1,346 research outputs found
The SLH framework for modeling quantum input-output networks
Many emerging quantum technologies demand precise engineering and control
over networks consisting of quantum mechanical degrees of freedom connected by
propagating electromagnetic fields, or quantum input-output networks. Here we
review recent progress in theory and experiment related to such quantum
input-output networks, with a focus on the SLH framework, a powerful modeling
framework for networked quantum systems that is naturally endowed with
properties such as modularity and hierarchy. We begin by explaining the
physical approximations required to represent any individual node of a network,
eg. atoms in cavity or a mechanical oscillator, and its coupling to quantum
fields by an operator triple . Then we explain how these nodes can be
composed into a network with arbitrary connectivity, including coherent
feedback channels, using algebraic rules, and how to derive the dynamics of
network components and output fields. The second part of the review discusses
several extensions to the basic SLH framework that expand its modeling
capabilities, and the prospects for modeling integrated implementations of
quantum input-output networks. In addition to summarizing major results and
recent literature, we discuss the potential applications and limitations of the
SLH framework and quantum input-output networks, with the intention of
providing context to a reader unfamiliar with the field.Comment: 60 pages, 14 figures. We are still interested in receiving
correction
Linear feedback stabilization of a dispersively monitored qubit
The state of a continuously monitored qubit evolves stochastically,
exhibiting competition between coherent Hamiltonian dynamics and diffusive
partial collapse dynamics that follow the measurement record. We couple these
distinct types of dynamics together by linearly feeding the collected record
for dispersive energy measurements directly back into a coherent Rabi drive
amplitude. Such feedback turns the competition cooperative, and effectively
stabilizes the qubit state near a target state. We derive the conditions for
obtaining such dispersive state stabilization and verify the stabilization
conditions numerically. We include common experimental nonidealities, such as
energy decay, environmental dephasing, detector efficiency, and feedback delay,
and show that the feedback delay has the most significant negative effect on
the feedback protocol. Setting the measurement collapse timescale to be long
compared to the feedback delay yields the best stabilization.Comment: 16 pages, 7 figure
Quantum filter for a class of non-Markovian quantum systems
In this paper we present a Markovian representation approach to constructing
quantum filters for a class of non-Markovian quantum systems disturbed by
Lorenztian noise. An ancillary system is introduced to convert white noise into
Lorentzian noise which is injected into a principal system via a direct
interaction. The resulting dynamics of the principal system are non-Markovian,
which are driven by the Lorentzian noise. By probing the principal system, a
quantum filter for the augmented system can be derived from standard theory,
where the conditional state of the principal system can be obtained by tracing
out the ancillary system. An example is provided to illustrate the
non-Markovian dynamics of the principal system.Comment: 8 pages, 7 figure
Nonlinear quantum input-output analysis using Volterra series
Quantum input-output theory plays a very important role for analyzing the
dynamics of quantum systems, especially large-scale quantum networks. As an
extension of the input-output formalism of Gardiner and Collet, we develop a
new approach based on the quantum version of the Volterra series which can be
used to analyze nonlinear quantum input-output dynamics. By this approach, we
can ignore the internal dynamics of the quantum input-output system and
represent the system dynamics by a series of kernel functions. This approach
has the great advantage of modelling weak-nonlinear quantum networks. In our
approach, the number of parameters, represented by the kernel functions, used
to describe the input-output response of a weak-nonlinear quantum network,
increases linearly with the scale of the quantum network, not exponentially as
usual. Additionally, our approach can be used to formulate the quantum network
with both nonlinear and nonconservative components, e.g., quantum amplifiers,
which cannot be modelled by the existing methods, such as the
Hudson-Parthasarathy model and the quantum transfer function model. We apply
our general method to several examples, including Kerr cavities, optomechanical
transducers, and a particular coherent feedback system with a nonlinear
component and a quantum amplifier in the feedback loop. This approach provides
a powerful way to the modelling and control of nonlinear quantum networks.Comment: 12 pages, 7 figure
Models and Feedback Stabilization of Open Quantum Systems
At the quantum level, feedback-loops have to take into account measurement
back-action. We present here the structure of the Markovian models including
such back-action and sketch two stabilization methods: measurement-based
feedback where an open quantum system is stabilized by a classical controller;
coherent or autonomous feedback where a quantum system is stabilized by a
quantum controller with decoherence (reservoir engineering). We begin to
explain these models and methods for the photon box experiments realized in the
group of Serge Haroche (Nobel Prize 2012). We present then these models and
methods for general open quantum systems.Comment: Extended version of the paper attached to an invited conference for
the International Congress of Mathematicians in Seoul, August 13 - 21, 201
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