Chiral Dynamics Near Intra- and Inter-Band Exceptional Points under Dissipative Spin-Orbital-Angular-Momentum Coupling

Abstract

We study the parametric chiral dynamics of atoms under dissipative spin-orbital-angular-momentum coupling (SOAMC). With atoms confined in the ring-shaped potential of the Laguerre-Gaussian Raman beams, the SOAMC not only couples the atomic center-of-mass angular momentum to the hyperfine spins, but also mixes different bands in the radial direction. This gives rise to a series of exceptional points of two types, the intra-band and the inter-band. Leveraging the topology of the spectral Riemann surface close to these exceptional points, we demonstrate the path-dependent chiral transfer of atoms to the higher-lying bands, by evolving the system along closed loops in the parameter space. Specifically, we illustrate two distinct scenarios, characterized by different mechanisms, where the atoms can be transferred to designated SOAMC-dressed bands. Our work demonstrates the rich exceptional structure in atom gases under dissipative SOAMC, and offers a novel route toward populating higher bands.

Figures (8)

• Figure 1: (a) Schematic level structure with spin-dependent atom loss. (b) The ac Stark shift of the Raman process $\chi (r)$ provides the ring-shaped confinement, while the Raman coupling $\Omega(r)$ drives transitions between distinct hyperfine states.
• Figure 2: Riemann surfaces of the real components of the eigenspectra, parameterized by $h$ and $\gamma$ in the $m=0$ sector. The right panels show the cross sections of the Riemann surfaces on the plane of $h=0$. The blue solid lines indicate the branch cuts, and red (black) dots mark intra-(inter-) band Eps. (a)(b) $\Omega_{0}/E_{0}=0.27$, (c)(d) $\Omega_{0}/E_{0}=0.82$, and (e)(f) $\Omega_{0}/E_{0}=1.37$. Other parameters are fixed as $l_{1}=4$, $l_{2}=-4$, $w=3a$, $R=15a$, and $\chi_{0}/E_{0}=-6.85$. We take $E_{0}=\hbar^{2}/(Ma^{2})$ as the unit of energy.
• Figure 3: (a) Schemaic evolution of $h$ and $\gamma$. Here, $\phi(t)=\pm 2\pi t /T+\pi$, where $+$ ($-$) corresponds to clockwise (counterclockwise) encircling. (b)(c)(d) The spectral trajectories under clockwise ($\circlearrowright$, red solid) and counterclockwise ($\circlearrowleft$, blue dashed) encircling at different Raman coupling $\Omega_0$. The values $\Omega_0/E_0=0.41,0.82$ and $1.37$ correspond to panels (b),(c) and (d), respectively. Purple dots indicate the initial points, green diamonds the final points, and the gray curves show the branch cuts. (e) The relation between ${\cal B}$ and the Raman coupling strength $\Omega_0$. The gray dashed lines correspond to the cases shown in (b)(c)(d). (f) The relation between ${\cal B}$ and the encircling time $T$. The gray dashed lines ($B=1$ and $B=6$) denote the lower dressed $s$ and the upper dressed $d$ bands. For panels (b)-(e), we fix $T E_0/\hbar=7.5$, while for panel (f), $\Omega_0/E_0=0.82$. All other parameters are identical to those in Fig. \ref{['Fig2']}, with $\rho/E_0=2.34$.
• Figure 4: Comparison of trajectories calculated from the effective and full Hamiltonians, for (a) $T E_0/\hbar=4$ and (b) $T E_0/\hbar=7.5$. The red (blue) solid lines denote the results of the two-band Hamiltonian for clockwise (counterclockwise) encircling, while the dark–gray (black-gray) dashed lines show the corresponding full-band results. Here, $\Omega_0/E_0=1.37$ and $\rho/E_0=2.34$. Other parameters are the same as those in Fig. \ref{['Fig2']}.
• Figure 5: (a) Schematic of the designed loops. The red, blue and black circles denotes the first, second and third loops with distinct encircling radius, and the corresponding dots mark their origins. (b) Spectral trajectories of the encircling. Here, $\rho_{k=1,2,3}=(4, 2.05, 3.5)E_0$, $T_{k=1,2,3}=(1.35, 3.2, 1.1)\hbar/E_0$ with $\Omega_0/E_0=1.37$. Other parameters are the same as those in Fig. \ref{['Fig2']}.