1Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching, Germany
2Nordita, Stockholm University and KTH Royal Institute of Technology, Hannes Alfvéns väg 12, SE-106 91 Stockholm, Sweden
3Institute for Theoretical Studies, ETH Zurich, 8092 Zurich, Switzerland
Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.
Abstract
The interaction between localized emitters and quantum fields, both in relativistic settings and in the case of ultra-strong couplings, requires non-perturbative methods beyond the rotating-wave approximation. In this work we employ chain-mapping methods to achieve a numerically exact treatment of the interaction between a localized emitter and a scalar quantum field. We extend the application range of these methods beyond emitter observables and apply them to study field observables. We first provide an overview of chain-mapping methods and their physical interpretation, and discuss the thermal double construction for systems coupled to thermal field states. Modelling the emitter as an Unruh-DeWitt particle detector, we then calculate the energy density emitted by a detector coupling strongly to the field. As a stimulating demonstration of the approach’s potential, we calculate the radiation emitted from an accelerated detector in the Unruh effect, which is closely related to the thermal double construction as we discuss. We comment on prospects and challenges of the method.
Featured image: Schematic overview of star-to-chain transformations
[embedded content]
Popular summary
The paper studies this type of theoretical model and explores computational methods to study the interactions between localized emitters and quantum fields, especially in relativistic and ultra-strong coupling scenarios. Utilizing so-called chain-mapping techniques, a numerically exact treatment of the problem is achieved. The paper advances computational techniques for light-matter interactions by extending these methods to both emitter and field observables. As an intriguing demonstration, the radiation emitted by an accelerated particle detector in the Unruh effect is calculated.
In the numerical findings, the errors introduced by numerical implementations of the chain-mapping can be carefully monitored. This contributes to a rich numerical toolbox for studying strong-coupling regimes in relativistic quantum information and quantum optics.
► BibTeX data
► References
[1] Heinz-Peter Breuer and F. Petruccione. “The theory of open quantum systems”. Oxford University Press. Oxford ; New York (2002).
https://doi.org/10.1093/acprof:oso/9780199213900.001.0001
[2] Heinz-Peter Breuer, Elsi-Mari Laine, Jyrki Piilo, and Bassano Vacchini. “Colloquium : Non-Markovian dynamics in open quantum systems”. Reviews of Modern Physics 88, 021002 (2016).
https://doi.org/10.1103/RevModPhys.88.021002
[3] Hendrik Weimer, Augustine Kshetrimayum, and Román Orús. “Simulation methods for open quantum many-body systems”. Reviews of Modern Physics 93, 015008 (2021).
https://doi.org/10.1103/RevModPhys.93.015008
[4] Martin V. Gustafsson, Thomas Aref, Anton Frisk Kockum, Maria K. Ekström, Göran Johansson, and Per Delsing. “Propagating phonons coupled to an artificial atom”. Science 346, 207–211 (2014).
https://doi.org/10.1126/science.1257219
[5] Gustav Andersson, Baladitya Suri, Lingzhen Guo, Thomas Aref, and Per Delsing. “Non-exponential decay of a giant artificial atom”. Nature Physics 15, 1123–1127 (2019).
https://doi.org/10.1038/s41567-019-0605-6
[6] A. González-Tudela, C. Sánchez Muñoz, and J. I. Cirac. “Engineering and Harnessing Giant Atoms in High-Dimensional Baths: A Proposal for Implementation with Cold Atoms”. Physical Review Letters 122, 203603 (2019).
https://doi.org/10.1103/PhysRevLett.122.203603
[7] Inés de Vega, Diego Porras, and J. Ignacio Cirac. “Matter-Wave Emission in Optical Lattices: Single Particle and Collective Effects”. Physical Review Letters 101, 260404 (2008).
https://doi.org/10.1103/PhysRevLett.101.260404
[8] S. Gröblacher, A. Trubarov, N. Prigge, G. D. Cole, M. Aspelmeyer, and J. Eisert. “Observation of non-Markovian micromechanical Brownian motion”. Nature Communications 6, 7606 (2015).
