Observation of non-Hermitian topology in cold Rydberg quantum gases

Abstract

The pursuit of topological phenomena in non-Hermitian systems has unveiled new physics beyond the conventional Hermitian paradigm, yet their realization in interacting many-body platforms remains a critical challenge. Exploring this interplay is essential to understand how strong interactions and dissipation collectively shape topological phases in open quantum systems. Here, we experimentally demonstrate non-Hermitian spectra topology in a dissipative Rydberg atomic gas and characterize parameters-dependent winding numbers. By increasing the interaction strength, the system evolves from Hermitian to non-Hermitian regime, accompanying emergence of trajectory loop in the complex energy plane. As the scanning time is varied, the spectra topology becomes twisted in the complex energy plane manifesting as a topology phase transition with the sign winding number changed. When preparing the system in different initial states, we can access a nontrivial fractional phase within a parameter space that globally possesses an integer winding. Furthermore, by changing the scanning direction, we observe the differentiated loops, revealing the breaking of chirality symmetry. This work establishes cold Rydberg gases as a versatile platform for exploring the rich interplay between non-Hermitian topology, strong interactions, and dissipative quantum dynamics.

Figures (5)

• Figure 1: Experimental diagram and energy spectral topology. (a) Energy level diagrams. Probe and coupling fields excite atoms from the ground state $\ket{g}$ to the Rydberg state $\ket{r}$. (b) Schematic diagram of the experimental setup. The probe beam is incident opposite to the coupling beam and focused in cold $\rm{^{85}Rb}$ atoms. MOT: magneto-optical trap, PMT: photomultiplier tube, DM: dichroic mirror. (c) Numerical simulations of Liouvillian eigenspectrum varying with parameter $\rm{Arg(Z)}$ on the complex energy plane, where $\text{Z}=\rm{\Delta_r}+i\rm{\Omega_{p}^2}$. The parameters are $\{ \rm{\Omega_c},\rm{\Delta _c},\gamma_{\rm{eff}},\gamma_1,\gamma_2 \}$ = $\{4,0,2,0.8,1.2\}$, $\rm{\Omega_p^2 }\in[0,6]$, and $\rm{\Delta _r} \in[-3,3]$. The enlarged view represents the eigenvalue $\lambda_{rr}$ of eigenstate $\rho_{rr}$. The upper panel shows the diagram of changing trends of parameters $\rm{\Omega^2 _p}$ and $\rm{\Delta _r}$.
• Figure 2: Non-Hermitian energy spectral topology. (a) Numerical simulation of the energy eigenvalue $\lambda_{rr}$ of Rydberg steady state versus $\rm{\gamma_{eff}}$ on the complex plane, where the parameters are $\{ \rm{\Omega_c},\rm{\Delta _c},\gamma_1,\gamma_2 \}$ = $\{4,0,0.8,1.2\}.$ The Liouvillian eigenspectrum forms a loop in the complex plane. (b-e) The evolution trajectory of Rydberg eigenstate in the complex energy plane is strongly correlated with the variation of probe transmission and the energy level detuning $\rm{\Delta_r}$ in the experiment varies with the parameter Arg(Z), where $\text{Z}=\rm{\Delta_r}+\mathit{i}\rm{\Omega^2_{p}}$ in the scanning time of $\rm{T_s}=18~\rm{\mu s}$. Panels (b), (c), (d), and (e) display the spectral features for $(\rm{\Omega_p}/2\pi)^2\in[0,1]~\rm{MHz}^2$, $(\rm{\Omega_p}/2\pi)^2\in[0,4]~\rm{MHz}^2$, $(\rm{\Omega_p}/2\pi)^2\in[0,10]~\rm{MHz}^2$, and $(\rm{\Omega_p}/2\pi)^2\in[0,20]~\rm{MHz}^2$ , respectively.
• Figure 3: Twisted topology. (a) The simulated $\rm{Im(\rho_{eg})}$ during the up-scan and down-scan processes of $\rm{\Omega_p^2}$ through Lindblad master equation. (b) Schematic diagram of the different winding numbers corresponding to the absorption- and dissipation-dominated spectra of the system. (c)-(h) The spectral trajectory of the transmitted signal and the energy level detuning $\rm{\Delta_r}$ in the experiment varies with the parameter Arg(Z). The scanning times are as follows: $\rm{T_s}=19~\rm{\mu s}$ in (c), $\rm{T_s}=15~\rm{\mu s}$ in (d), $\rm{T_s}=10~\rm{\mu s}$ in (e), $\rm{T_s}=6~\rm{\mu s}$ in (f), $\rm{T_s}=4~\rm{\mu s}$ in (g) and $\rm{T_s}=1~\rm{\mu s}$ in (h).
• Figure 4: Fractional winding phase and opposite winding. (a) The counterclockwise (CCW) scan paths of the parameters $\rm{\Omega_p^2}$ and $\rm{\Delta_r}$ with different starting points A and B. (b) The measured spectral topological trajectory and projection (the black line) under the CCW scan with Arg(Z) ranging from 0 $\sim 4\pi$. (c) and (d) are the measured spectral topological trajectories and projections (the black line) under the CCW scanning path. They correspond to the starting points A and B in panel (a), with Arg(Z) from $0.75\pi\sim 2.25\pi$ and $1.25\pi/4\sim 3.25\pi$, respectively. The winding number $\mathcal{W}_\lambda$ = 1 for (c) and $\mathcal{W}_\lambda$ = -1 for (d). In panel (c), the phase winding in the complex plane of the parameter space is $1.5\pi$ for a closed loop with $\mathcal{W}_\lambda$ = 1. (e-g) are measured spectral topological trajectories and projections for noise strengths $N$ = 0.02, 0.12, and 0.35, with a fixed $\rm{T_s}=35~\rm{\mu s}$. (h) The accumulated phase $\delta \phi$ for forming a quantized topological structure as a function of $N$. The red line represents the fitted curve using a piecewise function: $y$ = 1.5$\pi$ for $x \leq 0.12$, and $y = c-dx^2$ for $x > 0.12$ (c = 1.52$\pi$ and d = 3.9), and the grey region represents the rigidity regime to $N$.
• Figure 5: Chirality symmetry breaking. (a) The clockwise (CW) and counterclockwise (CCW) scan paths of the parameters $\rm{\Omega_p^2}$ and $\rm{\Delta_r}$, corresponding to the chiral operation. (b) The spectral topological trajectory and projection (the black line) under the CW scanning path. (c) The spectral topological trajectory and projection (the black line) under the CCW scanning path. (d, e) The projections of spectra under two different scanning paths on the parameter plane, at the condition of optical depth OD = 7.9 (d) and OD = 4.6 (e). The grey dash curve denotes the mirror curve of the projected topological trajectory under the CW scanning. (f) The nonreciprocity parameter $\eta$ as a function of OD, and the red curve is a function fit $y = L / [1 + e^{-k(x - x_0)}]$ ($L=0.78$, $k=1.0$, and $x_0=5.9$).