65 research outputs found
Lectures on dynamical models for quantum measurements
In textbooks, ideal quantum measurements are described in terms of the tested
system only by the collapse postulate and Born's rule. This level of
description offers a rather flexible position for the interpretation of quantum
mechanics. Here we analyse an ideal measurement as a process of interaction
between the tested system S and an apparatus A, so as to derive the properties
postulated in textbooks. We thus consider within standard quantum mechanics the
measurement of a quantum spin component by an apparatus A, being a
magnet coupled to a bath. We first consider the evolution of the density
operator of S+A describing a large set of runs of the measurement process. The
approach describes the disappearance of the off-diagonal terms ("truncation")
of the density matrix as a physical effect due to A, while the registration of
the outcome has classical features due to the large size of the pointer
variable, the magnetisation. A quantum ambiguity implies that the density
matrix at the final time can be decomposed on many bases, not only the one of
the measurement. This quantum oddity prevents to connect individual outcomes to
measurements, a difficulty known as the "measurement problem". It is shown that
it is circumvented by the apparatus as well, since the evolution in a small
time interval erases all decompositions, except the one on the measurement
basis. Once one can derive the outcome of individual events from quantum
theory, the so-called "collapse of the wave function" or the "reduction of the
state" appears as the result of a selection of runs among the original large
set. Hence nothing more than standard quantum mechanics is needed to explain
features of measurements. The employed statistical formulation is advocated for
the teaching of quantum theory.Comment: 43 pages, 5 figures. Lectures given in the "Advanced School on
Quantum Foundations and Open Quantum Systems", Joao Pessoa, Brazil, summer
2012. To appear in the proceedings and in IJMP
Multimode Fock states with large photon number: effective descriptions and applications in quantum metrology
We develop general tools to characterise and efficiently compute relevant
observables of multimode -photon states generated in non-linear decays in
one-dimensional waveguides. We then consider optical interferometry in a
Mach-Zender interferometer where a -mode photonic state enters in each arm
of the interferometer. We derive a simple expression for the Quantum Fisher
Information in terms of the average photon number in each mode, and show that
it can be saturated by number-resolved photon measurements that do not
distinguish between the different modes.Comment: 18 pages, 11 figures. V2: Minor change
Work and entropy production in generalised Gibbs ensembles
Recent years have seen an enormously revived interest in the study of
thermodynamic notions in the quantum regime. This applies both to the study of
notions of work extraction in thermal machines in the quantum regime, as well
as to questions of equilibration and thermalisation of interacting quantum
many-body systems as such. In this work we bring together these two lines of
research by studying work extraction in a closed system that undergoes a
sequence of quenches and equilibration steps concomitant with free evolutions.
In this way, we incorporate an important insight from the study of the dynamics
of quantum many body systems: the evolution of closed systems is expected to be
well described, for relevant observables and most times, by a suitable
equilibrium state. We will consider three kinds of equilibration, namely to (i)
the time averaged state, (ii) the Gibbs ensemble and (iii) the generalised
Gibbs ensemble (GGE), reflecting further constants of motion in integrable
models. For each effective description, we investigate notions of entropy
production, the validity of the minimal work principle and properties of
optimal work extraction protocols. While we keep the discussion general, much
room is dedicated to the discussion of paradigmatic non-interacting fermionic
quantum many-body systems, for which we identify significant differences with
respect to the role of the minimal work principle. Our work not only has
implications for experiments with cold atoms, but also can be viewed as
suggesting a mindset for quantum thermodynamics where the role of the external
heat baths is instead played by the system itself, with its internal degrees of
freedom bringing coarse-grained observables to equilibrium.Comment: 22 pages, 4 figures, improvements in presentatio
Strong coupling corrections in quantum thermodynamics
Quantum systems strongly coupled to many-body systems equilibrate to the
reduced state of a global thermal state, deviating from the local thermal state
of the system as it occurs in the weak-coupling limit. Taking this insight as a
starting point, we study the thermodynamics of systems strongly coupled to
thermal baths. First, we provide strong-coupling corrections to the second law
applicable to general systems in three of its different readings: As a
statement of maximal extractable work, on heat dissipation, and bound to the
Carnot efficiency. These corrections become relevant for small quantum systems
and always vanish in first order in the interaction strength. We then move to
the question of power of heat engines, obtaining a bound on the power
enhancement due to strong coupling. Our results are exemplified on the
paradigmatic situation of non-Markovian quantum Brownian motion.Comment: 20 pages, 3 figures, version two is substantially revised and
contains new result
Work Fluctuations in Slow Processes: Quantum Signatures and Optimal Control
This is the final version. Available from American Physical Society via the DOI in this recordAn important result in classical stochastic thermodynamics is the work fluctuation-dissipation relation (FDR), which states that the dissipated work done along a slow process is proportional to the resulting work fluctuations. We show that slowly driven quantum systems violate this FDR whenever quantum coherence is generated along the protocol, and we derive a quantum generalization of the work FDR. The additional quantum terms in the FDR are found to lead to a non-Gaussian work distribution. Fundamentally, our result shows that quantum fluctuations prohibit finding slow protocols that minimize both dissipation and fluctuations simultaneously, in contrast to classical slow processes. Instead, we develop a quantum geometric framework to find processes with an optimal trade-off between the two quantities.Engineering and Physical Sciences Research Council (EPSRC)National Science FoundationRoyal Societ
Collective operations can extremely reduce work fluctuations
We consider work extraction from copies of a quantum system. When the
same work-extraction process is implemented on each copy, the relative size of
fluctuations is expected to decay as . Here, we consider protocols
where the copies can be processed collectively, and show that in this case work
fluctuations can disappear exponentially fast in . As a consequence, a
considerable proportion of the average extractable work can be
obtained almost deterministically by globally processing a few copies of the
state. This is derived in the two canonical scenarios for work extraction: (i)
in thermally isolated systems, where corresponds to the energy
difference between initial and passive states, known as the ergotropy, and (ii)
in the presence of a thermal bath, where is given by the free
energy difference between initial and thermal states.Comment: 15 pages; 4 figures. v3: Minor change
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