Quantum scar

In physics, and especially quantum chaos, a quantum scar is a kind of quantum state with a high likelihood of existing in unstable classical periodic orbits in classically chaotic systems. The term also refers to the wave function of such a state, which is more formally defined by having an enhancement (i.e. increased norm squared) of an eigenfunction along unstable classical periodic orbits. Since the square-norm of quantum wavefunctions yield probability densities in the Copenhagen interpretation, the two notions correspond.

Quantum scars were discovered and explained in 1984 by Eric J. Heller[1] and are part of the large field of quantum chaos. Scars are unexpected in the sense that stationary classical distributions at the same energy are completely uniform in space with no special concentrations along periodic orbits, and quantum chaos theory of energy spectra gave no hint of their existence. Scars stand out to the eye in some eigenstates of classically chaotic systems, but are quantified by projection of the eigenstates onto certain test states, often Gaussians, having both average position and average momentum along the periodic orbit. These test states give a provably structured spectrum that reveals the necessity of scars, especially for the shorter and least unstable periodic orbits.[2][3]

Scars have been found and are important in membranes,[4] wave mechanics, optics,[5] microwave systems, water waves, and electronic motion in microstructures.

Scars have occurred in investigations for potential applications of Rydberg states to quantum computing, specifically acting as qubits for quantum simulation.[6][7] The particles of the system in an alternating ground state-Rydberg state configuration continually entangled and disentangled rather than remaining entangled and undergoing thermalization.[6][7][8] Systems of the same atoms prepared with other initial states did thermalize as expected.[7][8] The researchers dubbed the phenomenon "quantum many-body scarring".[9][10]

The area of quantum many-body scars is a subject of active research.[11][12]

Explanation

The causes of quantum scarring are not well understood.[6]

One possible proposed explanation is that quantum scars represent integrable systems, or nearly do so, and this could prevent thermalization from ever occurring.[13] This has drawn criticisms arguing that a non-integrable Hamiltonian underlies the theory.[14]

Recently, a series of works[15][16] has related the existence of quantum scarring to an algebraic structure known as dynamical symmetries.[17][18]

Potential applications to quantum computing
Further information: Quantum computing and Quantum error correction

Fault-tolerant quantum computers are desired, as any perturbations to qubit states can cause the states to thermalize, leading to loss of quantum information.[6] Scarring of qubit states is seen as a potential way to protect qubit states from outside disturbances leading to decoherence and information loss.