https://doi.org/10.1038/ncomms8606
[9] Javier del Pino, Florian A. Y. N. Schröder, Alex W. Chin, Johannes Feist, and Francisco J. Garcia-Vidal. “Tensor Network Simulation of Non-Markovian Dynamics in Organic Polaritons”. Physical Review Letters 121, 227401 (2018).
https://doi.org/10.1103/PhysRevLett.121.227401
[10] S.F. Huelga and M.B. Plenio. “Vibrations, quanta and biology”. Contemporary Physics 54, 181–207 (2013).
https://doi.org/10.1080/00405000.2013.829687
[11] Hong-Bin Chen, Neill Lambert, Yuan-Chung Cheng, Yueh-Nan Chen, and Franco Nori. “Using non-Markovian measures to evaluate quantum master equations for photosynthesis”. Scientific Reports 5, 12753 (2015).
https://doi.org/10.1038/srep12753
[12] Felix A. Pollock, César Rodríguez-Rosario, Thomas Frauenheim, Mauro Paternostro, and Kavan Modi. “Non-Markovian quantum processes: Complete framework and efficient characterization”. Physical Review A 97, 012127 (2018).
https://doi.org/10.1103/PhysRevA.97.012127
[13] Richard Lopp and Eduardo Martín-Martínez. “Quantum delocalization, gauge, and quantum optics: Light-matter interaction in relativistic quantum information”. Physical Review A 103, 013703 (2021).
https://doi.org/10.1103/PhysRevA.103.013703
[14] Barbara Šoda, Vivishek Sudhir, and Achim Kempf. “Acceleration-Induced Effects in Stimulated Light-Matter Interactions”. Physical Review Letters 128, 163603 (2022).
https://doi.org/10.1103/PhysRevLett.128.163603
[15] Sadao Nakajima. “On Quantum Theory of Transport Phenomena: Steady Diffusion”. Progress of Theoretical Physics 20, 948–959 (1958).
https://doi.org/10.1143/PTP.20.948
[16] Robert Zwanzig. “Ensemble Method in the Theory of Irreversibility”. The Journal of Chemical Physics 33, 1338–1341 (1960).
https://doi.org/10.1063/1.1731409
[17] Yoshitaka Tanimura and Ryogo Kubo. “Time Evolution of a Quantum System in Contact with a Nearly Gaussian-Markoffian Noise Bath”. Journal of the Physical Society of Japan 58, 101–114 (1989).
https://doi.org/10.1143/JPSJ.58.101
[18] Yoshitaka Tanimura. “Numerically “exact” approach to open quantum dynamics: The hierarchical equations of motion (HEOM)”. The Journal of Chemical Physics 153, 020901 (2020).
https://doi.org/10.1063/5.0011599
[19] Javier Prior, Alex W. Chin, Susana F. Huelga, and Martin B. Plenio. “Efficient Simulation of Strong System-Environment Interactions”. Physical Review Letters 105, 050404 (2010).
https://doi.org/10.1103/PhysRevLett.105.050404
[20] Alex W. Chin, Ángel Rivas, Susana F. Huelga, and Martin B. Plenio. “Exact mapping between system-reservoir quantum models and semi-infinite discrete chains using orthogonal polynomials”. Journal of Mathematical Physics 51, 092109 (2010).
https://doi.org/10.1063/1.3490188
[21] R.P Feynman and F.L Vernon. “The theory of a general quantum system interacting with a linear dissipative system”. Annals of Physics 24, 118–173 (1963).
https://doi.org/10.1016/0003-4916(63)90068-X
[22] Kenneth G. Wilson. “The renormalization group: Critical phenomena and the Kondo problem”. Reviews of Modern Physics 47, 773–840 (1975).
