type three-level atom systems N-linear (LaRa 5

6 The atom-cavity system N-linear Atom-Cavity system Our model is based schemes of stopped light in vapours (Chen Liu, et al. Nature 409(6819), 490(2001)). FIGURE: 1. A system of an gas cfined within an optical resator. The total Hamiltian of the cavity system fields to be applied is given by : H T = H atom + H field + H int. (1) Where H atom = i ω i i i, H field = ω c â â, H int = d. E are respectively the Hamiltians for the bare atom, the single cavity mode field, its interacti with electromagnetic fields. Solit-train storage retrieval in Λ-type three-level atom systems N-linear (LaRa 6

7 The atom-cavity system N-linear Atom-Cavity system Our model is based schemes of stopped light in vapours (Chen Liu, et al. Nature 409(6819), 490(2001)). FIGURE: 1. A system of an gas cfined within an optical resator. The total Hamiltian of the cavity system fields to be applied is given by : H T = H atom + H field + H int. (1) Where H atom = i ω i i i, H field = ω c â â, H int = d. E are respectively the Hamiltians for the bare atom, the single cavity mode field, its interacti with electromagnetic fields. Solit-train storage retrieval in Λ-type three-level atom systems N-linear (LaRa 6

8 The atom-cavity system N-linear Atom-Cavity system : Interacti with probe ctrol fields FIGURE: 2. Interacti of the cavity system with a probe coupling lasers. The Hamiltian of the three-level atom with the cavity fields of fig 2 in the rotating wave approximati (RWA) dipole approximati is given by : N N H T = κ â ˆb k + g âσ i ab + Ω(t)e iνt σ i ac + h.c. (2) k i=1 Here, σ ab = a b is the spin flip operator, â is the annihilati operator, g is the coupling cstant for the single-mode field, Ω(t) is the Rabi frequency of the classical driving field. i=1 Solit-train storage retrieval in Λ-type three-level atom systems N-linear (LaRa 7

9 Intracavity Electromagnetically Induced transparency (EIT) N-linear Electromagnetically Induced transparency FIGURE: 3. Explanati of the EIT theory. EIT is a interference effect that leads to the cancellati of light absorpti by an resance (S.E. Harris, Phys. Today 50, 36 (1997).) At two-phot resance the dressed system has new eigenstates : H new = { a, D, B } D = Ω b g N c g 2 N + Ω 2, B = g N b + Ω c g 2 N + Ω 2. (3) The dark state is decoupled from the two fields since H T D = 0. (4) Solit-train storage retrieval in Λ-type three-level atom systems N-linear (LaRa 8

10 Intracavity Electromagnetically Induced transparency (EIT) N-linear Electromagnetically Induced transparency FIGURE: 3. Explanati of the EIT theory. EIT is a interference effect that leads to the cancellati of light absorpti by an resance (S.E. Harris, Phys. Today 50, 36 (1997).) At two-phot resance the dressed system has new eigenstates : H new = { a, D, B } D = Ω b g N c g 2 N + Ω 2, B = g N b + Ω c g 2 N + Ω 2. (3) The dark state is decoupled from the two fields since H T D = 0. (4) Solit-train storage retrieval in Λ-type three-level atom systems N-linear (LaRa 8

11 Intracavity Electromagnetically Induced transparency (EIT) N-linear Electromagnetically Induced transparency FIGURE: 3. Explanati of the EIT theory. EIT is a interference effect that leads to the cancellati of light absorpti by an resance (S.E. Harris, Phys. Today 50, 36 (1997).) At two-phot resance the dressed system has new eigenstates : H new = { a, D, B } D = Ω b g N c g 2 N + Ω 2, B = g N b + Ω c g 2 N + Ω 2. (3) The dark state is decoupled from the two fields since H T D = 0. (4) Solit-train storage retrieval in Λ-type three-level atom systems N-linear (LaRa 8

12 N-linear single-phot The Model for storage retrieval process A representati of the interacti of the cavity EIT medium is depicted in Fig 2. FIGURE: 4. An optically dense medium cfined within a cavity. The state vector describing the cavity system with single-phot field is : Ψ(t) = b(t) b, 1, 0 k + a(t) a, 0, 0 k + c(t) c, 0, 0 k + ξ k (t) b, 0, 1 k, (5) The dark bright eigenstates of the cavity system is given by : D, 1 = i cos θ(t) b, 1 + i sin θ(t) c, 0, B = sin θ(t) b, 1 + cos θ(t) c, 0, (6) N-linear (LaRa Solit-train storage retrieval in Λ-type three-level atom systems 9 k

