Observation of Momentum Space Josephson Effects in Weakly Coupled Bose-Einstein Condensates.

The momentum space Josephson effect describes the supercurrent flow between weakly coupled Bose-Einstein condensates (BECs) at two discrete momentum states. Here, we experimentally observe this exotic phenomenon using a BEC with Raman-induced spin-orbit coupling, where the tunneling between two local band minima is implemented by the momentum kick of an additional optical lattice. A sudden quench of the Raman detuning induces coherent spin-momentum oscillations of the BEC, which is analogous to the ac Josephson effect. We observe both plasma and regular Josephson oscillations in different parameter regimes. The experimental results agree well with the theoretical model and numerical simulation and showcase the important role of nonlinear interactions. We also show that the measurement of the Josephson plasma frequency gives the Bogoliubov zero quasimomentum gap, which determines the mass of the corresponding pseudo-Goldstone mode, a long-sought phenomenon in particle physics. The observation of momentum space Josephson physics offers an exciting platform for quantum simulation and sensing utilizing momentum states as a synthetic degree.

Nonexponential Tunneling due to Mean-Field-Induced Swallowtails.

Typically, energy levels change without bifurcating in response to a change of a control parameter. Bifurcations can lead to loops or swallowtails in the energy spectrum. The simplest quantum Hamiltonian that supports swallowtails is a nonlinear 2×2 Hamiltonian with nonzero off-diagonal elements and diagonal elements that depend on the population difference of the two states. This work implements such a Hamiltonian experimentally using ultracold atoms in a moving one-dimensional optical lattice. Self-trapping and nonexponential tunneling probabilities, a hallmark signature of band structures that support swallowtails, are observed. The good agreement between theory and experiment validates the optical lattice system as a powerful platform to study, e.g., Josephson junction physics and superfluidity in ring-shaped geometries.