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arXiv:1212.2253

Incoherent light as a control resource: a route to complete controllability of quantum systems

Alexander Nikolaevich Pechen

Published Dec 10, 2012• 2 citations
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Abstract

We discuss the use of incoherent light as a resource to control the atomic dynamics and review the proposed in Phys. Rev. A 84, 042106 (2011) method for a controlled transfer between any pure and mixed states of quantum systems using a combination of incoherent and coherent light. Formally, the method provides a constructive proof for an approximate open-loop Markovian state-transfer controllability of quantum system in the space of all density matrices---the strongest possible degree of quantum state control.

DOI
10.48550/arxiv.1212.2253

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Conventional approaches for controlling open quantum systems use coherent control which affects the system's evolution through the Hamiltonian part of the dynamics. Such control, although being extremely efficient for a large variety of problems, has limited capabilities, e.g., if the initial and desired target states have density matrices with different spectra or if a control field needs to be designed to optimally transfer different initial states to the same target state. Recent research works suggest extending coherent control by including active manipulation of the non-unitary (i.e., incoherent) part of the evolution. This paper summarizes recent results specifically for incoherent control by the environment (e.g., incoherent radiation or a gaseous medium) with a kinematic description of controllability and landscape analysis.
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Coherence control was originally conceived by Shapiro and Brumer for closed quantum systems. In open quantum systems, the environment hampers or destroys coherence. Nevertheless, the Kurizki-Shapiro-Brumer coherent photocurrent control showed partial resilience to decoherence. Still, decoherence control is an essential prerequisite to our ability to fully exploit quantum coherence for any operational task. Yet decoherence control need not employ coherent fields: it may be incoherent. In operational tasks such as the preparation, transformation, transmission, and detection of quantumstates, environmental (bath) effects can be suppressed by dynamical decoupling, or by the more general incoherent dynamical control by modulation developed by our group. The resulting control dynamics must be Zeno-like in order to yield suppressed coupling to the bath in unitary operational tasks. There are however tasks which cannot be implemented by closed-system (unitary) evolution, in particular those involving a change of the system's entropy. Such tasks necessitate efficient coupling to a bath for their implementation. Examples are the use of measurements to cool (purify) a system, to equilibrate it, or harvest (and convert) energy from the environment. If the underlying dynamics is anti-Zeno like, enhancement of this coupling to the bath will occur and thereby facilitate the task, as discovered by us. A general task may also require state and energy transfer between non-interacting parties via shared modes of the bath. For such tasks, a more subtle interplay of Zeno and anti-Zeno dynamics may be optimal. We have therefore constructed a general framework for optimizing the way a system interacts with its environment to achieve a desired task. This optimization consists in adjusting a given “score” that quantifies the success of the task, such as the targeted fidelity, purity, entropy, energy or state transfer probability by dynamical modification of the system-bath coupling spectrum on demand.