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:cond-mat/0611584 · Physical Review Letters

Momentum Distribution Dynamics of a Tonks-Girardeau Gas: Bragg Reflections of a Quantum Many-Body Wave Packet

Robert Pezer, Hrvoje Buljan

Published Jun 14, 2007• 81 citations
arXivHTMLPDF

Abstract

The momentum distribution (MD) dynamics of a Tonks-Girardeau (TG) gas is studied in the context of Bragg reflections of a many-body wave packet. We find strong suppression of a Bragg reflection peak for a large and dense TG wave packet; our observation illustrates the dependence of the MD on the interactions and wave function symmetry. The MD is calculated from the reduced single-particle density matrix (RSPDM). We develop a method for calculating the RSPDM of a TG gas, which is operative for a large number of particles, and does not depend on the external potential and the state of the system. The method is based on a formula expressing the RSPDM via a dynamically evolving single-particle basis.

DOI
10.1103/physrevlett.98.240403

Related papers

Momentum distribution dynamics of a tonks-girardeau gas: Bragg reflections of a quantum many-body wavepacket

Robert Pezer, Hrvoje Buljan

The dynamics of the momentum distribution and the reduced single-particle density matrix (RSPDM) of a Tonks-Girardeau gas is studied in the context of Bragg-reflections of a manybody wavepacket.

Quantum Electronics and Laser Science Conference•May 1, 2007•1 citation

One-particle density matrix and momentum distribution of the out-of-equilibrium one-dimensional Tonks-Girardeau gas: Analytical results at large N

Stefano Scopa, Paola Ruggiero, Pasquale Calabrese +1 more

In one-dimensional (1D) quantum gases, the momentum distribution (MD) of the atoms is a standard experimental observable, routinely measured in various experimental setups. The MD is sensitive to correlations, and it is notoriously hard to compute theoretically for large numbers of atoms $N$, which often prevents direct comparison with experimental data. Here we report significant progress on this problem for the 1D Tonks-Girardeau (TG) gas in the asymptotic limit of large $N$, at zero temperature and driven out of equilibrium by a quench of the confining potential. We find an exact analytical formula for the one-particle density matrix $\ensuremath{\langle}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathrm{\ensuremath{\Psi}}}}^{\ifmmode\dagger\else\textdagger\fi{}}(x)\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathrm{\ensuremath{\Psi}}}({x}^{\ensuremath{'}})\ensuremath{\rangle}$ of the out-of-equilibrium TG gas in the $N\ensuremath{\rightarrow}\ensuremath{\infty}$ limit, valid on distances $|x\ensuremath{-}{x}^{\ensuremath{'}}|$ much larger than the interparticle distance. By comparing with time-dependent Bose-Fermi mapping numerics, we demonstrate that our analytical formula can be used to compute the out-of-equilibrium MD with great accuracy for a wide range of momenta (except in the tails of the distribution at very large momenta). For a quench from a double-well potential to a single harmonic well, which mimics a ``quantum Newton cradle'' setup, our method predicts the periodic formation of peculiar, multiply peaked, momentum distributions.

arXiv:2301.04094•Physical Review A•Jul 31, 2023•10 citations

Single-particle density matrix and the momentum distribution of dark “solitons” in a Tonks-Girardeau gas

Hrvoje Buljan, Karlo Lelas, Robert Pezer +1 more

We study the reduced single-particle density matrix (RSPDM), the momentum distribution, and natural orbitals and their occupancies of dark ``soliton'' (DS) states in a Tonks-Girardeau gas. DS states are specially tailored excited many-body eigenstates, which have a dark solitonic notch in their single-particle density. The momentum distribution of DS states has a characteristic shape with two sharp spikes. We find that the two spikes arise due to the high degree of correlation observed within the RSPDM between the mirror points ($x$ and $\ensuremath{-}x$) with respect to the dark notch at $x=0$; the correlations oscillate rather than decay as the points $x$ and $\ensuremath{-}x$ are being separated.

arXiv:0707.2196•Physical Review A•Oct 9, 2007•5 citations

The dynamics of Tonks–Girardeau gas excited by a pulse drive

Jia 佳 Li 李, Yajiang Hao

Abstract In this paper we study the dynamics of Tonks–Girardeau (TG) gases in a harmonic potential driven by a Gaussian pulse, which is in correspondence with the excitation dynamics of electrons in matter driven by an ultrashort laser pulse. The evolving dynamics of the TG gas are obtained with a Bose–Fermi mapping method combined with numerical techniques. We calculate the evolving dynamics of the occupation distribution of single-particle energy levels, the density distribution and the momentum distribution of the system. It is shown that the system arrives at a dynamically stable state at the end of driving. In the high-frequency regime, TG gases return back to the ground state, while in the low-frequency regime the population inversion exhibits that all atoms occupy high levels.

