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Measuring quantum geometry From superconducting qubits to spin chains

Measuring quantum geometry From superconducting qubits to spin chains. Michael Kolodrubetz , Physics Department, Boston University Theory collaborators: Anatoli Polkovnikov (BU), Vladimir Gritsev (Fribourg)

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Measuring quantum geometry From superconducting qubits to spin chains

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  1. Measuring quantum geometryFrom superconductingqubits to spin chains Michael Kolodrubetz, Physics Department, Boston University Theory collaborators: AnatoliPolkovnikov (BU), Vladimir Gritsev (Fribourg) Experimental collaborators: Michael Schroer, Will Kindel, KonradLehnert (JILA)

  2. The quantum geometric tensor

  3. The quantum geometric tensor

  4. The quantum geometric tensor • Geometric tensor

  5. The quantum geometric tensor • Geometric tensor • Real part = Quantum (Fubini-Study) metric tensor

  6. The quantum geometric tensor • Geometric tensor • Real part = Quantum (Fubini-Study) metric tensor • Imaginary part = Quantum Berry curvature

  7. Outline • Measuring the metric tensor • Transport experiments • Corrections to adiabaticity • Classification of quantum metric geometry • Invariance of geometry • Classification of singularities • Chern number of superconducting qubit • Berry curvature from slow ramps • Topological transition in a qubit

  8. Outline • Measuring the metric tensor • Transport experiments • Corrections to adiabaticity • Classification of quantum metric geometry • Invariance of geometry • Classification of singularities • Chern number of superconducting qubit • Berry curvature from slow ramps • Topological transition in a qubit

  9. Outline • Measuring the metric tensor • Transport experiments • Corrections to adiabaticity • Classification of quantum metric geometry • Invariance of geometry • Classification of singularities • Chern number of superconducting qubit • Berry curvature from slow ramps • Topological transition in a qubit

  10. Outline • Measuring the metric tensor • Transport experiments • Corrections to adiabaticity • Classification of quantum metric geometry • Invariance of geometry • Classification of singularities • Chern number of superconducting qubit • Berry curvature from slow ramps • Topological transition in a qubit

  11. The quantum geometric tensor Metric Tensor Berry curvature

  12. The quantum geometric tensor Metric Tensor Berry curvature

  13. The quantum geometric tensor • Real symmetric tensor Metric Tensor Berry curvature

  14. The quantum geometric tensor • Real symmetric tensor • Same as fidelity susceptibility Metric Tensor Berry curvature

  15. Measuring the metric tensor

  16. Measuring the metric tensor

  17. Measuring the metric tensor

  18. Measuring the metric tensor Generalized force

  19. Measuring the metric tensor Generalized force

  20. Measuring the metric tensor Generalized force

  21. Measuring the metric tensor Generalized force

  22. Measuring the metric tensor Generalized force

  23. Measuring the metric tensor Generalized force

  24. Measuring the metric tensor

  25. Measuring the metric tensor

  26. Measuring the metric tensor

  27. Measuring the metric tensor

  28. Measuring the metric tensor

  29. Measuring the metric tensor • For Bloch Hamiltonians, Neupert et al. pointed out relation tocurrent-current noise correlations [arXiv:1303.4643]

  30. Measuring the metric tensor • For Bloch Hamiltonians, Neupert et al. pointed out relation tocurrent-current noise correlations [arXiv:1303.4643] • Generalizable to other parameters/non-interacting systems

  31. Measuring the metric tensor • For Bloch Hamiltonians, Neupert et al. pointed out relation tocurrent-current noise correlations [arXiv:1303.4643] • Generalizable to other parameters/non-interacting systems

  32. Measuring the metric tensor

  33. Measuring the metric tensor REAL TIME

  34. Measuring the metric tensor REAL TIME IMAG. TIME

  35. Measuring the metric tensor REAL TIME IMAG. TIME

  36. Measuring the metric tensor REAL TIME IMAG. TIME

  37. Measuring the metric tensor • Real time extensions:

  38. Measuring the metric tensor • Real time extensions:

  39. Measuring the metric tensor • Real time extensions:

  40. Measuring the metric tensor • Real time extensions:

  41. Measuring the metric tensor • Real time extensions: (related the Loschmidt echo)

  42. Outline • Measuring the metric tensor • Transport experiments • Corrections to adiabaticity • Classification of quantum metric geometry • Invariance of geometry • Classification of singularities • Chern number of superconducting qubit • Berry curvature from slow ramps • Topological transition in a qubit

  43. Outline • Measuring the metric tensor • Transport experiments • Corrections to adiabaticity • Classification of quantum metric geometry • Invariance of geometry • Classification of singularities • Chern number of superconducting qubit • Berry curvature from slow ramps • Topological transition in a qubit

  44. Outline • Measuring the metric tensor • Transport experiments • Corrections to adiabaticity • Classification of quantum metric geometry • Invariance of geometry • Classification of singularities • Chern number of superconducting qubit • Berry curvature from slow ramps • Topological transition in a qubit

  45. Outline • Measuring the metric tensor • Transport experiments • Corrections to adiabaticity • Classification of quantum metric geometry • Invariance of geometry • Classification of singularities • Chern number of superconducting qubit • Berry curvature from slow ramps • Topological transition in a qubit

  46. Visualizing the metric Transverse field Anisotropy

  47. Visualizing the metric Transverse field Anisotropy

  48. Visualizing the metric Transverse field Anisotropy Global z-rotation

  49. Visualizing the metric

  50. Outline • Measuring the metric tensor • Transport experiments • Corrections to adiabaticity • Classification of quantum metric geometry • Invariance of geometry • Classification of singularities • Chern number of superconducting qubit • Berry curvature from slow ramps • Topological transition in a qubit

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