Lewis-Riesenfeld invariants and transitionless quantum driving

By Xi Chen, E. Torrontegui, Juan Gonzalo Muga. 2011

294 citations recorded by the source corpus.

Different methods have been recently put forward and implemented experimentally to inverse engineer the time-dependent Hamiltonian of a quantum system and accelerate slow adiabatic processes via nonadiabatic shortcuts. In the ''transitionless quantum driving'' proposed by Berry, shortcut Hamiltonians are designed so that the system follows exactly, in an arbitrarily short time, the approximate adiabatic path defined by a reference Hamiltonian. A different approach is based on first designing a Lewis-Riesenfeld invariant to carry the eigenstates of a Hamiltonian from specified initial to final configurations, again in an arbitrary time, and then constructing from the invariant the transient Hamiltonian that connects these boundary configurations. We show that the two approaches, apparently quite different in form and so far in results, are, in fact, strongly related and potentially equivalent, so that the inverse-engineering operations in one of them can be reinterpreted and understood in terms of the concepts and operations of the other one. We study, as explicit examples, expansions of time-dependent harmonic traps and the state preparation of two-level systems.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/5e04f3693c6f401badbbb8c47a67d35ceb420a3d

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Classical and Quantum Shortcuts to Adiabaticity for Scale-Invariant Driving (2014, methodology): “(9) and previous results derived for power-law traps [14, 28, 33].”
Accelerated quantum control using superadiabatic dynamics in a solid-state lambda system (2016, unknown): “ses are given by ΩÌ ÌºÍ:P; = Ωcos kà:P; o F8Ωqgl k:ç; o 7:ç; .>86:ç;. ΩÉ ÌºÍ:P; = Ωsin kà:P; o E amq k :ç; o7:ç; .>86:ç; (7) where we define P on the same interval >0,.?. See Supplementary Information for numerical results for MOD-SATD pulses. In order for Ω,É ÌºÍ:P; to not exceed the orig”
The Quantum Harmonic Otto Cycle (2016, result): “The invariant must satisfy [Ĥ, Î] = 0 for the initial τi and final τf times, then at these times the eigenstates of the invariant at the initial and final time of the adiabat are identical to those of the Hamiltonian [83, 84].”
Shortcuts to adiabaticity: Concepts, methods, and applications (2019, methodology): “There are as well many works studying and improving robustness in transport problems with respect to anharmonicities (Chen et al., 2011b; Torrontegui et al., 2011; Zhang et al., 2015b, 2016), and noise (Lu et al., 2014d, 2018), see Sec.”
Shortcuts to Adiabaticity (2012, methodology): “Chen et al. (2011b) have shown how to realise this bound by allowing the discontinuous acceleration of the trap at t = 0 and t = tf and also finite jumps in the trap position.”