17,074 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
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
Thermal correlators of anyons in two dimensions
The anyon fields have trivial -commutator for not integer.
For integer the commutators become temperature-dependent operator
valued distributions. The -point functions do not factorize as for quasifree
states.Comment: 14 pages, LaTeX (misprints corrected, a reference added
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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