2010
DOI: 10.1088/0953-4075/43/8/085509
|View full text |Cite
|
Sign up to set email alerts
|

Transitionless quantum drivings for the harmonic oscillator

Abstract: Abstract. Two methods to change a quantum harmonic oscillator frequency without transitions in a finite time are described and compared. The first method, a transitionless-tracking algorithm, makes use of a generalized harmonic oscillator and a non-local potential. The second method, based on engineering an invariant of motion, only modifies the harmonic frequency in time, keeping the potential local at all times.

Help me understand this report
View preprint versions

Search citation statements

Order By: Relevance

Paper Sections

Select...
1
1
1
1

Citation Types

4
168
0

Year Published

2012
2012
2018
2018

Publication Types

Select...
8
1

Relationship

0
9

Authors

Journals

citations
Cited by 128 publications
(172 citation statements)
references
References 26 publications
4
168
0
Order By: Relevance
“…The calculations forĤ C can be found from Ref. [15]. For a self-containing comparison with our classical theory, we first perform a similar calculation here.…”
Section: Discussionmentioning
confidence: 99%
See 1 more Smart Citation
“…The calculations forĤ C can be found from Ref. [15]. For a self-containing comparison with our classical theory, we first perform a similar calculation here.…”
Section: Discussionmentioning
confidence: 99%
“…This is important because (i) classical STA may help to design quantum STA (e.g., by quantizing the classical control field) and (ii) STA may be more general and robust than previously thought. Indeed, applying our formalism to a parametric oscillator, the control Hamiltonian is precisely the classical limit of an early quantum result [15].…”
Section: Introductionmentioning
confidence: 99%
“…(8,9). Specifically, the term ω 2 0 /(2b 2 ) is "kinetic" in the quantum scenario, and "potential" in the classical analogy.…”
Section: A Lower Bound For Time-averaged Non-adiabatic Energymentioning
confidence: 99%
“…We propose to repeat the experiment [28] with the same trajectory but a different potential depth and a different frequency. If they change according to (9,10), then fast frictionless expansion can be realized. So far, we have studied 1-D optical lattice with variable spacing.…”
Section: Accordion Latticementioning
confidence: 99%