1. University of California, Berkeley
EFFICIENT
POPULATION TRANSFER
IN A
MULTI-LEVEL ATOM
University of California, Berkeley
G. D. Chern
A. T. Nguyen
D. Budker
M. Zolotorev

2. OUTLINE Motivation Population Scheme Adiabatic Passage Calculations
Experimental Setup
Data
Experimental Results
Conclusions

3. SEARCH FOR PARITY NONCONSERVATON (PNC) IN ATOMIC DYSPROSIUM
MOTIVATION
SEARCH FOR PARITY NONCONSERVATON (PNC) IN ATOMIC DYSPROSIUM

4. PARITY TRANSFORMATION
Mirror reflection
Parity operator P and eigenstate Y(r)
P Y(r)= + Y(r)  Y(r) EVEN
P Y(r)= - Y(r)  Y(r) ODD
Interaction CONSERVES PARITY if
Y(r) simultaneously an
eigenstate of P and Hamiltonian H

5. Parity Nonconservation (PNC) in Atoms
CONSERVES PARITY:
Dominant electromagnetic interactions e- q g
Definite parity eigenstates

6. Smaller weak interactions between valence electron and nucleus
DOES NOT CONSERVE PARITY:
Smaller weak interactions between valence electron and nucleus e- q Z0
New eigenstates, e.g.

7. Why Dysprosium (Dy)? Pair of nearly-degenerate opposite parity states
 enhances mixing A
tA=7.9ms B
tB >200ms
3.1 MHz
Ground State
Energy (cm-1)
20,000
Isotopic comparisons:
Cancel Atomic Theory
Odd isotopes:
Anapole moment

8. Other Applications for Dy
Investigation of Sokolov effect
[B. B. Kadomtsev et al., Physica Scripta. 54, (1996)]
New PNC effects
[T. Gasenzer et al., European Journal of Phys. (1999)]

9. |Hw|=|2  3| Hz Atomic calculations predicted: Hw=70  40 Hz
[V. A. Dzuba et al., Phys. Rev. A 50, 3812 (1994)]
Using pulsed lasers, we reported:
|Hw|=|2  3| Hz
[A. T. Nguyen et al., Phys. Rev. A 56, 3453 (1997)]
Improve statistical sensitivity

10. POPULATION SCHEME 4f9 6s2 6p f J=9 1397 nm (.30(9) b.r.) B 4f9 5d2 6s
EVEN ODD
4f10 6s2 G
J=8
4f10 5d 6s2 A
J=10
4f9 6s2 6p f
J=9
e 4f9 5d 6s2
B 4f9 5d2 6s
833 nm
669 nm
1397 nm (.30(9) b.r.)

11. Send atomic beam across cw laser
laser beam
atomic beam
Consider a two-level atom
|g>
|e> w0
light
atomic states
Oscillations at Rabi freq. WR = d E
 50% prob. to be in excited state
Prob. to be in state |e>
time 1

12. [C. R. Ekstrom et al., Optics Comm. 123.505 (1996)]
PROBLEM: cw laser excites only small fraction of transverse atomic velocity distribution
# of atoms in state |g> vT
SOLUTION: diverge laser beam to match atomic beam divergence
[C. R. Ekstrom et al., Optics Comm (1996)]
diverging laser beam
atomic beam
Due to Doppler effect, almost entire distribution excited

13. ADIABATIC PASSAGE ADIABATIC PASSAGE: robust population technique
 Allows 100% prob. to be in excited state
Prob. to be in state |e>
time 1
Each atom “sees” change in detuning as it traverses laser beam
Analogous to adiabatic passage in NMR

14. “Dress” atomic states w/ photon states: |g, n> and |e, n-1>
Dressed Atom Model
Include atoms and light field in basis states
“Dress” atomic states w/ photon states: |g, n> and |e, n-1>
Eigenstates in dressed atom basis:
|1> and |2>
Detuning
Energy
|1>
|2>
|g, n>
|e, n-1>

15. Adiabatic Criteria
Change in detuning D is slow compared to Rabi frequency WR
Lifetime of upper state t is longer than time T for inversion to occur

16. CALCULATIONS
Hamiltonian:
Density Matrix:
Liouville Equation:

17. EXPERIMENTAL SETUP a) atomic beam produced by
effusive oven source at T=1500 K
b) atomic beam collimators
c) cylindrical lenses to diverge laser beams
d) spherical mirror to improve light collection
efficiency
e) interference filter(s)

18. DATA
First transition: state G  state e
833-nm fluorescence

19. Probe with 669-nm laser

20. EXPERIMENTAL RESULTS FIRST transition: ~50% efficiency
Limited only by insufficient laser power  need to double power
SECOND transition: ~80% efficiency
THIRD transition: 30% efficiency
determined by branching ratio

21. TOTAL EFFICIENCY: (~50%) * (~80%) * (30%) = ~12%
without lenses: < 0.5% efficiency
Efficiency easily improved w/:
more 833-nm laser power
1397-nm laser to stimulate transition

22. Pulsed lasers  cw lasers:
CONCLUSIONS
Pulsed lasers  cw lasers:
104 increase in duty cycle
With 20 h data taking time, this gives total factor of 102 increase in statistical sensitivity (10 mHz level)

23. PNC DETECTION
Stark-PNC Mixing A B + =
Stark Mixing Stark-PNC Mixing