By applying an external magnetic field, we have determined the population of the magnetic sublevels of photodissociated atoms from the intensities of atomic fluorescence lines split by the Zeeman effect. A preferential population of the magnetic sublevels of the atomic fragment Na(3 2P3/2), which arises from the direct photodissociation through the D1Π(continuum) state of the NaK molecule, has been observed. The results are explained by assuming the separability of electronic and nuclear motion during the dissociation. The observed results could be rationalized by the sum of the photodissociation amplitudes caused by excitation of the P, Q and R branches. The population of the magnetic sublevels of Rb(5 2P3/2) atoms produced by predissociation of the C1Πu state of the Rb2 molecule by the repulsive molecular state c3Σ+u has been determined from the Zeeman spectra of the emission Rb(5 2P3/2→ 5 2Sm′1/2). The observed results are interpreted by including the spin-orbit coupling between an excited level of the C1Πu state and levels of the c3Σ+u state and the effect of the external magnetic field.
Interference of atomic Bose-Einstein condensates, observed in free expansion experiments, is a basic characteristic of their quantum nature. The ability to produce synthetic spin-orbit coupling in Bose-Einstein condensates has recently opened a new research field. Here we theoretically describe interference of two noninteracting spin-orbit coupled Bose-Einstein condensates in an external synthetic magnetic field. We demonstrate that the spin-orbit and the Zeeman couplings strongly influence the interference pattern determined by the angle between the spins of the condensates, as can be seen in time-of-flight experiments. We show that a quantum backflow, being a subtle feature of the interference, is, nevertheless, robust against the spin-orbit coupling and applied synthetic magnetic field.
The interplay of non-Hermiticity and spin-orbit (SO) coupling has attracted great interest in condensed-matter physics, ultracold atomic physics, optics, and other fields. Here we study the ground states, collective modes, and free-expansion dynamics of non-Hermitian SO-coupled Bose-Einstein condensates (BECs) with momentum-dependent gain and loss in a harmonic trap. An efficient analytical method for revealing the impact of non-Hermiticity on the ground states and dynamics of SO-coupled BECs is proposed. A dispersion relation with effective mass
m2 that can be larger than 1, less than 1, or negative is engineered by the momentum-dependent gain and loss, which is distinct from the ordinary SO-coupled BECs, where
m2>1 always holds. Negative effective mass can lead to the self-interference effect of condensates, while
m2<1 means that condensates can gain a larger acceleration when they are subjected to a constant force. Interestingly, the high-order zero-point kinetic energies are derived analytically and confirmed numerically, establishing a link between the zero-point kinetic energy and dispersion relation. In particular, the second-order zero-point kinetic energy can be controlled by the effective mass
m2, which has an important impact on many phenomena of ultracold atomic physics. In addition, another key result is that the frequencies of dipole and breathing modes can exceed the values of traditional BECs without SO coupling when the effective mass
m2<1, showing that gain (loss) is a powerful tool for probing and controlling quantum systems. Moreover, the asymmetric free expansion and self-interference effect of the condensates caused by negative effective masses are observed, and it is found that the rate of expansion is controlled by the effective mass
m2. Our results show that the controllable gain-loss engineering in SO-coupled BECs provides a prospect to explore novel quantum many-body physics.