The role of singular control in frictionless atom cooling in a harmonic trapping potential

Type of publicationArticle (peer-reviewed) Shortcuts to adiabaticity let a system reach the results of a slow adiabatic process in a shorter time. We propose to quantify the "energy cost" of the shortcut by the energy consumption of the system enlarged by including the control device. A mechanical model where the dynamics of the system and control device can be explicitly described illustrates that a broad range of possible values for the consumption is possible, including zero (above the adiabatic energy increment) when friction is negligible and the energy given away as negative power is stored and reused by perfect regenerative braking.

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“…Similarly, at t f ,ẋ jumps fromẋ(t − f ) to zero. The acceleration thus includes Dirac δ impulses [29,32],…”

Section: H C (K(t)y(t)u) = K 0 G(y(t)u) + K T · F(y(t)u)mentioning

confidence: 99%

Energy consumption for shortcuts to adiabaticity

et al. 2017

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“…Since a basic aim of the shortcuts is to shorten the process time t f , some "price" in the form of high transient energies may be expected to be paid. Several articles have studied the energies and protocol times involved: their characterization; their mutual relation, which is not necessarily of the simple form of a time-energy uncertainty principle; and also their optimization under different constraints and conditions [8,12,14]. In this paper we build on these results and continue the analysis of the energies and times in STA processes.…”

Section: Introductionmentioning

confidence: 99%

“…(The first impulse always corresponds to a negative Delta, while the second may have the two signs [12].) The protocol (18) with Dirac impulses provides a formally elegant proof that the bound can indeed be reached, at least in principle, because, as the boundary conditions are satisfied, Eq.…”

Section: B the Energy Contribution From Dirac Impulsesmentioning

confidence: 99%

“…Some relevant expressions are provided in the Appendix. As well, "bang-singular-bang" solutions result from minimizing the time-averaged energy for the same constraints [12].…”

Section: A Invariant-based Inverse Engineeringmentioning

confidence: 99%

“…However the caps did contribute to the integral, actually half of the total time-averaged energy came from them, but the significance of this fact was not discussed. In [12] an alternative to the polynomial caps was put forward, namely, Dirac-delta impulses of the control function ω 2 (t) that switch the derivativesḃ(0…”

Section: B the Energy Contribution From Dirac Impulsesmentioning

confidence: 99%

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Transient Particle Energies in Shortcuts to Adiabatic Expansions of Harmonic Traps

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The expansion of a harmonic potential that holds a quantum particle may be realized without any final particle excitation but much faster than adiabatically via "shortcuts to adiabaticity" (STA). While ideally the process time can be reduced to zero, practical limitations and constraints impose minimal finite times for the externally controlled time-dependent frequency protocols. We examine the role of different time-averaged energies (total, kinetic, potential, non-adiabatic) and of the instantaneous power in characterizing or selecting different protocols. Specifically, we prove a virial theorem for STA processes, set minimal energies for specific times or viceversa, and discuss their realizability by means of Dirac impulses or otherwise.

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Robust Manipulation and Computation for Inhomogeneous Quantum Ensembles

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The role of singular control in frictionless atom cooling in a harmonic trapping potential

Cited by 3 publications

References 22 publications

Energy consumption for shortcuts to adiabaticity

Energy consumption for shortcuts to adiabaticity

Transient Particle Energies in Shortcuts to Adiabatic Expansions of Harmonic Traps

Robust Manipulation and Computation for Inhomogeneous Quantum Ensembles

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