389 research outputs found
Stabilizing Open Quantum Systems by Markovian Reservoir Engineering
We study open quantum systems whose evolution is governed by a master
equation of Kossakowski-Gorini-Sudarshan-Lindblad type and give a
characterization of the convex set of steady states of such systems based on
the generalized Bloch representation. It is shown that an isolated steady state
of the Bloch equation cannot be a center, i.e., that the existence of a unique
steady state implies attractivity and global asymptotic stability. Necessary
and sufficient conditions for the existence of a unique steady state are
derived and applied to different physical models including two- and four-level
atoms, (truncated) harmonic oscillators, composite and decomposable systems. It
is shown how these criteria could be exploited in principle for quantum
reservoir engineeing via coherent control and direct feedback to stabilize the
system to a desired steady state. We also discuss the question of limit points
of the dynamics. Despite the non-existence of isolated centers, open quantum
systems can have nontrivial invariant sets. These invariant sets are center
manifolds that arise when the Bloch superoperator has purely imaginary
eigenvalues and are closely related to decoherence-free subspaces.Comment: 16 pages, 4 figures, marginally revised version, mainly fixed some
notational inconsistencies that had crept in when we change the notation in
some figures without changing the captions and tex
Quantum simulation of zero temperature quantum phases and incompressible states of light via non-Markovian reservoir engineering techniques
We review recent theoretical developments on the stabilization of strongly
correlated quantum fluids of light in driven-dissipative photonic devices
through novel non-Markovian reservoir engineering techniques. This approach
allows to compensate losses and refill selectively the photonic population so
to sustain a desired steady-state. It relies in particular on the use of a
frequency-dependent incoherent pump which can be implemented, e.g., via
embedded two-level systems maintained at a strong inversion of population. As
specific applications of these methods, we discuss the generation of Mott
Insulator (MI) and Fractional Quantum Hall (FQH) states of light. As a first
step, we present the case of a narrowband emission spectrum and show how this
allows for the stabilization of MI and FQH states under the condition that the
photonic states are relatively flat in energy. As soon as the photonic
bandbwidth becomes comparable to the emission linewidth, important
non-equilibrium signatures and entropy generation appear. As a second step, we
review a more advanced configuration based on reservoirs with a broadband
frequency distribution, and we highlight the potential of this configuration
for the quantum simulation of equilibrium quantum phases at zero temperature
with tunable chemical potential. As a proof of principle we establish the
applicability of our scheme to the Bose-Hubbard model by confirming the
presence of a perfect agreement with the ground-state predictions both in the
Mott Insulating and superfluid regions, and more generally in all parts of the
parameter space. Future prospects towards the quantum simulation of more
complex configurations are finally outlined, along with a discussion of our
scheme as a concrete realization of quantum annealing
Stabilizing Entangled States with Quasi-Local Quantum Dynamical Semigroups
We provide a solution to the problem of determining whether a target pure
state can be asymptotically prepared using dissipative Markovian dynamics under
fixed locality constraints. Beside recovering existing results for a large
class of physically relevant entangled states, our approach has the advantage
of providing an explicit stabilization test solely based on the input state and
constraints of the problem. Connections with the formalism of frustration-free
parent Hamiltonians are discussed, as well as control implementations in terms
of a switching output-feedback law.Comment: 11 pages, no figure
Stabilizing Quantum States by Constructive Design of Open Quantum Dynamics
Based on recent work on the asymptotic behavior of controlled quantum
Markovian dynamics, we show that any generic quantum state can be stabilized by
devising constructively a simple Lindblad-GKS generator that can achieve global
asymptotic stability at the desired state. The applications of such result is
demonstrated by designing a direct feedback strategy that achieves global
stabilization of a qubit state encoded in a noise-protected subspace.Comment: Revised version with stronger proofs showing uniqueness can be
achieved in all cases by using the freedom to the choose diagonal elements of
both the Hamiltonian and Lindblad operator, and exploiting the fact that the
non-existence of two orthogonal eigenvectors of the Lindblad operator is
sufficient but not necessary for global asymptotic stability of the target
stat
Contraction and stability analysis of steady-states for open quantum systems described by Lindblad differential equations
For discrete-time systems, governed by Kraus maps, the work of D. Petz has
characterized the set of universal contraction metrics. In the present paper,
we use this characterization to derive a set of quadratic Lyapunov functions
for continuous-time systems, governed by Lindblad differential equations, that
have a steady-state with full rank. An extremity of this set is given by the
Bures metric, for which the quadratic Lyapunov function is obtained by
inverting a Sylvester equation. We illustrate the method by providing a strict
Lyapunov function for a Lindblad equation designed to stabilize a quantum
electrodynamic "cat" state by reservoir engineering. In fact we prove that any
Lindblad equation on the Hilbert space of the (truncated) harmonic oscillator,
which has a full-rank equilibrium and which has, among its decoherence
channels, a channel corresponding to the photon loss operator, globally
converges to that equilibrium.Comment: Submitted (10 pages, 1 figure
Using Spontaneous Emission of a Qubit as a Resource for Feedback Control
Persistent control of a transmon qubit is performed by a feedback protocol
based on continuous heterodyne measurement of its fluorescence. By driving the
qubit and cavity with microwave signals whose amplitudes depend linearly on the
instantaneous values of the quadratures of the measured fluorescence field, we
show that it is possible to stabilize permanently the qubit in any targeted
state. Using a Josephson mixer as a phase-preserving amplifier, it was possible
to reach a total measurement efficiency =35%, leading to a maximum of 59%
of excitation and 44% of coherence for the stabilized states. The experiment
demonstrates multiple-input multiple-output analog Markovian feedback in the
quantum regime.Comment: Supplementary material can be found as an ancillary objec
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
Engineering Stable Discrete-Time Quantum Dynamics via a Canonical QR Decomposition
We analyze the asymptotic behavior of discrete-time, Markovian quantum
systems with respect to a subspace of interest. Global asymptotic stability of
subspaces is relevant to quantum information processing, in particular for
initializing the system in pure states or subspace codes. We provide a
linear-algebraic characterization of the dynamical properties leading to
invariance and attractivity of a given quantum subspace. We then construct a
design algorithm for discrete-time feedback control that allows to stabilize a
target subspace, proving that if the control problem is feasible, then the
algorithm returns an effective control choice. In order to prove this result, a
canonical QR matrix decomposition is derived, and also used to establish the
control scheme potential for the simulation of open-system dynamics.Comment: 12 pages, 1 figur
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