Reentrant behavior of the breathing-mode-oscillation frequency in a one-dimensional Bose gas

Abstract

We calculate the breathing mode frequency $\omega$ in a one-dimensional Bose gas confined to a harmonic trap of frequency ${\omega }_z$. We predict Exciting temporal oscillations of the density distribution is a high-precision method for probing ultracold trapped atomic gases. Interaction effects in their many-body dynamics are particularly puzzling and counter-intuitive in one spatial dimension (1D) due to enhanced quantum correlations. We consider 1D quantum Bose gas in a parabolic trap at zero temperature and explain, analytically and numerically, how oscillation frequency depends on the number of particles, their repulsion and the trap strength. We identify the frequency with the energy difference between the ground state and a particular excited state. This way we avoided resolving the dynamical evolution of the system, simplifying the problem immensely. We find an excellent quantitative agreement of our results with the data from the Innsbruck experiment [Science 325, 1224 (2009)].

discussion of the experiments significantly extended, references added, Fig. 2 corrected

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• Tan's contact of a harmonically trapped one-dimensional Bose gas: strong-coupling expansion and conjectural approach at arbitrary interactions
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• Polarization angle dependence of the breathing modes in confined one-dimensional dipolar bosons
• Self-consistent determination of the many-body state of ultracold bosonic atoms in a one-dimensional harmonic trap
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