13 N-linear single-phot The Model for storage retrieval process A representati of the interacti of the cavity EIT medium is depicted in Fig 2. FIGURE: 4. An optically dense medium cfined within a cavity. The state vector describing the cavity system with single-phot field is : Ψ(t) = b(t) b, 1, 0 k + a(t) a, 0, 0 k + c(t) c, 0, 0 k + ξ k (t) b, 0, 1 k, (5) The dark bright eigenstates of the cavity system is given by : D, 1 = i cos θ(t) b, 1 + i sin θ(t) c, 0, B = sin θ(t) b, 1 + cos θ(t) c, 0, (6) N-linear (LaRa Solit-train storage retrieval in Λ-type three-level atom systems 9 k

14 N-linear single-phot Probability amplitude method for dark state populati retrieved field The equatis of moti in the interacti picture are : Ḋ(t) = κ cos θ(t) ξ k (t), ξ k (t) = i k ξ k (t) κ cos θ(t)d(t). (7) k For which their respective solutis are : D(t) = γ c t cos θ(τ)φ in (0, τ)e γ t 2 τ cos2 θ(τ )dτ dτ, (8) L t 0 γl Φ out (0, t) = c D(t 1) cos θ(t)e γ t 2 t dτ cos 2 θ(τ) 1. (9) The impedance matching cditi Φ out = Φ out = 0 is given by : d dt ln cos θ(t) + d dt ln Φ in(t) = γ 2 cos2 θ(t). (10) The soluti of the impedance cditi in terms of cos θ(t) is given by : cos θ(t) = 1 γ Φ in (t) t t 0 Φ 2 in (t )dt. (11) Solit-train storage retrieval in Λ-type three-level atom systems N-linear (LaRa 10

15 N-linear single-phot Probability amplitude method for dark state populati retrieved field The equatis of moti in the interacti picture are : Ḋ(t) = κ cos θ(t) ξ k (t), ξ k (t) = i k ξ k (t) κ cos θ(t)d(t). (7) k For which their respective solutis are : D(t) = γ c t cos θ(τ)φ in (0, τ)e γ t 2 τ cos2 θ(τ )dτ dτ, (8) L t 0 γl Φ out (0, t) = c D(t 1) cos θ(t)e γ t 2 t dτ cos 2 θ(τ) 1. (9) The impedance matching cditi Φ out = Φ out = 0 is given by : d dt ln cos θ(t) + d dt ln Φ in(t) = γ 2 cos2 θ(t). (10) The soluti of the impedance cditi in terms of cos θ(t) is given by : cos θ(t) = 1 γ Φ in (t) t t 0 Φ 2 in (t )dt. (11) Solit-train storage retrieval in Λ-type three-level atom systems N-linear (LaRa 10

16 N-linear single-phot Probability amplitude method for dark state populati retrieved field The equatis of moti in the interacti picture are : Ḋ(t) = κ cos θ(t) ξ k (t), ξ k (t) = i k ξ k (t) κ cos θ(t)d(t). (7) k For which their respective solutis are : D(t) = γ c t cos θ(τ)φ in (0, τ)e γ t 2 τ cos2 θ(τ )dτ dτ, (8) L t 0 γl Φ out (0, t) = c D(t 1) cos θ(t)e γ t 2 t dτ cos 2 θ(τ) 1. (9) The impedance matching cditi Φ out = Φ out = 0 is given by : d dt ln cos θ(t) + d dt ln Φ in(t) = γ 2 cos2 θ(t). (10) The soluti of the impedance cditi in terms of cos θ(t) is given by : cos θ(t) = 1 γ Φ in (t) t t 0 Φ 2 in (t )dt. (11) Solit-train storage retrieval in Λ-type three-level atom systems N-linear (LaRa 10