https://doi.org/10.1103/RevModPhys.47.773
[23] Matthias Vojta, Ning-Hua Tong, and Ralf Bulla. “Quantum Phase Transitions in the Sub-Ohmic Spin-Boson Model: Failure of the Quantum-Classical Mapping”. Physical Review Letters 94, 070604 (2005).
https://doi.org/10.1103/PhysRevLett.94.070604
[24] Ralf Bulla, Hyun-Jung Lee, Ning-Hua Tong, and Matthias Vojta. “Numerical renormalization group for quantum impurities in a bosonic bath”. Physical Review B 71, 045122 (2005).
https://doi.org/10.1103/PhysRevB.71.045122
[25] Ralf Bulla, Theo A. Costi, and Thomas Pruschke. “Numerical renormalization group method for quantum impurity systems”. Reviews of Modern Physics 80, 395–450 (2008).
https://doi.org/10.1103/RevModPhys.80.395
[26] Ahsan Nazir and Gernot Schaller. “The Reaction Coordinate Mapping in Quantum Thermodynamics”. In Felix Binder, Luis A. Correa, Christian Gogolin, Janet Anders, and Gerardo Adesso, editors, Thermodynamics in the Quantum Regime: Fundamental Aspects and New Directions. Pages 551–577. Fundamental Theories of Physics. Springer International Publishing, Cham (2018).
[27] Ricardo Puebla, Giorgio Zicari, Iñigo Arrazola, Enrique Solano, Mauro Paternostro, and Jorge Casanova. “Spin-Boson Model as A Simulator of Non-Markovian Multiphoton Jaynes-Cummings Models”. Symmetry 11, 695 (2019).
https://doi.org/10.3390/sym11050695
[28] Philipp Strasberg, Gernot Schaller, Neill Lambert, and Tobias Brandes. “Nonequilibrium thermodynamics in the strong coupling and non-Markovian regime based on a reaction coordinate mapping”. New Journal of Physics 18, 073007 (2016).
https://doi.org/10.1088/1367-2630/18/7/073007
[29] Guifré Vidal. “Efficient Simulation of One-Dimensional Quantum Many-Body Systems”. Physical Review Letters 93, 040502 (2004).
https://doi.org/10.1103/PhysRevLett.93.040502
[30] J. Ignacio Cirac, David Pérez-García, Norbert Schuch, and Frank Verstraete. “Matrix product states and projected entangled pair states: Concepts, symmetries, theorems”. Reviews of Modern Physics 93, 045003 (2021).
https://doi.org/10.1103/RevModPhys.93.045003
[31] M. P. Woods, M. Cramer, and M. B. Plenio. “Simulating Bosonic Baths with Error Bars”. Physical Review Letters 115, 130401 (2015).
https://doi.org/10.1103/PhysRevLett.115.130401
[32] M. P. Woods and M. B. Plenio. “Dynamical error bounds for continuum discretisation via Gauss quadrature rules—A Lieb-Robinson bound approach”. Journal of Mathematical Physics 57, 022105 (2016).
https://doi.org/10.1063/1.4940436
[33] F. Mascherpa, A. Smirne, S. F. Huelga, and M. B. Plenio. “Open Systems with Error Bounds: Spin-Boson Model with Spectral Density Variations”. Physical Review Letters 118, 100401 (2017).
https://doi.org/10.1103/PhysRevLett.118.100401
[34] Inés de Vega, Ulrich Schollwöck, and F. Alexander Wolf. “How to discretize a quantum bath for real-time evolution”. Physical Review B 92, 155126 (2015).
https://doi.org/10.1103/PhysRevB.92.155126
[35] Rahul Trivedi, Daniel Malz, and J. Ignacio Cirac. “Convergence Guarantees for Discrete Mode Approximations to Non-Markovian Quantum Baths”. Physical Review Letters 127, 250404 (2021).
https://doi.org/10.1103/PhysRevLett.127.250404
[36] Carlos Sánchez Muñoz, Franco Nori, and Simone De Liberato. “Resolution of superluminal signalling in non-perturbative cavity quantum electrodynamics”. Nature Communications 9, 1924 (2018).
