1 / 34

Non-perturbative dynamics in QFT: An application of the Unruh-DeWitt detector

Non-perturbative dynamics in QFT: An application of the Unruh-DeWitt detector. Antony Richard Lee In collaboration with David Edward Bruschi and Ivette Fuentes University of Nottingham. University of Sydney – August 2013.

carol
Download Presentation

Non-perturbative dynamics in QFT: An application of the Unruh-DeWitt detector

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Non-perturbative dynamics in QFT: An application of the Unruh-DeWitt detector Antony Richard Lee In collaboration with David Edward Bruschi and Ivette Fuentes University of Nottingham University of Sydney – August 2013

  2. Non-perturbative dynamics in QFT: An application of the Unruh-DeWitt detector • Introduction • RQI • Motivation • Objectives • Framework • Unitary dynamics • Symplectic formulation • Gaussian states • Application • Beam splitter • Down conversion • UdW detector • Conclusions • Presentation • Introduction • Relativistic quantum information, motivation, objectives • Framework • Unitary dynamics, symplectic formalism, Gaussian states • Application • Beam and down conversion Hamiltonian, quantum field theory, Unruh-DeWitt detector • Conclusions Antony Richard Lee – UoN – UoS

  3. Non-perturbative dynamics in QFT: An application of the Unruh-DeWitt detector • Introduction • RQI • Motivation • Objectives • Framework • Unitary dynamics • Symplectic formulation • Gaussian states • Application • Beam splitter • Down conversion • UdW detector • Conclusions • Relativistic quantum Information • Main questions? • How does relativity merge with quantum information? • Effects of gravity and quantum field theory on QI protocols? • New technologies? Antony Richard Lee – UoN – UoS

  4. Non-perturbative dynamics in QFT: An application of the Unruh-DeWitt detector • Introduction • RQI • Motivation • Objectives • Framework • Unitary dynamics • Symplectic formulation • Gaussian states • Application • Beam splitter • Down conversion • UdW detector • Conclusions • Relativistic quantum Information • Motivation • Implications for communication using quantum field theory • Fundamental limits on information exchange • Could help with quantum gravity experiments Antony Richard Lee – UoN – UoS

  5. Non-perturbative dynamics in QFT: An application of the Unruh-DeWitt detector • Introduction • RQI • Motivation • Objectives • Framework • Unitary dynamics • Symplectic formulation • Gaussian states • Application • Beam splitter • Down conversion • UdW detector • Conclusions • Relativistic quantum information • Objectives • Useful, tractable framework to pose and answer questions (see Nico’s talk) • Protocols that are possible only by combining relativity and QI • Use QI to provide new experiments Antony Richard Lee – UoN – UoS

  6. Non-perturbative dynamics in QFT: An application of the Unruh-DeWitt detector • Introduction • RQI • Motivation • Objectives • Framework • Unitary dynamics • Symplectic formulation • Gaussian states • Application • Beam splitter • Down conversion • UdW detector • Conclusions • Reasons for non-perturbative analysis? • How do quantum correlations evolve over time? • Interesting for QI, optics, RQI, quantum gravity, chemistry and biology • Want to examine dynamics in an exact manner in QFT • Want analytical control or few approximations • How to do this? Antony Richard Lee – UoN – UoS

  7. Non-perturbative dynamics in QFT: An application of the Unruh-DeWitt detector • Introduction • RQI • Motivation • Objectives • Framework • Unitary dynamics • Symplectic formulation • Gaussian states • Application • Beam splitter • Down conversion • UdW detector • Conclusions • Framework • Unitary Dynamics • System Hamiltonian • Schrödinger equation • Unitary equation • Formal Solution Antony Richard Lee – UoN – UoS

  8. Non-perturbative dynamics in QFT: An application of the Unruh-DeWitt detector • Introduction • RQI • Motivation • Objectives • Framework • Unitary dynamics • Symplectic formulation • Gaussian states • Application • Beam splitter • Down conversion • UdW detector • Conclusions • Framework • Explicit expression • How to compute • Use first order only? • Term by term? • Other? Antony Richard Lee – UoN – UoS

  9. Non-perturbative dynamics in QFT: An application of the Unruh-DeWitt detector • Introduction • RQI • Motivation • Objectives • Framework • Unitary dynamics • Symplectic formulation • Gaussian states • Application • Beam splitter • Down conversion • UdW detector • Conclusions • Framework • Symplectic Formulation • Quadratic Hamiltonian • Hilbert space replaced by phase space Antony Richard Lee – UoN – UoS

  10. Non-perturbative dynamics in QFT: An application of the Unruh-DeWitt detector • Introduction • RQI • Motivation • Objectives • Framework • Unitary dynamics • Symplectic formulation • Gaussian states • Application • Beam splitter • Down conversion • UdW detector • Conclusions • Framework • Symplectic Group • Structure • Can be formally extended to infinite dimensions (see Nico’s talk) Antony Richard Lee – UoN – UoS

