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.

{{Cite journal|last=Chen|first=X. |display-authors=etal |year=2010|title=Fast optimal frictionless atom cooling in harmonic traps: Shortcut to adiabaticity|journal=Physical Review Letters|volume=104|issue=6|pages=063002|doi=10.1103/PhysRevLett.104.063002|pmid=20366818|arxiv=0910.0709|bibcode=2010PhRvL.104f3002C |s2cid=1372315 }}

Their design can be achieved using a variety of techniques.{{Cite journal|last1=Guéry-Odelin|first1=D.|last2=Ruschhaupt|first2=A.|last3=Kiely|first3=A.|last4=Torrontegui|first4=E.|last5=Martínez-Garaot|first5=S.|last6=Muga|first6=J.G.|year=2019|title=Shortcuts to adiabaticity: Concepts, methods, and applications|url=https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.91.045001|journal=Reviews of Modern Physics|volume=91|issue=4|pages=045001|doi=10.1103/RevModPhys.91.045001|arxiv=1904.08448|bibcode=2019RvMP...91d5001G|hdl=10261/204556|s2cid=120374889|hdl-access=free}}

{{Cite book|last=Torrontegui|first=E. |title=Advances in Atomic, Molecular, and Optical Physics |display-authors=etal |year=2013|chapter=Shortcuts to adiabaticity|volume=62|pages=117–169|doi=10.1016/B978-0-12-408090-4.00002-5|series=Advances in Atomic, Molecular, and Optical Physics|isbn=9780124080904|citeseerx=10.1.1.752.9829|s2cid=118553513 }}

A universal approach is provided by counterdiabatic driving,

{{Cite journal|last1=Demirplak|first1=M.|last2=Rice|first2=S. A.|year=2003|title=Adiabatic Population Transfer with Control Fields|journal=The Journal of Physical Chemistry A|volume=107|issue=46|pages=9937–9945|doi=10.1021/jp030708a|bibcode=2003JPCA..107.9937D}}

also known as transitionless quantum driving.

{{Cite journal|last=Berry|first=M. V.|year=2009|title=Transitionless quantum driving|url=http://stacks.iop.org/1751-8121/42/i=36/a=365303|journal=Journal of Physics A: Mathematical and Theoretical|volume=42|issue=36|pages=365303|doi=10.1088/1751-8113/42/36/365303|bibcode=2009JPhA...42J5303B|s2cid=121345668 |url-access=subscription}}

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.

{{Cite journal|last1= Emmanouilidou|first1=A.

|bibcode=2000PhRvL..85.1626E

}}

Counterdiabatic driving has been demonstrated in the laboratory using a time-dependent quantum oscillator.

{{Cite journal|last1=An|first1=Shuoming|last2=Lv|first2=Dingshun|last3=del Campo|first3=Adolfo|last4=Kim|first4=Kihwan|year=2016|title=Shortcuts to adiabaticity by counterdiabatic driving for trapped-ion displacement in phase space|journal=Nature Communications|volume=7|pages=12999|doi=10.1038/ncomms12999|pmid=27669897|pmc=5052658|arxiv=1601.05551|bibcode=2016NatCo...712999A}}

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.

{{Cite journal |last = del Campo |first=A.

|title=Shortcuts to adiabaticity by counter-diabatic driving

|journal=Physical Review Letters

|volume=111

|issue=10

|pages=100502

|year=2013

|doi = 10.1103/PhysRevLett.111.100502|pmid=25166641

|arxiv=1306.0410

|bibcode=2013PhRvL.111j0502D

|s2cid=119271970

}}

{{Cite journal |last = Deffner |first=S.

|display-authors=etal

|title= Classical and quantum shortcuts to adiabaticity for scale-invariant driving

|journal=Physical Review X

|volume=4

|issue=2

|pages=021013

|year=2014

|doi = 10.1103/PhysRevX.4.021013|arxiv=1401.1184|bibcode=2014PhRvX...4b1013D

|s2cid=6758148

}}

{{Cite journal |last = Deng |first=S.

|display-authors=etal

|title=Shortcuts to adiabaticity in the strongly-coupled regime: nonadiabatic control of a unitary Fermi gas

|journal=Physical Review A

|volume=97

|pages=013628

|year=2018

|issue=1

|doi = 10.1103/PhysRevA.97.013628|arxiv=1610.09777

|bibcode=2018PhRvA..97a3628D

|s2cid=119264108

}}

STA have also found applications in finite-time quantum thermodynamics to suppress quantum friction.

