Controlling quantum chaos: time-dependent kicked rotor

• URL: http://arxiv.org/abs/2305.14187v2
• Date: Fri, 1 Sep 2023 20:35:17 GMT
• Title: Controlling quantum chaos: time-dependent kicked rotor
• Authors: Steven Tomsovic, Juan Diego Urbina, and Klaus Richter
• Abstract summary: In a recent letter [Phys.Rev.Lett. 130, 020201 (2023), a generalization of this targeting method to quantum systems was demonstrated. In this paper further details are given and an important quite general extension is established.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: One major objective of controlling classical chaotic dynamical systems is exploiting the system's extreme sensitivity to initial conditions in order to arrive at a predetermined target state. In a recent letter [Phys.~Rev.~Lett. 130, 020201 (2023)], a generalization of this targeting method to quantum systems was demonstrated using successive unitary transformations that counter the natural spreading of a quantum state. In this paper further details are given and an important quite general extension is established. In particular, an alternate approach to constructing the coherent control dynamics is given, which introduces a new time-dependent, locally stable control Hamiltonian that continues to use the chaotic heteroclinic orbits previously introduced, but without the need of countering quantum state spreading. Implementing that extension for the quantum kicked rotor generates a much simpler approximate control technique than discussed in the letter, which is a little less accurate, but far more easily realizable in experiments. The simpler method's error can still be made to vanish as $\hbar \rightarrow 0$.

Related papers

• Quantum ergodicity and scrambling in quantum annealers [0.0]
  We show that the unitary evolution operator describing the complete dynamics of quantum annealers is typically highly quantum chaotic. We observe that the Heisenberg dynamics of a quantum annealer leads to extensive operator spreading, a hallmark of quantum information scrambling.
  arXiv  Detail & Related papers  (2024-11-19T16:34:35Z)
• Controlling Many-Body Quantum Chaos: Bose-Hubbard systems [0.0]
  This work develops a quantum control application of many-body quantum chaos for ultracold bosonic gases trapped in optical lattices. In the technique known as targeting, instead of a hindrance to control, the instability becomes a resource. Explicit applications to custom state preparation and stabilization of quantum many-body scars are presented in one- and two-dimensional lattices.
  arXiv  Detail & Related papers  (2024-01-31T11:03:58Z)
• Universality of critical dynamics with finite entanglement [68.8204255655161]
  We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement. Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
  arXiv  Detail & Related papers  (2023-01-23T19:23:54Z)
• Controlling Quantum Chaos: Optimal Coherent Targeting [0.0]
  It is shown that a generalization to chaotic quantum systems is possible in the semiclassical regime. The procedure described here is applied to initially minimum uncertainty wave packets in the quantum kicked rotor.
  arXiv  Detail & Related papers  (2022-11-14T14:38:32Z)
• Quantum Lyapunov exponent in dissipative systems [68.8204255655161]
  The out-of-time order correlator (OTOC) has been widely studied in closed quantum systems. We study the interplay between these two processes. The OTOC decay rate is closely related to the classical Lyapunov.
  arXiv  Detail & Related papers  (2022-11-11T17:06:45Z)
• Canonically consistent quantum master equation [68.8204255655161]
  We put forth a new class of quantum master equations that correctly reproduce the state of an open quantum system beyond the infinitesimally weak system-bath coupling limit. Our method is based on incorporating the knowledge of the reduced steady state into its dynamics.
  arXiv  Detail & Related papers  (2022-05-25T15:22:52Z)
• 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)
• Robust Control Performance for Open Quantum Systems [0.0]
  A formalism is developed to measure performance based on the transmission of a dynamic perturbation or initial state preparation error. A difficulty arising from the singularity of the closed-loop Bloch equations for the quantum state is overcome by introducing the #-inversion lemma. Additional difficulties occur when symmetry gives rise to multiple open-loop poles, which under symmetry-breaking unfold into single eigenvalues.
  arXiv  Detail & Related papers  (2020-08-31T15:51:22Z)
• Sufficient conditions for adiabaticity in open quantum systems [0.0]
  We introduce sufficient conditions for the adiabatic approximation in open quantum systems. We first illustrate our results by showing that the adiabatic approximation for open systems is compatible with the description of quantum thermodynamics at thermal equilibrium. We also apply our sufficient conditions as a tool in quantum control, evaluating the adiabatic behavior for the Hamiltonians of both the Deutsch algorithm and the Landau-Zener model under decoherence.
  arXiv  Detail & Related papers  (2020-07-29T22:19:42Z)
• Quantum Zeno effect appears in stages [64.41511459132334]
  In the quantum Zeno effect, quantum measurements can block the coherent oscillation of a two level system by freezing its state to one of the measurement eigenstates. We show that the onset of the Zeno regime is marked by a $textitcascade of transitions$ in the system dynamics as the measurement strength is increased.
  arXiv  Detail & Related papers  (2020-03-23T18:17:36Z)
• Einselection from incompatible decoherence channels [62.997667081978825]
  We analyze an open quantum dynamics inspired by CQED experiments with two non-commuting Lindblad operators. We show that Fock states remain the most robust states to decoherence up to a critical coupling.
  arXiv  Detail & Related papers  (2020-01-29T14:15:19Z)

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.