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

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 76.8-98.4GHz 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

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

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

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

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

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

Buffer Gas Cooling In-Cell Dynamics Molecule Production Thermalization Ne 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.

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): 4803-4827

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

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

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

|Ψ⟩ Ω Ω |Ψ⟩

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)