Boson expansions and broken symmetry

Niels R. Walet, Abraham Klein

Eugene R. Marshalek, G. Alaga

Malte Weinberg, Ole Jürgensen, C. Ölschläger +3 more

We study several effects which lead to symmetry-broken momentum distributions of quantum gases released from optical lattices. In particular, we demonstrate that the interaction within the first milliseconds of the time-of-flight expansion can strongly alter the measurement of the initial atomic momentum distribution. For bosonic mixtures in state-dependent lattices, interspecies scattering processes lead to a symmetry breaking in momentum space. The underlying mechanism is identified to be diffraction of the matter wave from the total density lattice, which gives rise to a time-dependent interaction potential. Our findings are of fundamental relevance for the interpretation of time-of-flight measurements and for the study of exotic quantum phases such as the twisted superfluid. Beyond that, the observed matter-wave diffraction can also be used as an interferometric probe. In addition, we report on diffraction from the state-dependent standing light field, which leads to the same symmetry-broken momentum distributions, even for single component condensates.

Niels R. Walet, WALET, NR, Abraham Klein

Eugene R. Marshalek

The usefulness of perturbative expansions in deformed bosons has been limited by difficulties associated with zero-frequency (Goldstone) modes. A method developed earlier by Marshalek and Weneser to overcome these difficulties was restricted to the case in which the broken-symmetry generators commute. The present paper shows how to extend the method to the non-Abelian case of three-dimensional rotation of axially symmetric deformed systems. Application is made to a generic anharmonic Hamiltonian constructed from random-phase-approximation modes.

N. Dupuis

In systems with a spontaneously broken continuous symmetry, the perturbative loop expansion is plagued by infrared divergences due to the coupling between transverse and longitudinal fluctuations. As a result, the longitudinal susceptibility diverges and the self-energy becomes singular at low energy. We study the crossover from the high-energy Gaussian regime, where perturbation theory remains valid, to the low-energy Goldstone regime characterized by a diverging longitudinal susceptibility. We consider both the classical linear O (N) model and interacting bosons at zero temperature, using a variety of techniques: perturbation theory, hydrodynamic approach (i.e., for bosons, Popov's theory), large-N limit, and nonperturbative renormalization group. We emphasize the essential role of the Ginzburg momentum scale p{G}, below which the perturbative approach breaks down. Even though the action of (nonrelativistic) bosons includes a first-order time derivative term, we find remarkable similarities in the weak-coupling limit between the classical O(N) model and interacting bosons at zero temperature.