Abstract

We propose and analyze a scheme for adiabatic creation of maximum coherence of 0.5 with a controllable phase between a ground state and the excited state in a model Λ-structured atom using two short laser pulses. One of the pulses has constant carrier frequency quasi-resonant with transition between an initially empty ground and the excite states. The frequency of the second pulse is swept through the resonance with the adjacent transition between the initially populated ground state and the common excited state of the atom. We demonstrate high degree of robustness of the scheme against variation of parameters of the laser radiation in relatively broad region of values. The proposed scheme may find practical applications in the field of multi-photon ionization, high-order harmonics and Raman sideband generation, as well as in nonlinear wave mixing in coherently prepared media.

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References

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  1. A. S. Parkins, P. Marte, P. Zoller, and H. J. Kimble, “Synthesis of arbitrary quantum states via adiabatic transfer of Zeeman coherence,” Phys. Rev. Lett. 71(19), 3095–3098 (1993).
    [CrossRef] [PubMed]
  2. N. Sangouard, S. Guérin, L. P. Yatsenko, and T. Halfmann, “Preparation of coherent superposition in a three-state system by adiabatic passage,” Phys. Rev. A 70(1), 013415 (2004).
    [CrossRef]
  3. R. G. Unanyan, M. E. Pietrzyk, B. W. Shore, and K. Bergmann, “Adiabatic creation of coherent superposition states in atomic beams,” Phys. Rev. A 70(5), 053404 (2004).
    [CrossRef]
  4. G. P. Djotyan, J. S. Bakos, Z. Sörlei, J. Szigeti, and D. Dzsotjan, “Creation of a coherent superposition of quantum states by a single frequency-chirped short laser pulse,” J. Opt. Soc. Am. B 25(2), 166–174 (2008).
    [CrossRef]
  5. F. I. Gauthey, C. H. Keitel, P. L. Knight, and A. Maquet, “Role of initial coherence in the generation of harmonics and sidebands from a strongly driven two-level atom,” Phys. Rev. A 52(1), 525–540 (1995).
    [CrossRef] [PubMed]
  6. J. B. Watson, A. Sanpera, X. Chen, and K. Burnett, “Harmonic generation from a coherent superposition of states,” Phys. Rev. A 53(4), R1962–R1965 (1996).
    [CrossRef] [PubMed]
  7. R. R. Jones, “Multiphoton ionization enhancement usig two phase-coherent laser pulses,” Phys. Rev. Lett. 75(8), 1491–1494 (1995).
    [CrossRef] [PubMed]
  8. R. R. Jones, “Interference effects in the multiphoton ionization of sodium,” Phys. Rev. Lett. 74(7), 1091–1094 (1995).
    [CrossRef] [PubMed]
  9. A. K. Gupta and D. Neuhause, “Control of harmonic generation by initial-state preparation,” Chem. Phys. Lett. 290(4-6), 543–548 (1998).
    [CrossRef]
  10. D. B. Miloševic, “Theoretical analysis of high-order harmonic generation from a coherent superposition of states,” J. Opt. Soc. Am. B 23(2), 308–317 (2006).
    [CrossRef]
  11. C. Trallero-Herrero, J. L. Cohen, and T. Weinacht, “Strong-field atomic phase matching,” Phys. Rev. Lett. 96(6), 063603 (2006).
    [CrossRef] [PubMed]
  12. B. Wang, T. Cheng, X. Li, P. Fu, S. Chen, and J. Liu, “Pulse-duration dependence of high-order harmonic generation with coherent superposition state,” Phys. Rev. A 72(6), 063412 (2005).
    [CrossRef]
  13. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “EIT: Optics in coherent media,” Rev. Mod. Phys. 77(2), 633–673 (2005).
    [CrossRef]
  14. L. Dong, Y. Niu, Y. Xiang, S. Jin, and S. Gong, “Creation of an arbitrary coherent superposition state with chirped delayed pulses,” J. Phys. At. Mol. Opt. Phys. 43(3), 035401 (2010).
    [CrossRef]
  15. S. A. Malinovskaya, “Mode-selective excitation using ultrafast chirped laser pulses,” Phys. Rev. A 73(3), 033416 (2006).
    [CrossRef]

