Quantum Physics of Light-Matter Interactions, SS19, FAU

1. Claudiu Genes Max Planck Institute for the Science of Light (Erlangen, Germany) Lecture 12: Subradiance and superradiance Quantum Physics of Light-Matter Interactions, SS19, FAU

2. Structure • Master equation for the spontaneous emission of two two-level systems • Emergence of super- and subradiance • A few applications of subradiant states

3. Structure Master equation for the spontaneous emission of two two-level systems

4. The big picture Big quantization box – quantum electromagnetic vacuum Atomic, molecular system - +

5. The big picture Big quantization box – quantum electromagnetic vacuum Atomic, molecular system - +

6. The big picture Big quantization box – quantum electromagnetic vacuum Atomic, molecular system - + - +

7. The big picture Big quantization box – quantum electromagnetic vacuum Coupling strength

8. The big picture Big quantization box – quantum electromagnetic vacuum

9. The big picture Big quantization box – quantum electromagnetic vacuum

10. Eliminating the big box – reduced master equation for spontaneous emission Bare spontaneous emission rate • Open system dynamics Combining this with complexity – collective dynamics plays a big role

11. Eliminating the big box – reduced master equation for spontaneous emission Combining this with complexity – collective dynamics plays a big role

12. What about two two-level systems? Big quantization box – quantum electromagnetic vacuum Atomic, molecular system 1 Atomic, molecular system 2 - - + +

13. What about two two-level systems? Big quantization box – quantum electromagnetic vacuum Atomic, molecular system 1 Atomic, molecular system 2 - - + +

14. What about two two-level systems? Big quantization box – quantum electromagnetic vacuum Atomic, molecular system 1 Atomic, molecular system 2 - - + +

15. Spontaneous emission – master equation derivation Initial state Combining this with complexity – collective dynamics plays a big role

16. Spontaneous emission – master equation derivation Initial state Writing the equation of motion for the operator in the full Hilbert space Combining this with complexity – collective dynamics plays a big role

17. Spontaneous emission – master equation derivation Initial state Writing the equation of motion for the operator in the full Hilbert space Performing a unitary transformation to an interaction picture Combining this with complexity – collective dynamics plays a big role

18. Spontaneous emission – master equation derivation Initial state Writing the equation of motion for the operator in the full Hilbert space Performing a unitary transformation to an interaction picture The time dependent interaction Hamiltonian Where the forces (from the vacuum) are: Combining this with complexity – collective dynamics plays a big role

19. Spontaneous emission – master equation derivation Truncated equation for density operator: Tracing over the field states Combining this with complexity – collective dynamics plays a big role

20. Spontaneous emission – master equation derivation Truncated equation for density operator: Tracing over the field states Crucial terms: ...and three others like this one! Combining this with complexity – collective dynamics plays a big role

21. Spontaneous emission – master equation derivation Working it out: Combining this with complexity – collective dynamics plays a big role

22. Spontaneous emission – master equation derivation Working it out: vanish Combining this with complexity – collective dynamics plays a big role

23. Spontaneous emission – master equation derivation Working it out: vanish Combining this with complexity – collective dynamics plays a big role

24. Spontaneous emission – master equation derivation Working it out: Only non-vanishing contributions from: More explicitely Combining this with complexity – collective dynamics plays a big role

25. Spontaneous emission – master equation derivation ...a closer look... Combining this with complexity – collective dynamics plays a big role

26. Spontaneous emission – master equation derivation ...a closer look... Combining this with complexity – collective dynamics plays a big role

27. Spontaneous emission – master equation derivation ...a closer look... will lead to a delta function Real – leads to pure decay Combining this with complexity – collective dynamics plays a big role

28. Spontaneous emission – master equation derivation ...a closer look... will lead to a delta function Real – leads to pure decay Real part – decay and imaginary part – interaction Hamiltonian Combining this with complexity – collective dynamics plays a big role

29. Spontaneous emission – master equation derivation The previously derived result for independent atom spontaneous emission: Independent decay of two non-communicating atoms Combining this with complexity – collective dynamics plays a big role

30. Spontaneous emission – master equation derivation The previously derived result for independent atom spontaneous emission: Collective decay of two non-communicating atoms Combining this with complexity – collective dynamics plays a big role

31. Spontaneous emission – master equation derivation The previously derived result for independent atom spontaneous emission: Vacuum-mediated dipole-dipole interactions Combining this with complexity – collective dynamics plays a big role

32. Structure Emergence of super- and subradiance

33. Scalings with separation Scaling of mutual decay rate and dipole-dipole interaction strength with normalized separation

34. Diagonalizing the Hamiltonian Diagonalizing the interaction:

35. Diagonalizing the Hamiltonian Diagonalizing the interaction: Transformation

36. Diagonalizing the Hamiltonian Diagonalizing the interaction: Transformation ...and back... Result

37. Diagonalizing the Hamiltonian Diagonalizing the interaction: Transformation ...and back... Result Symmetric versus asymmetric states

38. Diagonalizing the decay terms Diagonalizing the Lindblad terms:

39. Diagonalizing the decay terms Diagonalizing the Lindblad terms:

40. Diagonalizing the decay terms Diagonalizing the Lindblad terms: Superradiant and subradiant states

41. Bare versus collective basis Subradiant rate: Superradiant rate:

42. Bare versus collective basis Subradiant rate: Superradiant rate: Subradiant/superradiant properties vary in space

43. Structure Application in metrology

44. The Bloch sphere Single system Bloch sphere N systems Bloch sphere

45. The Bloch sphere Single particle Bloch sphere N particles spin system

46. The Bloch sphere Single particle Bloch sphere N particles spin system • looking for common eigensystem of • collective spin operators

47. The Bloch sphere Single particle Bloch sphere N particles spin system • looking for common eigensystem of • collective spin operators Ramsey pulse

48. The Bloch sphere • states • degeneracy • space dimension

49. The Bloch sphere Diagonalization of the Lindblad term with

50. The Bloch sphere Diagonalization of the Lindblad term with