Principles for determining mechanistic pathways from observable quantum control data (original) (raw)
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Identifying mechanisms in the control of quantum dynamics through Hamiltonian encoding
Physical Review A, 2003
A variety of means are now available to design control fields for manipulating the evolution of quantum systems. However, the underlying physical mechanisms often remain obscure, especially in the cases of strong fields and high quantum state congestion. This paper proposes a method to quantitatively determine the various pathways taken by a quantum system in going from the initial state to the final target. The mechanism is revealed by encoding a signal in the system Hamiltonian and decoding the resultant nonlinear distortion of the signal in the system time-evolution operator. The relevant interfering pathways determined by this analysis give insight into the physical mechanisms operative during the evolution of the quantum system. A hierarchy of mechanism identification algorithms with increasing ability to extract more detailed pathway information is presented. The mechanism identification concept is presented in the context of analyzing computer simulations of controlled dynamics. As illustrations of the concept, mechanisms are identified in the control of several simple, discrete-state quantum systems. The mechanism analysis tools reveal the roles of multiple interacting quantum pathways to maximally take advantage of constructive and destructive interference. Similar procedures may be applied directly in the laboratory to identify control mechanisms without resort to computer modeling, although this extension is not addressed in this paper.
The Journal of Chemical Physics, 2008
Optimal control of quantum dynamics in the laboratory is proving to be increasingly successful. The control fields can be complex, and the mechanisms by which they operate have often remained obscure. Hamiltonian encoding ͑HE͒ has been proposed as a method for understanding mechanisms in quantum dynamics. In this context mechanism is defined in terms of the dominant quantum pathways leading to the final state of the controlled system. HE operates by encoding a special modulation into the Hamiltonian and decoding its signature in the dynamics to determine the dominant pathway amplitudes. Earlier work encoded the modulation directly into the Hamiltonian operators. This present work introduces the alternative scheme of field based HE, where the modulation is encoded into the control field and not directly into the Hamiltonian operators. This distinct form of modulation yields a new perspective on mechanism and is computationally faster than the earlier approach. Field based encoding is also an important step towards a laboratory based algorithm for HE as it is the only form of encoding that may be experimentally executed. HE is also extended to cover systems with noise and uncertainty and finally, a hierarchical algorithm is introduced to reveal mechanism in a stepwise fashion of ever increasing detail as desired. This new hierarchical algorithm is an improvement over earlier approaches to HE where the entire mechanism was determined in one stroke. The improvement comes from the use of less complex modulation schemes, which leads to fewer evaluations of Schrödinger's equation. A number of simulations are presented on simple systems to illustrate the new field based encoding technique for mechanism assessment.
Revealing quantum-control mechanisms through Hamiltonian encoding in different representations
Physical Review A, 2003
The Hamiltonian encoding is a means for revealing the mechanism of controlled quantum dynamics. In this context, the mechanism is defined by the dominant quantum pathways starting from the initial state and proceeding through a set of intermediate states to end at the final state. The nature and interpretation of the mechanism depends on the choice of the states to represent the dynamics. Alternative representations may provide distinct insights into the system mechanism, and representations producing fewer pathways are especially interesting. In addition, a suitable choice of representation may highlight the role of certain couplings in a system that would normally be masked by other, higher magnitude couplings. A simple three-level system is chosen for illustration, where different values for the Rabi frequencies lead to mechanistic analyses that are best described in terms of particular representations. As an examlple, the role of the nonadiabatic terms in stimulated Raman adiabatic passage dynamics is analyzed through the Hamiltonian encoding.