https://doi.org/10.1038/s41467-018-04339-w
[37] Neill Lambert, Shahnawaz Ahmed, Mauro Cirio, and Franco Nori. “Modelling the ultra-strongly coupled spin-boson model with unphysical modes”. Nature Communications 10, 1–9 (2019).
https://doi.org/10.1038/s41467-019-11656-1
[38] David D. Noachtar, Johannes Knörzer, and Robert H. Jonsson. “Nonperturbative treatment of giant atoms using chain transformations”. Physical Review A 106, 013702 (2022).
https://doi.org/10.1103/PhysRevA.106.013702
[39] C. A. Büsser, G. B. Martins, and A. E. Feiguin. “Lanczos transformation for quantum impurity problems in d -dimensional lattices: Application to graphene nanoribbons”. Physical Review B 88, 245113 (2013).
https://doi.org/10.1103/PhysRevB.88.245113
[40] Andrew Allerdt, C. A. Büsser, G. B. Martins, and A. E. Feiguin. “Kondo versus indirect exchange: Role of lattice and actual range of RKKY interactions in real materials”. Physical Review B 91, 085101 (2015).
https://doi.org/10.1103/PhysRevB.91.085101
[41] Andrew Allerdt and Adrian E. Feiguin. “A Numerically Exact Approach to Quantum Impurity Problems in Realistic Lattice Geometries”. Frontiers in Physics 7, 67 (2019).
https://doi.org/10.3389/fphy.2019.00067
[42] V. Bargmann. “On a Hilbert space of analytic functions and an associated integral transform part I”. Communications on Pure and Applied Mathematics 14, 187–214 (1961).
https://doi.org/10.1002/cpa.3160140303
[43] H. Araki and E. J. Woods. “Representations of the Canonical Commutation Relations Describing a Nonrelativistic Infinite Free Bose Gas”. Journal of Mathematical Physics 4, 637–662 (1963).
https://doi.org/10.1063/1.1704002
[44] Yasushi Takahashi and Hiroomi Umezawa. “THERMO FIELD DYNAMICS”. International Journal of Modern Physics B 10, 1755–1805 (1996).
https://doi.org/10.1142/S0217979296000817
[45] Inés de Vega and Mari-Carmen Bañuls. “Thermofield-based chain-mapping approach for open quantum systems”. Physical Review A 92, 052116 (2015).
https://doi.org/10.1103/PhysRevA.92.052116
[46] Dario Tamascelli, Andrea Smirne, James Lim, Susana F. Huelga, and Martin B. Plenio. “Efficient simulation of finite-temperature open quantum systems”. Physical Review Letters 123, 090402 (2019). arxiv:1811.12418.
https://doi.org/10.1103/PhysRevLett.123.090402
arXiv:1811.12418
[47] Gabriel T. Landi, Dario Poletti, and Gernot Schaller. “Nonequilibrium boundary-driven quantum systems: Models, methods, and properties”. Reviews of Modern Physics 94, 045006 (2022).
https://doi.org/10.1103/RevModPhys.94.045006
[48] Chu Guo, Ines de Vega, Ulrich Schollwöck, and Dario Poletti. “Stable-unstable transition for a Bose-Hubbard chain coupled to an environment”. Physical Review A 97, 053610 (2018).
https://doi.org/10.1103/PhysRevA.97.053610
[49] F. Schwarz, I. Weymann, J. von Delft, and A. Weichselbaum. “Nonequilibrium Steady-State Transport in Quantum Impurity Models: A Thermofield and Quantum Quench Approach Using Matrix Product States”. Physical Review Letters 121, 137702 (2018).
https://doi.org/10.1103/PhysRevLett.121.137702
[50] Tianqi Chen, Vinitha Balachandran, Chu Guo, and Dario Poletti. “Steady-state quantum transport through an anharmonic oscillator strongly coupled to two heat reservoirs”. Physical Review E 102, 012155 (2020).
