Download Raimar M. Sandner1,2, Markus Müller1,2,3, Andrew J. Daley1,2,4

Spatial Pauli blocking of spontaneous
emission in optical lattices
Preprint arXiv:1107.3375 (2011)
Raimar M. Sandner , Markus Müller
1,2
1,2,3
Institute for Quantum Optics and Quantum Information
of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria
SFB
Departamento de Física Teórica I
Universidad Complutense, 28040 Madrid, Spain
Department of Physics and Astronomy
University of Pittsburgh, Pittsburgh, Pennsylvania, 15260, USA
FoQuS
2
3
How?
and Peter Zoller
1,2
Institute for Theoretical Physics
University of Innsbruck, A-6020 Innsbruck, Austria
1
Goal
, Andrew J. Daley
1,2,4
Suppression of spontaneous emission by an
excited fermionic atom
4
Other methods to suppress spontaneous emission
Here: single atom blocks spontaneous emission on each site of a lattice
Lamb-Dicke regime:
• Engineering density of states of radiation modes (e.g.
Pauli exclusion principle: identical ground
state atom blocks dominant decay channel
confinement in trap
atom in cavity, in photonic bandgap, close to surface)
optical lattice with two atoms per site
•
Setup one atom excited, one in its ground state
•
• deep lattice, no tunneling on exp. timescales
• tight trapping in Lamb-Dicke regime
experimental demonstration of Pauli-blocked
•
Why? spontaneous emission conceptually interesting
• potential application as a tool: e.g. reservoir
• Single excited atom above Fermi sea of many trapped
ground state atoms [1]
optical wavelength of
emitted photon,
For the moment we assume
engineering and dissipative many-body state
preparation, photon wavepacket shaping
Limiting cases and corresponding experiments
Theoretical description
Alkaline earth-like atoms, 171Yb
weakly dipole allowed transition
Alkali atoms, dipole allowed transition
identical potential for ground- and excited state
excite atoms with fast pulse
(strong-excitation regime)
couple to lowest motional state
trap for excited state not important
Initial state
radiation field
Bath
System
creation (annihilation) operator
, Fermions:
Master equation in Born-Markov Approximation:
Experimental realization with alkaline-earth like atoms
general alkaline-earth properties
identical potential possible for ground- and excited
state (magic wavelength lattice):
two outer electrons, singlet and triplet
level structure
metastable, weakly dipole-allowed
due to hyperfine mixing, lifetime several tens
of seconds
dipole allowed, large decay
rate similar to alkali atoms
Center of mass motion of
atoms in harmonic trap
Protocol for alkaline-earth like atoms (observe the effect in a controllable way)
Here:
•
I: two atoms per lattice site in two nuclear spin states
•
II: excitation and nuclear spin flip
•
•
•
III: off-resonant weak dressing,
induced tunable (single particle) decay rate
compare also with [2]
Dipole-dipole interaction
(two-particle operator)
Order of magnitude:
for
for large detuning (
dip.-dip. interaction),
blocking ground state atom acts merely as spectator
Pauli-blocked induced decay rate
Recoil matrix elements
Expansion for small
Results
• For our initial state of interest
we have the initial decay rate
two-particle terms (dipole-dipole interaction and
• Additional
cross-damping terms) lead to more complex dynamics
• Tradeoff: tighter trap (smaller
interaction
) competes with larger dipole-dipole
Shape of the emitted photon wavepacket
Experimental realization with alkali atoms
Here:
Damping and recycling terms
•
initial state preparation (steps II and III) in strong
excitation regime
• motional state essentially unchanged
Description with a Weisskopf-Wigner ansatz
during excitation
• motion of excited atom negligible for decay timescales
• Pauli-blocked decay dynamics
• However: large dipole-dipole interaction, opens channels
which are not blocked, smaller
dipole-dipole interaction
Summary and outlook
and calculate the spatial
.
leads to larger
Literature
• Pauli exclusion principle can give rise to suppression
of spontaneous emission,
[1] T. Busch et. al., Europhys. Lett., 44,
1 (1998)
alkali atoms
[2] I. Reichenbach et. al., Phys. Rev. Lett., 99,
123001 (2007)
• Experimental realization with alkaline-earth and
• Possible application: photon wavepacket shaping,
reservoir engineering and dissipative many-body
state preparation, e.g. Diehl et. al. [3]:
We solve for the spectral distribution
intensity distribution
taken from [3]
[3] S. Diehl et. al., Phys. Rev. Lett., 105,
227001 (2010),
S. Diehl et. al., arXiv:1105.5947 (2011)
blocking atom in
blocking atom in superposition of
for the case
and
During the decay of the excited atom, the blocking atom oscillates in the
trap with a frequency , which imprints the spatial period
onto the
photon wavepacket.