  11. Non-perturbative dynamics in QFT: An application of the Unruh-DeWitt detector • Introduction • RQI • Motivation • Objectives • Framework • Unitary dynamics • Symplectic formulation • Gaussian states • Application • Beam splitter • Down conversion • UdW detector • Conclusions • Framework • How to find S from U? • Symplectic dynamics • Formal solution Antony Richard Lee – UoN – UoS

  12. Non-perturbative dynamics in QFT: An application of the Unruh-DeWitt detector • Introduction • RQI • Motivation • Objectives • Framework • Unitary dynamics • Symplectic formulation • Gaussian states • Application • Beam splitter • Down conversion • UdW detector • Conclusions • Framework • Solving the time ordering • Numerically • Another way? • Decomposition Antony Richard Lee – UoN – UoS

  13. Non-perturbative dynamics in QFT: An application of the Unruh-DeWitt detector • Introduction • RQI • Motivation • Objectives • Framework • Unitary dynamics • Symplectic formulation • Gaussian states • Application • Beam splitter • Down conversion • UdW detector • Conclusions • Framework • Solving the time ordering • Evolution equation • Can be rewritten as • Notation Antony Richard Lee – UoN – UoS

  14. Non-perturbative dynamics in QFT: An application of the Unruh-DeWitt detector • Introduction • RQI • Motivation • Objectives • Framework • Unitary dynamics • Symplectic formulation • Gaussian states • Application • Beam splitter • Down conversion • UdW detector • Conclusions • Framework • Solving the time ordering • Equating coefficients • Coupled, ordinary, highly-nonlinear equations Bruschiet al 2013 J. Phys. A: Math. Theor.46 Antony Richard Lee – UoN – UoS

  15. Non-perturbative dynamics in QFT: An application of the Unruh-DeWitt detector • Introduction • RQI • Motivation • Objectives • Framework • Unitary dynamics • Symplectic formulation • Gaussian states • Application • Beam splitter • Down conversion • UdW detector • Conclusions • Framework • Different Decompositions • Polar decomposition • Bloch-Messiah/ Euler decomposition • Active • Passive Antony Richard Lee – UoN – UoS

  16. Non-perturbative dynamics in QFT: An application of the Unruh-DeWitt detector • Introduction • RQI • Motivation • Objectives • Framework • Unitary dynamics • Symplectic formulation • Gaussian states • Application • Beam splitter • Down conversion • UdW detector • Conclusions • Gaussian States • Definitions • Characteristic function • 1st and 2nd moments • Vector and matrix form Antony Richard Lee – UoN – UoS

  17. Non-perturbative dynamics in QFT: An application of the Unruh-DeWitt detector • Introduction • RQI • Motivation • Objectives • Framework • Unitary dynamics • Symplectic formulation • Gaussian states • Application • Beam splitter • Down conversion • UdW detector • Conclusions • Gaussian States • Examples • Coherent state • Two-mode squeezed state • Thermal state Antony Richard Lee – UoN – UoS

  18. Non-perturbative dynamics in QFT: An application of the Unruh-DeWitt detector • Introduction • RQI • Motivation • Objectives • Framework • Unitary dynamics • Symplectic formulation • Gaussian states • Application • Beam splitter • Down conversion • UdW detector • Conclusions • Gaussian States • Gaussian transformations • Preserved by quadratic Hamiltonians • Gaussian state evolves to Gaussian state • Can compute dynamics non-perturbativley • Models many physical situations Antony Richard Lee – UoN – UoS

  19. Non-perturbative dynamics in QFT: An application of the Unruh-DeWitt detector • Introduction • RQI • Motivation • Objectives • Framework • Unitary dynamics • Symplectic formulation • Gaussian states • Application • Beam splitter • Down conversion • UdW detector • Conclusions • Application • Beam Splitter Hamiltonian • Lie algebra generators Antony Richard Lee – UoN – UoS

  20. Non-perturbative dynamics in QFT: An application of the Unruh-DeWitt detector • Introduction • RQI • Motivation • Objectives • Framework • Unitary dynamics • Symplectic formulation • Gaussian states • Application • Beam splitter • Down conversion • UdW detector • Conclusions • Application • Beam Splitter Hamiltonian • Symplectic decomposition Antony Richard Lee – UoN – UoS

  21. Non-perturbative dynamics in QFT: An application of the Unruh-DeWitt detector • Introduction • RQI • Motivation • Objectives • Framework • Unitary dynamics • Symplectic formulation • Gaussian states • Application • Beam splitter • Down conversion • UdW detector • Conclusions • Application • Beam Splitter equations • Ideal for numerical evaluation Antony Richard Lee – UoN – UoS

  22. Non-perturbative dynamics in QFT: An application of the Unruh-DeWitt detector • Introduction • RQI • Motivation • Objectives • Framework • Unitary dynamics • Symplectic formulation • Gaussian states • Application • Beam splitter • Down conversion • UdW detector • Conclusions • Application • Parametric down conversion Hamiltonian • Lie algebra generators Antony Richard Lee – UoN – UoS

