1. Yan Zhou, Anthony Colombo, David Grimes, Robert Field 2012.6.21 Cooperative effects in a dense Rydberg gas

2. Rydberg states Rydberg formula - A priori known energy Large dipole moment ~kiloDebye Pure electronic spectrum – core-nonpenetrating Rydberg electron: |∆ l |=1 Ion core: |∆N + |=0,|∆v + |=0 Resonance – the electron and ion-core Electronic-vibration interaction Electronic-rotation interaction Experimental methods Pulsed-Field Ionization Free Induction Decay

3. 5 cm Rydberg-Rydberg induced by CPmmW Direct transition detection: Free Induction Decay No high voltage ion detection system – Stray electric field 10 GHz bandwidth, ~100 kHz resolution Reliable relative intensities: 1% accuracy Manipulation by designed pulse sequence

4. We can now achieve >10:1 S:N in a single chirp Observing Rydberg–Rydberg transitions directly in Calcium gas Transition: 36p 36s Chirp: 10ns, 500MHz, 300 μW Acquisitions: 5000, 5min

5. Typical Ryd-Ryd spectrum – Time-domain Excitation: regular nutation envelope Max FID Min FID FID: Single exponential decay π /2 pulse – Maximum FID π pulse – Minimum FID

6. Typical Ryd-Ryd spectrum – Frequency domain Single sharp line 450kHz for He supersonic jet 250kHz for Ar supersonic jet

7. Strange behaviors N=5x10 5 cm -3 Intense but Short FID Weak but Long FID

8. Max FID Not π /2 Strange behaviors

9. N<1×10 5 /cm 3 N ~ 1×10 5 /cm 3 N ~ 3×10 5 /cm 3 Strange behaviors Side peak splittings ~ 500kHz Center Frequency shift ~ 200kHz

10. Cooperative effects – double-slit experiment * E 1 (t), W 1 * E 2 (t), W 2 E 1 (t), W 1 E 2 (t), W 2 E 1 (t)+E 2 (t), W 1 +W 2 E(t): damped oscillator, time-dependent W: energy, after spatial and time integrated Berman, P. R. (2010). American Journal of Physics, 78(12), 1323.

11. Cooperative effects – experimental results agree with the calculation Max FID Not π /2 Electric field/arb.u FID amplitude/arb.u 0.6 1.21.8 2.4 Pulse area / rad 3

12. Inverted two-level system – Superradiance and subradiance

13. Collisional cooling technique Temperature: < 5 K (trans and rot) Beam velocity: ~ 100 m/s Transverse Doppler at 100GHz: < 50 kHz Number density: 1×10 12 /pulse (10 9 cm -3 ) Shot-to-shot fluctuation: < 5%

14. Acknowledgment Barratt Park Kirill Kuyanov-Prozument Dave Patterson

15. Inverted Λ -type three-level system μ =5kD ( μ = 5D) μ = 4kD ( μ = 4D) Single mode radiation without cavity