2,725 research outputs found
All-optical versus electro-optical quantum-limited feedback
All-optical feedback can be effected by putting the output of a source cavity
through a Faraday isolator and into a second cavity which is coupled to the
source cavity by a nonlinear crystal. If the driven cavity is heavily damped,
then it can be adiabatically eliminated and a master equation or quantum
Langevin equation derived for the first cavity alone. This is done for an input
bath in an arbitrary state, and for an arbitrary nonlinear coupling. If the
intercavity coupling involves only the intensity (or one quadrature) of the
driven cavity, then the effect on the source cavity is identical to that which
can be obtained from electro-optical feedback using direct (or homodyne)
detection. If the coupling involves both quadratures, this equivalence no
longer holds, and a coupling linear in the source amplitude can produce a
nonclassical state in the source cavity. The analogous electro-optic scheme
using heterodyne detection introduces extra noise which prevents the production
of nonclassical light. Unlike the electro-optic case, the all-optical feedback
loop has an output beam (reflected from the second cavity). We show that this
may be squeezed, even if the source cavity remains in a classical state.Comment: 21 pages. This is an old (1994) paper, but one which I thought was
worth posting because in addition to what is described in abstract it has:
(1) the first formulation (to my knowledge) of quantum trajectories for an
arbitrary (i.e. squeezed, thermal etc.) broadband bath; (2) the prediction of
a periodic modification to the detuning and damping of an oscillator for the
simplest sort of all-optical feedback (i.e. a mirror) as seen in the recent
experiment "Forces between a Single Atom and Its Distant Mirror Image", P.
Bushev et al, Phys. Rev. Lett. 92, 223602 (2004
Weak Values, Quantum Trajectories, and the Stony-Brook Cavity QED experiment
Weak values as introduced by Aharonov, Albert and Vaidman (AAV) are ensemble
average values for the results of weak measurements. They are interesting when
the ensemble is preselected on a particular initial state and postselected on a
particular final measurement result. I show that weak values arise naturally in
quantum optics, as weak measurements occur whenever an open system is monitored
(as by a photodetector). I use quantum trajectory theory to derive a
generalization of AAV's formula to include (a) mixed initial conditions, (b)
nonunitary evolution, (c) a generalized (non-projective) final measurement, and
(d) a non-back-action-evading weak measurement. I apply this theory to the
recent Stony-Brook cavity QED experiment demonstrating wave-particle duality
[G.T. Foster, L.A. Orozco, H.M. Castro-Beltran, and H.J. Carmichael, Phys. Rev.
Lett. {85}, 3149 (2000)]. I show that the ``fractional'' correlation function
measured in that experiment can be recast as a weak value in a form as simple
as that introduced by AAV.Comment: 6 pages, no figures. To be published in Phys. Rev.
Feedback Control of Quantum Transport
The current through nanostructures like quantum dots can be stabilized by a
feedback loop that continuously adjusts system parameters as a function of the
number of tunnelled particles . At large times, the feedback loop freezes
the fluctuations of which leads to highly accurate, continuous single
particle transfers. For the simplest case of feedback acting simultaneously on
all system parameters, we show how to reconstruct the original full counting
statistics from the frozen distribution.Comment: 4 pages, 2 figure
Adaptive single-shot phase measurements: The full quantum theory
The phase of a single-mode field can be measured in a single-shot measurement
by interfering the field with an effectively classical local oscillator of
known phase. The standard technique is to have the local oscillator detuned
from the system (heterodyne detection) so that it is sometimes in phase and
sometimes in quadrature with the system over the course of the measurement.
This enables both quadratures of the system to be measured, from which the
phase can be estimated. One of us [H.M. Wiseman, Phys. Rev. Lett. 75, 4587
(1995)] has shown recently that it is possible to make a much better estimate
of the phase by using an adaptive technique in which a resonant local
oscillator has its phase adjusted by a feedback loop during the single-shot
measurement. In Ref.~[H.M. Wiseman and R.B. Killip, Phys. Rev. A 56, 944] we
presented a semiclassical analysis of a particular adaptive scheme, which
yielded asymptotic results for the phase variance of strong fields. In this
paper we present an exact quantum mechanical treatment. This is necessary for
calculating the phase variance for fields with small photon numbers, and also
for considering figures of merit other than the phase variance. Our results
show that an adaptive scheme is always superior to heterodyne detection as far
as the variance is concerned. However the tails of the probability distribution
are surprisingly high for this adaptive measurement, so that it does not always
result in a smaller probability of error in phase-based optical communication.Comment: 17 pages, LaTeX, 8 figures (concatenated), Submitted to Phys. Rev.
