Quantum fluctuations of a Bose-Josephson junction in a quasi-one-dimensional ring trap

Abstract

Using a Luttinger-liquid approach we study the quantum fluctuations of a Bose-Josephson junction, consisting of a Bose gas confined to a quasi one-dimensional ring trap which contains a localized repulsive potential barrier. For an infinite barrier we study the one-particle and two-particle static correlation functions. For the one-body density-matrix we obtain different power-law decays depending on the location of the probe points with respect to the position of the barrier. This quasi-long range order can be experimentally probed in principle using an interference measurement. The corresponding momentum distribution at small momenta is also shown to be affected by the presence of the barrier and to display the universal power-law behavior expected for an interacting 1D fluid. We also evaluate the particle density profile, and by comparing with the exact results in the Tonks-Girardeau limit we fix the nonuniversal parameters of the Luttinger-liquid theory. Once the parameters are determined from one-body properties, we evaluate the density-density correlation function, finding a remarkable agreement between the Luttinger liquid predictions and the exact result in the Tonks-Girardeau limit, even at the length scale of the Friedel-like oscillations which characterize the behavior of the density-density correlation function at intermediate distance. Finally, for a large but finite barrier we use the one-body correlation function to estimate the effect of quantum fluctuations on the renormalization of the barrier height, finding a reduction of the effective Josephson coupling energy, which depends on the length of the ring and on the interaction strength.

9 pages, 8 figures

References in corpus (9)

• Squeezing and entanglement in a Bose-Einstein condensate
• Direct Observation of Second Order Atom Tunnelling
• Observation of persistent flow of a Bose-Einstein condensate in a toroidal trap
• Bosonizing one-dimensional cold atomic gases
• Long Phase Coherence Time and Number Squeezing of two Bose-Einstein Condensates on an Atom Chip
• Preparing and probing atomic number states with an atom interferometer
• A ring trap for ultracold atoms
• Observing the Formation of Long-range Order during Bose-Einstein Condensation
• Motion of an impurity particle in an ultracold quasi-one-dimensional gas of hard-core bosons

Cited by in corpus (11)

• Damping of Josephson oscillations in strongly correlated one-dimensional atomic gases
• Strongly interacting trapped one-dimensional quantum gases: an exact solution
• Interacting atomic interferometry for rotation sensing approaching the Heisenberg Limit
• Metastable states and macroscopic quantum tunneling in a cold atom Josephson ring
• Universal shock-wave propagation in one-dimensional Bose fluids
• Macroscopic two-state systems in trapped atomic condensates
• Generalized harmonic-fluid approach for the off-diagonal correlations of a one-dimensional interacting Bose gas
• Exciton-polariton ring Josephson junction
• Time-resolved density correlations as probe of squeezing in toroidal Bose-Einstein condensates
• Minimal scattering entanglement in one-dimensional trapped gases
• Mesoscopic electron transport and atomic gases, a review of Frank W. J. Hekking's scientific work