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

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.

Quantum dynamics in a camel-back potential of a dc SQUID

We investigate the quantum dynamics of a quadratic-quartic anharmonic oscillator formed by a potential well between two potential barriers. We realize this novel potential shape with a superconducting circuit comprised of a loop interrupted by two Josephson junctions, with near-zero current bias and flux bias near half a flux quantum. We investigate escape out of the central well, which can occur via tunneling through either of the two barriers, and find good agreement with a generalized double-path macroscopic quantum tunneling theory. We also demonstrate that this system exhibits an optimal line in current and flux bias space along which the oscillator, which can be operated as a phase qubit, is insensitive to decoherence due to low-frequency current fluctuations.