17 N-linear single-phot Probability amplitude method for dark state populati retrieved field The equatis of moti in the interacti picture are : Ḋ(t) = κ cos θ(t) ξ k (t), ξ k (t) = i k ξ k (t) κ cos θ(t)d(t). (7) k For which their respective solutis are : D(t) = γ c t cos θ(τ)φ in (0, τ)e γ t 2 τ cos2 θ(τ )dτ dτ, (8) L t 0 γl Φ out (0, t) = c D(t 1) cos θ(t)e γ t 2 t dτ cos 2 θ(τ) 1. (9) The impedance matching cditi Φ out = Φ out = 0 is given by : d dt ln cos θ(t) + d dt ln Φ in(t) = γ 2 cos2 θ(t). (10) The soluti of the impedance cditi in terms of cos θ(t) is given by : cos θ(t) = 1 γ Φ in (t) t t 0 Φ 2 in (t )dt. (11) Solit-train storage retrieval in Λ-type three-level atom systems N-linear (LaRa 10

18 N-linear single-phot Normalized input field : Storage, retrieval observati of solit trains The D(t) output relati becomes : D(t) = c L 1 t Φ 2 t 0 in (t )dt Φ out (t) = Φ in (t) t Φ t in (t )dt 0 t1 t t 0 Φ 2 in t 0 Φ 2 in (τ)dτ. (12) (τ)dτ. (13) The multiplexed time-entangled phot trains, Φ in (t) is described mathematically by the normalized Jacobi dn functi given by (A. M. Dike, Journal of Optics 13, (2011)) : Φ in (t) = 2K(m ) π L ct dn 4K(m ) t π T, m, Φ in (t) = L ct sech ( ) 2t. (14) T Solit-train storage retrieval in Λ-type three-level atom systems N-linear (LaRa 11

19 single-phot N-linear FIGURE: 6.(a.) The periodic pulse solit train for m = 0.997, 0.998, (b.) Single high intensity pulse solit. (c.) (d.) Optimizati of the input pulses by decreasing the time dependence of cos θ(t). Solit-train storage retrieval in Λ-type three-level atom systems N-linear (LaRa 12

20 single-phot N-linear FIGURE: 7. (a.) Dark state populati described by a periodic kink solit. (b.) The particular case when m = 1 yields a single kink solit. (c.) (d.) Time reversal of cos θ(t) Solit-train storage retrieval in Λ-type three-level atom systems N-linear (LaRa 13

21 single-phot N-linear FIGURE: 8. (a.) Retrieval of periodic input single-phot solit pulses at t = 40T, (b.) Retrieval of single input solit pulse at t = 40T. FIGURE: 9. Retrieval of periodic input single-phot solit pulses at t = 40T. Solit-train storage retrieval in Λ-type three-level atom systems N-linear (LaRa 14

22 Cclusi N-linear Cclusi Coherent preparati of atoms by laser fields leads to the formati of a dark state that inevitably cause the system to become n-absorbing to these fields. We demstrated the formati of an EIT medium were e can store retrieve time-entangled high energy intensity phot pulses. By adiabatically switching off the ctrol field in an adiabatic fashi, these multiplexed time-entangled single-mode phots are respectively stored retrieved from the EIT system. This process portrays a ctinuously alternating storage coherent retrievals of phots in the dark state of of the 3-level Λ atom system. The subsequent storage such multiplexed phot states will play a great role in informati processing. Results of this presentati are currently submitted to Physical Review A (D. D. A. M. Dike : Solit-train storage retrieval in Λ-type three-level atom systems ). Solit-train storage retrieval in Λ-type three-level atom systems N-linear (LaRa 15

23 References N-linear References L. V. Hau, et al. Nature 397, 594(1999). M. Fleischhauer et al., Opt. comm. 179, 395(2000). M. D. Lukin, et al., Opt. Lett. 23, 295(1998). Chen Liu, et al. Nature 409(6819), 490(2001). S. E. Harris, Phys. Today 50, 36 (1997). M. O. Scully M.S. Zubairy, Quantum Optics (Cambridge University Press), A. M. Dike, Journal of Optics 13, , (2011) Solit-train storage retrieval in Λ-type three-level atom systems N-linear (LaRa 16

24 The End N-linear THANK YOU FOR YOUR KIND ATTENTION! Solit-train storage retrieval in Λ-type three-level atom systems N-linear (LaRa 17