2010 (1)

L. Dong, Y. Niu, Y. Xiang, S. Jin, and S. Gong, “Creation of an arbitrary coherent superposition state with chirped delayed pulses,” J. Phys. At. Mol. Opt. Phys. 43(3), 035401 (2010).
[CrossRef]

2008 (1)

2006 (3)

S. A. Malinovskaya, “Mode-selective excitation using ultrafast chirped laser pulses,” Phys. Rev. A 73(3), 033416 (2006).
[CrossRef]

D. B. Miloševic, “Theoretical analysis of high-order harmonic generation from a coherent superposition of states,” J. Opt. Soc. Am. B 23(2), 308–317 (2006).
[CrossRef]

C. Trallero-Herrero, J. L. Cohen, and T. Weinacht, “Strong-field atomic phase matching,” Phys. Rev. Lett. 96(6), 063603 (2006).
[CrossRef] [PubMed]

2005 (2)

B. Wang, T. Cheng, X. Li, P. Fu, S. Chen, and J. Liu, “Pulse-duration dependence of high-order harmonic generation with coherent superposition state,” Phys. Rev. A 72(6), 063412 (2005).
[CrossRef]

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “EIT: Optics in coherent media,” Rev. Mod. Phys. 77(2), 633–673 (2005).
[CrossRef]

2004 (2)

N. Sangouard, S. Guérin, L. P. Yatsenko, and T. Halfmann, “Preparation of coherent superposition in a three-state system by adiabatic passage,” Phys. Rev. A 70(1), 013415 (2004).
[CrossRef]

R. G. Unanyan, M. E. Pietrzyk, B. W. Shore, and K. Bergmann, “Adiabatic creation of coherent superposition states in atomic beams,” Phys. Rev. A 70(5), 053404 (2004).
[CrossRef]

1998 (1)

A. K. Gupta and D. Neuhause, “Control of harmonic generation by initial-state preparation,” Chem. Phys. Lett. 290(4-6), 543–548 (1998).
[CrossRef]

1996 (1)

J. B. Watson, A. Sanpera, X. Chen, and K. Burnett, “Harmonic generation from a coherent superposition of states,” Phys. Rev. A 53(4), R1962–R1965 (1996).
[CrossRef] [PubMed]

1995 (3)

R. R. Jones, “Multiphoton ionization enhancement usig two phase-coherent laser pulses,” Phys. Rev. Lett. 75(8), 1491–1494 (1995).
[CrossRef] [PubMed]

R. R. Jones, “Interference effects in the multiphoton ionization of sodium,” Phys. Rev. Lett. 74(7), 1091–1094 (1995).
[CrossRef] [PubMed]

F. I. Gauthey, C. H. Keitel, P. L. Knight, and A. Maquet, “Role of initial coherence in the generation of harmonics and sidebands from a strongly driven two-level atom,” Phys. Rev. A 52(1), 525–540 (1995).
[CrossRef] [PubMed]

1993 (1)

A. S. Parkins, P. Marte, P. Zoller, and H. J. Kimble, “Synthesis of arbitrary quantum states via adiabatic transfer of Zeeman coherence,” Phys. Rev. Lett. 71(19), 3095–3098 (1993).
[CrossRef] [PubMed]

Bakos, J. S.

Bergmann, K.

R. G. Unanyan, M. E. Pietrzyk, B. W. Shore, and K. Bergmann, “Adiabatic creation of coherent superposition states in atomic beams,” Phys. Rev. A 70(5), 053404 (2004).
[CrossRef]

Burnett, K.

J. B. Watson, A. Sanpera, X. Chen, and K. Burnett, “Harmonic generation from a coherent superposition of states,” Phys. Rev. A 53(4), R1962–R1965 (1996).
[CrossRef] [PubMed]

Chen, S.

