126 research outputs found
Analytic Solutions to Coherent Control of the Dirac Equation
A simple framework for Dirac spinors is developed that parametrizes
admissible quantum dynamics and also analytically constructs electromagnetic
fields, obeying Maxwell's equations, which yield a desired evolution. In
particular, we show how to achieve dispersionless rotation and translation of
wave packets. Additionally, this formalism can handle control interactions
beyond electromagnetic. This work reveals unexpected flexibility of the Dirac
equation for control applications, which may open new prospects for quantum
technologies
Dirac open quantum system dynamics: formulations and simulations
We present an open system interaction formalism for the Dirac equation.
Overcoming a complexity bottleneck of alternative formulations, our framework
enables efficient numerical simulations (utilizing a typical desktop) of
relativistic dynamics within the von Neumann density matrix and Wigner phase
space descriptions. Employing these instruments, we gain important insights
into the effect of quantum dephasing for relativistic systems in many branches
of physics. In particular, the conditions for robustness of Majorana spinors
against dephasing are established. Using the Klein paradox and tunneling as
examples, we show that quantum dephasing does not suppress negative energy
particle generation. Hence, the Klein dynamics is also robust to dephasing
Sampling-based learning control of inhomogeneous quantum ensembles
Compensation for parameter dispersion is a significant challenge for control
of inhomogeneous quantum ensembles. In this paper, we present a systematic
methodology of sampling-based learning control (SLC) for simultaneously
steering the members of inhomogeneous quantum ensembles to the same desired
state. The SLC method is employed for optimal control of the state-to-state
transition probability for inhomogeneous quantum ensembles of spins as well as
type atomic systems. The procedure involves the steps of (i) training
and (ii) testing. In the training step, a generalized system is constructed by
sampling members according to the distribution of inhomogeneous parameters
drawn from the ensemble. A gradient flow based learning and optimization
algorithm is adopted to find the control for the generalized system. In the
process of testing, a number of additional ensemble members are randomly
selected to evaluate the control performance. Numerical results are presented
showing the success of the SLC method.Comment: 8 pages, 9 figure
Sampling-based Learning Control for Quantum Systems with Uncertainties
Robust control design for quantum systems has been recognized as a key task
in the development of practical quantum technology. In this paper, we present a
systematic numerical methodology of sampling-based learning control (SLC) for
control design of quantum systems with uncertainties. The SLC method includes
two steps of "training" and "testing". In the training step, an augmented
system is constructed using artificial samples generated by sampling
uncertainty parameters according to a given distribution. A gradient flow based
learning algorithm is developed to find the control for the augmented system.
In the process of testing, a number of additional samples are tested to
evaluate the control performance where these samples are obtained through
sampling the uncertainty parameters according to a possible distribution. The
SLC method is applied to three significant examples of quantum robust control
including state preparation in a three-level quantum system, robust
entanglement generation in a two-qubit superconducting circuit and quantum
entanglement control in a two-atom system interacting with a quantized field in
a cavity. Numerical results demonstrate the effectiveness of the SLC approach
even when uncertainties are quite large, and show its potential for robust
control design of quantum systems.Comment: 11 pages, 9 figures, in press, IEEE Transactions on Control Systems
Technology, 201
The role of controllability in optimizing quantum dynamics
This paper discusses the important role of controllability played on the
complexity of optimizing quantum mechanical control systems. The study is based
on a topology analysis of the corresponding quantum control landscape, which is
referred to as the optimization objective as a functional of control fields. We
find that the degree of controllability is closely relevant with the ruggedness
of the landscape, which determines the search efficiency for global optima.
This effect is demonstrated via the gate fidelity control landscape of a system
whose controllability is restricted on a SU(2) dynamic symmetry group. We show
that multiple local false traps (i.e., non-global suboptima) exist even if the
target gate is realizable and that the number of these traps is increased by
the loss of controllability, while the controllable systems are always devoid
of false traps.Comment: 13 pages, 3 figure
Operational Dynamical Modeling of spin 1/2 relativistic particles: the Dirac equation and its classical limit
The formalism of Operational Dynamical Modeling [Phys. Rev. Lett. {\bf 109},
190403 (2012)] is employed to analyze dynamics of spin half relativistic
particles. We arrive at the Dirac equation from specially constructed
relativistic Ehrenfest theorems by assuming that the coordinates and momenta do
not commute. Forbidding creation of antiparticles and requiring the
commutativity of the coordinates and momenta lead to classical Spohn's equation
[Ann. Phys. {\bf 282}, 420 (2000)]. Moreover, Spohn's equation turns out to be
the classical Koopman-von Neumann theory underlying the Dirac equation
Integration of Carbon, Nitrogen, and Oxygen Metabolism in Escherichia coli--Final Report
A key challenge for living systems is balancing utilization of multiple elemental nutrients, such as carbon, nitrogen, and oxygen, whose availability is subject to environmental fluctuations. As growth can be limited by the scarcity of any one nutrient, the rate at which each nutrient is assimilated must be sensitive not only to its own availability, but also to that of other nutrients. Remarkably, across diverse nutrient conditions, E. coli grows nearly optimally, balancing effectively the conversion of carbon into energy versus biomass. To investigate the link between the metabolism of different nutrients, we quantified metabolic responses to nutrient perturbations using LC-MS based metabolomics and built differential equation models that bridge multiple nutrient systems. We discovered that the carbonaceous substrate of nitrogen assimilation, ñ-ketoglutarate, directly inhibits glucose uptake and that the upstream glycolytic metabolite, fructose-1,6-bisphosphate, ultrasensitively regulates anaplerosis to allow rapid adaptation to changing carbon availability. We also showed that NADH controls the metabolic response to changing oxygen levels. Our findings support a general mechanism for nutrient integration: limitation for a nutrient other than carbon leads to build-up of the most closely related product of carbon metabolism, which in turn feedback inhibits further carbon uptake
Quantum tracking control of the orientation of symmetric top molecules
The goal of quantum tracking control is to identify shaped fields to steer
observable expectation values along designated time-dependent tracks. The
fields are determined via an iteration-free procedure, which is based on
inverting the underlying dynamical equations governing the controlled
observables. In this article, we generalize the ideas in Phys. Rev. A 98,
043429 (2018) to the task of orienting symmetric top molecules in 3D. To this
end, we derive equations for the control fields capable of directly tracking
the expected value of the 3D dipole orientation vector along a desired path in
time. We show this framework can be utilized for tracking the orientation of
linear molecules as well, and present numerical illustrations of these
principles for symmetric top tracking control problems
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