Extension of Noether’s theorem in T-symmetry systems and its experimental demonstration in an optical setup
Noether’s theorem is one of the fundamental laws in physics, relating the symmetry of a physical system to its constant of motion and conservation law. On the other hand, there exist a variety of non-Hermitian parity-time ( T )-symmetric systems, which exhibit novel quantum properties and have attra...
Saved in:
Published in | Science China. Physics, mechanics & astronomy Vol. 66; no. 4; p. 240312 |
---|---|
Main Authors | , , , , , , |
Format | Journal Article |
Language | English |
Published |
Beijing
Science China Press
01.04.2023
Springer Nature B.V |
Subjects | |
Online Access | Get full text |
Cover
Loading…
Summary: | Noether’s theorem is one of the fundamental laws in physics, relating the symmetry of a physical system to its constant of motion and conservation law. On the other hand, there exist a variety of non-Hermitian parity-time (
T
)-symmetric systems, which exhibit novel quantum properties and have attracted increasing interest. In this work, we extend Noether’s theorem to a class of significant
T
-symmetry systems for which the eigenvalues of the
T
-symmetry Hamiltonian
H
^
T
change from purely real numbers to purely imaginary numbers, and introduce a generalized expectation value of an operator based on biorthogonal quantum mechanics. We find that the generalized expectation value of a time-independent operator is a constant of motion when the operator presents a standard symmetry in the
T
-symmetry unbroken regime, or a chiral symmetry in the
T
-symmetry broken regime. In addition, we experimentally investigate the extended Noether’s theorem in
T
-symmetry single-qubit and two-qubit systems using an optical setup. Our experiment demonstrates the existence of the constant of motion and reveals how this constant of motion can be used to judge whether the
T
-symmetry of a system is broken. Furthermore, a novel phenomenon of masking quantum information is first observed in a
T
-symmetry two-qubit system. This study not only contributes to full understanding of the relation between symmetry and conservation law in
T
-symmetry physics, but also has potential applications in quantum information theory and quantum communication protocols. |
---|---|
ISSN: | 1674-7348 1869-1927 |
DOI: | 10.1007/s11433-022-2067-x |