B. Wang, T. Cheng, X. Li, P. Fu, S. Chen, and J. Liu, “Pulse-duration dependence of high-order harmonic generation with coherent superposition state,” Phys. Rev. A 72(6), 063412 (2005).
[CrossRef]

Chen, X.

J. B. Watson, A. Sanpera, X. Chen, and K. Burnett, “Harmonic generation from a coherent superposition of states,” Phys. Rev. A 53(4), R1962–R1965 (1996).
[CrossRef] [PubMed]

Cheng, T.

B. Wang, T. Cheng, X. Li, P. Fu, S. Chen, and J. Liu, “Pulse-duration dependence of high-order harmonic generation with coherent superposition state,” Phys. Rev. A 72(6), 063412 (2005).
[CrossRef]

Cohen, J. L.

C. Trallero-Herrero, J. L. Cohen, and T. Weinacht, “Strong-field atomic phase matching,” Phys. Rev. Lett. 96(6), 063603 (2006).
[CrossRef] [PubMed]

Djotyan, G. P.

Dong, L.

L. Dong, Y. Niu, Y. Xiang, S. Jin, and S. Gong, “Creation of an arbitrary coherent superposition state with chirped delayed pulses,” J. Phys. At. Mol. Opt. Phys. 43(3), 035401 (2010).
[CrossRef]

Dzsotjan, D.

Fleischhauer, M.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “EIT: Optics in coherent media,” Rev. Mod. Phys. 77(2), 633–673 (2005).
[CrossRef]

Fu, P.

B. Wang, T. Cheng, X. Li, P. Fu, S. Chen, and J. Liu, “Pulse-duration dependence of high-order harmonic generation with coherent superposition state,” Phys. Rev. A 72(6), 063412 (2005).
[CrossRef]

Gauthey, F. I.

F. I. Gauthey, C. H. Keitel, P. L. Knight, and A. Maquet, “Role of initial coherence in the generation of harmonics and sidebands from a strongly driven two-level atom,” Phys. Rev. A 52(1), 525–540 (1995).
[CrossRef] [PubMed]

Gong, S.

L. Dong, Y. Niu, Y. Xiang, S. Jin, and S. Gong, “Creation of an arbitrary coherent superposition state with chirped delayed pulses,” J. Phys. At. Mol. Opt. Phys. 43(3), 035401 (2010).
[CrossRef]

Guérin, S.

N. Sangouard, S. Guérin, L. P. Yatsenko, and T. Halfmann, “Preparation of coherent superposition in a three-state system by adiabatic passage,” Phys. Rev. A 70(1), 013415 (2004).
[CrossRef]

Gupta, A. K.

A. K. Gupta and D. Neuhause, “Control of harmonic generation by initial-state preparation,” Chem. Phys. Lett. 290(4-6), 543–548 (1998).
[CrossRef]

Halfmann, T.

N. Sangouard, S. Guérin, L. P. Yatsenko, and T. Halfmann, “Preparation of coherent superposition in a three-state system by adiabatic passage,” Phys. Rev. A 70(1), 013415 (2004).
[CrossRef]

Imamoglu, A.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “EIT: Optics in coherent media,” Rev. Mod. Phys. 77(2), 633–673 (2005).
[CrossRef]

Jin, S.

L. Dong, Y. Niu, Y. Xiang, S. Jin, and S. Gong, “Creation of an arbitrary coherent superposition state with chirped delayed pulses,” J. Phys. At. Mol. Opt. Phys. 43(3), 035401 (2010).
[CrossRef]

Jones, R. R.

R. R. Jones, “Multiphoton ionization enhancement usig two phase-coherent laser pulses,” Phys. Rev. Lett. 75(8), 1491–1494 (1995).
[CrossRef] [PubMed]

R. R. Jones, “Interference effects in the multiphoton ionization of sodium,” Phys. Rev. Lett. 74(7), 1091–1094 (1995).
[CrossRef] [PubMed]

Keitel, C. H.

