The Cosmological Signature of Covariant Bandlimitation
Aidan Chatwin-Davies, University of Waterloo and Macquarie University
In quantum gravity, it is widely expected that the classical notion of distance should break down on small enough scales, or in other words, that a semiclassical effective theory of quantum matter and curved spacetime should possess a natural ultraviolet (UV) cutoff. A further challenge consists of reconciling such a cutoff with Lorentz invariance. This reconciliation is achieved by a proposed information-theoretic cutoff on eld degrees of freedom which consists of a covariant generalization of bandlimitation in Shannon sampling theory. Here we analyse the impact of this covariant UV cutoff on the inflationary fluctuation spectrum of a scalar eld in de Sitter space. Accordingly, we discuss the covariant cutoff 's observational signature in the Cosmic Microwave Background in light of our analysis.
Locality and entanglement in bandlimited quantum field theory
Jason Pye, University of Waterloo
We consider a model for a Planck scale ultraviolet cutoff which is
based on Shannon sampling. Shannon sampling originated in information theory, where it expresses the equivalence of continuous and discrete
representations of information. When applied to quantum eld theory,
Shannon sampling expresses a hard ultraviolet cutoff in the form of a
bandlimitation. This introduces nonlocality at the cutoff scale in a way
that is more subtle than a simple discretization of space: quantum fields
can then be represented as either living on continuous space or, entirely
equivalently, as living on any one lattice whose average spacing is sufficiently small. We explicitly calculate vacuum entanglement entropies in 1+1 dimensions and we nd a transition between logarithmic and linear
scaling of the entropy, which is the expected 1+1 dimensional analog of
the transition from an area to a volume law. We also use entanglement
entropy and mutual information as measures to probe in detail the
localizability of the eld degrees of freedom. We nd that, even though
neither translation nor rotation invariance are broken, each eld degree
of freedom occupies an incompressible volume of space, indicating a finite
information density.
Using quantum energy teleportation to create exotic spacetimes
Nicholas Funai, Perimeter Institute for Theoretical Physics
In general relativity the energy conditions [1] are imposed to disallow spacetime geometries that violate singularity theorems, and to ban 'exotic' solutions to Einstein equations such as closed timelike curves or warp drives. These conditions do not seem far-fetched in classical theory since matter fields reasonably obey these conditions from rst principles. However quantum fields are known to locally violate these conditions, e.g.
through phenomena such as the Casimir effect or in squeezed states.
In 2008 Masahiro Hotta proposed a protocol for transporting energy between two localized observers A and B through a eld without any energy propagating through the eld from A to B [2, 3, 4, 5, 6, 7]. When this
protocol is applied to a vacuum state of a eld the local energy density in the eld achieves negative values, violating the weak energy condition.
We use quantum energy teleportation as a means to create states of a relativistic scalar eld that have local negative energy densities. Namely, we use a slightly modified version of this protocol [8] (Local operations
on the eld and quantum communication) as an ansatz for operationally creating quantum eld states whose energy density violates energy conditions and resembles exotic spacetimes such as the Alcubierre metric.
In particular, we manipulate the eld locally through Unruh-Dewitt particle detectors. We nd that in 1+1 dimensional Minkowski spacetime the energy density distribution obeys a simple relation with the position
smearing functions of the particle detectors. By controlling the detectors smearing, we are able to control the negative energy density distribution in the eld. For higher dimensional systems where gravity is not trivial,
we nd that the energy density is dependent on the ne details of the coupling of the detectors and the eld, which, in principle, could yield more control of the `on demand' violations of the energy conditions. This
protocol shows promise in being a simple procedure to generate custom negative energy distributions.
This work was done in collaboration with Eduardo Martin-Martinez.
References
[1] Erik Curiel. A Primer on Energy Conditions. 2014. URL http://arxiv.org/abs/1405.0403.
[2] Masahiro Hotta. Quantum measurement information as a key to energy extraction from local vacuums. Phys. Rev. D, 78:045006, Aug 2008. doi: 10.1103/PhysRevD.78.045006. URL http://link.aps.org/doi/10.1103/PhysRevD.78.045006.
[3] Masahiro Hotta. Quantum Energy Teleportation with Electromagnetic Field: Discrete vs. Continuous Variables. 2009. URL http://arxiv.org/abs/0908.2674v2.
