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Robust open-loop stabilization of Fock states by time-varying quantum interactions

Alain Sarlette UGent and Pierre Rouchon (2012) Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, Proceedings. p.30-35
abstract
A quantum harmonic oscillator (spring subsystem) is stabilized towards a target Fock state by reservoir engineering. This passive and open-loop stabilization works by consecutive and identical Hamiltonian interactions with auxiliary systems, here three-level atoms (the auxiliary ladder subsystem), followed by a partial trace over these auxiliary atoms. A scalar control input governs the interaction, defining which atomic transition in the ladder subsystem is in resonance with the spring subsystem. We use it to build a time-varying interaction with individual atoms, that combines three non-commuting steps. We show that the resulting reservoir robustly stabilizes any initial spring state distributed between 0 and 4n+3 quanta of vibrations towards a pure target Fock state of vibration number n. The convergence proof relies on the construction of a strict Lyapunov function for the Kraus map induced by this reservoir setting on the spring subsystem. Simulations with realistic parameters corresponding to the quantum electrodynamics setup at Ecole Normale Supérieure further illustrate the robustness of the method.
Please use this url to cite or link to this publication:
author
organization
year
type
conference
publication status
published
subject
keyword
discrete-time, stabilization methods, open-loop control systems, photons, quantum physics, Hilbert spaces., Lyapunov function
in
Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, Proceedings
pages
30 - 35
publisher
International Federation of Automatic Control (IFAC)
conference name
Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control (LHMNLC - 2012)
conference location
Bertinoro, Italy
conference start
2012-08-29
conference end
2012-08-31
ISBN
9781622763689
language
English
UGent publication?
yes
classification
C1
copyright statement
I have transferred the copyright for this publication to the publisher
id
2912997
handle
http://hdl.handle.net/1854/LU-2912997
date created
2012-06-20 09:49:34
date last changed
2015-01-13 15:21:28
@inproceedings{2912997,
  abstract     = {A quantum harmonic oscillator (spring subsystem) is stabilized towards a target Fock state by reservoir engineering. This passive and open-loop stabilization works by consecutive and identical Hamiltonian interactions with auxiliary systems, here three-level atoms (the auxiliary ladder subsystem), followed by a partial trace over these auxiliary atoms. A scalar control input governs the interaction, defining which atomic transition in the ladder subsystem is in resonance with the spring subsystem. We use it to build a time-varying interaction with individual atoms, that combines three non-commuting steps. We show that the resulting reservoir robustly stabilizes any initial spring state distributed between 0 and 4n+3 quanta of vibrations towards a pure target Fock state of vibration number n. The convergence proof relies on the construction of a strict Lyapunov function for the Kraus map induced by this reservoir setting on the spring subsystem. Simulations with realistic parameters corresponding to the quantum electrodynamics setup at Ecole Normale Sup{\'e}rieure further illustrate the robustness of the method.},
  author       = {Sarlette, Alain and Rouchon, Pierre},
  booktitle    = {Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, Proceedings},
  isbn         = {9781622763689},
  keyword      = {discrete-time,stabilization methods,open-loop control systems,photons,quantum physics,Hilbert spaces.,Lyapunov function},
  language     = {eng},
  location     = {Bertinoro, Italy},
  pages        = {30--35},
  publisher    = {International Federation of Automatic Control (IFAC)},
  title        = {Robust open-loop stabilization of Fock states by time-varying quantum interactions},
  year         = {2012},
}

Chicago
Sarlette, Alain, and Pierre Rouchon. 2012. “Robust Open-loop Stabilization of Fock States by Time-varying Quantum Interactions.” In Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, Proceedings, 30–35. International Federation of Automatic Control (IFAC).
APA
Sarlette, A., & Rouchon, P. (2012). Robust open-loop stabilization of Fock states by time-varying quantum interactions. Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, Proceedings (pp. 30–35). Presented at the Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control (LHMNLC - 2012), International Federation of Automatic Control (IFAC).
Vancouver
1.
Sarlette A, Rouchon P. Robust open-loop stabilization of Fock states by time-varying quantum interactions. Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, Proceedings. International Federation of Automatic Control (IFAC); 2012. p. 30–5.
MLA
Sarlette, Alain, and Pierre Rouchon. “Robust Open-loop Stabilization of Fock States by Time-varying Quantum Interactions.” Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, Proceedings. International Federation of Automatic Control (IFAC), 2012. 30–35. Print.