Project A06: Representation of quantum correlations in complex systems

In this project we will estimate the quantum entanglement present in mixed states of many particle systems using the expectation values of experimentally accessible observables and Bell inequalities for entangled states of neutral atoms will be found. Algorithms to simulate the dissipative dynamics of many body systems will be developed and fluctuations of many particle systems studied. Noise in analogue quantum algorithms for quantum simulation will also be modelled. Finally, the metrological characterisation of quantum devices will be studied providing feedback schemes, engineered states for quantum frequency metrology, and improved noise reduction schemes for quantum devices with memory.

Introduction

In the second funding period our goal was to build on the foundations laid in the first round, namely, our development of variational methods to study many body quantum systems out of equilibrium. Particular emphasis was given to the study of complex quantum systems out of equilibrium, particularly with a view to the next generation of NISQ devices. We engineered strongly entangled states of complex quantum systems such as dilute atomic gases and trapped ions, and designed robust metrological schemes approaching the Heisenberg limit.

Project A06 contributed to the core research goals of DQ-mat by providing fundamental theoretical methods to manipulate and characterise quantum systems, enhance metrology, and explore many-body physics.

Results

In the second funding phase we aimed to delve deeper into the intricate realm of quantum many-body systems far from equilibrium, building on the insights gained in the initial period. These systems, exemplified by optical and atomic clocks, as well as emerging NISQ devices, posed complex challenges. The project’s core objectives revolved around understanding these systems from various angles, integrating known methods to explore new frontiers.

One objective involved pioneering a noncommutative extension of the cumulant expansion, enabling systematic corrections to mean-field theory. Here waveguide QED was the focus of intensive investigations. The central result during the second funding period was an improved mean-field theory based on higher-order cumulant expansions to describe the experimentally relevant, but theoretically elusive, regime of weak coupling and strong driving of large ensembles for chiral waveguide QED.

Another goal centered on developing classical simulation methods for complex quantum many-body systems, especially in the presence of defects and disorder. Advanced tensor network techniques took the spotlight, addressing gaps left by previous methods, notably in variational approaches. It was demonstrated, using novel tensor network methods, that many body disordered systems states feature periodic high-fidelity revivals of the full wavefunction and local observables that oscillate indefinitely. Thus these systems neither  equilibrate nor thermalise, in contrast to previous expectations from the literature.

In summary, A06 completely and comprehensively achieved all of the proposed objectives. It will be concluded at the end of the second funding period in 2024.


