Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1710.01637 · Physical Review A

Quantum dynamics of two trapped bosons following infinite interaction quenches

Leonhard M. A. Kehrberger, Valentin Bolsinger, Peter Schmelcher

Published Jan 10, 2018• 25 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.97.013606

Related papers

Quench dynamics of two one-dimensional harmonically trapped bosons bridging attraction and repulsion

Laura Budewig, S. I. Mistakidis, Peter Schmelcher

We unravel the nonequilibrium quantum dynamics of two harmonically confined bosons in one spatial dimension when performing an interaction quench from finite repulsive to attractive interaction strengths and vice versa. A closed analytical form of the expansion coefficients of the time-evolved two-body wavefunction is derived, while its dynamics is determined in terms of an expansion over the postquench eigenstates. For both quench scenarios the temporal evolution is analysed by inspecting the one- and two-body reduced density matrices and densities, the momentum distribution and the fidelity. Resorting to the fidelity spectrum and the eigenspectrum we identify the dominant eigenstates of the system that govern the dynamics. Monitoring the dynamics of the above-mentioned observables we provide signatures of the energetically higher-lying states triggered by the quench.

arXiv:1812.10985•Molecular Physics•Feb 6, 2019•21 citations

Analytical treatment of the interaction quench dynamics of two bosons in a two-dimensional harmonic trap

G. Bougas, S. I. Mistakidis, Peter Schmelcher

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.

arXiv:1905.10320•Physical Review A•Nov 4, 2019•19 citations

Stationary and dynamical properties of two harmonically trapped bosons in the crossover from two dimensions to one

G. Bougas, S. I. Mistakidis, G. M. Alshalan +1 more

We unravel the stationary properties and the interaction quench dynamics of two bosons, confined in a two-dimensional anisotropic harmonic trap. A transcendental equation is derived giving access to the energy spectrum and revealing the dependence of the energy gaps on the anisotropy parameter. The relation between the two- and one-dimensional scattering lengths as well as the Tan contacts is established. The contact, capturing the two-body short-range correlations, shows an increasing tendency for a larger anisotropy. Subsequently, the interaction quench dynamics from attractive to repulsive values and vice versa is investigated for various anisotropies. A closed analytical form of the expansion coefficients of the two-body wave function, during the time evolution is constructed. The response of the system is studied by means of the time-averaged fidelity, the spectra of the spatial extent of the cloud in each direction, and the one-body density. It is found that as the anisotropy increases, the system becomes less perturbed independently of the interactions, while for fixed anisotropy quenches toward the noninteracting regime perturb the system in the most efficient manner. Furthermore, we identify that in the tightly confined direction more frequencies are involved in the dynamics stemming from higher lying excited states.

arXiv:2001.10722•Physical Review A•Jul 15, 2020•14 citations

Sudden quench of harmonically trapped mass-imbalanced fermions

D. K. Nandy, Tomasz Sowiński

Dynamical properties of two-component mass-imbalanced few-fermion systems confined in a one-dimensional harmonic trap following a sudden quench of interactions are studied. It is assumed that initially the system is prepared in the non-interacting ground state and then, after a sudden quench of interactions, the unitary evolution is governed by interacting many-body Hamiltonian. By careful analysis of the evolution of the Loschmidt echo, density distributions of the components, and entanglement entropy between them, the role of mass imbalance and particle number imbalance on the system's evolution stability are investigated. All the quantities studied manifest a dramatic dependence on the number of heavy and lighter fermions in each component at a given quench strength. The results may have implications for upcoming experiments on fermionic mixtures with a well-defined and small number of particles.

arXiv:2209.05870•Scientific Reports•Nov 16, 2022•2 citations

Two-body quench dynamics of harmonically trapped interacting particles

A. D. Kerin, A. Martin

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.

