39 research outputs found
Nonlinearity in Single Photon Detection: Modeling and Quantum Tomography
Single Photon Detectors are integral to quantum optics and quantum
information. Superconducting Nanowire based detectors exhibit new levels of
performance, but have no accepted quantum optical model that is valid for
multiple input photons. By performing Detector Tomography, we improve the
recently proposed model [M.K. Akhlaghi and A.H. Majedi, IEEE Trans. Appl.
Supercond. 19, 361 (2009)] and also investigate the manner in which these
detectors respond nonlinearly to light, a valuable feature for some
applications. We develop a device independent model for Single Photon Detectors
that incorporates this nonlinearity
The phase sensitivity of a fully quantum three-mode nonlinear interferometer
We study a nonlinear interferometer consisting of two consecutive parametric
amplifiers, where all three optical fields (pump, signal and idler) are treated
quantum mechanically, allowing for pump depletion and other quantum phenomena.
The interaction of all three fields in the final amplifier leads to an
interference pattern from which we extract the phase uncertainty. We find that
the phase uncertainty oscillates around a saturation level that decreases as
the mean number of input pump photons increases. For optimal interaction
strengths, we also find a phase uncertainty below the shot-noise level and
obtain a Heisenberg scaling . This is in contrast to the conventional
treatment within the parametric approximation, where the Heisenberg scaling is
observed as a function of the number of down-converted photons inside the
interferometer.Comment: 8 pages, 7 figure
Quantum metrology timing limits of the Hong-Ou-Mandel interferometer and of general two-photon measurements
We examine the precision limits of Hong-Ou-Mandel (HOM) timing measurements,
as well as precision limits applying to generalized two-photon measurements. As
a special case, we consider the use of two-photon measurements using photons
with variable bandwidths and frequency correlations. When the photon bandwidths
are not equal, maximizing the measurement precision involves a trade-off
between high interference visibility and strong frequency anticorrelations,
with the optimal precision occuring when the photons share non-maximal
frequency anticorrelations. We show that a generalized measurement has
precision limits that are qualitatively similar to those of the HOM measurement
whenever the generalized measurement is insensitive to the net delay of both
photons. By examining the performance of states with more general frequency
distributions, our analysis allows for engineering of the joint spectral
amplitude for use in realistic situations, in which both photons may not have
ideal spectral properties.Comment: 12 pages, 6 figures; resubmissio
Direct measurement of general quantum states using weak measurement
Recent work [J.S. Lundeen et al. Nature, 474, 188 (2011)] directly measured
the wavefunction by weakly measuring a variable followed by a normal (i.e.
`strong') measurement of the complementary variable. We generalize this method
to mixed states by considering the weak measurement of various products of
these observables, thereby providing the density matrix an operational
definition in terms of a procedure for its direct measurement. The method only
requires measurements in two bases and can be performed `in situ', determining
the quantum state without destroying it.Comment: This is a later and very different version of arXiv:1110.0727v3
[quant-ph]. New content: a method to directly measure each element of the
density matrix, specific Hamiltonians to weakly measure the product of
non-commuting observables, and references to recent related wor
Direct Measurement of the Quantum Wavefunction
Central to quantum theory, the wavefunction is the complex distribution used
to completely describe a quantum system. Despite its fundamental role, it is
typically introduced as an abstract element of the theory with no explicit
definition. Rather, physicists come to a working understanding of the
wavefunction through its use to calculate measurement outcome probabilities via
the Born Rule. Presently, scientists determine the wavefunction through
tomographic methods, which estimate the wavefunction that is most consistent
with a diverse collection of measurements. The indirectness of these methods
compounds the problem of defining the wavefunction. Here we show that the
wavefunction can be measured directly by the sequential measurement of two
complementary variables of the system. The crux of our method is that the first
measurement is performed in a gentle way (i.e. weak measurement) so as not to
invalidate the second. The result is that the real and imaginary components of
the wavefunction appear directly on our measurement apparatus. We give an
experimental example by directly measuring the transverse spatial wavefunction
of a single photon, a task not previously realized by any method. We show that
the concept is universal, being applicable both to other degrees of freedom of
the photon (e.g. polarization, frequency, etc.) and to other quantum systems
(e.g. electron spin-z quantum state, SQUIDs, trapped ions, etc.). Consequently,
this method gives the wavefunction a straightforward and general definition in
terms of a specific set of experimental operations. We expect it to expand the
range of quantum systems scientists are able to characterize and initiate new
avenues to understand fundamental quantum theory