Coherence in Spontaneous Emission

1. Coherence in Spontaneous Emission Creston Herold July 8, 2013 JQI Summer School (1st annual!)

2. Emission from collective (many-body) dipole • Super-radiance, sub-radiance JQI Summer School

3. Gross, M. and S. Heroche. Physics Reports 93, 301–396 (1982). JQI Summer School

4. Emission from collective (many-body) dipole • Super-radiance, sub-radiance • Nuclear magnetic resonance (NMR) • Duan, Lukin, Cirac, Zoller (DLCZ) protocol JQI Summer School

5. Classical: Dipole Antenna JQI Summer School

6. Simple Quantum Example ? Spontaneous emission rate JQI Summer School

7. Matrix Form: 2 atoms JQI Summer School

8. Matrix Form: 3 atoms JQI Summer School

9. Overview • Write Hamiltonian for collection of atoms and their interaction with EM field • Build intuition for choice of basis • Energy states (eigenspectrum) • Simplify couplings by choosing better basis • Effects of system size, atomic motion • Experimental examples throughout! JQI Summer School

10. Formalism: Atomic States Depends on CoMcoords. e.g. kinetic energy internal energy commutes with all the (motion, collisions don’t change internal state) So we can choose simultaneous energy eigenstates: (operates on CoMcoords. only) JQI Summer School

11. Formalism: Atomic States degeneracy: JQI Summer School

12. Formalism: Atom-Light Interaction momentum conjugate to Field interaction with jth atom: (here, dipole approx. but results general!) is an odd operator, must be off-diagonal in representation with internal E diagonal: constant vectors For gas of small extent (compared to wavelength): JQI Summer School

13. Formalism:Better Basis “cooperation” number Each of the states is connected to many others through spontaneous emission/absorption (any “spin” could flip). As with angular momentum, and commute; therefore we can reorganize into eigenstates of : degeneracy: JQI Summer School

14. Formalism:Better Basis Determine all the eigenstates by starting with the largest : and applying the lowering operator, lowering operator normalization Once done with , construct states with making them orthogonal to ; apply lowering operator. Repeat (repeat, repeat, …); note the rapidly increasing degeneracy! JQI Summer School

15. Spontaneous Emission Rates Through judicious choice of basis, the field-atom interaction connects each of the states to two other states, with . Spontaneous emission rate is square of matrix element (lower sign): where is the single atom spontaneous emission rate (set ). JQI Summer School

16. Level Diagram collective states, single photon transitions! JQI Summer School

17. Examples: Collective Coherence 2-atom Rydberg blockade demonstration: 2-atom, 1.38(3)x faster! single atom Gaëtan, A. et al. Nature Physics 5, 115 (2009) [Browaeys & Grangier] See also E. Urban et al. Nature Physics 5, 110 (2009) [Walker & Saffman] JQI Summer School

18. Examples: Collective Coherence “many-body Rabi oscillations … in regime of Rydberg excitation blockade by just one atom.” Neff = 148 Neff = 243 Neff = 397 Neff = 456 Shared DAMOP 2013 thesis prize! Dudin, Y.et al. Nature Physics 8, 790 (2012) [Kuzmich] JQI Summer School

19. Example: Subradiance • Takasu, Y. et al. “Controlled Production of Subradiant States of a Diatomic Molecule in an Optical Lattice.” Phys. Rev. Lett.108, 173002 (2012). [Takahashi & Julienne] • “The difficulty of creating and studying the subradiant state comes from its reduced radiative interaction.” • Observe controlled production of subradiant (1g) and superradiant (0u) Yb2 molecules, starting from 2-atom Mott insulator phase in 3-d optical lattice. (Yb is “ideal” for observing pure subradiant state because it has no ground state electronic structure). • Control which states are excited by laser detuning. Subradiant state has sub-kHz linewidth! Making is potentially useful for many-body spectroscopy… JQI Summer School

20. Extended Cloud Have to keep spatial extent of field: • Directionality to coherence, emission • Same general approach applies • Eigenstates for particular (incomplete) • Include rest of to complete basis (decoherence, can change “cooperation number” ) constant vectors JQI Summer School

21. Extended Cloud JQI Summer School

22. Extended Cloud Incorporate spatial phase into raising/lowering operators: Generate eigenfunctions of For specific, fixed Rate per solid angle: JQI Summer School

23. Extended Cloud • OK for fixed atoms, but I said we’d consider motion! • We’ve incorporated CoM coordinates into , the “cooperation” operator; does not commute with ! • Thus, these are not stationary eigenstates of . • Classically, relative motion of radiators causes decoherence, but radiators with a common velocity will not decohere. • Quantum mechanically, analogous simultaneous eigenstates of and are found with: JQI Summer School

24. Extended Cloud • The states are not complete. • e.g. state after emitting/absorbing a photon with is not one of . • We can complete set of states “by adding all other orthogonal plane wave states, each being characterized by a definite momentum and internal energy for each molecule.” i.e. sets of with their own JQI Summer School

25. DLCZ protocol Speedup! Strong pump (se) recalls single eg photon JQI Summer School

26. DLCZ, storage times H. J. Kimball. Nature 453, 1029 (2008) • 2-node entanglement realized by Chou et al. Science316, 1316 (2007). [Kimball] • Ever longer storage times: • 3 us: Black et al. Phys. Rev. Lett. 95, 133601 (2005). [Vuletic] • 6 ms: Zhao et al. Nat. Phys.5, 100(2008). [Kuzmich] • 13 s: Dudinet al. Phys. Rev. A 87, 031801 (2013). [Kuzmich] JQI Summer School

27. References [1] Dicke, R. H. “Coherence in Spontaneous Radiation Processes.” Phys. Rev.93, 99-110 (1954). [2] Gross, M. and S. Haroche. “Superradiance: An essay on the theory of collective spontaneous emission.” Physics Reports 93, 301–396 (1982). [3] Gaëtan, A. et al. “Observation of collective excitation of two individual atoms in the Rydberg blockade regime.” Nature Physics 5, 115-118 (2009); also E. Urban et al. “Observation of Rydberg blockade between two atoms.” Nature Physics 5, 110-114 (2009). [4] Dudin, Y. et al. “Observation of coherent many-body Rabi oscillations.” Nature Physics 8, 790 (2012). [5]Takasu, Y. et al. “Controlled Production of Subradiant States of a Diatomic Molecule in an Optical Lattice.” Phys. Rev. Lett.108, 173002 (2012). [6] Duan, L., M. Lukin, J. I. Cirac, P. Zoller. “Long-distance quantum communication with atomic ensembles and linear optics.” Nature414, 413-418 (2001). [7] Chou, C. et al. “Functional quantum nodes for entanglement distribution over scalable quantum networks.” Science316, 1316-1320 (2007). [8] Kimball, H. J. “The quantum internet.” Nature453, 1023-1030 (2008). [9] Black, A. et al. “On-Demand Superradiant Conversion of Atomic Spin Gratings into Single Photons with High Efficiency.” Phys. Rev. Lett. 95 133601 (2005). [10] Zhao, R., Y. Dudin, et al. “Long-lived quantum memory.” Nature Physics 5, 100 (2008). [11] Dudin, Y. et al. “Light storage on the time scale of a minute.” Phys. Rev. A87, 031801 (2013). JQI Summer School

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29. Rydberg Blockade JQI Summer School