Shortcuts to adiabaticity (STA) are fast control protocols to drive the dynamics of system without relying on the adiabatic theorem. The concept of STA was introduced in a 2010 paper by Xi Chen et al.[1] Their design can be achieved using a variety of techniques.[2][3] A universal approach is provided by counterdiabatic driving,[4] also known as transitionless quantum driving.[5] Motivated by one of authors systematic study of dissipative Landau-Zener transition, the key idea was demonstrated earlier by a group of scientists from China, Greece and USA in 2000, as steering an eigenstate to destination. [6] Counterdiabatic driving has been demonstrated in the laboratory using a time-dependent quantum oscillator. [7]

The use of counterdiabatic driving requires to diagonalize the system Hamiltonian, limiting its use in many-particle systems. In the control of trapped quantum fluids, the use of symmetries such as scale invariance and the associated conserved quantities has allowed to circumvent this requirement.[8][9][10] STA have also found applications in finite-time quantum thermodynamics to suppress quantum friction.[11] Fast nonadiabatic strokes of a quantum engine have been implemented using a three-dimensional interacting Fermi gas.[12][13]

The use of STA has also been suggested to drive a quantum phase transition.[14] In this context, the Kibble-Zurek mechanism predicts the formation of topological defects. While the implementation of counterdiabatic driving across a phase transition requires complex many-body interactions, feasible approximate controls can be found.[15][16][17]

Outside of physics, STA have been applied to population genetics to derive a formalism to admit finite time control of the speed and trajectory in evolving populations, with an eye towards manipulating large populations of organisms causing human disease as an evolutionary therapy method, or toward more efficient directed evolution. [18]

