19 research outputs found
Dynamical Casimir effect in curved spacetime
A boundary undergoing relativistic motion can create particles from quantum
vacuum fluctuations in a phenomenon known as the dynamical Casimir effect. We
examine the creation of particles, and more generally the transformation of
quantum field states, due to boundary motion in curved spacetime. We provide a
novel method enabling the calculation of the effect for a wide range of
trajectories and spacetimes. We apply this to the experimental scenario used to
detect the dynamical Casimir effect, now adopting the Schwarzschild metric, and
find novel resonances in particle creation as a result of the spacetime
curvature. Finally, we discuss a potential enhancement of the effect for the
phonon field of a Bose-Einstein condensate.Comment: 17 pages, 0 figures, 2 appendice
Universal quantum modifications to general relativistic time dilation in delocalised clocks
The theory of relativity associates a proper time with each moving object via
its world line. In quantum theory however, such well-defined trajectories are
forbidden. After introducing a general characterisation of quantum clocks, we
demonstrate that, in the weak-field, low-velocity limit, all "good" quantum
clocks experience time dilation as dictated by general relativity when their
state of motion is classical (i.e. Gaussian). For nonclassical states of
motion, on the other hand, we find that quantum interference effects may give
rise to a significant discrepancy between the proper time and the time measured
by the clock. The universality of this discrepancy implies that it is not
simply a systematic error, but rather a quantum modification to the proper time
itself. We also show how the clock's delocalisation leads to a larger
uncertainty in the time it measures -- a consequence of the unavoidable
entanglement between the clock time and its center-of-mass degrees of freedom.
We demonstrate how this lost precision can be recovered by performing a
measurement of the clock's state of motion alongside its time reading.Comment: 7 + 10 pages. V3: accepted versio
On the feasibility of detecting quantum delocalization effects on gravitational redshift in optical clocks
We derive the predicted time dilation of delocalized atomic clocks in an
optical lattice setup in the presence of a gravitational field to leading order
in quantum relativistic corrections. We investigate exotic quantum states of
motion whose gravitational time dilation is outside of the realm of classical
general relativity, finding a regime where optical lattice
clocks currently in development would comfortably be able to detect this
quantum effect (if the technical challenge of generating such states can be
met). We provide a detailed experimental protocol and analyse the effects of
noise on our predictions. We also show that the magnitude of our predicted
quantum gravitational time dilation effect remains just out of detectable reach
for the current generation of optical lattice clocks. Our
calculations agree with the predicted time dilation of classical general
relativity when restricting to Gaussian states
Quantum Relativity of Subsystems
One of the most basic notions in physics is the partitioning of a system into
subsystems, and the study of correlations among its parts. In this work, we
explore these notions in the context of quantum reference frame (QRF)
covariance, in which this partitioning is subject to a symmetry constraint. We
demonstrate that different reference frame perspectives induce different sets
of subsystem observable algebras, which leads to a gauge-invariant,
frame-dependent notion of subsystems and entanglement. We further demonstrate
that subalgebras which commute before imposing the symmetry constraint can
translate into non-commuting algebras in a given QRF perspective after symmetry
imposition. Such a QRF perspective does not inherit the distinction between
subsystems in terms of the corresponding tensor factorizability of the
kinematical Hilbert space and observable algebra. Since the condition for this
to occur is contingent on the choice of QRF, the notion of subsystem locality
is frame-dependent.Comment: 8+9 pages, 1 figur
Equivalence of Approaches to Relational Quantum Dynamics in Relativistic Settings
We have previously shown that three approaches to relational quantum dynamics—relational Dirac observables, the Page-Wootters formalism and quantum deparametrizations—are equivalent. Here we show that this “trinity” of relational quantum dynamics holds in relativistic settings per frequency superselection sector. Time according to a clock subsystem is defined via a positive operator-valued measure (POVM) that is covariant with respect to the group generated by its (quadratic) Hamiltonian. This differs from the usual choice of a self-adjoint clock observable conjugate to the clock momentum. It also resolves Kuchař\u27s criticism that the Page-Wootters formalism yields incorrect localization probabilities for the relativistic particle when conditioning on a Minkowski time operator. We show that conditioning instead on the covariant clock POVM results in a Newton-Wigner type localization probability commonly used in relativistic quantum mechanics. By establishing the equivalence mentioned above, we also assign a consistent conditional-probability interpretation to relational observables and deparametrizations. Finally, we expand a recent method of changing temporal reference frames, and show how to transform states and observables frequency-sector-wise. We use this method to discuss an indirect clock self-reference effect and explore the state and temporal frame-dependence of the task of comparing and synchronizing different quantum clocks
