Phase diagrams of tunable spin-orbit coupled Bose-Einstein condensates
Abstract
We analytically calculate phase boundaries of tunable spin-orbit coupled BECs with effective two-body interactions by using variational method. Phase diagrams for periodically driving 87Rb and 23Na systems are presented, respectively, which display several characteristic features contrast with those of undriven systems. In the 87Rb BECs, the critical density nc (density at quantum tricritical point) can be dramatically reduced in some parameter regions, thus the prospect of observing this intriguing quantum tricritical point is greatly enlarged. Moreover, a series of quantum tricritical points emerge quasi-periodically with increasing the Raman coupling strength for fixed 87Rb density. In the 23Na BECs, two hyperfine states of 23Na atoms can be miscible due to driving under proper parameters. As a result, 23Na systems can stay in the stripe phase with small Raman frequency at typical density. This expands the region of stripe phase in the phase diagram. In addition, there is no quantum tricritical point in such 23Na system , which is different from 87Rb system.