Entanglement-enhanced measurement of a completely unknown phase
The high-precision interferometric measurement of an unknown phase is the
basis for metrology in many areas of science and technology. Quantum
entanglement provides an increase in sensitivity, but present techniques have
only surpassed the limits of classical interferometry for the measurement of
small variations about a known phase. Here we introduce a technique that
combines entangled states with an adaptive algorithm to precisely estimate a
completely unspecified phase, obtaining more information per photon that is
possible classically. We use the technique to make the first ab initio
entanglement-enhanced optical phase measurement. This approach will enable
rapid, precise determination of unknown phase shifts using interferometry.Comment: 6 pages, 4 figure
In-loop squeezing is real squeezing to an in-loop atom
Electro-optical feedback can produce an in-loop photocurrent with arbitrarily
low noise. This is not regarded as evidence of `real' squeezing because
squeezed light cannot be extracted from the loop using a linear beam splitter.
Here I show that illuminating an atom (which is a nonlinear optical element)
with `in-loop' squeezed light causes line-narrowing of one quadrature of the
atom's fluorescence. This has long been regarded as an effect which can only be
produced by squeezing. Experiments on atoms using in-loop squeezing should be
much easier than those with conventional sources of squeezed light.Comment: 4 pages, 2 figures, submitted to PR
Using weak values to experimentally determine "negative probabilities" in a two-photon state with Bell correlations
Bipartite quantum entangled systems can exhibit measurement correlations that
violate Bell inequalities, revealing the profoundly counter-intuitive nature of
the physical universe. These correlations reflect the impossibility of
constructing a joint probability distribution for all values of all the
different properties observed in Bell inequality tests. Physically, the
impossibility of measuring such a distribution experimentally, as a set of
relative frequencies, is due to the quantum back-action of projective
measurements. Weakly coupling to a quantum probe, however, produces minimal
back-action, and so enables a weak measurement of the projector of one
observable, followed by a projective measurement of a non-commuting observable.
By this technique it is possible to empirically measure weak-valued
probabilities for all of the values of the observables relevant to a Bell test.
The marginals of this joint distribution, which we experimentally determine,
reproduces all of the observable quantum statistics including a violation of
the Bell inequality, which we independently measure. This is possible because
our distribution, like the weak values for projectors on which it is built, is
not constrained to the interval [0, 1]. It was first pointed out by Feynman
that, for explaining singlet-state correlations within "a [local] hidden
variable view of nature ... everything works fine if we permit negative
probabilities". However, there are infinitely many such theories. Our method,
involving "weak-valued probabilities", singles out a unique set of
probabilities, and moreover does so empirically.Comment: 9 pages, 3 figure
Measuring Which-Path Information with Coupled Electronic Mach-Zehnder Interferometers
We theoretically investigate a generalized "which-path" measurement on an
electronic Mach-Zehnder Interferometer (MZI) implemented via Coulomb coupling
to a second electronic MZI acting as a detector. The use of contextual values,
or generalized eigenvalues, enables the precise construction of which-path
operator averages that are valid for any measurement strength from the
available drain currents. The form of the contextual values provides direct
physical insight about the measurement being performed, providing information
about the correlation strength between system and detector, the measurement
inefficiency, and the proper background removal. We find that the detector
interferometer must display maximal wave-like behavior to optimally measure the
particle-like which-path information in the system interferometer,
demonstrating wave-particle complementarity between the system and detector. We
also find that the degree of quantum erasure that can be achieved by
conditioning on a specific detector drain is directly related to the ambiguity
of the measurement. Finally, conditioning the which-path averages on a
particular system drain using the zero frequency cross-correlations produces
conditioned averages that can become anomalously large due to quantum
interference; the weak coupling limit of these conditioned averages can produce
both weak values and detector-dependent semi-weak values.Comment: 17 pages, 12 figures, published version including appendi
The simplest demonstrations of quantum nonlocality
We investigate the complexity cost of demonstrating the key types of nonclassical correlations-Bell inequality violation, Einstein, Podolsky, Rosen (EPR)-steering, and entanglement-with independent agents, theoretically and in a photonic experiment. We show that the complexity cost exhibits a hierarchy among these three tasks, mirroring the recently discovered hierarchy for how robust they are to noise. For Bell inequality violations, the simplest test is the well-known Clauser-Horne-Shimony-Holt test, but for EPR-steering and entanglement the tests that involve the fewest number of detection patterns require nonprojective measurements. The simplest EPR-steering test requires a choice of projective measurement for one agent and a single nonprojective measurement for the other, while the simplest entanglement test uses just a single nonprojective measurement for each agent. In both of these cases, we derive our inequalities using the concept of circular two-designs. This leads to the interesting feature that in our photonic demonstrations, the correlation of interest is independent of the angle between the linear polarizers used by the two parties, which thus require no alignment
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