Ensemble qubit controllability with a single control via adiabatic and rotating wave approximations

• URL: http://arxiv.org/abs/2003.05831v2
• Date: Mon, 10 May 2021 12:08:35 GMT
• Title: Ensemble qubit controllability with a single control via adiabatic and rotating wave approximations
• Authors: R\'emi Robin, Nicolas Augier, Ugo Boscain, Mario Sigalotti
• Abstract summary: We show how it is possible to control an ensemble of spin systems by a single real-valued inversion control. As a byproduct of this result, we prove that it is possible to control an ensemble of spin systems by a single real-valued control.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In the physics literature it is common to see the rotating wave approximation andthe adiabatic approximation used "in cascade" to justify the use of chirped pulses for two-level quantum systems driven by one external field, in particular when the resonance frequency of the system is not known precisely. Both approximations need relatively long time and are essentially based on averaging theory of dynamical systems. Unfortunately, the two approximations cannot be done independently since, in a sense, the two time scales interact. The purpose of this paper is to study how the cascade of the two approximations can be justified and how large becomes the final time as the fidelity goes to one, while preserving the robustness of the adiabatic strategy. Our first result, based on high-order averaging techniques, gives a precise quantification of the uncertainty interval of the resonance frequency for which the population inversion works. As a byproduct of this result, we prove that it is possible to control an ensemble of spin systems by a single real-valued control, providing a non-trivial extension of a celebrated result of ensemble controllability with two controls by Khaneja and Li.

Related papers

• On the validity of the rotating wave approximation for coupled harmonic oscillators [34.82692226532414]
  We solve the dynamics analytically by employing tools from symplectic geometry. We find that the squeezing present in the full Hamiltonian and in the initial state governs the deviation from the approximated evolution. We also show that the rotating wave approximation is recovered for resonant frequencies and vanishing coupling to frequency ratio.
  arXiv  Detail & Related papers  (2024-03-22T16:51:53Z)
• Stochastic action for the entanglement of a noisy monitored two-qubit system [55.2480439325792]
  We study the effect of local unitary noise on the entanglement evolution of a two-qubit system subject to local monitoring and inter-qubit coupling. We construct a Hamiltonian by incorporating the noise into the Chantasri-Dressel-Jordan path integral and use it to identify the optimal entanglement dynamics. Numerical investigation of long-time steady-state entanglement reveals a non-monotonic relationship between concurrence and noise strength.
  arXiv  Detail & Related papers  (2024-03-13T11:14:10Z)
• Optimal State Manipulation for a Two-Qubit System Driven by Coherent and Incoherent Controls [77.34726150561087]
  State preparation is important for optimal control of two-qubit quantum systems. We exploit two physically different coherent control and optimize the Hilbert-Schmidt target density matrices.
  arXiv  Detail & Related papers  (2023-04-03T10:22:35Z)
• Pulse-controlled qubit in semiconductor double quantum dots [57.916342809977785]
  We present a numerically-optimized multipulse framework for the quantum control of a single-electron charge qubit. A novel control scheme manipulates the qubit adiabatically, while also retaining high speed and ability to perform a general single-qubit rotation.
  arXiv  Detail & Related papers  (2023-03-08T19:00:02Z)
• Autonomous coherence protection of a two-level system in a fluctuating environment [68.8204255655161]
  We re-examine a scheme originally intended to remove the effects of static Doppler broadening from an ensemble of non-interacting two-level systems (qubits) We demonstrate that this scheme is far more powerful and can also protect a single (or even an ensemble) qubit's energy levels from noise which depends on both time and space.
  arXiv  Detail & Related papers  (2023-02-08T01:44:30Z)
• On optimization of coherent and incoherent controls for two-level quantum systems [77.34726150561087]
  This article considers some control problems for closed and open two-level quantum systems. The closed system's dynamics is governed by the Schr"odinger equation with coherent control. The open system's dynamics is governed by the Gorini-Kossakowski-Sudarshan-Lindblad master equation.
  arXiv  Detail & Related papers  (2022-05-05T09:08:03Z)
• Quantum approach to the thermalization of the toppling pencil interacting with a finite bath [0.0]
  We investigate the longstanding problem of thermalization of quantum systems coupled to an environment. The long-time average of the double-well energy is found to be a monotonously decaying function.
  arXiv  Detail & Related papers  (2021-11-19T12:30:34Z)
• Quantum coherence, correlations and nonclassical states in the two-qubit Rabi model with parametric oscillator [0.0]
  Quantum coherence and quantum correlations are studied in a strongly interacting system composed of two qubits and a parametric medium. We employ the adiabatic approximation approach to analytically solve the system. The reconstructed states are observed to be nearly pure generalized Bell states.
  arXiv  Detail & Related papers  (2021-06-12T11:16:40Z)
• Sideband transitions in a two-mode Josephson circuit driven beyond the rotating wave approximation [0.0]
  We experimentally, numerically, and analytically explore strongly driven two-mode Josephson circuits in the regime of strong driving and large detuning. We find that the breakdown of the rotating wave approximation in the regime studied does not lead to qualitatively different dynamics. This is an interesting consequence compared to the carrier transition case, where the breakdown of the RWA results in qualitatively different time evolution of the quantum state.
  arXiv  Detail & Related papers  (2020-11-30T07:51:48Z)
• Assessment of weak-coupling approximations on a driven two-level system under dissipation [58.720142291102135]
  We study a driven qubit through the numerically exact and non-perturbative method known as the Liouville-von equation with dissipation. We propose a metric that may be used in experiments to map the regime of validity of the Lindblad equation in predicting the steady state of the driven qubit.
  arXiv  Detail & Related papers  (2020-11-11T22:45:57Z)
• Floquet theory for temporal correlations and spectra in time-periodic open quantum systems: Application to squeezed parametric oscillation beyond the rotating-wave approximation [0.0]
  We propose a method to compute two-time correlations and corresponding spectral densities of time-periodic open quantum systems. We show how the quantum Langevin equations for the fluctuations can be efficiently integrated by partitioning the time domain into one-period duration intervals.
  arXiv  Detail & Related papers  (2020-05-17T13:25:04Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.