F. I. Gauthey, C. H. Keitel, P. L. Knight, and A. Maquet, “Role of initial coherence in the generation of harmonics and sidebands from a strongly driven two-level atom,” Phys. Rev. A 52(1), 525–540 (1995).
[CrossRef] [PubMed]

Kimble, H. J.

A. S. Parkins, P. Marte, P. Zoller, and H. J. Kimble, “Synthesis of arbitrary quantum states via adiabatic transfer of Zeeman coherence,” Phys. Rev. Lett. 71(19), 3095–3098 (1993).
[CrossRef] [PubMed]

Knight, P. L.

F. I. Gauthey, C. H. Keitel, P. L. Knight, and A. Maquet, “Role of initial coherence in the generation of harmonics and sidebands from a strongly driven two-level atom,” Phys. Rev. A 52(1), 525–540 (1995).
[CrossRef] [PubMed]

Li, X.

B. Wang, T. Cheng, X. Li, P. Fu, S. Chen, and J. Liu, “Pulse-duration dependence of high-order harmonic generation with coherent superposition state,” Phys. Rev. A 72(6), 063412 (2005).
[CrossRef]

Liu, J.

B. Wang, T. Cheng, X. Li, P. Fu, S. Chen, and J. Liu, “Pulse-duration dependence of high-order harmonic generation with coherent superposition state,” Phys. Rev. A 72(6), 063412 (2005).
[CrossRef]

Malinovskaya, S. A.

S. A. Malinovskaya, “Mode-selective excitation using ultrafast chirped laser pulses,” Phys. Rev. A 73(3), 033416 (2006).
[CrossRef]

Maquet, A.

F. I. Gauthey, C. H. Keitel, P. L. Knight, and A. Maquet, “Role of initial coherence in the generation of harmonics and sidebands from a strongly driven two-level atom,” Phys. Rev. A 52(1), 525–540 (1995).
[CrossRef] [PubMed]

Marangos, J. P.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “EIT: Optics in coherent media,” Rev. Mod. Phys. 77(2), 633–673 (2005).
[CrossRef]

Marte, P.

A. S. Parkins, P. Marte, P. Zoller, and H. J. Kimble, “Synthesis of arbitrary quantum states via adiabatic transfer of Zeeman coherence,” Phys. Rev. Lett. 71(19), 3095–3098 (1993).
[CrossRef] [PubMed]

Miloševic, D. B.

Neuhause, D.

A. K. Gupta and D. Neuhause, “Control of harmonic generation by initial-state preparation,” Chem. Phys. Lett. 290(4-6), 543–548 (1998).
[CrossRef]

Niu, Y.

L. Dong, Y. Niu, Y. Xiang, S. Jin, and S. Gong, “Creation of an arbitrary coherent superposition state with chirped delayed pulses,” J. Phys. At. Mol. Opt. Phys. 43(3), 035401 (2010).
[CrossRef]

Parkins, A. S.

A. S. Parkins, P. Marte, P. Zoller, and H. J. Kimble, “Synthesis of arbitrary quantum states via adiabatic transfer of Zeeman coherence,” Phys. Rev. Lett. 71(19), 3095–3098 (1993).
[CrossRef] [PubMed]

Pietrzyk, M. E.

R. G. Unanyan, M. E. Pietrzyk, B. W. Shore, and K. Bergmann, “Adiabatic creation of coherent superposition states in atomic beams,” Phys. Rev. A 70(5), 053404 (2004).
[CrossRef]

Sangouard, N.

N. Sangouard, S. Guérin, L. P. Yatsenko, and T. Halfmann, “Preparation of coherent superposition in a three-state system by adiabatic passage,” Phys. Rev. A 70(1), 013415 (2004).
[CrossRef]

Sanpera, A.

J. B. Watson, A. Sanpera, X. Chen, and K. Burnett, “Harmonic generation from a coherent superposition of states,” Phys. Rev. A 53(4), R1962–R1965 (1996).
[CrossRef] [PubMed]

Shore, B. W.

