Abstract

Conditions for obtaining maximal enhancement of optical lattice vibrations by a train of picosecond light pulses, including its dependence on the relaxation time of a material system, are found by using density matrix formalism.

© 1978 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. H. Piekara, in Coherence and Quantum Optics, L. Mandel, E. Wolf, Eds. (Plenum, New York, 1973), p. 533.
    [CrossRef]
  2. A. H. Piekara, Jpn. J. Appl. Phys. Suppl. 14, 1 (1975).
    [CrossRef]
  3. A. H. Piekara, B. Ratajska, Acta Phys. Pol. A53, 115 (1978).
  4. J. Ducuing, “Quantum Optics,” in Proceedings International School of Physics Enrico Fermi, R. J. Glauber, Ed. (Varenna, 1967).
  5. N. Bloembergen, Nonlinear Optics (Benjamin, New York, 1965).
  6. R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957).
    [CrossRef]
  7. A. H. Piekara, B. Ratajska, Opt. Laser Technol. (1978).
  8. A. H. Piekara, J. S. Moore, M. S. Feld, Phys. Rev. A 9, 1403 (1974).
    [CrossRef]
  9. K. Nava, R. Arzt, I. Ciccarello, K. Dransfeld, Phys. Rev. A 134, 581 (1964).
  10. T. O. Woodruff, X. Ehrenreich, Phys. Rev. 123, 1553 (1961).
    [CrossRef]

1978 (2)

A. H. Piekara, B. Ratajska, Opt. Laser Technol. (1978).

A. H. Piekara, B. Ratajska, Acta Phys. Pol. A53, 115 (1978).

1975 (1)

A. H. Piekara, Jpn. J. Appl. Phys. Suppl. 14, 1 (1975).
[CrossRef]

1974 (1)

A. H. Piekara, J. S. Moore, M. S. Feld, Phys. Rev. A 9, 1403 (1974).
[CrossRef]

1964 (1)

K. Nava, R. Arzt, I. Ciccarello, K. Dransfeld, Phys. Rev. A 134, 581 (1964).

1961 (1)

T. O. Woodruff, X. Ehrenreich, Phys. Rev. 123, 1553 (1961).
[CrossRef]

1957 (1)

R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957).
[CrossRef]

Arzt, R.

K. Nava, R. Arzt, I. Ciccarello, K. Dransfeld, Phys. Rev. A 134, 581 (1964).

Bloembergen, N.

N. Bloembergen, Nonlinear Optics (Benjamin, New York, 1965).

Ciccarello, I.

K. Nava, R. Arzt, I. Ciccarello, K. Dransfeld, Phys. Rev. A 134, 581 (1964).

Dransfeld, K.

K. Nava, R. Arzt, I. Ciccarello, K. Dransfeld, Phys. Rev. A 134, 581 (1964).

Ducuing, J.

J. Ducuing, “Quantum Optics,” in Proceedings International School of Physics Enrico Fermi, R. J. Glauber, Ed. (Varenna, 1967).

Ehrenreich, X.

T. O. Woodruff, X. Ehrenreich, Phys. Rev. 123, 1553 (1961).
[CrossRef]

Feld, M. S.

A. H. Piekara, J. S. Moore, M. S. Feld, Phys. Rev. A 9, 1403 (1974).
[CrossRef]

Kubo, R.

R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957).
[CrossRef]

Moore, J. S.

A. H. Piekara, J. S. Moore, M. S. Feld, Phys. Rev. A 9, 1403 (1974).
[CrossRef]

Nava, K.

K. Nava, R. Arzt, I. Ciccarello, K. Dransfeld, Phys. Rev. A 134, 581 (1964).

Piekara, A. H.