{{Cite journal |last = del Campo |first=A.

|display-authors=etal

|title=More bang for your buck: Towards super-adiabatic quantum engines

|journal=Scientific Reports

|volume=4

|pages=6208

|year=2014

|doi = 10.1038/srep06208|pmid=25163421

|pmc=4147366

|bibcode=2014NatSR...4E6208C

}}

Fast nonadiabatic strokes of a quantum engine have been implemented using a three-dimensional interacting Fermi gas.

{{Cite journal|last=Deng|first=S. |display-authors=etal |year=2018|title=Superadiabatic quantum friction suppression in finite-time thermodynamics|journal=Science Advances|volume=4|issue=4|pages=eaar5909|doi=10.1126/sciadv.aar5909|pmid=29719865|pmc=5922798 |arxiv=1711.00650 |bibcode=2018SciA....4.5909D }}

{{Cite journal|last=Diao|first=P. |display-authors=etal |year=2018|title=Shortcuts to adiabaticity in Fermi gases|journal=New Journal of Physics|volume=20|issue=10|pages=105004|doi=10.1088/1367-2630/aae45e|arxiv=1807.01724 |bibcode=2018NJPh...20j5004D |doi-access=free}}

The use of STA has also been suggested to drive a quantum phase transition.

{{Cite journal |last1 = del Campo |first1=A.

|last2=Rams |first2= M. M.

|last3=Zurek |first3= W. H.

|title=Assisted finite-rate adiabatic passage across a quantum critical point: Exact solution for the quantum Ising model

|journal=Physical Review Letters

|volume=109

|issue=11

|pages=115703

|year=2012

|doi = 10.1103/PhysRevLett.109.115703|pmid=23005647

|arxiv=1206.2670

|bibcode=2012PhRvL.109k5703D

|doi-access=free

}}

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.

{{Cite journal|last=Takahashi|first=K.|year=2013|title=Transitionless quantum driving for spin systems|journal=Physical Review E|volume=87|issue=6|pages=062117|arxiv=1209.3153|doi=10.1103/PhysRevE.87.062117|pmid=23848637|bibcode=2013PhRvE..87f2117T|s2cid=28545144}}

{{Cite journal|last=Saberi|first=H. |display-authors=etal |year=2014|title=Adiabatic tracking of quantum many-body dynamics|journal=Physical Review A|volume=90|issue=6|pages=060301(R)|doi=10.1103/PhysRevA.90.060301|arxiv=1408.0524 |bibcode=2014PhRvA..90f0301S |doi-access=free}}

{{Cite journal|last=Campbell|first=S. |display-authors=etal |year=2015|title=Shortcut to Adiabaticity in the Lipkin-Meshkov-Glick Model|journal=Physical Review Letters|volume=114|issue=17|pages=177206|doi=10.1103/PhysRevLett.114.177206|pmid=25978261|arxiv=1410.1555 |bibcode=2015PhRvL.114q7206C |hdl=10447/126172|s2cid=22450078 |url=https://pure.qub.ac.uk/portal/en/publications/shortcut-to-adiabaticity-in-the-lipkinmeshkovglick-model(dc95203b-5cf5-491d-80fb-1b397baeb9d4).html |hdl-access=free}}

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.

{{Cite journal|last=Iram|first=S.|year=2021|title=Controlling the speed and trajectory of evolution with counterdiabatic driving|journal=Nature Physics|volume=17|issue=1 |pages=135–142|doi=10.1038/s41567-020-0989-3|arxiv=1912.03764 |bibcode=2021NatPh..17..135I }}

References

Category:Quantum mechanics