Chiral supersolid and dissipative time crystal in Rydberg-dressed Bose-Einstein condensates with Raman-induced spin-orbit coupling

Abstract

Spin-orbit coupling (SOC) is one of the crucial factors that affect the chiral symmetry of matter by causing the spatial symmetry breaking of the system. We find that Raman-induced SOC can induce a chiral supersolid phase with a helical antiskyrmion lattice in balanced Rydberg-dressed two-component Bose-Einstein condensates (BECs) in a harmonic trap by modulating the Raman coupling strength. This is in stark contrast to the mirror symmetric supersolid phase containing skyrmion-antiskyrmion lattice pair for the case of Rashba SOC. Two ground-state phase diagrams are presented as a function of the Rydberg interaction and the Raman-induced SOC. It is shown that the interplay among Raman-induced SOC, Rydberg interactions, and nonlinear contact interactions favors rich ground-state structures, including half-quantum vortex phase, stripe supersolid phase, toroidal stripe phase with a central Anderson-Toulouse coreless vortex, checkerboard supersolid phase, mirror symmetric supersolid phase, chiral supersolid phase and standing-wave supersolid phase. In addition, the effects of rotation and in-plane quadrupole magnetic field on the ground state of the system are analyzed. In these two cases, the chiral supersolid phase is broken and the ground state tends to form a miscible phase. Furthermore, we demonstrate that when the initial state is a chiral supersolid phase the rotating harmonic trapped system sustains dissipative continuous time crystal by studying the rotational dynamic behaviors of the system.

Figures (4)

• Figure 1: (Color online) Typical density distribution (left), phase distribution (middle) and spin texture (right) of the system for (a) $\widetilde{C}_{6}=1500$, $\kappa=4$, $\Omega _{R}=0$ and (b) $\widetilde{C}_{6}=1500$, $\kappa=4$, $\Omega _{R}=10$. The arrows in the spin texture represent the transverse spin vector ($S_{x}$, $S_{y}$) and the color of each arrow indicates the magnitude of $S_{z}$. The square and circle in the spin texture denote a skyrmion and an antiskyrmion, respectively. Here each panel is a square, and the range and scale of the vertical axis are the same as those of the horizontal axis. The unit length is $R_{c}$.
• Figure 2: (Color online) (a) Ground-state phase diagram as the function of the SOC strength $\kappa$ and the Rydberg interaction strength $\widetilde{C}_{6}$ for two-component BECs with Raman-induced SOC and balanced Rydberg interactions in a harmonic trap, where the Raman coupling strength $\Omega _{R}=10$. (b) Ground-state phase diagram with respect to $\Omega _{R}$ and $\widetilde{C}_{6}$, where $\kappa=4$. The background color in (a) and (b) indicates the magnitude of $\left\langle L_{z}\right\rangle$. (c) The first four rows denote typical density distributions and phase distributions of various ground-state phases, where (I)-(VII) correspond to the half-quantum vortex (HQV) phase, stripes supersolid (SSS) phase, toroidal stripe (TS) phase with a central Anderson-Toulouse coreless vortex, checkerboard supersolid (CBSS) phase, mirror-symmetric supersolid (MSSS) phase with skyrmion-antiskyrmion lattice pair, chiral supersolid (CSS) phase with a helical antiskyrmion lattice, and standing-wave supersolid (SWSS) phase, respectively. The last row corresponds to the momentum distribution of the system. The relevant parameters are (I) $\widetilde{C}_{6}=10$, $\kappa=2$, $\Omega _{R}=10$, (II) $\widetilde{C}_{6}=10$, $\kappa=6$, $\Omega _{R}=10$, (III) $\widetilde{C}_{6}=250$, $\kappa=6$, $\Omega _{R}=10$, (IV) $\widetilde{C}_{6}=1000$, $\kappa=6$, $\Omega _{R}=10$, (V) $\widetilde{C}_{6}=1500$, $\kappa=4$, $\Omega _{R}=0$, (VI) $\widetilde{C}_{6}=1500$, $\kappa=4$, $\Omega _{R}=10$, and (VII) $\widetilde{C}_{6}=1500$, $\kappa=7$, $\Omega _{R}=10$. The unit length in the first to fourth rows of Fig. 2(c) is $R_{c}$.
• Figure 3: (Color online) (a) Ground-state density distribution, phase distribution and spin texture of rotating two-component BECs with Raman-induced SOC and Rydberg interactions, where the rotation frequency $\Omega _{r}=0.8$, $\widetilde{C}_{6}=1500$, $\kappa=4$, and $\Omega _{R}=10$. (b) Ground-state density distribution, phase distribution and spin texture of non-rotating two-component BECs with Raman-induced SOC and Rydberg interactions in an in-plane quadrupole magnetic field, where the quadrupole field strength $B=6$, $\widetilde{C}_{6}=1500$, $\kappa=4$, and $\Omega _{R}=10$. The arrows in the spin texture represent the transverse spin vector ($S_{x}$, $S_{y}$) and the color of each arrow indicates the magnitude of $S_{z}$. The square, circle, pentagon, and hexagon in the spin texture denote a skyrmion, an antiskyrmion, a half-skyrmion, and a half-antiskyrmion, respectively. Here each panel in (a) and (b) is a square, and the range and scale of the vertical axis are the same as those of the horizontal axis. The unit length in Figs. 3(a)-3(b) is $R_{c}$. (c) and (d) The miscibility $\eta$ as a function of $\Omega _{r}$ and $B$ for $\widetilde{C}_{6}=1500$, $\kappa=4$, and $\Omega _{R}=10$, respectively. The insets in Fig. 3(c) and Fig. 3(d) are the density distributions of the system for $\Omega _{r}=0.1$ and for $B=0.5$, respectively.
• Figure 4: (Color online) (a)--(d) Temporal evolution of the average orbital angular momentum per atom $\left\langle L_{z}\right\rangle$ for (a) $\widetilde{C}_{6}=250$, $\kappa=4$, $\Omega _{R}=16$, (b) $\widetilde{C}_{6}=1500$, $\kappa=4$, $\Omega _{R}=0$, (c) $\widetilde{C}_{6}=1500$, $\kappa=4$, $\Omega _{R}=10$, and (d) $\widetilde{C}_{6}=1500$, $\kappa=7$, $\Omega _{R}=10$. The insets in the upper right corners of panels (a)-(c) illustrate the local enlargements of the red dotted frames, respectively. The component density distributions at specific moments are shown in panels (a)-(d). (e) The temporal evolution of the density distribution corresponding to the red dotted frame in panel (c). Here $t$ and $\left\langle L_{z}\right\rangle$ are in units of $\tau$ and $\hbar$, respectively. The unit length in Fig. 4(e) is $R_{c}$.