1. Buffer Gas Cooled Molecule Source for CPmmW Spectroscopy
Yan Zhou, David Grimes, Timothy J Barnum, Ethan Klein, Robert W Field
Department of Chemistry, MIT
ISMS – 19 June 2014
Development of buffer gas cooling apparatus for use with CPmmW spectrometer, highlight why these 2 techniques particularly powerful in study of Rydberg states

2. Chirped Pulse millimeter-Wave
10MHz
Rb Osc
4.2GHz
PDRO
6.2GHz
2-18GHz
Synthesizer
AWG710
4.2Gs/s
T7000 Scope
12.5GHz
clock LO IF RF  x2 x6
Variable Attenuators
Band pass
Notch
0.2-2 GHz
Chirped pulse
Molecular beam i ii
iii iv v vi
vii
viii ix x xi
xii
xiii
xiv xv
xvi
xvii
xviii
xix xx
xxi
xxii
xxiv
xxviii
xxix
xxx
GHz
30mW
xxiii
xxv
xxvi
xxvii
Direct detection of transitions via Free Induction Decay
20 GHz bandwidth ÷ 50 kHz resolution = 400,000 resolution elements
Reliable relative intensities
Manipulation by designed pulse sequence

3. Chirped Pulse millimeter-Wave
Short time phase stability
Long time phase stability
Broadband chirp, arbitrary pulse sequence, Time-domain and frequency domain FID
Modifiable chirp shape
Tunable chirp rate

4. Bolometer-detected absorption
Chirped Pulse millimeter-Wave
Bolometer-detected absorption
Chirped Pulse
CPmmW Merit Ratio
= (100/50)(1500/670)2(4000/100) = 400

5. Rotational transitions: µ ~ 1 D → Limited by power
CPmmW for Rydberg States
Broadband
Low power
Rotational transitions: µ ~ 1 D → Limited by power
Rydberg-Rydberg transitions: µ ~ 1 kD → Intermediate coupling regime: Nearly maximum polarization
We have shown that CPmmW works pretty well for rotation spectrum, and how about Rydberg spectrum? It is even better. We know that if we stretch a narrow band pulse to a broad band pulse, we will lose power for a specific frequency component. In this formula, we increase the chirp rate, we can increase the pulse bandwidth, but we will lose the polarization, that is what we detect. To compensate this loss, we have to increase the electric field. So for rotational spectrum, the limitation is always power. But for Rydberg state, mu is kD instead of 1D. So it is always pretty easy to saturate a Rydberg transition with a short broad bandwidth pulse.
Rydberg systems well suited for CPmmW spectroscopy

6. Absorptive vs Emissive Transitions
Intensity/arb. units
Intensity/arb. units
1.08(2) π
0.04(2) π
Distinguish absorption vs emission in Rydberg-Rydberg transitions. Bloch vector model provides intuitive explanation of these transient nutation phenomena. Absorptive transitions are 180° out of phase with the stimulating radiation resulting in destructive interference, while emissive transitions interfere constructively, giving above patterns. This provides a method for distinguishing btwn these types of transitions, like quadrature phase detection, but which takes advantage of the time domain information and phase stability provided by CPmmW. Moreover, this phase shift holds in the case of chirped pulses or very short pulses where the curvature of the chirp is not impacted as in single frequency chirps.
Time/µs
Time/ns
36s
36p
41f
43d

7. Supersonic Beam Volume: 3cm x 3cm x 10 cm ~ 100cm3
generator
detector
TOF
LIF
Volume: 3cm x 3cm x 10 cm ~ 100cm3
Atomic Rydberg states: 107
Beam velocity: 1800 m/s (He), 600 m/s (Ar)
No skimmer, Doppler broadening > 400 kHz
ablation laser
pump lasers

8. Buffer Gas Cooling In-Cell Dynamics Molecule Production ThermalizationNe
In-Cell Dynamics L
Molecule Production
Thermalization
Diffusion
Extraction d
𝛾 𝑐𝑒𝑙𝑙 ≡ 𝜏 𝑑𝑖𝑓𝑓 𝜏 𝑝𝑢𝑚𝑝 ∝ 1 𝐿
Thermalization estimate: Buffer gas 10x lighter than species, Ablated species 100x hotter than buffer, need ~50 collisions. Typical thermalization times just a few milliseconds. Diffusion and extraction times both in range 1-10 ms.

9. Hutzler et al. Chem. Rev. 112(2012): 4803-4827
Buffer Gas Cooling
Beam Formation
𝑅𝑒= 𝐹 𝑖𝑛𝑒𝑟𝑡𝑖𝑎𝑙 𝐹 𝑣𝑖𝑠𝑐𝑜𝑢𝑠 ∝ 𝑑 𝑎𝑝𝑒𝑟𝑡𝑢𝑟𝑒
Effusive: Re ≲ 1
Partially Hydrodynamic: 1 ≲ Re ≲ 100
Supersonic: Re ≳ 100
Reynolds number scales linearly with in-cell buffer gas density, buffer gas flow rate, number of collisions near aperture
Hutzler et al. Chem. Rev. 112(2012):

10. Buffer Gas Cooling Volume: 3cm x 3cm x 20 cm ~ 200cm3
detector
generator 4K Ne
pump lasers
20K
90% Ni mesh
40K
ablation laser
Volume: 3cm x 3cm x 20 cm ~ 200cm3
Number of Rydberg states: 1010 atoms /108 molecules
Beam velocity: 150m/s, Doppler broadening ~ 30 kHz

11. Rydberg-Rydberg Transitions: Ba Atoms
75kHz
150kHz
Intensity/ arb. units
FID amplitude/ arb. units
Time/µs
Frequency on Scope/ GHz
Single shot spectroscopy possible
New physics available for interrogation:
Propagation of radiation through an extended sample
Superradiance/cooperative effects
Coming up: FID of Molecular Rydberg-Rydberg Transitions

12. Questions? Justin Neill (UVa) Brooks Pate (UVa)
Dave Patterson (Harvard)
John Doyle (Harvard)
John Barry (Yale)
Dave DeMille (Yale)
Questions?

13. |Ψ⟩ Ω Ω
|Ψ⟩

14. 2𝕽 𝐧 𝟑 Δν
𝓁+1→ 𝓁+2
𝓁→ 𝓁+1
𝓁+2→ 𝓁+3 n
n+1 𝓁
(𝓁+1)
(𝓁+2)
(𝓁+3)