arXiv:2005.01235•Physical Review A•Aug 11, 2020•9 citations

Probing the out-of-equilibrium dynamics of two interacting atoms

Tim Keller, Thomás Fogarty

We study the out-of-equilibrium dynamics of two interacting atoms in a one-dimensional harmonic trap after a quench by a tightly pinned impurity atom. We make use of an approximate variational calculation called the Lagrange-mesh method to solve the Schr\"odinger equation as a function of interparticle interaction and impurity quench strength. We investigate the out-of-equilibrium dynamics by calculating the Loschmidt echo which quantifies the irreversibility of the system following the quench, while its probability distribution after long times can be used to identify distinct dynamical regimes. These quantities are related to the spectral function which describes the full dynamical spectrum, and we show through a thorough examination of the parameter space the existence of distinct scattering states and collective oscillations. This work demonstrates how these dynamics are strongly dependent on the interaction strength between the atoms and may be tuned to observe the establishment of the orthogonality catastrophe in few-body systems.

arXiv:1608.03038•Physical Review A•Dec 19, 2016•17 citations
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 unravel the nonequilibrium quantum dynamics of two harmonically confined bosons in one spatial dimension when performing an interaction quench from finite repulsive to attractive interaction strengths and vice versa. A closed analytical form of the expansion coefficients of the time-evolved two-body wavefunction is derived, while its dynamics is determined in terms of an expansion over the postquench eigenstates. For both quench scenarios the temporal evolution is analysed by inspecting the one- and two-body reduced density matrices and densities, the momentum distribution and the fidelity. Resorting to the fidelity spectrum and the eigenspectrum we identify the dominant eigenstates of the system that govern the dynamics. Monitoring the dynamics of the above-mentioned observables we provide signatures of the energetically higher-lying states triggered by the quench.
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 unravel the stationary properties and the interaction quench dynamics of two bosons, confined in a two-dimensional anisotropic harmonic trap. A transcendental equation is derived giving access to the energy spectrum and revealing the dependence of the energy gaps on the anisotropy parameter. The relation between the two- and one-dimensional scattering lengths as well as the Tan contacts is established. The contact, capturing the two-body short-range correlations, shows an increasing tendency for a larger anisotropy. Subsequently, the interaction quench dynamics from attractive to repulsive values and vice versa is investigated for various anisotropies. A closed analytical form of the expansion coefficients of the two-body wave function, during the time evolution is constructed. The response of the system is studied by means of the time-averaged fidelity, the spectra of the spatial extent of the cloud in each direction, and the one-body density. It is found that as the anisotropy increases, the system becomes less perturbed independently of the interactions, while for fixed anisotropy quenches toward the noninteracting regime perturb the system in the most efficient manner. Furthermore, we identify that in the tightly confined direction more frequencies are involved in the dynamics stemming from higher lying excited states.
Dynamical properties of two-component mass-imbalanced few-fermion systems confined in a one-dimensional harmonic trap following a sudden quench of interactions are studied. It is assumed that initially the system is prepared in the non-interacting ground state and then, after a sudden quench of interactions, the unitary evolution is governed by interacting many-body Hamiltonian. By careful analysis of the evolution of the Loschmidt echo, density distributions of the components, and entanglement entropy between them, the role of mass imbalance and particle number imbalance on the system's evolution stability are investigated. All the quantities studied manifest a dramatic dependence on the number of heavy and lighter fermions in each component at a given quench strength. The results may have implications for upcoming experiments on fermionic mixtures with a well-defined and small number of particles.
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 study the out-of-equilibrium dynamics of two interacting atoms in a one-dimensional harmonic trap after a quench by a tightly pinned impurity atom. We make use of an approximate variational calculation called the Lagrange-mesh method to solve the Schr\"odinger equation as a function of interparticle interaction and impurity quench strength. We investigate the out-of-equilibrium dynamics by calculating the Loschmidt echo which quantifies the irreversibility of the system following the quench, while its probability distribution after long times can be used to identify distinct dynamical regimes. These quantities are related to the spectral function which describes the full dynamical spectrum, and we show through a thorough examination of the parameter space the existence of distinct scattering states and collective oscillations. This work demonstrates how these dynamics are strongly dependent on the interaction strength between the atoms and may be tuned to observe the establishment of the orthogonality catastrophe in few-body systems.