Bound to Unbound State Route and Propagation of Dark Solitons showing Acoustical Memory

The dark and bright solitons in different systems are already known. If the intrinsic field is only considered, then the modal dynamics for small oscillations could be characterized by the bound state in a limited range of frequency, revealed via associated Legendre polynomial. The pairing and interplay between the dark and bright solitons occur. The disappearance of the bound state after a critical frequency gives rise to dark solitons in the unbound states that propagate through the domains. In a two-part partition function based on our Hamiltonian, a frequency-temperature relation is worked out. Above the upper boundary of the bound states, the estimated frequencies of dark solitons at 300K and 319K match with those experimentally found for ‘acoustical memory’. In 2002 in PRL (89 (2002) 115506), the experimental evidence was shown by McPherson, Ostrovskii and Breazeale at University of Mississippi (USA). 

     In a nonlinear system (e.g. LN), solitons are basically considered as phonons that have both optical and acoustic branches in the dispersion curve, as nonlinearity arises from the anharmonicity of the inter-atomic forces including the quantized vibrations, i.e. phonons. While both bright and dark solitons are sensitive to optical excitations, dark solitons manly respond to acoustic stimulation or pulses that is a subject matter of this paper. Hence, the same material (LN) may respond to optical pulses in one frequency range and then in another frequency range, it could also remember sound and respond to an acoustic pulse, as has been demonstrated in PRL in 2002. For soliton dynamics, in the low frequency range, the bound state will predominate and in the higher range, the phonon mode takes over in the unbound state, and here these are the main issues for dark soliton that guides not only optical experiments but also plays a role in acoustic emission. In another paper in PRB (64 (2001) 064302), an experiment with picosecond ultrasonic pulse technique was done on different crystalline solids and the usefulness of solitons via KdV equation was shown. In the present work, different soliton solutions and their respective responses to ultrasonic waves are not discussed.

A I P-Advances 4, 087101 (2014).

Keywords: Dark and Bright Solitons, Bound and Unbound States, Acoustic Memory.