We investigate degenerate quantum gases in one dimension, trapped in a harmonic potential which is split centrally by a point-like potential. Since the single-particle eigenfunctions of such a system are known for all strengths of the central potential, the dynamics for non-interacting fermionic gases and low-density, strongly interacting bosonic gases can be investigated exactly using the Fermi–Bose mapping theorem. We calculate the exact many-particle ground state wavefunctions for both particle species, investigate soliton-like solutions, and compare the bosonic system to the well known physics of Bose gases described by the Gross–Pitaevskii equation. We also address the experimentally important questions of the creation and detection of such states.We investigate degenerate quantum gases in one dimension, trapped in a harmonic potential which is split centrally by a point-like potential. Since the single-particle eigenfunctions of such a system are known for all strengths of the central potential, the dynamics for non-interacting fermionic gases and low-density, strongly interacting bosonic gases can be investigated exactly using the Fermi–Bose mapping theorem. We calculate the exact many-particle ground state wavefunctions for both particle species, investigate soliton-like solutions, and compare the bosonic system to the well known physics of Bose gases described by the Gross–Pitaevskii equation. We also address the experimentally important questions of the creation and detection of such states.

arXiv:cond-mat/0301200Journal of Physics B Atomic Molecular and Optical PhysicsJun 5, 200341 citations

Multi-Particle Correlation Functions in a Trapped Bose Gas

N. M. Bogoliubov

Journal of Mathematical SciencesApr 4, 20031 citation

Symplectic tomography of ultracold gases in tight waveguides

Adolfo del Campo, Vladimir I. Man’ko, Giuseppe Marmo

The phase space is the natural ground to smoothly extrapolate between local and nonlocal correlation functions. With this objective, we introduce the symplectic tomography of many-body quantum gases in tight waveguides, and concentrate on the reduced single-particle symplectic tomogram (RSPST) whose marginals are the density profile and momentum distribution. We present an operational approach to measure the RSPST from the time evolution of the density profile after shutting off the interactions in a variety of relevant situations: Free expansion, fall under gravity, and oscillations in a harmonic trap. From the RSPST, the one-body density matrix of the trapped state can be reconstructed.The phase space is the natural ground to smoothly extrapolate between local and nonlocal correlation functions. With this objective, we introduce the symplectic tomography of many-body quantum gases in tight waveguides, and concentrate on the reduced single-particle symplectic tomogram (RSPST) whose marginals are the density profile and momentum distribution. We present an operational approach to measure the RSPST from the time evolution of the density profile after shutting off the interactions in a variety of relevant situations: Free expansion, fall under gravity, and oscillations in a harmonic trap. From the RSPST, the one-body density matrix of the trapped state can be reconstructed.

arXiv:0803.4158Physical Review AAug 13, 200811 citations

Study of weakly interacting trapped Bose gas

Renu Bala, K. N. Pathak

The European Physical Journal BOct 1, 20160 citations

Universal energy functionals for trapped Fermi gases in low dimensions

Jiansen Zhang, Shina Tan

We study a system of trapped two-component Fermi gases with a zero-range interaction in two dimensions or one dimension. We calculate the one-particle density matrices of these systems at small displacements, from which we show that the $N$ -body energies are linear functionals of the occupation probabilities of single-particle energy eigenstates. A universal energy functional was first derived in 2011 [S. Tan, Phys. Rev. Lett. 107, 145302 (2011)] for trapped zero-range interacting two-component Fermi gases in three dimensions. We also calculate the asymptotic behaviors of the occupation probabilities of single-particle energy eigenstates at high energies.We study a system of trapped two-component Fermi gases with a zero-range interaction in two dimensions or one dimension. We calculate the one-particle density matrices of these systems at small displacements, from which we show that the $N$-body energies are linear functionals of the occupation probabilities of single-particle energy eigenstates. A universal energy functional was first derived in 2011 [S. Tan, Phys. Rev. Lett. 107, 145302 (2011)] for trapped zero-range interacting two-component Fermi gases in three dimensions. We also calculate the asymptotic behaviors of the occupation probabilities of single-particle energy eigenstates at high energies.

arXiv:2312.00325Physical Review AApr 16, 20240 citations

N

-body energies are linear functionals of the occupation probabilities of single-particle energy eigenstates. A universal energy functional was first derived in 2011 [S. Tan, Phys. Rev. Lett. 107, 145302 (2011)] for trapped zero-range interacting two-component Fermi gases in three dimensions. We also calculate the asymptotic behaviors of the occupation probabilities of single-particle energy eigenstates at high energies.