https://doi.org/10.1103/PhysRevE.102.012155
[51] Angus J. Dunnett and Alex W. Chin. “Matrix Product State Simulations of Non-Equilibrium Steady States and Transient Heat Flows in the Two-Bath Spin-Boson Model at Finite Temperatures”. Entropy 23, 77 (2021).
https://doi.org/10.3390/e23010077
[52] Thibaut Lacroix, Angus Dunnett, Dominic Gribben, Brendon W. Lovett, and Alex Chin. “Unveiling non-Markovian spacetime signaling in open quantum systems with long-range tensor network dynamics”. Physical Review A 104, 052204 (2021).
https://doi.org/10.1103/PhysRevA.104.052204
[53] Angela Riva, Dario Tamascelli, Angus J. Dunnett, and Alex W. Chin. “Thermal cycle and polaron formation in structured bosonic environments”. Physical Review B 108, 195138 (2023).
https://doi.org/10.1103/PhysRevB.108.195138
[54] W. G. Unruh. “Notes on black-hole evaporation”. Physical Review D 14, 870–892 (1976).
https://doi.org/10.1103/PhysRevD.14.870
[55] B. S. DeWitt. “Quantum gravity: The new synthesis”. In Stephen Hawking and W. Israel, editors, General Relativity : An Einstein Centenary Survey. Page 680. Cambridge University Press, Cambridge Eng; New York (1979).
[56] B. L. Hu, Shih-Yuin Lin, and Jorma Louko. “Relativistic quantum information in detectors–field interactions”. Classical and Quantum Gravity 29, 224005 (2012).
https://doi.org/10.1088/0264-9381/29/22/224005
[57] Luís C. B. Crispino, Atsushi Higuchi, and George E. A. Matsas. “The Unruh effect and its applications”. Reviews of Modern Physics 80, 787–838 (2008).
https://doi.org/10.1103/RevModPhys.80.787
[58] R. B. Mann and T. C. Ralph. “Relativistic quantum information”. Classical and Quantum Gravity 29, 220301 (2012).
https://doi.org/10.1088/0264-9381/29/22/220301
[59] Shih-Yuin Lin and B. L. Hu. “Accelerated detector-quantum field correlations: From vacuum fluctuations to radiation flux”. Physical Review D 73, 124018 (2006).
https://doi.org/10.1103/PhysRevD.73.124018
[60] D. J. Raine, D. W. Sciama, and P. G. Grove. “Does a Uniformly Accelerated Quantum Oscillator Radiate?”. Proceedings: Mathematical and Physical Sciences 435, 205–215 (1991).
[61] F. Hinterleitner. “Inertial and Accelerated Particle Detectors with Back-Reaction in Flat Space-Time”. Annals of Physics 226, 165–204 (1993).
https://doi.org/10.1006/aphy.1993.1066
[62] S. Massar, R. Parentani, and R. Brout. “On the problem of the uniformly accelerated oscillator”. Classical and Quantum Gravity 10, 385 (1993).
https://doi.org/10.1088/0264-9381/10/2/020
[63] S. Massar and R. Parentani. “From vacuum fluctuations to radiation. I. Accelerated detectors”. Physical Review D 54, 7426–7443 (1996).
https://doi.org/10.1103/PhysRevD.54.7426
[64] Jürgen Audretsch and Rainer Müller. “Radiation from a uniformly accelerated particle detector: Energy, particles, and the quantum measurement process”. Physical Review D 49, 6566–6575 (1994).
https://doi.org/10.1103/PhysRevD.49.6566
[65] Hyeong-Chan Kim and Jae Kwan Kim. “Radiation from a uniformly accelerated harmonic oscillator”. Physical Review D 56, 3537–3547 (1997).
https://doi.org/10.1103/PhysRevD.56.3537
[66] Hyeong-Chan Kim. “Quantum field and uniformly accelerated oscillator”. Physical Review D 59, 064024 (1999).