Systematically Identifying Mechanisms in the Control of Quantum Dynamics
IFAC Proceedings Volumes, 2003
This paper introduces a method to quantitatively determine the various pathways taken by a qua ntum system ill going from the initial st ate to the fin al t arget. The mechanism is revealed by encoding a signal in the s~'ste m Hamiltonian and decoding the resultant nonlinear distortion of the signal in the system time evolution operator , The releva nt interfering pathways determined by this a nalysis give insight into the physical mechanisms operative during the evolution of the quantum s,\'stem. The mechanism analysis t ools reveal the roles of multiple interacting qu antum pathwa:vs to maximally take advantage of constructive and destructive interference,
Understanding the role of respresentation in controlled quantum-dynamical mechanism analysis
Physical Review A, 2008
Hamiltonian Encoding ͑HE͒ has been proposed as a technique for analyzing the mechanism of controlled quantum dynamics, where mechanism is understood in terms of the set of amplitudes of the dominant pathways connecting the initial and final states of the system. The choice of representation for the system wave function is often motivated by seeking simplicity for the structure of the Hamiltonian and not necessarily for the generated dynamics. However, the mechanism revealed by HE is strongly dependent on the basis in which the wave function is represented. The degree of mechanistic complexity is indicated by the relevant orders of the Dyson series contributing to the dynamics. An appropriate choice of representation can yield a simpler view of the dynamical mechanism by shifting some of the complexity into the representation itself. In this work the choice of representation is set up as the solution to a variational optimization problem. For unconstrained basis transformations, the optimization of the representation is formally equivalent to solving the time-dependent Schrödinger equation; different constrained basis transformations provide distinct dynamical perspectives. Specific constrained variational Ansätze are compared and analyzed by performing HE on several simple Hamiltonians with an observation of the extent to which the mechanism assessment varies with representation. The general variational formulation for determining representation can flexibly admit other Ansätze with the ultimate aim of balancing the ease of determining and understanding the representation with the reduction in mechanistic complexity.
Mechanistic Analysis of Optimal Dynamic Discrimination of Similar Quantum Systems
The Journal of Physical Chemistry A, 2004
Optimal dynamic discrimination (ODD) was recently introduced as a technique for maximally drawing out and detecting the differences between similar quantum systems by exploiting their controllable dynamical properties. As a simulation of ODD, optimal fields were found that successfully discriminated among similar species, but the underlying mechanisms of the process remained obscure. Hamiltonian encoding (HE) has been introduced as a technique for identifying the mechanisms of controlled quantum dynamics. The results of a HE based simulation analysis of ODD are presented in this paper. Different types and degrees of constructive and destructive interference are shown to underly the controlled discrimination processes. In general, it is found that successful discrimination relies on more complex interfering pathways for increasingly similar systems or increasing numbers of similar quantum systems.
Physical Review A, 2009
We develop a general approach for monitoring and controlling evolution of open quantum systems. In contrast to the master equations describing time evolution of density operators, here, we formulate a dynamical equation for the evolution of the process matrix acting on a system. This equation is applicable to non-Markovian and/or strong coupling regimes. We propose two distinct applications for this dynamical equation. We first demonstrate identification of quantum Hamiltonians generating dynamics of closed or open systems via performing process tomography. In particular, we argue how one can efficiently estimate certain classes of sparse Hamiltonians by performing partial tomography schemes. In addition, we introduce a novel optimal control theoretic setting for manipulating quantum dynamics of Hamiltonian systems, specifically for the task of decoherence suppression.
Modelling of quantum mechanical control systems
Mathematical Modelling
A program of studies of quantum mechanical control systems is initiated. Following the historical development of quantum mechanics, the quantum control model is obtained from a corresponding classical structure. Second order linear and bilinear control systems as well as first order linear control systems are investigated; it is further demonstrated that the analysis may be extended to some nonlinear control problems. The results derived for these systems form an interesting example of the general theory of quantization.
A Mechanistic Reading of Quantum Laser Theory
The Frontiers Collection, 2015
I want to show that the quantum theory of laser radiation provides a good example of a mechanistic explanation in a quantum physical setting. Although the physical concepts and analytical strategies I will outline in the following do admittedly go somewhat beyond high school knowledge, I think it worth going some way into the state-of-the-art treatment of the laser, rather than remaining at a superficial pictorial level. In the course of the ensuing exposition of laser theory, I want to show that the basic equations and the methods for solving them can, despite their initially inaccessible appearance, be closely matched to mechanistic ideas at every stage.