3,954 research outputs found
Proof of the Standard Quantum Limit for Monitoring Free-Mass Position
The measurement result of the moved distance for a free mass m during the
time t between two position measurements cannot be predicted with uncertainty
smaller than sqrt{hbar t/2m}. This is formulated as a standard quantum limit
(SQL) and it has been proven to always hold for the following position
measurement: a probe is set in a prescribed position before the measurement.
Just after the interaction of the mass with the probe, the probe position is
measured, and using this value, the measurement results of the pre-measurement
and post-measurement positions are estimated.Comment: 4 pages, no figur
Quantum Control Landscapes
Numerous lines of experimental, numerical and analytical evidence indicate
that it is surprisingly easy to locate optimal controls steering quantum
dynamical systems to desired objectives. This has enabled the control of
complex quantum systems despite the expense of solving the Schrodinger equation
in simulations and the complicating effects of environmental decoherence in the
laboratory. Recent work indicates that this simplicity originates in universal
properties of the solution sets to quantum control problems that are
fundamentally different from their classical counterparts. Here, we review
studies that aim to systematically characterize these properties, enabling the
classification of quantum control mechanisms and the design of globally
efficient quantum control algorithms.Comment: 45 pages, 15 figures; International Reviews in Physical Chemistry,
Vol. 26, Iss. 4, pp. 671-735 (2007
Quantum Parrondo's game with random strategies
We present a quantum implementation of Parrondo's game with randomly switched
strategies using 1) a quantum walk as a source of ``randomness'' and 2) a
completely positive (CP) map as a randomized evolution. The game exhibits the
same paradox as in the classical setting where a combination of two losing
strategies might result in a winning strategy. We show that the CP-map scheme
leads to significantly lower net gain than the quantum walk scheme
Classical Correlations and Entanglement in Quantum Measurements
We analyze a quantum measurement where the apparatus is initially in a mixed
state. We show that the amount of information gained in a measurement is not
equal to the amount of entanglement between the system and the apparatus, but
is instead equal to the degree of classical correlations between the two. As a
consequence, we derive an uncertainty-like expression relating the information
gain in the measurement and the initial mixedness of the apparatus. Final
entanglement between the environment and the apparatus is also shown to be
relevant for the efficiency of the measurement.Comment: to appear in Physical Review Letter
Correlated interaction fluctuations in photosynthetic complexes
The functioning and efficiency of natural photosynthetic complexes is
strongly influenced by their embedding in a noisy protein environment, which
can even serve to enhance the transport efficiency. Interactions with the
environment induce fluctuations of the transition energies of and interactions
between the chlorophyll molecules, and due to the fact that different
fluctuations will partially be caused by the same environmental factors,
correlations between the various fluctuations will occur. We argue that
fluctuations of the interactions should in general not be neglected, as these
have a considerable impact on population transfer rates, decoherence rates and
the efficiency of photosynthetic complexes. Furthermore, while correlations
between transition energy fluctuations have been studied, we provide the first
quantitative study of the effect of correlations between interaction
fluctuations and transition energy fluctuations, and of correlations between
the various interaction fluctuations. It is shown that these additional
correlations typically lead to changes in interchromophore transfer rates,
population oscillations and can lead to a limited enhancement of the light
harvesting efficiency
Nonmonotonic energy harvesting efficiency in biased exciton chains
We theoretically study the efficiency of energy harvesting in linear exciton
chains with an energy bias, where the initial excitation is taking place at the
high-energy end of the chain and the energy is harvested (trapped) at the other
end. The efficiency is characterized by means of the average time for the
exciton to be trapped after the initial excitation. The exciton transport is
treated as the intraband energy relaxation over the states obtained by
numerically diagonalizing the Frenkel Hamiltonian that corresponds to the
biased chain. The relevant intraband scattering rates are obtained from a
linear exciton-phonon interaction. Numerical solution of the Pauli master
equation that describes the relaxation and trapping processes, reveals a
complicated interplay of factors that determine the overall harvesting
efficiency. Specifically, if the trapping step is slower than or comparable to
the intraband relaxation, this efficiency shows a nonmonotonic dependence on
the bias: it first increases when introducing a bias, reaches a maximum at an
optimal bias value, and then decreases again because of dynamic (Bloch)
localization of the exciton states. Effects of on-site (diagonal) disorder,
leading to Anderson localization, are addressed as well.Comment: 9 pages, 6 figures, to appear in Journal of Chemical Physic
Tuning phase transition between quantum spin Hall and ordinary insulating phases
An effective theory is constructed for analyzing a generic phase transition
between the quantum spin Hall and the insulator phases. Occurrence of
degeneracies due to closing of the gap at the transition are carefully
elucidated. For systems without inversion symmetry the gap-closing occurs at
\pm k_0(\neq G/2) while for systems with inversion symmetry, the gap can close
only at wave-numbers k=G/2, where G is a reciprocal lattice vector. In both
cases, following a unitary transformation which mixes spins, the system is
represented by two decoupled effective theories of massive two-component
fermions having masses of opposite signs. Existence of gapless helical modes at
a domain wall between the two phases directly follows from this formalism. This
theory provides an elementary and comprehensive phenomenology of the quantum
spin Hall system.Comment: 6 pages, 2 figures, to appear in Phys. Rev.
