Journal
PHYSICAL REVIEW LETTERS
Volume 129, Issue 18, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.129.173601
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Funding
- National Natural Science Foundation of China [61960206003, 61825502, 61827826, 62061160487, 12204462]
- Innovation Program for Quantum Science and Technology [2021ZD0303200]
- Fundamental Research Funds for the Central Universities
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This study quantifies the edge states and localization lengths in topological phase transitions through measuring the survival probability. The experiment provides an alternative approach for characterizing topological phase transitions and extracting critical exponents.
Edge states in topological phase transitions have been observed in various platforms. To date, verification of the edge states and the associated topological invariant are mostly studied, and yet a quantitative measurement of topological phase transitions is still lacking. Here, we show the direct measurement of edge states and their localization lengths from survival probability. We employ photonic waveguide arrays to demonstrate the topological phase transitions based on the Su-Schrieffer-Heeger model. By measuring the survival probability at the lattice boundary, we show that in the long-time limit, the survival probability is P = (1 - e(-2/xi loc))(2), where xi(loc) is the localization length. This length derived from the survival probability is compared with the distance from the transition point, yielding a critical exponent of nu = 0.94 +/- 0.04 at the phase boundary. Our experiment provides an alternative route to characterizing topological phase transitions and extracting their key physical quantities.
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