R. G. Unanyan, M. E. Pietrzyk, B. W. Shore, and K. Bergmann, “Adiabatic creation of coherent superposition states in atomic beams,” Phys. Rev. A 70(5), 053404 (2004).
[CrossRef]

Sörlei, Z.

Szigeti, J.

Trallero-Herrero, C.

C. Trallero-Herrero, J. L. Cohen, and T. Weinacht, “Strong-field atomic phase matching,” Phys. Rev. Lett. 96(6), 063603 (2006).
[CrossRef] [PubMed]

Unanyan, R. G.

R. G. Unanyan, M. E. Pietrzyk, B. W. Shore, and K. Bergmann, “Adiabatic creation of coherent superposition states in atomic beams,” Phys. Rev. A 70(5), 053404 (2004).
[CrossRef]

Wang, B.

B. Wang, T. Cheng, X. Li, P. Fu, S. Chen, and J. Liu, “Pulse-duration dependence of high-order harmonic generation with coherent superposition state,” Phys. Rev. A 72(6), 063412 (2005).
[CrossRef]

Watson, J. B.

J. B. Watson, A. Sanpera, X. Chen, and K. Burnett, “Harmonic generation from a coherent superposition of states,” Phys. Rev. A 53(4), R1962–R1965 (1996).
[CrossRef] [PubMed]

Weinacht, T.

C. Trallero-Herrero, J. L. Cohen, and T. Weinacht, “Strong-field atomic phase matching,” Phys. Rev. Lett. 96(6), 063603 (2006).
[CrossRef] [PubMed]

Xiang, Y.

L. Dong, Y. Niu, Y. Xiang, S. Jin, and S. Gong, “Creation of an arbitrary coherent superposition state with chirped delayed pulses,” J. Phys. At. Mol. Opt. Phys. 43(3), 035401 (2010).
[CrossRef]

Yatsenko, L. P.

N. Sangouard, S. Guérin, L. P. Yatsenko, and T. Halfmann, “Preparation of coherent superposition in a three-state system by adiabatic passage,” Phys. Rev. A 70(1), 013415 (2004).
[CrossRef]

Zoller, P.

A. S. Parkins, P. Marte, P. Zoller, and H. J. Kimble, “Synthesis of arbitrary quantum states via adiabatic transfer of Zeeman coherence,” Phys. Rev. Lett. 71(19), 3095–3098 (1993).
[CrossRef] [PubMed]

Chem. Phys. Lett. (1)

A. K. Gupta and D. Neuhause, “Control of harmonic generation by initial-state preparation,” Chem. Phys. Lett. 290(4-6), 543–548 (1998).
[CrossRef]

J. Opt. Soc. Am. B (2)

J. Phys. At. Mol. Opt. Phys. (1)

L. Dong, Y. Niu, Y. Xiang, S. Jin, and S. Gong, “Creation of an arbitrary coherent superposition state with chirped delayed pulses,” J. Phys. At. Mol. Opt. Phys. 43(3), 035401 (2010).
[CrossRef]

Phys. Rev. A (6)

S. A. Malinovskaya, “Mode-selective excitation using ultrafast chirped laser pulses,” Phys. Rev. A 73(3), 033416 (2006).
[CrossRef]

B. Wang, T. Cheng, X. Li, P. Fu, S. Chen, and J. Liu, “Pulse-duration dependence of high-order harmonic generation with coherent superposition state,” Phys. Rev. A 72(6), 063412 (2005).
[CrossRef]

F. I. Gauthey, C. H. Keitel, P. L. Knight, and A. Maquet, “Role of initial coherence in the generation of harmonics and sidebands from a strongly driven two-level atom,” Phys. Rev. A 52(1), 525–540 (1995).
[CrossRef] [PubMed]

J. B. Watson, A. Sanpera, X. Chen, and K. Burnett, “Harmonic generation from a coherent superposition of states,” Phys. Rev. A 53(4), R1962–R1965 (1996).
[CrossRef] [PubMed]