Trinity of relational quantum dynamics
The problem of time in quantum gravity calls for a relational solution. Using quantum reduction maps, we establish a previously unknown equivalence between three approaches to relational quantum dynamics: (1) relational observables in the clock-neutral picture of Dirac quantization, (2) Page and Wootters’ (PW) Schrödinger picture formalism, and (3) the relational Heisenberg picture obtained via symmetry reduction. Constituting three faces of the same dynamics, we call this equivalence the trinity. In the process, we develop a quantization procedure for relational Dirac observables using covariant positive operator-valued measures which encompass nonideal clocks and resolve the nonmonotonicity issue of realistic quantum clocks reported by Unruh and Wald. The quantum reduction maps reveal this procedure as the quantum analog of gauge-invariantly extending gauge-fixed quantities. We establish algebraic properties of these relational observables. We extend a recent “clock-neutral” approach to changing temporal reference frames, transforming relational observables and states, and demonstrate a clock dependent temporal nonlocality effect. We show that Kuchař’s criticism, alleging that the conditional probabilities of the PW formalism violate the constraint, is incorrect. They are a quantum analog of a gauge-fixed description of a gauge-invariant quantity and equivalent to the manifestly gauge-invariant evaluation of relational observables in the physical inner product. The trinity furthermore resolves a previously reported normalization ambiguity and clarifies the role of entanglement in the PW formalism. The trinity finally permits us to resolve Kuchař’s criticism that the PW formalism yields wrong propagators by showing how conditional probabilities of relational observables give the correct transition probabilities. Unlike previous proposals, our resolution does not invoke approximations, ideal clocks or ancilla systems, is manifestly gauge invariant, and easily extends to an arbitrary number of conditionings
Landauer vs. Nernst: What is the True Cost of Cooling a Quantum System?
Thermodynamics connects our knowledge of the world to our capability to
manipulate and thus to control it. This crucial role of control is exemplified
by the third law of thermodynamics, Nernst's unattainability principle, stating
that infinite resources are required to cool a system to absolute zero
temperature. But what are these resources and how should they be utilised? And
how does this relate to Landauer's principle that famously connects information
and thermodynamics? We answer these questions by providing a framework for
identifying the resources that enable the creation of pure quantum states. We
show that perfect cooling is possible with Landauer energy cost given infinite
time or control complexity. However, such optimal protocols require complex
unitaries generated by an external work source. Restricting to unitaries that
can be run solely via a heat engine, we derive a novel Carnot-Landauer limit,
along with protocols for its saturation. This generalises Landauer's principle
to a fully thermodynamic setting, leading to a unification with the third law
and emphasising the importance of control in quantum thermodynamics.Comment: 15 pages, 4 figures, 46 pages of appendice
Equivalence of Approaches to Relational Quantum Dynamics in Relativistic Settings
We have previously shown that three approaches to relational quantum dynamics—relational Dirac observables, the Page-Wootters formalism and quantum deparametrizations—are equivalent. Here we show that this “trinity” of relational quantum dynamics holds in relativistic settings per frequency superselection sector. Time according to a clock subsystem is defined via a positive operator-valued measure (POVM) that is covariant with respect to the group generated by its (quadratic) Hamiltonian. This differs from the usual choice of a self-adjoint clock observable conjugate to the clock momentum. It also resolves Kuchař's criticism that the Page-Wootters formalism yields incorrect localization probabilities for the relativistic particle when conditioning on a Minkowski time operator. We show that conditioning instead on the covariant clock POVM results in a Newton-Wigner type localization probability commonly used in relativistic quantum mechanics. By establishing the equivalence mentioned above, we also assign a consistent conditional-probability interpretation to relational observables and deparametrizations. Finally, we expand a recent method of changing temporal reference frames, and show how to transform states and observables frequency-sector-wise. We use this method to discuss an indirect clock self-reference effect and explore the state and temporal frame-dependence of the task of comparing and synchronizing different quantum clocks