[PPT] - Testing quantum mechanics fundamental principles with time PowerPoint Presentation

SLIDE 1

Testing quantum mechanics fundamental principles with time projection chambers

Jean-Marc Sparenberg, David Gaspard, Ruben Ceulemans1

Nuclear Physics and Quantum Physics, ´ Ecole polytechnique de Bruxelles, Universit´ e libre de Bruxelles, Belgium

Workshop on Active Targets and Time Projection Chambers for High-intensity and Heavy-ion beams in Nuclear Physics (ACTAR-TPC’18), GDS-ENSAR2, 17-19 January 2018, Santiago de Compostela, Spain

1Master’s thesis student 2015-2016, KU Leuven Jean-Marc Sparenberg (ULB) Quantum Mechanics Foundations with TPC ACTAR-TPC’18 1 / 13

SLIDE 2

1

The Mott problem. . . revisited for time projection chambers

2

Project: deterministic quantum statistical detector model

3

First results for a one-dimensional detector model

4

Conclusions and open questions

Jean-Marc Sparenberg (ULB) Quantum Mechanics Foundations with TPC ACTAR-TPC’18 2 / 13

SLIDE 3

The Mott problem. . . revisited for time projection chambers

The Mott problem: α particle in a cloud chamber [Mott 1929]

S-wave α emitter in Wilson cloud chamber Spherical highly non local wave function ψ(r) = eikr

r

But linear classical tracks detected, because of

◮ measurement?

(wave function reduction)

◮ or simply decoherence?

4 2 2 4 X 4 2 2 4 Y

[Wilson 1912]

Jean-Marc Sparenberg (ULB) Quantum Mechanics Foundations with TPC ACTAR-TPC’18 3 / 13

SLIDE 4

The Mott problem. . . revisited for time projection chambers

Do you recognize Wilson?

Solvay conference, Brussels 1927

Jean-Marc Sparenberg (ULB) Quantum Mechanics Foundations with TPC ACTAR-TPC’18 4 / 13

SLIDE 5

The Mott problem. . . revisited for time projection chambers

When does decoherence take place in a TPC?

1 Imagine any matter-wave interferometry

(Young-type) experiment in an empty time projection chamber and measure interference pattern

2 Increase pressure continuously. . .

check pattern

3 Switch on voltage. . .

check pattern

4 Switch on electronics readout. . .

check pattern

5 Become aware of tracks. . .

check pattern

electron biprism [Tonomura et al. 1989]

incoming beam segmented plane gas volume range E field

ACTAR TPC principle [CDR 2012]

Jean-Marc Sparenberg (ULB) Quantum Mechanics Foundations with TPC ACTAR-TPC’18 5 / 13

SLIDE 6

The Mott problem. . . revisited for time projection chambers

A similar experiment for (heavy!) molecules

Matter-wave interferences for fullerene molecules [Hornberger,

Zeilinger et al. PRL 2003]

Collisional decoherence due to background gas

◮ fringe visibility

V (p) = V0e−p/p0

◮ decoherence pressure p0 ◮ effective cross section σeff

Gas dependence well understood

Jean-Marc Sparenberg (ULB) Quantum Mechanics Foundations with TPC ACTAR-TPC’18 6 / 13

SLIDE 7

Project: deterministic quantum statistical detector model

1

The Mott problem. . . revisited for time projection chambers

2

Project: deterministic quantum statistical detector model

3

First results for a one-dimensional detector model

4

Conclusions and open questions

Jean-Marc Sparenberg (ULB) Quantum Mechanics Foundations with TPC ACTAR-TPC’18 7 / 13

SLIDE 8

Project: deterministic quantum statistical detector model

Inspired by [Mott 1929]’s original question: why no multiple tracks?

◮ because of state-space structure ◮ in “unaided” wave mechanics

New question: why a particular track?

◮ hypothesis: because of detector

microscopic state [JMS et al. 2013] (fixed atom positions in simplest case)

◮ deterministic statistical mechanics

α-particle source Unexcited atom Hit/excited/ionized atom Directly related to slowing-down (stopping power) through

◮ (in)elastic scattering ◮ ionization

First revisited as a 1D model with contact interactions

[Carlone et al. 2015]

Jean-Marc Sparenberg (ULB) Quantum Mechanics Foundations with TPC ACTAR-TPC’18 8 / 13

SLIDE 9

First results for a one-dimensional detector model

1

The Mott problem. . . revisited for time projection chambers

2

Project: deterministic quantum statistical detector model

3

First results for a one-dimensional detector model

4

Conclusions and open questions

Jean-Marc Sparenberg (ULB) Quantum Mechanics Foundations with TPC ACTAR-TPC’18 9 / 13

