Shortcuts to adiabaticity

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]

References
  1. Chen, X.; et al. (2010). "Fast optimal frictionless atom cooling in harmonic traps: Shortcut to adiabaticity". Phys. Rev. Lett. 104 (6): 063002. arXiv:0910.0709. doi:10.1103/PhysRevLett.104.063002. PMID 20366818.
  2. Guéry-Odelin, D.; Ruschhaupt, A.; Kiely, A.; Torrontegui, E.; Martínez-Garaot, S.; Muga, J.G. (2019). "Shortcuts to adiabaticity: Concepts, methods, and applications". Rev. Mod. Phys. 91: 045001. doi:10.1103/RevModPhys.91.045001. hdl:10261/204556.
  3. Torrontegui, E.; et al. (2013). Shortcuts to adiabaticity. Adv. At. Mol. Opt. Phys. Advances in Atomic, Molecular, and Optical Physics. 62. pp. 117–169. CiteSeerX 10.1.1.752.9829. doi:10.1016/B978-0-12-408090-4.00002-5. ISBN 9780124080904.
  4. Demirplak, M.; Rice, S. A. (2003). "Adiabatic Population Transfer with Control Fields". J. Phys. Chem. A. 107 (46): 9937–9945. doi:10.1021/jp030708a.
  5. Berry, M. V. (2009). "Transitionless quantum driving". Journal of Physics A: Mathematical and Theoretical. 42 (36): 365303. doi:10.1088/1751-8113/42/36/365303.
  6. Emmanouilidou, A.; Zhao, X.-G.; Ao, A.; Niu, Q. (2000). "Steering an Eigenstate to Destination". Phys. Rev. Lett. 85 (8): 1626–1629. doi:10.1103/PhysRevLett.85.1626.
  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. doi:10.1038/ncomms12999. PMC 5052658. PMID 27669897.
  8. del Campo, A. (2013). "Shortcuts to adiabaticity by counter-diabatic driving". Phys. Rev. Lett. 111 (10): 100502. arXiv:1306.0410. doi:10.1103/PhysRevLett.111.100502. PMID 25166641.
  9. Deffner, S.; et al. (2014). "Classical and quantum shortcuts to adiabaticity for scale-invariant driving". Phys. Rev. X. 4 (2): 021013. arXiv:1401.1184. doi:10.1103/PhysRevX.4.021013.
  10. Deng, S.; et al. (2018). "Shortcuts to adiabaticity in the strongly-coupled regime: nonadiabatic control of a unitary Fermi gas". Phys. Rev. A. 97: 013628. arXiv:1610.09777. doi:10.1103/PhysRevA.97.013628.
  11. del Campo, A.; et al. (2014). "More bang for your buck: Towards super-adiabatic quantum engines". Sci. Rep. 4: 6208. 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. doi:10.1126/sciadv.aar5909. PMC 5922798. PMID 29719865.
  13. Diao, P.; et al. (2018). "Shortcuts to adiabaticity in Fermi gases". New J. Phys. 20 (10): 105004. 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". Phys. Rev. Lett. 109 (11): 115703. doi:10.1103/PhysRevLett.109.115703. PMID 23005647.
  15. Takahashi, K. (2013). "Transitionless quantum driving for spin systems". Phys. Rev. E. 87 (6): 062117. arXiv:1209.3153. doi:10.1103/PhysRevE.87.062117. PMID 23848637.
  16. Saberi, H.; et al. (2014). "Adiabatic tracking of quantum many-body dynamics". Phys. Rev. A. 90 (6): 060301(R). doi:10.1103/PhysRevA.90.060301.
  17. Campbell, S.; et al. (2015). "Shortcut to Adiabaticity in the Lipkin-Meshkov-Glick Model". Phys. Rev. Lett. 114 (17): 177206. doi:10.1103/PhysRevLett.114.177206. hdl:10447/126172. PMID 25978261.


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