Coherence in Spontaneous Emission Creston Herold July 8, 2013 JQI Summer School (1 st annual!)
Dec 22, 2015
Coherence in Spontaneous Emission
Creston Herold
July 8, 2013JQI Summer School (1st annual!)
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• Emission from collective (many-body) dipole• Super-radiance, sub-radiance
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Gross, M. and S. Heroche. Physics Reports 93, 301–396 (1982).
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• Emission from collective (many-body) dipole• Super-radiance, sub-radiance• Nuclear magnetic resonance (NMR)• Duan, Lukin, Cirac, Zoller (DLCZ) protocol
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Classical: Dipole Antenna
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Simple Quantum Example
?
Spontaneous emission rate
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Matrix Form: 2 atoms
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Matrix Form: 3 atoms
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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!
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Formalism: Atomic States
Depends on CoM coords.e.g. kinetic energy
So we can choose simultaneous energy eigenstates:
commutes with all the (motion, collisions don’t change internal state)
(operates on CoM coords. only)
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internal energy
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Formalism: Atomic States
degeneracy:
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Formalism: Atom-Light Interaction
Field interaction with jth atom:(here, dipole approx. but results general!)
momentum conjugate to
is an odd operator, must be off-diagonal in representation with internal E diagonal:
constant vectors
For gas of small extent (compared to wavelength):
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Formalism: Better BasisEach of the states is connected to many others throughspontaneous emission/absorption (any “spin” could flip).
As with angular momentum, and commute; therefore we can reorganize into eigenstates of :
“cooperation” number
degeneracy:
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Formalism: Better BasisDetermine all the eigenstates by starting with the largest :
and applying the lowering operator,
lowering operatornormalization
Once done with , construct states with making them orthogonal to ; apply lowering operator.
Repeat (repeat, repeat, …); note the rapidly increasing degeneracy!
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Spontaneous Emission RatesThrough 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 ).
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Level Diagram
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collective states,single photon transitions!
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Examples: Collective Coherence2-atom Rydberg blockade demonstration:
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Gaëtan, A. et al. Nature Physics 5, 115 (2009) [Browaeys & Grangier]See also E. Urban et al. Nature Physics 5, 110 (2009) [Walker &
Saffman]
single atom2-atom, 1.38(3)x faster!
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Examples: Collective Coherence“many-body Rabi oscillations … in regime of Rydberg excitation blockade by just one atom.”
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Dudin, Y. et al. Nature Physics 8, 790 (2012) [Kuzmich]
Shared DAMOP 2013 thesis prize!
Neff = 148
Neff = 243
Neff = 397
Neff = 456
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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…
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Extended Cloud
• 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
Have to keep spatial extent of field:
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Extended Cloud
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Extended Cloud
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Incorporate spatial phase into raising/lowering operators:
Rate per solid angle:
Generate eigenfunctions of
For specific, fixed
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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:
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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.”
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i.e. sets of with their own
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DLCZ protocol
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Speedup!
Strong pump (s e) recalls single e g photon
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DLCZ, storage times
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• 2-node entanglement realized by Chou et al. Science 316, 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: Dudin et al. Phys. Rev. A 87,
031801 (2013). [Kuzmich]
H. J. Kimball. Nature 453, 1029 (2008)
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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.” Nature 414, 413-418 (2001).
[7] Chou, C. et al. “Functional quantum nodes for entanglement distribution over scalable quantum networks.” Science 316, 1316-1320 (2007).
[8] Kimball, H. J. “The quantum internet.” Nature 453, 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. A 87, 031801 (2013).
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Rydberg Blockade
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