SLIDE 10

First results for a one-dimensional detector model

Why no multiple track? [Carlone et al. 2015, JMS & DG arXiv 2016]

Spin model Hamiltonian for two-level atoms at fixed positions xn H = − 2 2m∂2

x free particle

+

N

n=1

εn

atoms

+

N

n=1

βn γn γn βn

δ(x − xn)
contact coupling

,

◮ ε, β, γ to be related to realistic physical values ◮ state-space structure: 2N-dimensional spinor Ψ

One particle with 2 symmetric atoms: no left and right excitation

|Ψs(x, t)|2 x x x x source State space |Ψs(x, t)|2 x x x x source State space no multiple excitation

Jean-Marc Sparenberg (ULB) Quantum Mechanics Foundations with TPC ACTAR-TPC’18 10 / 13

SLIDE 11

First results for a one-dimensional detector model

Why a particular track (no-coupling case)?

x

incoming x1 R0 T1 x2 R1 T2 x3 R2 T3

. . .

xN RN TN+1

Single-sided detector, N atoms Stationary transmission probability P, energy E = k2 Band-like perfect transmission when equally-spaced mesh Anderson localisation (reflection) when random positions ⇒ detected trajectories determined by perfect-transmission conditions?

3 6 9 1

k P N = 1 N = 2 N = 3 N = 6

ǫ = γ = 0, β = 2, xn = n

5 10 15 20 25 30 1

k P

N = 1 N = 3 periodic N = 3 aperiodic

ǫ = γ = 0, β = 10, xn = n [Ceulemans, Master thesis 2016]

Jean-Marc Sparenberg (ULB) Quantum Mechanics Foundations with TPC ACTAR-TPC’18 11 / 13

SLIDE 12

First results for a one-dimensional detector model

Why a particular track (coupled case)?

R3 T 3

1

R3

1

T 3

2

11

R2 T 2

1

R2

1

T 2

2

10

R1 T 1

1

R1

1

T 1

2

01

incoming x1 R0 T 0

1

x2 R0

1

T 0

2

00 x

No perfect transmission anymore (already with two atoms!) ⇒ phase-space localisation Adds up to Anderson localisation (analysis in progress)

2 4 6 8 10 12 14 16 18 20 0.2 0.4 0.6 0.8 1

k P

i |Ri

0|2

i |T i

2|2

ǫ = β = 0, γ = 5, N = 2, x2 − x1 = 10/3 ǫ = 0, β = 10, γ = 100, N = 10, xn = n [Ceulemans, Master thesis 2016]

Jean-Marc Sparenberg (ULB) Quantum Mechanics Foundations with TPC ACTAR-TPC’18 12 / 13

SLIDE 13

Conclusions and open questions

New research project: deterministic quantum statistical model for quantum particle in gaseous environment

◮ new approach to decoherence, localisation and measurement problems ◮ best tested with matter-wave interferometry

(new experiment welcome!)

Promising one-dimensional preliminary model

◮ Anderson localisation ◮ phase-space localisation ◮ short-term project: realistic ordrers of magnitudes

⇒ new corrections to Bethe formula in Bragg peak? (experimental data welcome!)

Longer-term projects

◮ 3D model: reduced Anderson localisation but enhanced phase-space

localisation?

◮ interest for atmospheric cloud formation [CLOUD@CERN]? Jean-Marc Sparenberg (ULB) Quantum Mechanics Foundations with TPC ACTAR-TPC’18 13 / 13

SLIDE 14

Conclusions and open questions Jean-Marc Sparenberg (ULB) Quantum Mechanics Foundations with TPC ACTAR-TPC’18 14 / 13

SLIDE 15

Conclusions and open questions

References

1 ACTAR TPC: Conceptual Design Report, D28, GANIL internal report

(2012)

2 R. Carlone, R. Figari and C. Negulescu, Comm. Comput. Phys. 18

(2015) 247

3 CLOUD experiment, Cosmic Leaving OUtdoor Droplets, CERN,

http://cloud.web.cern.ch

4 K. Hornberger et al., Phys. Rev. Lett. 90 (2003) 160401 5 N. F. Mott, Proc. Roy. Soc. A126 (1929) 79 6 J.-M. Sparenberg and D. Gaspard, arXiv:1609.03217 [quant-ph] 7 J.-M. Sparenberg, R. Nour and A. Man¸

co, EPJ web of conferences 58 (2013) 01016

8 A. Tonomura et al., Am. J. Phys. 57 (1989) 117 9 C. T. R. Wilson, Proc. Roy. Soc. 87 (1912) 292 Jean-Marc Sparenberg (ULB) Quantum Mechanics Foundations with TPC ACTAR-TPC’18 15 / 13