A. H. Piekara, B. Ratajska, Opt. Laser Technol. (1978).

A. H. Piekara, B. Ratajska, Acta Phys. Pol. A53, 115 (1978).

A. H. Piekara, Jpn. J. Appl. Phys. Suppl. 14, 1 (1975).
[CrossRef]

A. H. Piekara, J. S. Moore, M. S. Feld, Phys. Rev. A 9, 1403 (1974).
[CrossRef]

A. H. Piekara, in Coherence and Quantum Optics, L. Mandel, E. Wolf, Eds. (Plenum, New York, 1973), p. 533.
[CrossRef]

Ratajska, B.

A. H. Piekara, B. Ratajska, Acta Phys. Pol. A53, 115 (1978).

A. H. Piekara, B. Ratajska, Opt. Laser Technol. (1978).

Woodruff, T. O.

T. O. Woodruff, X. Ehrenreich, Phys. Rev. 123, 1553 (1961).
[CrossRef]

Acta Phys. Pol. (1)

A. H. Piekara, B. Ratajska, Acta Phys. Pol. A53, 115 (1978).

J. Phys. Soc. Jpn. (1)

R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957).
[CrossRef]

Jpn. J. Appl. Phys. Suppl. (1)

A. H. Piekara, Jpn. J. Appl. Phys. Suppl. 14, 1 (1975).
[CrossRef]

Opt. Laser Technol. (1)

A. H. Piekara, B. Ratajska, Opt. Laser Technol. (1978).

Phys. Rev. (1)

T. O. Woodruff, X. Ehrenreich, Phys. Rev. 123, 1553 (1961).
[CrossRef]

Phys. Rev. A (2)

A. H. Piekara, J. S. Moore, M. S. Feld, Phys. Rev. A 9, 1403 (1974).
[CrossRef]

K. Nava, R. Arzt, I. Ciccarello, K. Dransfeld, Phys. Rev. A 134, 581 (1964).

Other (3)

A. H. Piekara, in Coherence and Quantum Optics, L. Mandel, E. Wolf, Eds. (Plenum, New York, 1973), p. 533.
[CrossRef]

J. Ducuing, “Quantum Optics,” in Proceedings International School of Physics Enrico Fermi, R. J. Glauber, Ed. (Varenna, 1967).

N. Bloembergen, Nonlinear Optics (Benjamin, New York, 1965).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1
Fig. 1

Enhancement of mean square vibrational amplitude as a function of time for different values of relaxation time at optimal excitation (Δt = ½δt). Curves 1–4 correspond to the following relaxation times: τ = 10δt, 3δt, δt, ¼δt.

Fig. 2
Fig. 2

Resonance curves for relative change of amplitude as the function of n, the number of pulses for different ratios ( δ t ) / τ = 1 2 , 1 10 , 1 20 , 1 100, assuming ( K E ¯ 2 ) / ( m ω 0 2 ) = 0.01.

Equations (31)

