Abstract

We have simultaneously excited a coherent and a squeezed phonon field in SrTiO3 using femtosecond laser pulses and stimulated Raman scattering. The frequency of the coherent state (~ 1.3 THz) is that of the A 1g-component of the soft mode responsible for the cubic-tetragonal phase transformation at ≈ 110 K. The squeezed field involves a continuum of transverse acoustic phonons dominated by a narrow peak in the density of states at ~ 6.9 THz.

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References

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  1. R. Merlin, Generating coherent THz phonons with light pulses, Solid State Commun. 102, 207-220 (1997).
    [CrossRef]
  2. G. A. Garrett, A. G. Rojo, A. K. Sood, J. F. Whitaker and R. Merlin, Vacuum squeezing of solids: macroscopic quantum states driven by light pulses, Science 275, 1638-1640 (1997).
    [CrossRef] [PubMed]
  3. See, e. g., D. F. Walls and G. J. Wilburn, Quantum Optics (Springer, Berlin, 1994), chap. 2.
  4. P. A. Fleury, J. F. Scott and J. M. Worlock, Soft phonon modes and the 110 0 K phase transition in SrTiO3, Phys. Rev. Lett. 21, 16-19 (1968).
    [CrossRef]
  5. K. A. Mller and H. Burkard, SrTiO3: an intrinsic quantum paraelectric below 4 K, Phys. Rev. B 19, 3593-3602 (1979).
    [CrossRef]
  6. See: W. Zhong and D. Vanderbilt, Effect of quantum fluctuations on structural phase transitions in SrTiO3 and BaTiO3, Phys. Rev. B 53, 5047-5050 (1996), and references therein.
    [CrossRef]
  7. P. A. Fleury and J. M. Worlock, Electric-Field-Induced Raman scattering in SrTiO3 and BaTiO3, Phys. Rev. 174, 613-623 (1968)
    [CrossRef]
  8. D. E. Grupp and A. M. Goldman, Giant piezoelectric effect in strontium titanate at cryogenic temperatures, Science 276, 392-394 (1997).
    [CrossRef] [PubMed]
  9. H. Uwe and T. Sakudo, Stress-induced ferroelectricity and soft modes in SrTiO3, Phys. Rev. B 13, 271-286 (1976).
    [CrossRef]
  10. W. G. Nielsen and J. G. Skinner, Raman spectrum of strontium titanate, J. Chem. Phys. 48, 2240-2248 (1968).
    [CrossRef]
  11. W. G. Stirling, Neutron inelastic scattering study of the lattice dynamics of strontium titanate: harmonic models, J. Phys. C 5, 2711-2730 (1972).
    [CrossRef]

Other

R. Merlin, Generating coherent THz phonons with light pulses, Solid State Commun. 102, 207-220 (1997).
[CrossRef]

G. A. Garrett, A. G. Rojo, A. K. Sood, J. F. Whitaker and R. Merlin, Vacuum squeezing of solids: macroscopic quantum states driven by light pulses, Science 275, 1638-1640 (1997).
[CrossRef] [PubMed]

See, e. g., D. F. Walls and G. J. Wilburn, Quantum Optics (Springer, Berlin, 1994), chap. 2.

P. A. Fleury, J. F. Scott and J. M. Worlock, Soft phonon modes and the 110 0 K phase transition in SrTiO3, Phys. Rev. Lett. 21, 16-19 (1968).
[CrossRef]

K. A. Mller and H. Burkard, SrTiO3: an intrinsic quantum paraelectric below 4 K, Phys. Rev. B 19, 3593-3602 (1979).
[CrossRef]

See: W. Zhong and D. Vanderbilt, Effect of quantum fluctuations on structural phase transitions in SrTiO3 and BaTiO3, Phys. Rev. B 53, 5047-5050 (1996), and references therein.
[CrossRef]

P. A. Fleury and J. M. Worlock, Electric-Field-Induced Raman scattering in SrTiO3 and BaTiO3, Phys. Rev. 174, 613-623 (1968)
[CrossRef]

D. E. Grupp and A. M. Goldman, Giant piezoelectric effect in strontium titanate at cryogenic temperatures, Science 276, 392-394 (1997).
[CrossRef] [PubMed]

H. Uwe and T. Sakudo, Stress-induced ferroelectricity and soft modes in SrTiO3, Phys. Rev. B 13, 271-286 (1976).
[CrossRef]

W. G. Nielsen and J. G. Skinner, Raman spectrum of strontium titanate, J. Chem. Phys. 48, 2240-2248 (1968).
[CrossRef]

W. G. Stirling, Neutron inelastic scattering study of the lattice dynamics of strontium titanate: harmonic models, J. Phys. C 5, 2711-2730 (1972).
[CrossRef]

Supplementary Material (3)

» Media 1: MOV (55 KB)     
» Media 2: MOV (56 KB)     
» Media 3: MOV (162 KB)     

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Figures (2)

Fig. 1.
Fig. 1.

Schematic diagram showing a unitary cell containing two atoms. The averaged relative position between the atoms is labeled r, the instantaneous displacement with respect to the equilibrium position is indicated by u, and the dashed circles represent the square root of the variance 〈u 2〉. The following links show animations illustrating motion associated with coherent, squeezed, and combined coherent-squeezed fields. [Media 1] [Media 2] [Media 3]

Fig. 2.
Fig. 2.

(a) Normalized transmitted intensity of the probe pulse as a function of the delay for the A 1g-symmetry configuration. (b) Fourier transform of the time-domain data.

Equations (8)

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χ 1 = 1 2 ( χ Q 0 ) Q 0
χ 2 ( q ) = 1 4 ( 2 χ Q q 2 ) Q q 2 .
d 2 Q 0 d t 2 + Ω 0 2 Q 0 = 1 2 ( χ Q 0 ) E ( t ) 2 = F .
ν 2 = 1 2 ( 2 χ Q 0 ) E ( t ) 2 .
d 3 Q q 2 d t 3 + 4 [ Ω q 2 + ν 2 ] d Q q 2 dt = 2 d ( ν 2 ) dt Q q 2 .
Q 0 = 2 W 0 ( χ Q 0 ) sin ( Ω 0 t )
Q q 2 ( t ) Q q 2 ( 0 ) [ 1 + 2 W q ( 2 χ Q q 2 ) sin ( 2 Ω q t ) ] .
Ψ + = exp ( q 2 i W q σ q 2 [ χ 1 δ q , 0 + χ 2 ( q ) ] ) Ψ .

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