  23. Non-perturbative dynamics in QFT: An application of the Unruh-DeWitt detector • Introduction • RQI • Motivation • Objectives • Framework • Unitary dynamics • Symplectic formulation • Gaussian states • Application • Beam splitter • Down conversion • UdW detector • Conclusions • Application • Parametric down conversion Hamiltonian • Symplectic decomposition Antony Richard Lee – UoN – UoS

  24. Non-perturbative dynamics in QFT: An application of the Unruh-DeWitt detector • Introduction • RQI • Motivation • Objectives • Framework • Unitary dynamics • Symplectic formulation • Gaussian states • Application • Beam splitter • Down conversion • UdW detector • Conclusions • Application • Parametric down conversion equations • Simple expressions • Allows for exact solutions • Numerically stable Antony Richard Lee – UoN – UoS

  25. Non-perturbative dynamics in QFT: An application of the Unruh-DeWitt detector • Introduction • RQI • Motivation • Objectives • Framework • Unitary dynamics • Symplectic formulation • Gaussian states • Application • Beam splitter • Down conversion • UdW detector • Conclusions • Application – Quantum Field Theory • Spacetime coordinates • Quantum field • Expand in basis of solutions Antony Richard Lee – UoN – UoS

  26. Non-perturbative dynamics in QFT: An application of the Unruh-DeWitt detector • Introduction • RQI • Motivation • Objectives • Framework • Unitary dynamics • Symplectic formulation • Gaussian states • Application • Beam splitter • Down conversion • UdW detector • Conclusions • Application • Quantisation • Works for Dirac, Electromagnetic and higher spin fields Antony Richard Lee – UoN – UoS

  27. Non-perturbative dynamics in QFT: An application of the Unruh-DeWitt detector • Introduction • RQI • Motivation • Objectives • Framework • Unitary dynamics • Symplectic formulation • Gaussian states • Application • Beam splitter • Down conversion • UdW detector • Conclusions • Application • Unruh-DeWitt detector • Comoving coordinates Antony Richard Lee – UoN – UoS

  28. Non-perturbative dynamics in QFT: An application of the Unruh-DeWitt detector • Introduction • RQI • Motivation • Objectives • Framework • Unitary dynamics • Symplectic formulation • Gaussian states • Application • Beam splitter • Down conversion • UdW detector • Conclusions • Application • Unruh-DeWitt detector • Detector couples linearly to field operator Antony Richard Lee – UoN – UoS

  29. Non-perturbative dynamics in QFT: An application of the Unruh-DeWitt detector Trajectory Constant acceleration Antony Richard Lee – UoN – UoS

  30. Non-perturbative dynamics in QFT: An application of the Unruh-DeWitt detector • Introduction • RQI • Motivation • Objectives • Framework • Unitary dynamics • Symplectic formulation • Gaussian states • Application • Beam splitter • Down conversion • UdW detector • Conclusions • Application • Unruh-DeWitt detector • Normally compute transition rate to first order in perturbation theory • Inertial trajectories cannot excite the detector from its vacuum state • Accelerated detectors predict the “Unruh effect” Antony Richard Lee – UoN – UoS

  31. Non-perturbative dynamics in QFT: An application of the Unruh-DeWitt detector • Introduction • RQI • Motivation • Objectives • Framework • Unitary dynamics • Symplectic formulation • Gaussian states • Application • Beam splitter • Down conversion • UdW detector • Conclusions • Application • Unruh-DeWitt detector (inertial) Brown et. al. Phys. Rev. D 87, 084062 (2013) Bruschiet al 2013 J. Phys. A: Math. Theor.46 Antony Richard Lee – UoN – UoS

  32. Non-perturbative dynamics in QFT: An application of the Unruh-DeWitt detector • Introduction • RQI • Motivation • Objectives • Framework • Unitary dynamics • Symplectic formulation • Gaussian states • Application • Beam splitter • Down conversion • UdW detector • Conclusions • Application • Unruh-DeWitt detector (acc.) Brown et. al. Phys. Rev. D 87, 084062 (2013) Antony Richard Lee – UoN – UoS

  33. Non-perturbative dynamics in QFT: An application of the Unruh-DeWitt detector • Introduction • RQI • Motivation • Objectives • Framework • Unitary dynamics • Symplectic formulation • Gaussian states • Application • Beam splitter • Down conversion • UdW detector • Conclusions • Conclusions • Introduced RQI • Motivation • Objectives • Introduced a novel way to approach quantum dynamics • Analyse quadratic bosonic Hamiltonians • Can be used in quantum field theory • Powerful and efficient for Gaussian quantum information • Opens door to other questions in RQI Antony Richard Lee – UoN – UoS

  34. Thanks! (Stick around for Nico’s talk)

More Related