Testing quantum mechanics fundamental principles with time projection chambers Ruben Ceulemans 1 Jean-Marc Sparenberg, David Gaspard, 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 1 Master’s thesis student 2015-2016, KU Leuven Jean-Marc Sparenberg (ULB) Quantum Mechanics Foundations with TPC ACTAR-TPC’18 1 / 13
The Mott problem. . . revisited for time projection chambers 1 Project: deterministic quantum statistical detector model 2 First results for a one-dimensional detector model 3 Conclusions and open questions 4 Jean-Marc Sparenberg (ULB) Quantum Mechanics Foundations with TPC ACTAR-TPC’18 2 / 13
The Mott problem. . . revisited for time projection chambers The Mott problem: α particle in a cloud chamber [Mott 1929] 4 2 S -wave α emitter in Wilson 0 Y cloud chamber 2 Spherical highly non local wave function ψ ( r ) = e ikr 4 r 4 2 0 2 4 X But linear classical tracks detected, because of ◮ measurement? (wave function reduction) ◮ or simply decoherence? [Wilson 1912] Jean-Marc Sparenberg (ULB) Quantum Mechanics Foundations with TPC ACTAR-TPC’18 3 / 13
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
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 electron biprism 3 Switch on voltage. . . [Tonomura et al. 1989] check pattern gas volume 4 Switch on electronics readout. . . E field check pattern incoming range beam 5 Become aware of tracks. . . segmented plane check pattern ACTAR TPC principle [CDR 2012] Jean-Marc Sparenberg (ULB) Quantum Mechanics Foundations with TPC ACTAR-TPC’18 5 / 13
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 ) = V 0 e − p/p 0 ◮ decoherence pressure p 0 ◮ effective cross section σ eff Gas dependence well understood Jean-Marc Sparenberg (ULB) Quantum Mechanics Foundations with TPC ACTAR-TPC’18 6 / 13
Project: deterministic quantum statistical detector model The Mott problem. . . revisited for time projection chambers 1 Project: deterministic quantum statistical detector model 2 First results for a one-dimensional detector model 3 Conclusions and open questions 4 Jean-Marc Sparenberg (ULB) Quantum Mechanics Foundations with TPC ACTAR-TPC’18 7 / 13
Project: deterministic quantum statistical detector model 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 α -particle source microscopic state [JMS et al. 2013] Unexcited atom (fixed atom positions in simplest case) Hit/excited/ionized atom ◮ deterministic statistical mechanics 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
First results for a one-dimensional detector model The Mott problem. . . revisited for time projection chambers 1 Project: deterministic quantum statistical detector model 2 First results for a one-dimensional detector model 3 Conclusions and open questions 4 Jean-Marc Sparenberg (ULB) Quantum Mechanics Foundations with TPC ACTAR-TPC’18 9 / 13
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 x n � ε n � β n N N � � H = − � 2 0 γ n � � 2 m∂ 2 + + δ ( x − x n ) , x 0 0 γ n β n n =1 n =1 � �� � � �� � � �� � free particle atoms contact coupling ◮ ε , β , γ to be related to realistic physical values ◮ state-space structure: 2 N -dimensional spinor Ψ One particle with 2 symmetric atoms: no left and right excitation | Ψ s ( x, t ) | 2 | Ψ s ( x, t ) | 2 no multiple excitation x x State space State space x x x x x x source source Jean-Marc Sparenberg (ULB) Quantum Mechanics Foundations with TPC ACTAR-TPC’18 10 / 13
First results for a one-dimensional detector model Why a particular track (no-coupling case)? incoming 1 . . . R 0 T 1 R 1 T 2 R 2 T 3 R N T N +1 x 1 x 2 x 3 x N x P Single-sided detector, N atoms N = 1 N = 2 N = 3 Stationary transmission N = 6 0 3 6 9 probability P , energy E = k 2 k ǫ = γ = 0 , β = 2 , x n = n Band-like perfect transmission 1 when equally-spaced mesh Anderson localisation P (reflection) when random positions N = 1 N = 3 periodic N = 3 aperiodic 0 5 10 15 20 25 30 ⇒ detected trajectories determined k ǫ = γ = 0 , β = 10 , � x n � = n by perfect-transmission conditions? [Ceulemans, Master thesis 2016] Jean-Marc Sparenberg (ULB) Quantum Mechanics Foundations with TPC ACTAR-TPC’18 11 / 13
First results for a one-dimensional detector model Why a particular track (coupled case)? R 3 T 3 R 3 T 3 11 0 1 1 2 1 � i | R i 0 | 2 � i | T i 2 | 2 0 . 8 0 . 6 R 2 T 2 R 2 T 2 10 0 1 1 2 P 0 . 4 0 . 2 R 1 T 1 R 1 T 1 01 0 1 1 2 0 0 2 4 6 8 10 12 14 16 18 20 k incoming ǫ = β = 0 , γ = 5 , N = 2 , x 2 − x 1 = 10 / 3 R 0 T 0 R 0 T 0 00 0 1 1 2 x x 1 x 2 No perfect transmission anymore (already with two atoms!) ⇒ phase-space localisation Adds up to Anderson localisation ǫ = 0 , β = 10 , γ = 100 , N = 10 , � x n � = n (analysis in progress) [Ceulemans, Master thesis 2016] Jean-Marc Sparenberg (ULB) Quantum Mechanics Foundations with TPC ACTAR-TPC’18 12 / 13
Conclusions and open questions 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
Conclusions and open questions Jean-Marc Sparenberg (ULB) Quantum Mechanics Foundations with TPC ACTAR-TPC’18 14 / 13
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
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