References

  1. ↑ Chen, X.; et al. (2010). "Fast optimal frictionless atom cooling in harmonic traps: Shortcut to adiabaticity". Physical Review Letters. 104 (6): 063002. arXiv:0910.0709. Bibcode:2010PhRvL.104f3002C. doi:10.1103/PhysRevLett.104.063002. PMID 20366818. S2CID 1372315.
  2. ↑ Guéry-Odelin, D.; Ruschhaupt, A.; Kiely, A.; Torrontegui, E.; Martínez-Garaot, S.; Muga, J.G. (2019). "Shortcuts to adiabaticity: Concepts, methods, and applications". Reviews of Modern Physics. 91 (4): 045001. arXiv:1904.08448. Bibcode:2019RvMP...91d5001G. doi:10.1103/RevModPhys.91.045001. hdl:10261/204556. S2CID 120374889.
  3. ↑ Torrontegui, E.; et al. (2013). "Shortcuts to adiabaticity". Advances in Atomic, Molecular, and Optical Physics. Advances in Atomic, Molecular, and Optical Physics. Vol. 62. pp. 117–169. CiteSeerX 10.1.1.752.9829. doi:10.1016/B978-0-12-408090-4.00002-5. ISBN 9780124080904. S2CID 118553513.
  4. ↑ Demirplak, M.; Rice, S. A. (2003). "Adiabatic Population Transfer with Control Fields". The Journal of Physical Chemistry A. 107 (46): 9937–9945. Bibcode:2003JPCA..107.9937D. doi:10.1021/jp030708a.
  5. ↑ Berry, M. V. (2009). "Transitionless quantum driving". Journal of Physics A: Mathematical and Theoretical. 42 (36): 365303. Bibcode:2009JPhA...42J5303B. doi:10.1088/1751-8113/42/36/365303. S2CID 121345668.
  6. ↑ Emmanouilidou, A.; Zhao, X.-G.; Ao, A.; Niu, Q. (2000). "Steering an Eigenstate to Destination". Physical Review Letters. 85 (8): 1626–1629. Bibcode:2000PhRvL..85.1626E. doi:10.1103/PhysRevLett.85.1626. PMID 10970574.
  7. ↑ An, Shuoming; Lv, Dingshun; del Campo, Adolfo; Kim, Kihwan (2016). "Shortcuts to adiabaticity by counterdiabatic driving for trapped-ion displacement in phase space". Nature Communications. 7: 12999. arXiv:1601.05551. Bibcode:2016NatCo...712999A. doi:10.1038/ncomms12999. PMC 5052658. PMID 27669897.
  8. ↑ del Campo, A. (2013). "Shortcuts to adiabaticity by counter-diabatic driving". Physical Review Letters. 111 (10): 100502. arXiv:1306.0410. Bibcode:2013PhRvL.111j0502D. doi:10.1103/PhysRevLett.111.100502. PMID 25166641. S2CID 119271970.
  9. ↑ Deffner, S.; et al. (2014). "Classical and quantum shortcuts to adiabaticity for scale-invariant driving". Physical Review X. 4 (2): 021013. arXiv:1401.1184. Bibcode:2014PhRvX...4b1013D. doi:10.1103/PhysRevX.4.021013. S2CID 6758148.
  10. ↑ Deng, S.; et al. (2018). "Shortcuts to adiabaticity in the strongly-coupled regime: nonadiabatic control of a unitary Fermi gas". Physical Review A. 97 (1): 013628. arXiv:1610.09777. Bibcode:2018PhRvA..97a3628D. doi:10.1103/PhysRevA.97.013628. S2CID 119264108.
  11. ↑ del Campo, A.; et al. (2014). "More bang for your buck: Towards super-adiabatic quantum engines". Scientific Reports. 4: 6208. Bibcode:2014NatSR...4E6208C. doi:10.1038/srep06208. PMC 4147366. PMID 25163421.
  12. ↑ Deng, S.; et al. (2018). "Superadiabatic quantum friction suppression in finite-time thermodynamics". Science Advances. 4 (4): eaar5909. arXiv:1711.00650. Bibcode:2018SciA....4.5909D. doi:10.1126/sciadv.aar5909. PMC 5922798. PMID 29719865.
  13. ↑ Diao, P.; et al. (2018). "Shortcuts to adiabaticity in Fermi gases". New Journal of Physics. 20 (10): 105004. arXiv:1807.01724. Bibcode:2018NJPh...20j5004D. doi:10.1088/1367-2630/aae45e.
  14. ↑ del Campo, A.; Rams, M. M.; Zurek, W. H. (2012). "Assisted finite-rate adiabatic passage across a quantum critical point: Exact solution for the quantum Ising model". Physical Review Letters. 109 (11): 115703. arXiv:1206.2670. Bibcode:2012PhRvL.109k5703D. doi:10.1103/PhysRevLett.109.115703. PMID 23005647.
  15. ↑ Takahashi, K. (2013). "Transitionless quantum driving for spin systems". Physical Review E. 87 (6): 062117. arXiv:1209.3153. Bibcode:2013PhRvE..87f2117T. doi:10.1103/PhysRevE.87.062117. PMID 23848637. S2CID 28545144.
  16. ↑ Saberi, H.; et al. (2014). "Adiabatic tracking of quantum many-body dynamics". Physical Review A. 90 (6): 060301(R). arXiv:1408.0524. Bibcode:2014PhRvA..90f0301S. doi:10.1103/PhysRevA.90.060301.
  17. ↑ Campbell, S.; et al. (2015). "Shortcut to Adiabaticity in the Lipkin-Meshkov-Glick Model". Physical Review Letters. 114 (17): 177206. arXiv:1410.1555. Bibcode:2015PhRvL.114q7206C. doi:10.1103/PhysRevLett.114.177206. hdl:10447/126172. PMID 25978261. S2CID 22450078.
  18. ↑ Iram, S. (2021). "Controlling the speed and trajectory of evolution with counterdiabatic driving". Nature Physics. 17 (1): 135–142. arXiv:1912.03764. Bibcode:2021NatPh..17..135I. doi:10.1038/s41567-020-0989-3.


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