81 research outputs found
Quantum Measurements: a modern view for quantum optics experimentalists
In these notes, based on lectures given as part of the Les Houches summer
school on Quantum Optics and Nanophotonics in August, 2013, I have tried to
give a brief survey of some important approaches and modern tendencies in
quantum measurement. I wish it to be clear from the outset that I shy
explicitly away from the "quantum measurement problem," and that the present
treatment aims to elucidate the theory and practice of various ways in which
measurements can, in light of quantum mechanics, be carried out; and various
formalisms for describing them. While the treatment is by necessity largely
theoretical, the emphasis is meant to be on an experimental "perspective" on
measurement -- that is, to place the priority on the possibility of gaining
information through some process, and then attempting to model that process
mathematically and consider its ramifications, rather than stressing a
particular mathematical definition as the {\it sine qua non} of measurement.
The textbook definition of measurement as being a particular set of
mathematical operations carried out on particular sorts of operators has been
so well drilled into us that many have the unfortunate tendency of saying "that
experiment can't be described by projections onto the eigenstates of a
Hermitian operator, so it is not really a measurement," when of course any
practitioner of an experimental science such as physics should instead say
"that experiment allowed us to measure something, and if the standard theory of
measurement does not describe it, the standard theory of measurement is
incomplete." Idealisations are important, but when the real world breaks the
approximations made in the theory, it is the theory which must be fixed, and
not the real world.Comment: Notes based on lectures given at the 101st Les Houches summer school,
on "Quantum Optics and Nanophotonics", August 2013, to be published by Oxford
University Pres
Beating Rayleigh's Curse by Imaging Using Phase Information
Any imaging device such as a microscope or telescope has a resolution limit,
a minimum separation it can resolve between two objects or sources; this limit
is typically defined by "Rayleigh's criterion", although in recent years there
have been a number of high-profile techniques demonstrating that Rayleigh's
limit can be surpassed under particular sets of conditions. Quantum information
and quantum metrology have given us new ways to approach measurement ; a new
proposal inspired by these ideas has now re-examined the problem of trying to
estimate the separation between two poorly resolved point sources. The "Fisher
information" provides the inverse of the Cramer-Rao bound, the lowest variance
achievable for an unbiased estimator. For a given imaging system and a fixed
number of collected photons, Tsang, Nair and Lu observed that the Fisher
information carried by the intensity of the light in the image-plane (the only
information available to traditional techniques, including previous
super-resolution approaches) falls to zero as the separation between the
sources decreases; this is known as "Rayleigh's Curse." On the other hand, when
they calculated the quantum Fisher information of the full electromagnetic
field (including amplitude and phase information), they found it remains
constant. In other words, there is infinitely more information available about
the separation of the sources in the phase of the field than in the intensity
alone. Here we implement a proof-of-principle system which makes use of the
phase information, and demonstrate a greatly improved ability to estimate the
distance between a pair of closely-separated sources, and immunity to
Rayleigh's curse
Multidimensional quantum information based on single-photon temporal wavepackets
We propose a multidimensional quantum information encoding approach based on
temporal modulation of single photons, where the Hilbert space can be spanned
by an in-principle infinite set of orthonormal temporal profiles. We analyze
two specific realizations of such modulation schemes, and show that error rate
per symbol can be smaller than 1% for practical implementations. Temporal
modulation may enable multidimensional quantum communication over the existing
fiber optical infrastructure, as well as provide an avenue for probing
high-dimensional entanglement approaching the continuous limit.Comment: 11 pages, 5 figure
Experimental demonstration of a time-domain multidimensional quantum channel
We present the first experimental realization of a flexible multidimensional
quantum channel where the Hilbert space dimensionality can be controlled
electronically. Using electro-optical modulators (EOM) and narrow-band optical
filters, quantum information is encoded and decoded in the temporal degrees of
freedom of photons from a long-coherence-time single-photon source. Our results
demonstrate the feasibility of a generic scheme for encoding and transmitting
multidimensional quantum information over the existing fiber-optical
telecommunications infrastructure.Comment: 14 pages, 4 figure
Enhanced Probing of Fermion Interaction Using Weak Value Amplification
We propose a scheme for enhanced probing of an interaction between two single