Publications

Showing results 21 - 39 out of 39

Nitzschke D, Schulte M, Niemann M, Cornejo JM, Ulmer S, Lehnert R et al. Elementary laser‐less quantum logic operations with (anti‐)protons in penning traps. Advanced Quantum Technologies. 2020 Jun 16;3(11):1900133. doi: 10.1002/qute.201900133
Osborne TJ, Stiegemann DE. Dynamics for holographic codes. Journal of High Energy Physics. 2020 Apr 23;2020(4):154. doi: 10.48550/arXiv.1706.08823, 10.1007/JHEP04(2020)154
Prasad AS, Hinney J, Mahmoodian S, Hammerer K, Rind S, Schneeweiss P et al. Correlating photons using the collective nonlinear response of atoms weakly coupled to an optical mode. Nature Photonics. 2020 Dec;14(12):719–722 . Epub 2020 Sept 21. doi: 10.1038/s41566-020-0692-z
Raghunandan M, Wolf F, Ospelkaus C, Schmidt PO, Weimer H. Initialization of quantum simulators by sympathetic cooling. Science advances. 2020 Mar 6;6(10):eaaw9268. doi: 10.1126/sciadv.aaw9268
Schulte M, Lisdat C, Schmidt PO, Sterr U, Hammerer K. Prospects and challenges for squeezing-enhanced optical atomic clocks. Nature Communications. 2020 Nov 24;11(1):5955. doi: 10.1038/s41467-020-19403-7
Schulte M, Martínez-Lahuerta VJ, Scharnagl MS, Hammerer K. Ramsey interferometry with generalized one-axis twisting echoes. Quantum. 2020 May 15;4:268-286. doi: 10.48550/arXiv.1911.11801, 10.22331/q-2020-05-15-268, 10.15488/9960
Schwonnek R, Werner RF. The Wigner distribution of n arbitrary observables. Journal of mathematical physics. 2020 Aug 4;61(8):082103. doi: 10.1063/1.5140632
Cedzich C, Geib T, Werner AH, Werner RF. Quantum walks in external gauge fields. Journal of Mathematical Physics. 2019 Jan;60(1):012107. Epub 2019 Jan 28. doi: 10.48550/arXiv.1808.10850, 10.1063/1.5054894
Nitsche T, Geib T, Stahl C, Lorz L, Cedzich C, Barkhofen S et al. Eigenvalue Measurement of Topologically Protected Edge states in Split-Step Quantum Walks. New Journal of Physics. 2019 Apr;21(4):043031. Epub 2019 Apr 15. doi: 10.48550/arXiv.1811.09520, 10.1088/1367-2630/ab12fa, 10.15488/10404
Werner RF, Farrelly T. Uncertainty from Heisenberg to Today. Foundations of Physics. 2019 Jun 15;49(6):460-491. Epub 2019 May 30. doi: 10.48550/arXiv.1904.06139, 10.1007/s10701-019-00265-z
Wolf F, Shi C, Heip JC, Gessner M, Pezzè L, Smerzi A et al. Motional Fock states for quantum-enhanced amplitude and phase measurements with trapped ions. Nature Communications. 2019 Jul 2;10(1):2929. Epub 2019 Jul 2. doi: 10.48550/arXiv.1807.01875, 10.1038/s41467-019-10576-4
Zarantonello G, Hahn H, Schulte M, Bautista-Salvador A, Werner RF, Hammerer K et al. Robust and Resource-Efficient Microwave Near-Field Entangling ^{9}Be^{+} Gate. Physical review letters. 2019 Dec 31;123(26):260503. Epub 2019 Dec 26. doi: 10.48550/arXiv.1911.03954, 10.1103/PhysRevLett.123.260503
Beer K, Osborne TJ. Contextuality and bundle diagrams. Physical Review A. 2018 Nov 20;98(5):052124. doi: 10.1103/PhysRevA.98.052124
Bény C, Chubb CT, Farrelly T, Osborne TJ. Energy cost of entanglement extraction in complex quantum systems. Nature Communications. 2018 Sept 17;9:3792. doi: 10.48550/arXiv.1711.06658, 10.1038/s41467-018-06153-w, 10.15488/4224
Cedzich C, Geib T, Grünbaum FA, Stahl C, Velázquez L, Werner AH et al. The Topological Classification of One-Dimensional Symmetric QuantumWalks. Annales Henri Poincaré. 2018 Feb;19(2):325–383. Epub 2017 Nov 28. doi: 10.48550/arXiv.1611.04439, 10.1007/s00023-017-0630-x
Nikolova A, Brennen GK, Osborne TJ, Milburn GJ, Stace TM. Relational time in anyonic systems. Physical Review A. 2018 Mar;97(3):030101. Epub 2018 Mar 12. doi: 10.1103/PhysRevA.97.030101, 10.15488/9158
Schulte M, Lörch N, Schmidt PO, Hammerer KJ. Photon-recoil spectroscopy: Systematic shifts and nonclassical enhancements. Physical Review A. 2018 Dec;98(6):063808. Epub 2018 Dec 5. doi: 10.48550/arXiv.1807.08309, 10.1103/PhysRevA.98.063808
Schwonnek R, Dammeier L, Werner RF. State-independent Uncertainty Relations and Entanglement Detection in Noisy Systems. Phys. Rev. Lett. 2017 Oct 27;119(17):170404. doi: 10.1103/PhysRevLett.119.170404
Zoubi H, Hammerer K. Quantum Nonlinear Optics in Optomechanical Nanoscale Waveguides. Physical Review Letters. 2017 Sept 21;119(12):123602. doi: 10.1103/PhysRevLett.119.123602
All publications of the Collaborative Research Centre

Project leader

Prof. Dr. Tobias J. Osborne
Address
Appelstraße 2
30167 Hannover
Address
Appelstraße 2
30167 Hannover
Prof. Dr. Reinhard Werner
Address
Schneiderberg 32
30167 Hannover
Building
Room
021
Address
Schneiderberg 32
30167 Hannover
Building
Room
021
Prof. Dr. Klemens Hammerer
Address
Appelstraße 2
30167 Hannover
Building
Room
114
Address
Appelstraße 2
30167 Hannover
Building
Room
114

Staff

Tobias Geib
Tobias Geib
Dmytro Bondarenko
Dmytro Bondarenko
Victoria-Sophie Schmiesing
Victoria-Sophie Schmiesing