Two-body quench dynamics of harmonically trapped interacting particles

Abstract

We consider the quantum evolution of a pair of interacting atoms in a three dimensional isotropic trap where the interaction strength is quenched from one value to another. Using exact solutions of the static problem we are able to evaluate time-dependent observables such as the overlap between initial and final states and the expectation value of the separation between the two atoms. In the case where the interaction is quenched from the non-interacting regime to the strongly interacting regime, or vice versa, we are able to obtain analytic results. Examining the overlap between the initial and final states we show that when the interaction is quenched from the non-interacting to strongly interacting regimes the early time dependence is ∝ 1 − αt 3/2 which is consistent with theoretical work in the untrapped single impurity many-body limit.

Energetics of three interacting mass-imbalanced bodies in a three-dimensional spherical harmonic trap

“…We have provided results for both fermionic systems with mass imbalance and bosonic systems where by definition there is no mass imbalance. In each case these results can be used to investigate physical phenomena such as quench dynamics [6,[9][10][11][12][13][14][15][16][17][18] and the derivation of the equation of state of such a gas [19][20][21][22][23].…”

“…The foundation of such studies is the investigation of the properties of few-body systems [1][2][3][4][5][6][7][8]. Through solutions of the few-body problem it is possible to calculate the thermodynamics of many-body quantum gases [6,[9][10][11][12][13][14][15][16][17][18] and the quench dynamics of few-body systems [19][20][21][22][23]. Significant research has been undertaken [11,[24][25][26] into the study of the interacting three-body problem for both Bose and Fermi gases trapped in three-dimensional spherically symmetric harmonic traps.…”

Reduced density matrix approach to ultracold few-fermion systems in one dimension

“…Further extensions using this methodology could include spin imbalanced systems, where N ↑ = N ↓ , as well as mass-imbalanced systems. Minor imbalances in these systems can be exaggerated to permit the study of single impurities in otherwise homogeneous systems [123][124][125]. Alternate interactions, such as soft-core or dipolar interactions can be analysed with this method also.…”

Reduced density matrix approach to ultracold few-fermion systems in one dimension

“…Further extensions using this methodology could include spin imbalanced systems, where N ↑ = N ↓ , as well as mass-imbalanced systems. Minor imbalances in these systems can be exaggerated to permit the study of single impurities in otherwise homogeneous systems [99][100][101]. Alternate interactions, such as soft-core, dipolar, or Coulombic interactions can be analysed with this method also.…”