fermions based on weak-value amplification. The scheme is applied to measuring
the anisotropic electron-hole exchange interaction strength in semiconductor
quantum dots, where both spin and energy are mapped onto emitted photons. We
study the effect of dephasing of the probe on the weak-value-enhanced
measurement. We find that in the limit of slow noise, weak-value amplification
provides a unique tool for enhanced-precision measurement of few-fermion
systems
Observation of the Nonlinear Phase Shift Due to Single Post-Selected Photons
Over the past years, there have been many efforts towards generating
interactions between two optical beams so strong that they could be observed at
the level of individual photons. Such strong interactions, beyond opening up a
new regime in optics, could lead to technologies such as all-optical quantum
information processing. However, the extreme weakness of photon-photon
scattering has hindered any attempt to observe such interactions at the level
of single particles. Here we implement a strong optical nonlinearity using
electromagnetically-induced transparency and slow light, and directly measure
the resulting nonlinear phase shift for individual photons. This is done by
illuminating the sample with a weak classical pulse with as few as 0.5 photons
per pulse on average, and using post-selection to determine whether a given
pulse contained (approximately) 0 or 1 photons. We present clear data showing
the quantized dependence of a probe beam's measured phase shift on the
post-selection result, for a range of input pulse intensities. We believe that
this represents the first direct measurement of the cross-phase shift due to
single photons
A Note on Different Definitions of Momentum Disturbance
In [1], Busch et al. showed that it is possible to construct an
error-disturbance relation having the same form as Heisenberg's original
heuristic definition[2], in contrast to the theory proposed by Ozawa[3] which
we and others recently confirmed experimentally[4,5]. With Ozawa's definitions
of measurement error and disturbance, a relation of Heisenberg's form is not in
general valid, and a new error-disturbance relationship can be derived. Here we
explain the different physical significance of the two definitions, and suggest
that Ozawa's definition better corresponds to the usual understanding of the
disturbance that Heisenberg discussed
Transcoherent states: Optical states for maximal generation of atomic coherence
Quantum technologies are built on the power of coherent superposition. Atomic
coherence is typically generated from optical coherence, most often via Rabi
oscillations. However, canonical coherent states of light create imperfect
resources; a fully-quantized description of " pulses" shows
that the atomic superpositions generated remain entangled with the light. We
show that there are quantum states of light that generate coherent atomic
states perfectly, with no residual atom-field entanglement. These states can be
found for arbitrarily short times and approach slightly-number-squeezed
pulses in the limit of large intensities; similar ideal states
can be found for any pulses, requiring more number
squeezing with increasing . Moreover, these states can be repeatedly used as
"quantum catalysts" to successfully generate coherent atomic states with high
probability. From this perspective we have identified states that are "more
coherent" than coherent states.Comment: 11 pages including 5 figures and 2 appendice
Tunneling takes less time when it's less probable
How much time does a tunneling particle spend in a barrier? A Larmor clock,
one proposal to answer this question, measures the interaction between the
particle and the barrier region using an auxiliary degree of freedom of the
particle to clock the dwell time inside the barrier. We report on precise
Larmor time measurements of an ultra-cold gas of Rb atoms tunneling
through an optical barrier. The data capture distinctive features that confirm
longstanding predictions of tunneling times. In particular, we demonstrate that
atoms spend less time tunneling through higher barriers and that this time
decreases for lower energy particles. For the lowest measured incident energy,
at least of transmitted atoms tunneled through the barrier, spending an
average of ms inside. This is ms faster than atoms traversing
the same barrier with energy close to the barrier's peak and ms faster
than when the atoms traverse a barrier with less energy
Interaction-assisted quantum tunneling of a Bose-Einstein condensate out of a single trapping well
We experimentally study tunneling of Bose-condensed Rb atoms prepared
in a quasi-bound state and observe a non-exponential decay caused by
interatomic interactions. A combination of a magnetic quadrupole trap and a
thin barrier created using a blue-detuned sheet of light is
used to tailor traps with controllable depth and tunneling rate. The escape
dynamics strongly depend on the mean-field energy, which gives rise to three
distinct regimes--- classical spilling over the barrier, quantum tunneling, and
decay dominated by background losses. We show that the tunneling rate depends
exponentially on the chemical potential. Our results show good agreement with
numerical solutions of the 3D Gross-Pitaevskii equation
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