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arXiv:2208.05666 · Physical Review A

Effects of Efimov states on quench dynamics in a three-boson trapped system

A. D. Kerin, A. Martin

Published Dec 21, 2022• 2 citations
arXivHTMLPDF

Abstract

We investigate the effects of Efimov states on the postquench dynamics of a system of three identical bosons with contact interactions in a spherically symmetric three-dimensional harmonic trap. The quench we consider is in the $s$-wave contact interaction, and we focus on quenches from the noninteracting to strongly interacting regimes and vice versa. The calculations use the hyperspherical solutions of the three-body problem and enable us to evaluate the semianalytical results of the Ramsey and particle separation, postquench. In the case where the interactions are quenched from the noninteracting to strongly interacting regime we find convergent aperiodic solutions for both the Ramsey signal and the particle separation. In contrast, for quenches from the strongly interacting regime to the noninteracting regime both the Ramsey signal and particle separation are periodic functions. However, in this case we find that the solutions for the particle separation diverge, indicating that in such a system large oscillations may be observable.

DOI
10.1103/physreva.106.063316

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We investigate the effects of Efimov states on the postquench dynamics of a system of three identical bosons with contact interactions in a spherically symmetric three-dimensional harmonic trap. The quench we consider is in the sss-wave contact interaction, and we focus on quenches from the noninteracting to strongly interacting regimes and vice versa. The calculations use the hyperspherical solutions of the three-body problem and enable us to evaluate the semianalytical results of the Ramsey and particle separation, postquench. In the case where the interactions are quenched from the noninteracting to strongly interacting regime we find convergent aperiodic solutions for both the Ramsey signal and the particle separation. In contrast, for quenches from the strongly interacting regime to the noninteracting regime both the Ramsey signal and particle separation are periodic functions. However, in this case we find that the solutions for the particle separation diverge, indicating that in such a system large oscillations may be observable.
We consider a system of two identical fermions of general mass interacting with a third distinguishable particle via a contact interaction within an isotropic three-dimensional harmonic trap. We calculate time-dependent observables of the system after it is quenched in sss-wave scattering length. To do this we use exact closed-form mass-imbalanced hyperspherical solutions to the static three-body problem. These exact solutions enable us to calculate two time-dependent observables, the Ramsey signal and particle separation, after the system undergoes a quench from noninteracting to the unitary regime or vice versa.
Abstract We consider a system of three particles, either three identical bosons or two identical fermions plus an impurity, within a three-dimensional isotropic trap interacting via a contact interaction. Using two approaches, one using an infinite sum of basis states for the wavefunction and the other a closed form wavefunction, we calculate the allowable energy eigenstates of the system as a function of the interaction strength, including the strongly and weakly interacting limits. For the fermionic case this is done while maintaining generality regarding particle masses. We find that the two methods of calculating the spectrum are in excellent agreement in the strongly interacting limit. However the infinite sum approach is unable to uniquely specify the energy of Efimov states, but in the strongly interacting limit there is, to a high degree of accuracy, a correspondence between the three-body parameter required by the boundary condition of the closed form approach and the summation truncation order required by the summation approach. This specification of the energies and wavefunctions forms the basis with which thermodynamic variables such as the virial coefficients or Tan contacts, or dynamic phenomena like quench dynamics can be calculated.
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 noninteracting 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 noninteracting to strongly interacting regimes the early time dependence dynamics are consistent with theoretical work in the single impurity many-body limit. When the system is quenched from the strongly to noninteracting regime we predict large oscillations in the separation between the two atoms, which arises from a logarithmic divergence due to the zero-range nature of the interaction potential.
We investigate the quantum dynamics of two bosons, trapped in a two-dimensional harmonic trap, upon quenching arbitrarily their interaction strength and thereby covering the entire energy spectrum. Utilizing the exact analytical solution of the stationary system, we derive a closed analytical form of the expansion coefficients of the time-evolved two-body wave function, whose dynamics is determined by an expansion over the postquench eigenstates. The emergent dynamical response of the system is analyzed in detail by inspecting several observables such as the fidelity, the reduced one-body densities, the radial probability density of the relative wave function in both real and momentum space, and the Tan contact, which unveils the existence of short range two-body correlations. When the system is initialized in its bound state, it is perturbed in the most efficient manner as compared to any other initial configuration. Moreover, starting from an interacting ground state, the two-boson response is enhanced for quenches toward the noninteracting limit.
We investigate the quantum dynamics of two identical bosons in a one-dimensional harmonic trap following an interaction quench from zero to infinite interaction strength and vice versa. For both quench scenarios, closed analytical expressions for the temporal evolution of the wave function as well as the Loschmidt echo are found and the dynamics of the momentum density as well as the reduced single-particle density matrix are analyzed. We observe a crossover of these quantities between bosonic, ``symmetrized'' fermionic, and fermionic properties. Furthermore, several combined quenches are analyzed as well.
We consider the evolution of two contact-interacting harmonically trapped particles following an arbitrary quench in interaction strength. We focus on the change in system energy, the work, associated with the quench. When quenching from any nonzero interaction strength to zero interaction strength we observe that the work done and particle separation diverge. In particular, the divergent behavior arises always and exclusively when quenching to\mathit{to}to the noninteracting regime. We demonstrate that the source of the divergence is its instantaneous nature. This validates and builds upon previous work that found divergent behavior arises when quenching from the strongly interacting limit to the noninteracting limit in both the two- and three-body cases.