[4] Masahiro Hotta. A Brief Introduction to Quantum Energy Teleportation. 2010. URL http://arxiv.org/abs/1008.0188v1.
[5] Masahiro Hotta. Controlled hawking process by quantum energy teleportation. Phys. Rev. D, 81:044025, Feb 2010. doi: 10.1103/PhysRevD.81.044025. URL http://link.aps.org/doi/10.1103/PhysRevD.81.044025.
[6] Masahiro Hotta. Quantum Energy Teleportation: An Introductory Review. 2011. URL http://arxiv.org/abs/1101.3954v1.
[7] Masahiro Hotta, Jiro Matsumoto, and Go Yusa. Quantum Energy Teleportation without Limit of Distance. 2013. URL http://arxiv.org/abs/1305.3955v2.
[8] Guillaume Verdon-Akzam, Eduardo Martn-Martnez, and Achim Kempf. Asymptotically Limitless Quantum Energy Teleportation via Qudit Probes. 2015. URL http://arxiv.org/abs/1510.03751.
On thermalization timescales, KMS detailed balance and AntiUnruh phenomena
José de Ramón Rivera, Universidad Complutense de Madrid
According to the Unruh effect, an accelerated detector “heats up” as it accelerates. However, it has recently been found that its response can be actually suppressed by its accelerationwhen interacting with a field vacuum only for finite times (this is known as Anti-Unruh phenomenon [1]). This was particularly surprising in the light of the fact that the detector’s finite-time response seemed to satisfy a simplified KMS-like
condition [2], in particular that the ratio of the detector excitation and deexcitation rate follows an exponential law with thedetector’s gap.
We will show that this is a manifestation of a more general phenomenon where a cold atomic probe interacting with a quantum field in a hotter thermal state can be cooled down as the temperature of the field increases when the interaction times are comparable to the probe’s
Heisenberg time. We demonstrate that the “Anti-Unruh effect” reported in [1] will always appear for sufficiently short interaction times.
We will further analyze these Anti-Unruh phenomena from the perspective of the detailed-balance condition [2,3,4] and thermalization timescales. Namely, we will show that below the atomic Heisenberg time, the KMS-like condition as stated above does not imply detailed balance. We will show that the complete detailed balance condition can be expressed as the usual KMS-like condition stated above plus finite time corrections. We will
finally discuss the validity of KMS temperature estimators for finite timescales, and in particular for timescales comparable and below the Heisenberg time of the detector.
Work in collaboration with: Luis J. Garay and Eduardo MartínMartínez
[1] W. Brenna, R. B. Mann, E. MartínMartínez, ArXiv:1504.02468. Phys. Lett. B (in press)
[2] S. Takagi, Progr. Theoret. Phys. Suppl. 88, 1 (1986)
[3] R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957).
[4] P. C. Martin and J. Schwinger, Phys. Rev. 115, 1342 (1959)
Asymptotically Limitless Quantum Energy Teleportation
Guillaume Verdon-Akzam, Institute for Quantum Computing, University of Waterloo
We propose a modified quantum energy teleportation scheme that uses arbitrary-dimensional qudit probes and polynomially localized Hamiltonians. We find that with an appropriate scaling of parameters, the teleported energy scales with the teleportation distance more favorably than the nonlocal tails of the Hamiltonians. We show that by allowing the exchange of arbitrary amounts of information between agents and in a suitable limit, an arbitrarily large amount of energy can be teleported through a massless quantum field initialized in vacuum. Finally, we generalize this protocol to other Gaussian initial states for the field and discuss implications for black hole thermodynamics.
Accelerating in a Thermal Bath
Eric G. Brown, ICFO - Institute of Photonic Sciences
In this talk I will present some preliminary calculations examining the response of an observer uniformly accelerating in a Minkowski thermal bath, rather than in the vacuum state. One of the primary questions of interest in such a scenario is whether an observer is able to distinguish the two sources of thermal noise; that coming from the bath and that coming from the Unruh response. Aside from theoretical interest, such a question is potentially very important for experimental attempts at detecting the Unruh effect. The answer found is that, indeed, the two responses are distinguishable, contrary to previous claims. In addition we find, interestingly, that accelerating may act to amplify the thermal fluctuations of the field in addition to the usual Unruh effect. We will briefly discuss consequences of this finding and look at future directions.
