Decoherence of the radiation from an accelerated quantum source - - PowerPoint PPT Presentation

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Decoherence of the radiation from an accelerated quantum source T.C.Ralph School of Maths & Physics University of Queensland Mathematical Motivation Radiation from accelerated objects has been studied for a long time, but... ... mostly

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Decoherence of the radiation from an accelerated quantum source

T.C.Ralph School of Maths & Physics University of Queensland

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Mathematical Motivation Radiation from accelerated

bjects has been studied for a

long time, but... ... mostly solutions are: numerical; perturbative; and suffer from infra-red and ultra- violet divergences.

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Mathematical Motivation

Problems arise from the detector model and non-unitary interactions

tegrat , |0i.

U

Start in vacuum Single–mode unitary

D

Matched displacement Broadband detector Solve for expectation values in the Heisenberg Picture

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Mathematical Motivation

Problems arise from the detector model and non-unitary interactions

tegrat , |0i.

U

Start in vacuum Single–mode unitary

D

Matched displacement Broadband detector Solve for expectation values in the Heisenberg Picture

Inertial frame Inertial frame accelerated frame

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Mathematical Motivation

For example: accelerated mirror

tegrat , |0i.

M D

Solve for expectation values in the Heisenberg Picture

Inertial frame Inertial frame accelerated frame

1 + 8(1 − cos θ)IcIs V =

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Physical Motivation

tegrat , |0i.

U

Start in vacuum Single–mode unitary

D

Matched displacement Broadband detector Solve for expectation values in the Heisenberg Picture

Pure state in, Unitary interaction, Pure state out!

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Physical Motivation

tegrat , |0i.

U

Start in vacuum Single–mode unitary

D

Matched displacement Broadband detector Solve for expectation values in the Heisenberg Picture

Inertial frame Inertial frame accelerated frame

Pure state in, Unitary interaction, Pure state out...?

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“Decoherence of the radiation from an accelerated quantum source” Daiqin Su, T.C.Ralph, arXiv:1705.07432 “Quantum circuit model for non-inertial objects: a uniformly accelerated mirror ” Daiqin Su, C. T. Marco Ho, Robert Mann, Timothy C. Ralph New Journal of Physics 19, 063017 (2017)

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Overview * An accelerating quantum source * Calculating the quantum statistics * Decoherence

squeezed source

* Relationship to Black-Hole information paradox?

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Overview * An accelerating quantum source

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Overview * Calculating the quantum statistics

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Radiation from accelerated objects

Particle radiated by the accelerated

bject, detected

by inertial

bservers

Standard method: perturbation theory Feynman diagrams, renormalisation, etc.

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Minkowski modes and Rindler modes

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Rindler modes

Minkowski modes and Rindler modes

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Unruh modes

Rindler modes Unruh modes

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Relations between three sets of modes

Minkowski operators Unruh operators Rindler operators

left-moving and right-moving modes two mode squeezer

Unruh modes share the same vacuum with Minkowski modes

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Unruh modes

Rindler modes Unruh modes

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Quantum circuit model: accelerated mirror

Daiqin Su, et al, New Journal of Physics 19, 063017 (2017)

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Quantum circuit model: accelerated time independent interaction

Daiqin Su, et al, New Journal of Physics 19, 063017 (2017)

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Circuit for time dependent interactions

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Penrose diagram of the problem

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Self-Homodyne detection

Inertial detector

e ˆ N = R dk ˆ a†

kˆ

ak.

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Self-Homodyne detection

Inertial detector

e ˆ N = R dk ˆ a†

kˆ

ak.

Many two-level atoms

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Self-Homodyne detection

Inertial detector

e ˆ N = R dk ˆ a†

kˆ

ak.

Inhomogeneously broadened Many two-level atoms

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Self-Homodyne detection

Inertial detector

e ˆ N = R dk ˆ a†

kˆ

ak.

Inhomogeneously broadened Many two-level atoms

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Self-Homodyne detection

Inertial detector

e ˆ N = R dk ˆ a†

kˆ

ak.

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Accelerated displacement

Displacement

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Accelerated displacement

Displacement Unruh modes

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Accelerated displacement

Displacement Unruh modes Minkowski modes Displacement amplitude Coherent state as observed by inertial observers

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Overview II * Decoherence

squeezed source

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Accelerated single-mode squeezer

Single-mode squeezer

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Accelerated single-mode squeezer

Single-mode squeezer

Maximum & minimum variance

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Accelerated single-mode squeezer

Red circle:

vacuum noise

Blue ellipse

variance

f
utput

state

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Accelerated single-mode squeezer

non-unitary

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Accelerated single-mode squeezer

non-unitary two sets of Unruh modes

ne set of

Minkowski modes

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Accelerated single-mode squeezer

non-unitary two sets of Unruh modes

ne set of

Minkowski modes

interference information lost

photon detector

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Overview II * Relationship to Black-Hole information paradox?

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Black hole information paradox

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Black hole information paradox

A pure initial state A mixed final state

black hole formation black hole evaporation

Unitary evolution is violated in the presence of gravity?

S. Hawking , Phys. Rev. D 14, 2460(1976)

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acknowledgeme ments

Marco Ho Daiqin Su Daiqin Su, et al, New Journal of Physics 19, 063017 (2017) Daiqin Su, T.C.Ralph, arXiv:1705.07432 Rob Mann

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Decoherence of Entanglement

Entanglement No Entanglement EN r 2πω0/a

˜ ν− = e−2r + 4Ic(Ic − 1)(e−r − 1)2.

EN = max[0, − log2(˜ ν−)],

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Localised wave packet modes

5 3

Localised wave packet modes

Localised unitary operator

Transformation of single frequency modes

mixing of different frequency modes

finite bandwidth localised in time

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