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Coherent Population Trapping in Rb atoms.Tianchu(Alex) Liang, Dr. John R. Brandenberger, Lawrence University, Appleton, WI

Why trapping:

• Trapping means to control the particles.• Experimental Physics--->Explore Structure &

dynamics--->Trapping.

History of Trapping:

• Began in the 1970s• Usually involves lasers.• Examples:– 1. Optical Trapping– 2. Magneto-Optical Trapping– 3. Magnetic Trapping

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Special Kind of Trapping: Coherent Population Trapping

• Special: Not spatial trapping, but trapping in energy levels.

• Applications: Miniature Atomic Clock, Quantum Information Processing, etc.

More about Coherent Population Trapping:

Ground StateExcited State

|2>

|1>

|3>

Resonant Frequency f1

Resonant Frequency f2

Fixed at resonant frequency f1

Scans through resonant frequency f2

Rb Vapor Cell

Detector

Constant level of absorption for a fixed resonant f1

Absorption increases as frequency gets closer to resonant f2

Get greedier, we want more excited atoms :

|1>

|3>

Resonant Frequency f1

Resonant Frequency f2

|2>

Get greedier, we want more atoms excited:Laser#1: Fixed Frequency f1Laser#2: Scanning Frequency f2

Detector

|1> |3>

Fixed Frequency f1

Scanning Frequency f2

|2>???

Astonishing Result:

One laser locked on f1, the other laser scans throughf2

Theoretical explanation:

• Quantum mechanical interference– Atoms being trapped in the superposition state of

two ground states: |ψ>=|1>-|3>. • Use density matrix to account for the CPT

phenomenon.

Theoretical Lineshapes: Quantum mechanical point of view for stationary atoms:

Credit to: Coherent Trapping of Atomic Populations byH.R. Gray, R.M. Whitley, and C.R. Stroud,Jr.

Ideal Case:• Assume stationary atoms• Ideal Intensity profile of the beam

By Maple

Theoretical Lineshapes: Based on density matrix analysis taking into account the Doppler Effect

Credit to: Electromagnetically induced transparency in a three-level Lambda-type system in rubidium atoms by Yong-qing Li and Min Xiao

By MATLAB

ExperimentDesign:

• Fix one(f1), scans the other(f2);

• Expect to see a dip .• How does CPT

width, depth depend on the power of one laser(f1,optical-pumping).

One laser locked on f1, the other laser scans throughf2

Experimental set-up

Experimental Data

Experimental Data

Compare to Theoretical

Compare to Theoretical

Conclusion & what’s next:

• CPT width, depth increase as laser power increases.• Experimental data on CPT width vs laser power does

not quite agree with theoretical prediction.

Next:• Acquire more data.• More theoretical work needs to be done.• What exactly determines the shape of the CPT

dip?

Acknowledgements:

• Professor John R.Brandenberger• Skran Summer Research Fellowship• Lawrence University

Thanks!