Entanglement of quantum clocks through gravity
Esteban Castro-Ruiz, University of Vienna
Esteban Castro-Ruiz,1, 2 Flaminia Giacomini,1, 2 and Caslav Brukner1, 2
1 Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria
2 Institute of Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria
In general relativity, the picture of spacetime assigns an ideal clock to each worldline. Being ideal, gravitational effects due to these clocks are ignored and the flow of time according to one clock is not affected by the presence of clocks along nearby worldlines. However, if time is defined operationally, as a pointer position of a physical clock that obeys the principles of general relativity and quantum mechanics, such a picture is at most a convenient fiction. Specifically, we show that the general relativistic mass-energy equivalence implies gravitational interaction between the clocks, while the quantum mechanical superposition of energy eigenstates leads to a non-fixed metric background. Based only on the assumption that both principles hold in this situation, we show that the clocks necessarily get entangled through time dilation effect, which eventually leads to a loss of coherence of a single clock. Hence, the time as measured by a single clock is not well-defined. However, the general relativistic notion of time is recovered in the classical limit of clocks.
On decoherence under gravity: a perspective from the Equivalence Principle
Belinda Pang, California Institute of Technology
In Nature Phys. 11, 668 (2015) (Ref. [1]), a composite particle prepared in a pure initial quantum state and propagated in a uniform gravitational field is shown to undergo a decoherence process at a rate determined by the gravitational acceleration. By assuming Einstein's Equivalence Principle to be valid, we demonstrate, first in a Lorentz frame with accelerating detectors, and then directly in the Lab frame with uniform gravity, that the dephasing between the different internal states arise not from gravity but rather from differences in their rest mass, and the mass dependence of the de Broglie wave's dispersion relation. We provide an alternative view to the situation considered by Ref. [1], where we propose that gravity plays a kinematic role in the loss of fringe visibility by giving the detector a transverse velocity relative to the particle beam; visibility can be easily recovered by giving the screen an appropriate uniform velocity. We finally propose that dephasing due to gravity may in fact take place for certain modifications to the gravitational potential where the Equivalence Principle is violated.
Unruh effect as a two-mode Gaussian channel
Krzysztof Lorek, University of Warsaw
We describe the Unruh effect using the formalism of Gaussian channels and apply it to the Minkowski vacuum state. We show in detail how the vacuum state transforms, when measured with a pair of localized observables that are relativistically accelerated. In particular we analytically determine all the elements of the covariance matrix of the resulting output of the channel. Our calculations involve the two accelerations and their directions, as well as the spatial separation between the observers, as independent parameters.
Effects of acceleration on fermionic Gaussian states
Benedikt Richter, LMU Munich and IST Lisbon
We study the effects of acceleration on fermionic Gaussian states of localized modes. We consider two wave-packets in a Gaussian state and transform these to an accelerated frame of reference. In particular, we formulate the action of this transformation as a fermionic quantum channel. Thereby, the acceleration, as well as the mutual separation of the two observers, can take arbitrary values. Having developed the general framework for the fermionic case, we study the entanglement of the vacuum. We then investigate the entanglement in even Bell states. Finally, we compare our findings to the bosonic case that was investigated recently.
Joint work with Yasser Omar and Andrzej Dragan.
Spatial entanglement of nonvacuum Gaussian states
Filip Kiałka, University of Warsaw
Filip Kiałka*, Mehdi Ahmadi, and Andrzej Dragan
Institute of Theoretical Physics, Faculty of Physics,
University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
The vacuum state of a relativistic quantum field contains entanglement between regions separated by spacelike intervals. Such spatial entanglement can be revealed using an operational method introduced in Ann. Phys. 351, 112 (2014) and Phys. Rev. D 91, 016005 (2015). In this approach, a cavity is instantaneously divided into halves by introduction of an extra perfect mirror. Causal separation of the two regions of the cavity reveals nonlocal spatial correlations present in the field, which can be quantified by measuring particles generated in the process. We use this method to study spatial entanglement properties of nonvacuum Gaussian field states. In particular we show how to enhance the amount of harvested spatial entanglement by an appropriate choice of the initial state of the field in the cavity. We find a counterintuitive influence of the initial entanglement between cavity modes on spatial entanglement which is revealed by dividing the cavity in half.
* fk322204@okwf.fuw.edu.pl