46 research outputs found
The multi-time correlation functions, free white noise, and the generalized Poisson statistics in the low density limit
In the present paper the low density limit of the non-chronological multitime
correlation functions of boson number type operators is investigated. We prove
that the limiting truncated non-chronological correlation can be computed using
only a sub-class of diagrams associated to non-crossing pair partitions and
thus coincide with the non-truncated correlation functions of suitable free
number operators. The independent in the limit subalgebras are found and the
limiting statistics is investigated. In particular, it is found that the
cumulants of certain elements coincide in the limit with the cumulants of the
Poisson distribution. An explicit representation of the limiting correlation
functions and thus of the limiting algebra is constructed in a special case
through suitably defined quantum white noise operators.Comment: 14 page
Engineering arbitrary pure and mixed quantum states
This work addresses a fundamental problem of controllability of open quantum
systems, meaning the ability to steer arbitrary initial system density matrix
into any final density matrix. We show that under certain general conditions
open quantum systems are completely controllable and propose the first, to the
best of our knowledge, deterministic method for a laboratory realization of
such controllability which allows for a practical engineering of arbitrary pure
and mixed quantum states. The method exploits manipulation by the system with a
laser field and a tailored nonequilibrium and time-dependent state of the
surrounding environment. As a physical example of the environment we consider
incoherent light, where control is its spectral density. The method has two
specifically important properties: it realizes the strongest possible degree of
quantum state control --- complete density matrix controllability which is the
ability to steer arbitrary pure and mixed initial states into any desired pure
or mixed final state, and is "all-to-one", i.e. such that each particular
control can transfer simultaneously all initial system states into one target
state
White noise approach to the low density limit of a quantum particle in a gas
The white noise approach to the investigation of the dynamics of a quantum
particle interacting with a dilute and in general non-equilibrium gaseous
environment in the low density limit is outlined. The low density limit is the
kinetic Markovian regime when only pair collisions (i.e., collisions of the
test particle with one particle of the gas at one time moment) contribute to
the dynamics. In the white noise approach one first proves that the appropriate
operators describing the gas converge in the sense of appropriate matrix
elements to certain operators of quantum white noise. Then these white noise
operators are used to derive quantum white noise and quantum stochastic
equations describing the approximate dynamics of the total system consisting of
the particle and the gas. The derivation is given ab initio, starting from the
exact microscopic quantum dynamics. The limiting dynamics is described by a
quantum stochastic equation driven by a quantum Poisson process. This equation
then applied to the derivation of quantum Langevin equation and linear
Boltzmann equation for the reduced density matrix of the test particle. The
first part of the paper describes the approach which was developed by L.
Accardi, I.V. Volovich and the author and uses the Fock-antiFock (or GNS)
representation for the CCR algebra of the gas. The second part presents the
approach to the derivation of the limiting equations directly in terms of the
correlation functions, without use of the Fock-antiFock representation. This
approach simplifies the derivation and allows to express the strength of the
quantum number process directly in terms of the one-particle -matrix.Comment: This preprint is a minor modification of the published pape
Quantum measurements as a control resource
We discuss the use of back-action of quantum measurements as a resource for
controlling quantum systems and review its application to optimal approximation
of quantum anti-Zeno effect
Incoherent light as a control resource: a route to complete controllability of quantum systems
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.Comment: An updated version of the published Conference Paper for the OSA
Optics and Photonics Congress 2012: High Intensity Lasers and High Field
Phenomena. Section 4 is adde
Quantum multipole noise
Quantum multipole noise is defined as a family of creation and annihilation
operators with commutation relations proportional to derivatives of delta
function of difference of the times, . In this paper an explicit operator representation of the
quantum multipole noise is constructed in a suitable pseudo-Hilbert space
(i.e., in a Hilbert space with indefinite metric). For making this
representation, we introduce a class of Hilbert spaces obtained as completion
of the Schwartz space in specific norms. Using this representation, we obtain
an asymptotic expansion as a series in quantum multipole noise for multitime
correlation functions which describe the dynamics of open quantum systems
weakly interacting with a reservoir
Coherent control of a qubit is trap-free
There is a strong interest in optimal manipulating of quantum systems by
external controls. Traps are controls which are optimal only locally but not
globally. If they exist, they can be serious obstacles to the search of
globally optimal controls in numerical and laboratory experiments, and for this
reason the analysis of traps attracts considerable attention. In this paper we
prove that for a wide range of control problems for two-level quantum systems
all locally optimal controls are also globally optimal. Hence we conclude that
two-level systems in general are trap-free. In particular, manipulating
qubits---two-level quantum systems forming a basic building block for quantum
computation---is free of traps for fundamental problems such as the state
preparation and gate generation
Trap-free manipulation in the Landau-Zener system
The analysis of traps, i.e., locally but not globally optimal controls, for
quantum control systems has attracted a great interest in recent years. The
central problem that has been remained open is to demonstrate for a given
system either existence or absence of traps. We prove the absence of traps and
hence completely solve this problem for the important tasks of unconstrained
manipulation of the transition probability and unitary gate generation in the
Landau-Zener system---a system with a wide range of applications across
physics, chemistry and biochemistry. This finding provides the first example of
a controlled quantum system which is completely free of traps. We also discuss
the impact of laboratory constraints due to decoherence, noise in the control
pulse, and restrictions on the available controls which when being sufficiently
severe can produce traps
On critical points of the objective functional for maximization of qubit observables
We study unconstrained control of a two-level quantum system and analyse
critical points of the objective functional which represents quantum average of
system observable at some final time . In Proc. Steklov Inst. Math. 285,
233-240 (2014) it was shown that all maxima and minima of the objective
functional are global if (in suitable units). In the present work we
show that all maxima and minima are global as soon as . Hence we
reduce by the factor of two the minimal time for which traps, i.e., local but
not global maxima or minima of the objective functional, do not exist
Are there traps in quantum control landscapes?
There has been great interest in recent years in quantum control landscapes.
Given an objective that depends on a control field the
dynamical landscape is defined by the properties of the Hessian at the critical points .
We show that contrary to recent claims in the literature the dynamical control
landscape can exhibit trapping behavior due to the existence of special
critical points and illustrate this finding with an example of a 3-level
-system. This observation can have profound implications for both
theoretical and experimental quantum control studies