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 http://phylabs.berkeley.edu/budker

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

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

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

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

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.

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

Other Applications for Dy Investigation of Sokolov effect [B. B. Kadomtsev et al., Physica Scripta. 54, 156-162 (1996)] New PNC effects [T. Gasenzer et al., European Journal of Phys. (1999)]

|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

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.)

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

[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. 123.505 (1996)] diverging laser beam atomic beam Due to Doppler effect, almost entire distribution excited

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

“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>

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

CALCULATIONS Hamiltonian: Density Matrix: Liouville Equation:

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)

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

Probe with 669-nm laser

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

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

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)

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