N. Sangouard, S. Guérin, L. P. Yatsenko, and T. Halfmann, “Preparation of coherent superposition in a three-state system by adiabatic passage,” Phys. Rev. A 70(1), 013415 (2004).
[CrossRef]

R. G. Unanyan, M. E. Pietrzyk, B. W. Shore, and K. Bergmann, “Adiabatic creation of coherent superposition states in atomic beams,” Phys. Rev. A 70(5), 053404 (2004).
[CrossRef]

Phys. Rev. Lett. (4)

C. Trallero-Herrero, J. L. Cohen, and T. Weinacht, “Strong-field atomic phase matching,” Phys. Rev. Lett. 96(6), 063603 (2006).
[CrossRef] [PubMed]

R. R. Jones, “Multiphoton ionization enhancement usig two phase-coherent laser pulses,” Phys. Rev. Lett. 75(8), 1491–1494 (1995).
[CrossRef] [PubMed]

R. R. Jones, “Interference effects in the multiphoton ionization of sodium,” Phys. Rev. Lett. 74(7), 1091–1094 (1995).
[CrossRef] [PubMed]

A. S. Parkins, P. Marte, P. Zoller, and H. J. Kimble, “Synthesis of arbitrary quantum states via adiabatic transfer of Zeeman coherence,” Phys. Rev. Lett. 71(19), 3095–3098 (1993).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “EIT: Optics in coherent media,” Rev. Mod. Phys. 77(2), 633–673 (2005).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Schematic of Λ-like atom with two acting laser fields: one with chirped frequency and the other one with constant carrier frequency.

Fig. 2
Fig. 2

Dynamics of the states populations in the laser field (a), and absolute value of the coherence created between the states | 2 and | 3 (b). Parameters applied are: the peak Rabi frequencies Ω 1 ( 0 ) = Ω 2 ( 0 ) = 15 G H z , chirp speed β = 5 G H z / n s , detuning of the field with constant carrier frequency Δ 0 = 0 , and duration of the pulses τ p = 1.5 n s .

Fig. 3
Fig. 3

Color plot of the absolute value of the created coherence versus the speed of the chirp and the peak Rabi frequency Ω 2 ( 0 ) of the laser pulse with constant carrier frequency (in logarithmic scale): Ω 2 ( 0 ) = η · Ω 1 ( 0 ) with a fixed value of the peak Rabi frequency of the chirped laser pulse Ω 1 = 15 G H z . Other parameters applied are: τ p = 3 n s , Δ 0 = 0 .

Fig. 4
Fig. 4

The phase of the coherence between the initially empty ground and excited states in π-radians. (a)- in the case of positive chirp β = 5 G H z / n s , and (b)- in the case of negative chirp β = 5 G H z / n s . Other parameters applied are the same as in Fig. 2.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

| ψ = n = 1 3 a n ( t ) | n ,
E ( t ) = E 1 ( t ) e 1 exp [ i ω L 1 ( t ) d t ] + E 2 ( t ) e 2 exp [ i ω L 2 0 t ] + c . c . ,
H ^ = ( ε ( t ) Ω 1 ( t ) 0 Ω 1 * ( t ) 0 Ω 2 * ( t ) 0 Ω 2 ( t ) Δ 0 ) ,
| b 1 = | 1 ,         | b + = ( | 2 + | 3 ) / 2 ,         | b = ( | 2 | 3 ) / 2 ,
b 1 = a 1 , b + = ( a 2 + a 3 ) / 2 , b = ( a 2 a 3 ) / 2 .
i d d b ¯ = H ^ b b ¯
H ^ b = ( ε ( t ) Ω 1 ( t ) / 2 Ω 1 ( t ) / 2 Ω 1 ( t ) / 2 Ω 2 ( t ) Δ 0 / 2 Δ 0 / 2 Ω 1 ( t ) / 2 Δ 0 / 2 [ Ω 2 ( t ) + Δ 0 / 2 ] ) .

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