20,251 research outputs found
Stochastic dynamics of a Josephson junction threshold detector
We generalize the stochastic path integral formalism by considering
Hamiltonian dynamics in the presence of general Markovian noise. Kramers'
solution of the activation rate for escape over a barrier is generalized for
non-Gaussian driving noise in both the overdamped and underdamped limit. We
apply our general results to a Josephson junction detector measuring the
electron counting statistics of a mesoscopic conductor. Activation rate
dependence on the third current cumulant includes an additional term
originating from the back-action of the measurement circuit.Comment: 5 pages, 2 figures, discussion of experiment added, typos correcte
Stochastic path integral formalism for continuous quantum measurement
We generalize and extend the stochastic path integral formalism and action
principle for continuous quantum measurement introduced in [A. Chantasri, J.
Dressel and A. N. Jordan, Phys. Rev. A {\bf 88}, 042110 (2013)], where the
optimal dynamics, such as the most-likely paths, are obtained by extremizing
the action of the path integral. In this work, we apply exact functional
methods as well as develop a perturbative approach to investigate the
statistical behaviour of continuous quantum measurement, with examples given
for the qubit case. For qubit measurement with zero qubit Hamiltonian, we find
analytic solutions for average trajectories and their variances while
conditioning on fixed initial and final states. For qubit measurement with
unitary evolution, we use the perturbation method to compute expectation
values, variances, and multi-time correlation functions of qubit trajectories
in the short-time regime. Moreover, we consider continuous qubit measurement
with feedback control, using the action principle to investigate the global
dynamics of its most-likely paths, and finding that in an ideal case, qubit
state stabilization at any desired pure state is possible with linear feedback.
We also illustrate the power of the functional method by computing correlation
functions for the qubit trajectories with a feedback loop to stabilize the
qubit Rabi frequency.Comment: 24 pages, 4 figures and 1 tabl
Sufficient conditions for uniqueness of the weak value
We review and clarify the sufficient conditions for uniquely defining the
generalized weak value as the weak limit of a conditioned average using the
contextual values formalism introduced in Dressel J, Agarwal S and Jordan A N
2010 Phys. Rev. Lett. 104, 240401. We also respond to criticism of our work in
[arXiv:1105.4188v1] concerning a proposed counter-example to the uniqueness of
the definition of the generalized weak value. The counter-example does not
satisfy our prescription in the case of an underspecified measurement context.
We show that when the contextual values formalism is properly applied to this
example, a natural interpretation of the measurement emerges and the unique
definition in the weak limit holds. We also prove a theorem regarding the
uniqueness of the definition under our sufficient conditions for the general
case. Finally, a second proposed counter-example in [arXiv:1105.4188v6] is
shown not to satisfy the sufficiency conditions for the provided theorem.Comment: 17 pages, final published respons
Entanglement Energetics at Zero Temperature
We show how many-body ground state entanglement information may be extracted
from sub-system energy measurements at zero temperature. Generically, the
larger the measured energy fluctuations are, the larger the entanglement is.
Examples are given with the two-state system and the harmonic oscillator.
Comparisons made with recent qubit experiments show this type of measurement
provides another method to quantify entanglement with the environment.Comment: 4 pages, 2 figure
Preferential duplication graphs
We consider a preferential duplication model for growing random graphs, extending previous models of duplication graphs by selecting the vertex to be duplicated with probability proportional to its degree. We show that a special case of this model can be analysed using the same stochastic approximation as for vertex-reinforced random walks, and show that 'trapping' behaviour can occur, such that the descendants of a particular group of initial vertices come to dominate the graph
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