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

H E = 1 2 K E ¯ 2 x 2 ,
K = 192 ( + 2 3 ) 2 α 2 a 5 ( 1 4 α a 3 ) 3 ,
H = H 0 + H E = 1 2 p 2 m + 1 2 m ω 0 2 ( 1 K E ¯ 2 m ω 0 2 ) x 2 .
ω = ω 0 ( 1 K E ¯ 2 m w 0 2 ) 1 / 2 .
d ρ d t = 1 i ћ [ H , ρ ] + ( d ρ d t ) d ,
( d ρ d t ) d
( d ρ d t ) d = ρ ρ 0 τ .
ρ 0 = 1 Z exp ( H 0 k T ) ,
ρ ( t ) = ρ 0 + Δ ρ ( t ) ,
Δ ρ ( t ) = exp ( i ћ H t ) Δ ρ ( t ) exp ( i ћ H t ) exp ( t τ ) ,
d Δ ρ ( t ) d t = 1 i ћ exp ( t τ ) [ H , ρ 0 ( t ) ] ,
ρ 0 ( t ) = exp ( i ћ H t ) ρ 0 exp ( i ћ H t ) ,
Δ ρ | t = 0 = 0.
ρ ( t ) = ρ 0 + 1 i ћ 0 t exp [ ( t t ) τ ] [ H , ρ 0 ( t t ) ] d t .
A ( t ) = A 0 + 1 i ћ 0 t exp [ ( t t ) τ ] [ A ( t t ) , H ] 0 d t ,
A ( t t ) = exp [ i ћ H ( t t ) ] A ( 0 ) exp [ i ћ H ( t t ) ] ,
d A d t = 1 i ћ [ A , H ] .
A ( t t ) = x 2 ( t t ) = x 2 ( 0 ) cos 2 ω ( t t ) + p 2 ( 0 ) m 2 ω 2 sin 2 ω ( t t ) + x ( 0 ) p ( 0 ) m ω sin 2 ω ( t t ) ,
x 2 ( t ) = x 2 0 { 1 + K E ¯ 2 m ω 0 2 ω 0 2 4 ω 2 + 1 τ 2 [ 1 exp ( t τ ) × cos 2 ω t exp ( t τ ) 1 ω τ sin 2 ω t ] } ,
x 2 0 = 1 ( m ω 0 ) 2 p 2 0 .
x 2 = x 2 0 [ 1 + 1 4 K E ¯ 2 m ω 2 ] ,
E ¯ 2 ( t ) = { E ¯ 2 for n δ t t n δ t + Δ t , n = 0,1,2 , , 0 for ( n 1 ) δ t + Δ t t n δ t , n = 1,2,3 , ,
ρ n [ ( n 1 ) δ t + Δ t ] = ρ 0 + k = 0 n 1 exp ( k δ t τ ) × exp ( i ћ H 0 k δ t ) Δ ρ ( Δ t ) exp ( i ћ H 0 k δ t ) .
x n 2 [ ( n 1 ) δ t + Δ t ] = x 2 0 { 1 + 1 4 K E ¯ 2 m ( ω 2 + 1 4 τ 2 ) k = 0 n 1 exp ( k δ t τ ) × [ cos 2 ω 0 k δ t exp ( Δ t τ ) cos 2 ( ω 0 k δ t + ω Δ t ) + 1 ω τ sin 2 ω 0 k δ t 1 ω τ exp ( Δ t τ ) sin 2 ( ω 0 k δ t + ω Δ t ) ] } .
x n 2 = x 2 0 { 1 + 1 2 K E ¯ 2 m ω 2 sin ω Δ t × sin ω Δ t + exp ( δ t τ ) sin ( 2 ω 0 δ t ω Δ t ) exp ( n δ t τ ) sin ( 2 n ω 0 δ t + ω Δ t ) + exp [ ( n + 1 ) δ t τ ] sin [ 2 ( n 1 ) ω 0 δ t + ω Δ t ] 1 2 exp ( δ t τ ) cos 2 ω 0 δ t + exp ( 2 δ t τ ) } .
x 2 = x 2 0 ( 1 + 1 2 K E ¯ 2 m ω 2 sin 2 ω Δ t ) .
Δ t = π 2 ω ( 2 k + 1 ) , k = 0,1,2 ,
x 2 = x 2 0 { 1 + 1 4 K E ¯ 2 m ω 2 sin ω Δ t cos ( ω 0 δ t ω Δ t ) exp ( n δ t τ ) cos [ ( 2 n 1 ) ω 0 δ t + ω Δ t ] sin ω 0 δ t } .
δ t = k 1 π ω 0 = k 1 T 0 2 , Δ t = ( 2 k 2 + 1 ) π 2 ω = ( 2 k 2 + 1 ) T 0 4 ( 1 K E 2 ¯ m ω 0 2 ) 1 / 2 ,
x 2 = x 2 0 { 1 + 1 4 K E ¯ 2 m ω 2 [ 1 + exp ( n δ t τ ) ( 2 n 1 ) ] } .
x 2 = x 2 0 { 1 + 1 4 K E ¯ 2 m ω 2 [ 1 + exp ( 1 δ t 2 τ ) τ δ t ] } .

Metrics