See also

References
  1. Heller, Eric J. (15 October 1984). "Bound-State Eigenfunctions of Classically Chaotic Hamiltonian Systems: Scars of Periodic Orbits". Physical Review Letters. 53 (16): 1515–1518. Bibcode:1984PhRvL..53.1515H. doi:10.1103/PhysRevLett.53.1515.
  2. Antonsen, T. M.; Ott, E.; Chen, Q.; Oerter, R. N. (1 January 1995). "Statistics of wave-function scars". Physical Review E. 51 (1): 111–121. Bibcode:1995PhRvE..51..111A. doi:10.1103/PhysRevE.51.111. PMID 9962623.
  3. Kaplan, L.; Heller, E.J. (April 1998). "Linear and Nonlinear Theory of Eigenfunction Scars". Annals of Physics. 264 (2): 171–206. arXiv:chao-dyn/9809011. Bibcode:1998AnPhy.264..171K. doi:10.1006/aphy.1997.5773.
  4. Arcos, E.; Báez, G.; Cuatláyol, P. A.; Prian, M. L. H.; Méndez-Sánchez, R. A.; Hernández-Saldaña, H. (1998-06-09). "Vibrating soap films: An analog for quantum chaos on billiards". American Journal of Physics. 66 (7): 601–607. arXiv:chao-dyn/9903002. Bibcode:1998AmJPh..66..601A. doi:10.1119/1.18913. ISSN 0002-9505.
  5. Bies, W. E.; Kaplan, L.; Heller, E. J. (2001-06-13). "Scarring effects on tunneling in chaotic double-well potentials". Physical Review E. 64 (1): 016204. arXiv:nlin/0007037. Bibcode:2001PhRvE..64a6204B. doi:10.1103/PhysRevE.64.016204. PMID 11461364. S2CID 18108592.
  6. "Quantum Scarring Appears to Defy Universe's Push for Disorder". Quanta Magazine. March 20, 2019. Retrieved March 24, 2019.
  7. Lukin, Mikhail D.; Vuletić, Vladan; Greiner, Markus; Endres, Manuel; Zibrov, Alexander S.; Soonwon Choi; Pichler, Hannes; Omran, Ahmed; Levine, Harry (November 30, 2017). "Probing many-body dynamics on a 51-atom quantum simulator". Nature. 551 (7682): 579–584. arXiv:1707.04344. Bibcode:2017Natur.551..579B. doi:10.1038/nature24622. ISSN 1476-4687. PMID 29189778. S2CID 205261845.
  8. Turner, C. J.; Michailidis, A. A.; Abanin, D. A.; Serbyn, M.; Papić, Z. (October 22, 2018). "Quantum scarred eigenstates in a Rydberg atom chain: Entanglement, breakdown of thermalization, and stability to perturbations". Physical Review B. 98 (15): 155134. arXiv:1806.10933. Bibcode:2018PhRvB..98o5134T. doi:10.1103/PhysRevB.98.155134. S2CID 51746325.
  9. Papić, Z.; Serbyn, M.; Abanin, D. A.; Michailidis, A. A.; Turner, C. J. (May 14, 2018). "Weak ergodicity breaking from quantum many-body scars" (PDF). Nature Physics. 14 (7): 745–749. Bibcode:2018NatPh..14..745T. doi:10.1038/s41567-018-0137-5. ISSN 1745-2481. S2CID 51681793.
  10. Ho, Wen Wei; Choi, Soonwon; Pichler, Hannes; Lukin, Mikhail D. (January 29, 2019). "Periodic Orbits, Entanglement, and Quantum Many-Body Scars in Constrained Models: Matrix Product State Approach". Physical Review Letters. 122 (4): 040603. arXiv:1807.01815. Bibcode:2019PhRvL.122d0603H. doi:10.1103/PhysRevLett.122.040603. PMID 30768339. S2CID 73441462.
  11. Lin, Cheng-Ju; Motrunich, Olexei I. (2019). "Exact Quantum Many-body Scar States in the Rydberg-blockaded Atom Chain". Physical Review Letters. 122 (17): 173401. arXiv:1810.00888. doi:10.1103/PhysRevLett.122.173401. PMID 31107057. S2CID 85459805.
  12. Moudgalya, Sanjay; Regnault, Nicolas; Bernevig, B. Andrei (2018-12-27). "Entanglement of Exact Excited States of AKLT Models: Exact Results, Many-Body Scars and the Violation of Strong ETH". Physical Review B. 98 (23): 235156. arXiv:1806.09624. doi:10.1103/PhysRevB.98.235156. ISSN 2469-9950.
  13. Khemani, Vedika; Laumann, Chris R.; Chandran, Anushya (2019). "Signatures of integrability in the dynamics of Rydberg-blockaded chains". Physical Review B. 99 (16): 161101. arXiv:1807.02108. Bibcode:2018arXiv180702108K. doi:10.1103/PhysRevB.99.161101. S2CID 119404679.
  14. Choi, Soonwon; Turner, Christopher J.; Pichler, Hannes; Ho, Wen Wei; Michailidis, Alexios A.; Papić, Zlatko; Serbyn, Maksym; Lukin, Mikhail D.; Abanin, Dmitry A. (2019). "Emergent SU(2) dynamics and perfect quantum many-body scars". Physical Review Letters. 122 (22): 220603. arXiv:1812.05561. doi:10.1103/PhysRevLett.122.220603. PMID 31283292. S2CID 119494477.
  15. Moudgalya, Sanjay; Regnault, Nicolas; Bernevig, B. Andrei (2020-08-20). "$\ensuremath{\eta}$-pairing in Hubbard models: From spectrum generating algebras to quantum many-body scars". Physical Review B. 102 (8): 085140. arXiv:2004.13727. doi:10.1103/PhysRevB.102.085140. S2CID 216641904.
  16. Bull, Kieran; Desaules, Jean-Yves; Papić, Zlatko (2020-04-27). "Quantum scars as embeddings of weakly broken Lie algebra representations". Physical Review B. 101 (16): 165139. doi:10.1103/PhysRevB.101.165139. S2CID 210861174.
  17. Buča, Berislav; Tindall, Joseph; Jaksch, Dieter (2019-04-15). "Non-stationary coherent quantum many-body dynamics through dissipation". Nature Communications. 10 (1): 1730. doi:10.1038/s41467-019-09757-y. ISSN 2041-1723. PMC 6465298. PMID 30988312.
  18. Medenjak, Marko; Buča, Berislav; Jaksch, Dieter (2020-07-20). "Isolated Heisenberg magnet as a quantum time crystal". Physical Review B. 102 (4): 041117. arXiv:1905.08266. doi:10.1103/PhysRevB.102.041117. S2CID 160009779.
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