https://doi.org/10.1103/PhysRevD.59.064024
[67] Erickson Tjoa. “Non-perturbative simple-generated interactions with a quantum field for arbitrary Gaussian states” (2023).
https://doi.org/10.1103/PhysRevD.108.045003
[68] Eric G. Brown, Eduardo Martín-Martínez, Nicolas C. Menicucci, and Robert B. Mann. “Detectors for probing relativistic quantum physics beyond perturbation theory”. Physical Review D 87, 084062 (2013).
https://doi.org/10.1103/PhysRevD.87.084062
[69] David Edward Bruschi, Antony R. Lee, and Ivette Fuentes. “Time evolution techniques for detectors in relativistic quantum information”. Journal of Physics A: Mathematical and Theoretical 46, 165303 (2013).
https://doi.org/10.1088/1751-8113/46/16/165303
[70] Wolfram Research, Inc. “Mathematica, Version 12.3.1”. Champaign, IL, 2022.
[71] Sebastian Paeckel, Thomas Köhler, Andreas Swoboda, Salvatore R. Manmana, Ulrich Schollwöck, and Claudius Hubig. “Time-evolution methods for matrix-product states”. Annals of Physics 411, 167998 (2019).
https://doi.org/10.1016/j.aop.2019.167998
[72] Lucas Hackl and Eugenio Bianchi. “Bosonic and fermionic Gaussian states from Kähler structures”. SciPost Physics Core 4, 025 (2021). arxiv:2010.15518.
https://doi.org/10.21468/SciPostPhysCore.4.3.025
arXiv:2010.15518
[73] N. D. Birrell and P. C. W. Davies. “Quantum Fields in Curved Space”. Cambridge Monographs on Mathematical Physics. Cambridge University Press. Cambridge (1982).
https://doi.org/10.1017/CBO9780511622632
[74] Dario Tamascelli. “Excitation dynamics in chain-mapped environments”. Entropy 22, 1320 (2020). arxiv:2011.11295.
https://doi.org/10.3390/e22111320
arXiv:2011.11295
[75] Robert H. Jonsson, Eduardo Martín-Martínez, and Achim Kempf. “Quantum signaling in cavity QED”. Physical Review A 89, 022330 (2014).
https://doi.org/10.1103/PhysRevA.89.022330
[76] Eduardo Martín-Martínez. “Causality issues of particle detector models in QFT and quantum optics”. Physical Review D 92, 104019 (2015).
https://doi.org/10.1103/PhysRevD.92.104019
[77] Robert M. Wald. “Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics”. Chicago Lectures in Physics. University of Chicago Press. Chicago, IL (1994).
[78] Shin Takagi. “On the Response of a Rindler-Particle Detector”. Progress of Theoretical Physics 72, 505–512 (1984).
https://doi.org/10.1143/PTP.72.505
[79] Izrail Solomonovich Gradshteyn and Iosif Moiseevich Ryzhik. “Table of Integrals, Series, and Products (Eighth Edition)”. Academic press. (2014).
https://doi.org/10.1016/c2010-0-64839-5
Cited by
Could not fetch Crossref cited-by data during last attempt 2024-01-30 14:00:51: Could not fetch cited-by data for 10.22331/q-2024-01-30-1237 from Crossref. This is normal if the DOI was registered recently. On SAO/NASA ADS no data on citing works was found (last attempt 2024-01-30 14:00:52).
This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.
- SEO Powered Content & PR Distribution. Get Amplified Today.
- PlatoData.Network Vertical Generative Ai. Empower Yourself. Access Here.
- PlatoAiStream. Web3 Intelligence. Knowledge Amplified. Access Here.
- PlatoESG. Carbon, CleanTech, Energy, Environment, Solar, Waste Management. Access Here.
- PlatoHealth. Biotech and Clinical Trials Intelligence. Access Here.
- Source: https://quantum-journal.org/papers/q-2024-01-30-1237/