Journal of Physics B Atomic Molecular and Optical Physics•Dec 16, 2024•0 citations

The dynamics of Tonks-Girardeau gas excited by a pulse drive

Jia Li, Yajiang Hao

In this paper we study the dynamics of Tonks-Girardeau (TG) gases in a harmonic potential driven by Gaussian pulse, which is a correspondence of the excitation dynamics of electrons in matters driven by ultrashort laser pulse. The evolving dynamics of TG gas are obtained with Bose-Fermi mapping method combined with the numerical techniques. We calculate the evolving dynamics of occupation distribution of single-particle energy levels, density distribution and momentum distribution of the system. It is shown that the system arrived at a dynamically stable state at the end of driving. At high-frequency regime TG gases return back to ground state while at low-frequency regime the population inversion exhibits and all atoms occupy high levels.

arXiv:2406.17997•Jun 26, 2024•0 citations

One-dimensional magnetized Tonks–Girardeau gas properties in an external magnetic field

Zhao Liang Wang, An Min Wang

With Girardeau's Fermi–Bose mapping, we have constructed the eigenstates of the Tonks–Girardeau (TG) gas in an external magnetic field. When the number of bosons N is commensurate with the number of potential cycles M , the probability of this TG gas in the ground state is bigger than the TG gas raised by Girardeau in 1960. Through the comparison of properties between this TG gas and Fermi gas, we find that the following issues are always the same: their average value of particle coordinates and potential energies, system total momenta, single-particle densities and pair distribution functions. But the reduced single-particle density matrices and their momentum distributions between them are different.

arXiv:1001.0116•Journal of Physics A Mathematical and Theoretical•Mar 29, 2010•2 citations
The momentum distribution (MD) dynamics of a Tonks-Girardeau (TG) gas is studied in the context of Bragg reflections of a many-body wave packet. We find strong suppression of a Bragg reflection peak for a large and dense TG wave packet; our observation illustrates the dependence of the MD on the interactions and wave function symmetry. The MD is calculated from the reduced single-particle density matrix (RSPDM). We develop a method for calculating the RSPDM of a TG gas, which is operative for a large number of particles, and does not depend on the external potential and the state of the system. The method is based on a formula expressing the RSPDM via a dynamically evolving single-particle basis.
In one-dimensional (1D) quantum gases, the momentum distribution (MD) of the atoms is a standard experimental observable, routinely measured in various experimental setups. The MD is sensitive to correlations, and it is notoriously hard to compute theoretically for large numbers of atoms NNN, which often prevents direct comparison with experimental data. Here we report significant progress on this problem for the 1D Tonks-Girardeau (TG) gas in the asymptotic limit of large NNN, at zero temperature and driven out of equilibrium by a quench of the confining potential. We find an exact analytical formula for the one-particle density matrix $\ensuremath{\langle}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathrm{\ensuremath{\Psi}}}}^{\ifmmode\dagger\else\textdagger\fi{}}(x)\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathrm{\ensuremath{\Psi}}}({x}^{\ensuremath{'}})\ensuremath{\rangle}$ of the out-of-equilibrium TG gas in the $N\ensuremath{\rightarrow}\ensuremath{\infty}$ limit, valid on distances $|x\ensuremath{-}{x}^{\ensuremath{'}}|$ much larger than the interparticle distance. By comparing with time-dependent Bose-Fermi mapping numerics, we demonstrate that our analytical formula can be used to compute the out-of-equilibrium MD with great accuracy for a wide range of momenta (except in the tails of the distribution at very large momenta). For a quench from a double-well potential to a single harmonic well, which mimics a ``quantum Newton cradle'' setup, our method predicts the periodic formation of peculiar, multiply peaked, momentum distributions.
We study the reduced single-particle density matrix (RSPDM), the momentum distribution, and natural orbitals and their occupancies of dark ``soliton'' (DS) states in a Tonks-Girardeau gas. DS states are specially tailored excited many-body eigenstates, which have a dark solitonic notch in their single-particle density. The momentum distribution of DS states has a characteristic shape with two sharp spikes. We find that the two spikes arise due to the high degree of correlation observed within the RSPDM between the mirror points (xxx and $\ensuremath{-}x$) with respect to the dark notch at x=0x=0x=0; the correlations oscillate rather than decay as the points xxx and $\ensuremath{-}x$ are being separated.
Abstract In this paper we study the dynamics of Tonks–Girardeau (TG) gases in a harmonic potential driven by a Gaussian pulse, which is in correspondence with the excitation dynamics of electrons in matter driven by an ultrashort laser pulse. The evolving dynamics of the TG gas are obtained with a Bose–Fermi mapping method combined with numerical techniques. We calculate the evolving dynamics of the occupation distribution of single-particle energy levels, the density distribution and the momentum distribution of the system. It is shown that the system arrives at a dynamically stable state at the end of driving. In the high-frequency regime, TG gases return back to the ground state, while in the low-frequency regime the population inversion exhibits that all atoms occupy high levels.
In this paper we study the dynamics of Tonks-Girardeau (TG) gases in a harmonic potential driven by Gaussian pulse, which is a correspondence of the excitation dynamics of electrons in matters driven by ultrashort laser pulse. The evolving dynamics of TG gas are obtained with Bose-Fermi mapping method combined with the numerical techniques. We calculate the evolving dynamics of occupation distribution of single-particle energy levels, density distribution and momentum distribution of the system. It is shown that the system arrived at a dynamically stable state at the end of driving. At high-frequency regime TG gases return back to ground state while at low-frequency regime the population inversion exhibits and all atoms occupy high levels.
With Girardeau's Fermi–Bose mapping, we have constructed the eigenstates of the Tonks–Girardeau (TG) gas in an external magnetic field. When the number of bosons N is commensurate with the number of potential cycles M , the probability of this TG gas in the ground state is bigger than the TG gas raised by Girardeau in 1960. Through the comparison of properties between this TG gas and Fermi gas, we find that the following issues are always the same: their average value of particle coordinates and potential energies, system total momenta, single-particle densities and pair distribution functions. But the reduced single-particle density matrices and their momentum distributions between them are different.