| Citation: | LIN Yu-Hao, YAN Kai, TAN Jia, CAO Zhao-Liang, HAO Xiang. Witnessing quantum phase transition in a non-Hermitian trapped ion system via quantum Fisher information[J]. Chinese Optics, 2024, 17(6): 1467-1475. doi: 10.37188/CO.EN-2024-0017
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Quantum Fisher information is used to witness the quantum phase transition in a non-Hermitian trapped ion system with balanced gain and loss, from the viewpoint of quantum parameter estimation. We formulate a general non-unitary dynamic of any two-level non-Hermitian system in the form of state vector. The sudden change in the dynamics of quantum Fisher information occurs at an exceptional point characterizing quantum criticality. The dynamical behaviors of quantum Fisher information are classified into two different ways which depends on whether the system is located in symmetry unbroken or broken phase regimes. In the phase regime where parity and time reversal symmetry are unbroken, the oscillatory evolution of quantum Fisher information is presented, achieving better quantum measurement precision. In the broken phase regime, quantum Fisher information undergoes the monotonically decreasing behavior. The maximum value of quantum estimation precision is obtained at the exceptional point. It is found that the two distinct kinds of behaviors can be verified by quantum entropy and coherence. Utilizing quantum Fisher information to witness phase transition in the non-Hermitian system is emphasized. The results may have potential applications to non-Hermitian quantum information technology.
| [1] |
ÖZDEMIR Ş K, ROTTER S, NORI F, et al. Parity–time symmetry and exceptional points in photonics[J]. Nature Materials, 2019, 18(8): 783-798. doi: 10.1038/s41563-019-0304-9
|
| [2] |
FENG L, WONG Z J, MA R M, et al. Single-mode laser by parity-time symmetry breaking[J]. Science, 2014, 346(6212): 972-975. doi: 10.1126/science.1258479
|
| [3] |
SUNADA S. Enhanced response of non-Hermitian photonic systems near exceptional points[J]. Physical Review A, 2018, 97(4): 043804. doi: 10.1103/PhysRevA.97.043804
|
| [4] |
LÜ X Y, JING H, MA J Y, et al. PT-symmetry-breaking chaos in optomechanics[J]. Physical Review Letters, 2015, 114(25): 253601.
|
| [5] |
LU T X, ZHANG H L, ZHANG Q, et al. Exceptional-point-engineered cavity magnomechanics[J]. Physical Review A, 2021, 103(6): 063708. doi: 10.1103/PhysRevA.103.063708
|
| [6] |
GUO A, SALAMO G J, DUCHESNE D, et al. Observation of PT-symmetry breaking in complex optical potentials[J]. Physical Review Letters, 2009, 103(9): 093902. doi: 10.1103/PhysRevLett.103.093902
|
| [7] |
CHEN W J, KAYA ÖZDEMIR Ş, ZHAO G M, et al. Exceptional points enhance sensing in an optical microcavity[J]. Nature, 2017, 548(7666): 192-196. doi: 10.1038/nature23281
|
| [8] |
XU H, LAI D G, QIAN Y B, et al. Optomechanical dynamics in the PT-and broken-PT-symmetric regimes[J]. Physical Review A, 2021, 104(5): 053518. doi: 10.1103/PhysRevA.104.053518
|
| [9] |
SU ZH X, YAO E X, HUANG L L, et al. Optical topological characteristics of two dimensional artificial metamaterials[J]. Chinese Optics, 2021, 14(4): 955-967. (in Chinese). doi: 10.37188/CO.2021-0074
|
| [10] |
RANGANI JAHROMI H, LO FRANCO R. Searching for exceptional points and inspecting non-contractivity of trace distance in (anti)-PT symmetric systems[J]. Quantum Information Processing, 2022, 21(4): 155. doi: 10.1007/s11128-022-03475-z
|
| [11] |
PIRES D P, MACRÌ T. Probing phase transitions in non-Hermitian systems with multiple quantum coherences[J]. Physical Review B, 2021, 104(15): 155141. doi: 10.1103/PhysRevB.104.155141
|
| [12] |
GUO Y N, WANG G Y. Witnessing criticality in non-Hermitian systems via entopic uncertainty relation[J]. New Journal of Physics, 2022, 24: 093035. doi: 10.1088/1367-2630/ac91ea
|
| [13] |
BENDER C M, BOETTCHER S, MEISINGER P N. PT-symmetric quantum mechanics[J]. Journal of Mathematical Physics, 1999, 40(5): 2201-2229. doi: 10.1063/1.532860
|
| [14] |
LU X M, WANG X G, SUN C P. Quantum Fisher information flow and non-Markovian processes of open systems[J]. Physical Review A, 2010, 82(4): 042103. doi: 10.1103/PhysRevA.82.042103
|
| [15] |
ZHONG W, SUN ZH, MA J, et al. Fisher information under decoherence in Bloch representation[J]. Physical Review A, 2013, 87(2): 022337. doi: 10.1103/PhysRevA.87.022337
|
| [16] |
YU X L, ZHANG CH J. Quantum parameter estimation of non-Hermitian systems with optimal measurements[J]. Physical Review A, 2023, 108(2): 022215. doi: 10.1103/PhysRevA.108.022215
|
| [17] |
ZLOSHCHASTIEV K G. Non-Hermitian Hamiltonians and stability of pure states[J]. The European Physical Journal D, 2015, 69(11): 253. doi: 10.1140/epjd/e2015-60384-0
|
| [18] |
MINGANTI F, MIRANOWICZ A, CHHAJLANY R W, et al. Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: the effects of quantum jumps[J]. Physical Review A, 2019, 100(6): 062131. doi: 10.1103/PhysRevA.100.062131
|
| [19] |
WANG W CH, ZHOU Y L, ZHANG H L, et al. Observation of PT-symmetric quantum coherence in a single-ion system[J]. Physical Review A, 2021, 103(2): L020201.
|
| [20] |
MIRI M A, ALÙ A. Exceptional points in optics and photonics[J]. Science, 2019, 363(6422): eaar7709.
|
| [21] |
SERGI A, GIAQUINTA P V. Linear quantum entropy and non-Hermitian Hamiltonians[J]. Entropy, 2016, 18(12): 451. doi: 10.3390/e18120451
|
| [22] |
SERGI A, ZLOSHCHASTIEV K G. Quantum entropy of systems described by non-Hermitian Hamiltonians[J]. Journal of Statistical Mechanics: Theory and Experiment, 2016, 2016: 033102. doi: 10.1088/1742-5468/2016/03/033102
|
| [23] |
BAUMGRATZ T, CRAMER M, PLENIO M B. Quantifying coherence[J]. Physical Review Letters, 2014, 113(14): 140401. doi: 10.1103/PhysRevLett.113.140401
|
| [24] |
STRELTSOV A, ADESSO G, PLENIO M B. Colloquium: quantum coherence as a resource[J]. Reviews of Modern Physics, 2017, 89(4): 041003. doi: 10.1103/RevModPhys.89.041003
|
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