1,233 research outputs found
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
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
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
Weak values are universal in von Neumann measurements
We refute the widely held belief that the quantum weak value necessarily
pertains to weak measurements. To accomplish this, we use the transverse
position of a beam as the detector for the conditioned von Neumann measurement
of a system observable. For any coupling strength, any initial states, and any
choice of conditioning, the averages of the detector position and momentum are
completely described by the real parts of three generalized weak values in the
joint Hilbert space. Higher-order detector moments also have similar weak value
expansions. Using the Wigner distribution of the initial detector state, we
find compact expressions for these weak values within the reduced system
Hilbert space. As an application of the approach, we show that for any
Hermite-Gauss mode of a paraxial beam-like detector these expressions reduce to
the real and imaginary parts of a single system weak value plus an additional
weak-value-like contribution that only affects the momentum shift.Comment: 7 pages, 3 figures, includes Supplementary Materia
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