Universal Uncertainty Principle in the Measurement Operator Formalism
Heisenberg's uncertainty principle has been understood to set a limitation on
measurements; however, the long-standing mathematical formulation established
by Heisenberg, Kennard, and Robertson does not allow such an interpretation.
Recently, a new relation was found to give a universally valid relation between
noise and disturbance in general quantum measurements, and it has become clear
that the new relation plays a role of the first principle to derive various
quantum limits on measurement and information processing in a unified
treatment. This paper examines the above development on the noise-disturbance
uncertainty principle in the model-independent approach based on the
measurement operator formalism, which is widely accepted to describe a class of
generalized measurements in the field of quantum information. We obtain
explicit formulas for the noise and disturbance of measurements given by the
measurement operators, and show that projective measurements do not satisfy the
Heisenberg-type noise-disturbance relation that is typical in the gamma-ray
microscope thought experiments. We also show that the disturbance on a Pauli
operator of a projective measurement of another Pauli operator constantly
equals the square root of 2, and examine how this measurement violates the
Heisenberg-type relation but satisfies the new noise-disturbance relation.Comment: 11 pages. Based on the author's invited talk at the 9th International
Conference on Squeezed States and Uncertainty Relations (ICSSUR'2005),
Besancon, France, May 2-6, 200
Transferring elements of a density matrix
We study restrictions imposed by quantum mechanics on the process of matrix
elements transfer. This problem is at the core of quantum measurements and
state transfer. Given two systems \A and \B with initial density matrices
and , respectively, we consider interactions that lead to
transferring certain matrix elements of unknown into those of the
final state of \B. We find that this process eliminates the
memory on the transferred (or certain other) matrix elements from the final
state of \A. If one diagonal matrix element is transferred, , the memory on each non-diagonal element
is completely eliminated from the final density operator of
\A. Consider the following three quantities \Re \la_{a\not =b}, \Im
\la_{a\not =b} and \la_{aa}-\la_{bb} (the real and imaginary part of a
non-diagonal element and the corresponding difference between diagonal
elements). Transferring one of them, e.g., \Re\tir_{a\not = b}=\Re\la_{a\not =
b}, erases the memory on two others from the final state of \A.
Generalization of these set-ups to a finite-accuracy transfer brings in a
trade-off between the accuracy and the amount of preserved memory. This
trade-off is expressed via system-independent uncertainty relations which
account for local aspects of the accuracy-disturbance trade-off in quantum
measurements.Comment: 9 pages, 2 table
Designing Dirac points in two-dimensional lattices
We present a framework to elucidate the existence of accidental contacts of
energy bands, particularly those called Dirac points which are the point
contacts with linear energy dispersions in their vicinity. A generalized
von-Neumann-Wigner theorem we propose here gives the number of constraints on
the lattice necessary to have contacts without fine tuning of lattice
parameters. By counting this number, one could quest for the candidate of Dirac
systems without solving the secular equation. The constraints can be provided
by any kinds of symmetry present in the system. The theory also enables the
analytical determination of k-point having accidental contact by selectively
picking up only the degenerate solution of the secular equation. By using these
frameworks, we demonstrate that the Dirac points are feasible in various
two-dimensional lattices, e.g. the anisotropic Kagome lattice under inversion
symmetry is found to have contacts over the whole lattice parameter space.
Spin-dependent cases, such as the spin-density-wave state in LaOFeAs with
reflection symmetry, are also dealt with in the present scheme.Comment: 15pages, 9figures (accepted to Phys. Rev. B
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