Observation of Non-Hermitian Edge Burst Effect in One-Dimensional Photonic Quantum Walk

Non-Hermitian systems can exhibit unique quantum phases without any Hermitian counterparts. For example, the latest theoretical studies predict a new surprising phenomenon that bulk bands can localize and dissipate prominently at the system boundary, which is dubbed the non-Hermitian edge burst effect. Here we realize a one-dimensional non-Hermitian Su-Schrieffer-Heeger lattice with bulk translation symmetry implemented with a photonic quantum walk. Employing time-resolved single-photon detection to characterize the chiral motion and boundary localization of bulk bands, we determine experimentally that the dynamics underlying the non-Hermitian edge burst effect is due to the interplay of non-Hermitian skin effect and imaginary band gap closing. This new non-Hermitian physical effect deepens our understanding of quantum dynamics in open quantum systems.

Figure 1

The non-Hermitian SSH lattice model. (a) We draw the non-Hermitian SSH lattice model as two sublattices with the nearest neighbor coupling $U_1$ and $U_2$. The dissipation $\mathrm{\Gamma }$ occurs only via the superposition state $|n,-⟩=(|n,A⟩-|n,B⟩)/\sqrt{2}$. Then we can describe the single particle transport in this lattice by the Floquet operator $F=U_2{U}_1\mathrm{\Gamma }$. (b) The respective energy spectra with intercell hopping paramter $t_2=0.40$ and $\gamma =2.00$. Inset: the maxima of the imaginary gaps and the NHSE parameter $\kappa$ versus intercell hopping parameter $t_1$.

Figure 2

Schematic of the experimental setup. (a) To implement the photonic quantum walk, we couple 10% energy of laser pulses ($\lambda =1560\mathrm{nm}$) into an optical loop via a beam splitter (BS). We pass them through a customized polarizing beam splitter (CPBS) to induce dissipation $\mathrm{\Gamma }$, a pair of half-wave plates ($H_1$ and $H_2$) to implement the intracell tunneling $U_1$, then through an unbalanced Mach-Zehnder interferometer (MZI), an electro-optical-modulator (EOM), and the second MZI to implement the intercell tunneling $U_2$ (see main text and Supplemental Material [54]). We apply time-resolved single-photon detection to the dissipation from the CPBS. We note that the time sequences for the laser diode, the EOM, and the single-photon detecter are precisely synchronized. Additionally, an erbium-doped fiber amplifier (EDFA) is integrated into the loop to mitigate the optical loss. (b) An illustration to realize the Floquet operator in Eq. (1), here creating an edge at the boundary of the lattices to implement the OBC.

Figure 3

Experimental measurements of photon dissipations. (a) and (b) Photon dissipation probabilities $p(n,m)$ with $|{\varphi }_0⟩=|10,+⟩$, $N=17$, $t_1=t_2=0.4$ in (a), and $t_1=0.88$, $t_2=0.4$ in (b). Left (right) panel: experimental (theoretical) results with high (low) dissipation in red (blue). (c) and (d) Accumulated dissipations $P(n)$ that correspond, respectively, to (a) and (b), with experimental (thoretical) results drawn in red (blue). Error bars stand for 1 standard deviation.

Figure 4

Characteristic features of the non-Hermitian edge burst effect. (a) $P_{\mathrm{edge}}/P_{\min }$ versus intercell hopping parameter $t_1$. Smooth lines from top to bottom are numerical results with $(n_0,N)=(100,200),(20,40),(10,17),(5,17)$, respectively. Filled dots: the respective experimental results. (b) The scaling relation. Red smooth lines (numerical) and red solid dots (experimental) are for $t_1=t_2$. Red dashed line is the scaling relation with ${\alpha }_{\mu }=1.08$. Inset: Red smooth line is the numerical result and red dashed line is the scaling relation with ${\alpha }_{\mu }=1.03$ for $n\le 500$. Respectively, blue lines (numerical) and blue solid dots (experimental) are for $t_1>t_2$. Error bars stand for 1 standard deviation. (c) Quasienergy spectrum $\overline{\epsilon }$ under OBC for the system described by the unitary Floquet operator $U_2{U}_1$ with $t_2=0.4$. A pair of zero-energy edge states are seen in the parameter region of $0<t_1<t_2$, and a topological phase transition occurs at $t_1=t_2$.