Chirped-Pulse Millimeter-Wave Spectroscopy, Dynamics, and Manipulation of Rydberg–Rydberg Transitions by Anthony P. Colombo Submitted to the Department of Chemistry in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 2013 (cid:13)c Massachusetts Institute of Technology 2013. All rights reserved. Author .............................................................. Department of Chemistry May 15, 2013 Certified by.......................................................... Robert W. Field Haslam and Dewey Professor of Chemistry Thesis Supervisor Accepted by......................................................... Robert W. Field Chairman, Departmental Committee on Graduate Students 2 This doctoral thesis has been examined by a Committee of the Department of Chemistry that included Professor Robert G. Griffin .......................................... Chairperson, Thesis Committee Professor Sylvia T. Ceyer............................................ Member, Thesis Committee Professor Robert W. Field ........................................... Thesis Supervisor 4 Chirped-Pulse Millimeter-Wave Spectroscopy, Dynamics, and Manipulation of Rydberg–Rydberg Transitions by Anthony P. Colombo Submitted to the Department of Chemistry on May 15, 2013, in partial fulfillment of the requirements for the degree of Doctor of Philosophy Abstract The chirped-pulse millimeter-wave (CPmmW) technique is applied to transitions be- tween Rydberg states, and calcium atoms are used as the initial test system. The unique feature of Rydberg–Rydberg transitions is that they have enormous electric dipole transition moments: ∼5 kiloDebye at n∗ ∼ 45, where n∗ is the effective prin- cipal quantum number. After polarization by a mm-wave pulse in the 70–84 GHz frequencyregion, theexcitedtransitionsre-radiatefreeinductiondecay(FID)attheir resonant frequencies, and the FID is heterodyne-detected by the CPmmW spectrom- eter. Data collection and averaging are performed in the time domain. The spectral resolution is ∼100 kHz. Because of the large transition dipole moments, the available mm-wave power is sufficient to polarize the entire bandwidth of the spectrometer (12 GHz) in each pulse, and high-resolution survey spectra may be collected. Both absorptive and emissive transitions are observed, and they are distinguished by the phase of their FID relative to that of the excitation pulse. With the combination of the large transition dipole moments and direct monitoring of transitions, dynam- ics are observed, such as transient nutations from the interference of the excitation pulse with the polarization that it induces in the sample. Transient nutations also provide information about the sample, such as the dipole moment and the number density of Rydberg states. Since the waveform produced by the mm-wave source may be precisely controlled, states with high angular momentum may be populated by a sequence of pulses while recording the results of these manipulations in the time domain. Also, the superradiant decay of the Rydberg sample is probed both directly throughFIDandindirectlyusingphotonechoes. Prospectsforfurthermanipulations, such as adiabatic rapid passage, composite pulses, and optical/mm-wave stimulated Raman adiabatic passage, are evaluated. The application of the CPmmW technique to transitions between Rydberg states of molecules is discussed. Thesis Supervisor: Robert W. Field Title: Haslam and Dewey Professor of Chemistry 5 6 Acknowledgments First, I will acknowledge my research advisor, Bob Field. I am confident that the most enduring thing that I have learned from Bob (other than how to turn a scientific phrase) is to always apply the simplest model conceivable to a problem first: Even when the simple approach fails, there is still something to learn from how it fails. For most of my time in the Field Group, I have worked closely with Yan Zhou. I always appreciated his enthusiasm and his insight, and working with him has been excellent. We also worked with Kirill Prozument on the early Rydberg millimeter- wave experiments. In particular, he came up with the approach of using a large interaction volume that initially got things working. I have also enjoyed working closely with David Grimes since he joined the Rydberg Project. Steve Coy helped me especially with developing the phase extraction procedure discussed in Chapter 3. Jeff Kay and Vladimir Petrovi´c introduced me to the Rydberg Project when I was a new graduate student in the group. BarrattParkdesignedandassembledthechirped-pulsemillimeter-wavespectrom- eter described in this thesis. We benefited from collaborating with Brooks Pate and Justin Neill on importing the chirped-pulse method into the Field Group as well. I interacted substantially with a few other members of the Singlet Project: Josh Bara- ban, Bryan Changala, and Adam Steeves, who were willing to provide input and assistance on many issues. Josh Middaugh also gave a helping hand whenever asked. The Rydberg Project has been supported by the National Science Foundation. For three years, I was supported by a Department of Homeland Security Graduate Fellowship. 7 8 Contents 1 Introduction 19 1.1 Properties of Rydberg states . . . . . . . . . . . . . . . . . . . . . . . 19 1.2 Millimeter-wave spectroscopy of Rydberg states: Advantages and chal- lenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.3 The chirped-pulse millimeter-wave technique . . . . . . . . . . . . . . 23 1.4 ApplicationoftheCPmmWtechniquetothestudyofRydberg–Rydberg transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 1.5 Thesis overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2 Design principles and implementation of the CPmmW method for Rydberg–Rydberg transitions 27 2.1 Excitation schemes for Rydberg–Rydberg transitions . . . . . . . . . 28 2.2 The chirped-pulse millimeter-wave spectrometer . . . . . . . . . . . . 30 2.2.1 The mm-wave generation arm . . . . . . . . . . . . . . . . . . 30 2.2.2 The pulse/FID detection arm . . . . . . . . . . . . . . . . . . 32 2.3 The laser/mm-wave interaction region . . . . . . . . . . . . . . . . . 33 2.3.1 The guiding design principle: Large interaction volume . . . . 34 2.3.2 Experimental implementation . . . . . . . . . . . . . . . . . . 34 2.4 Pulsed-field ionization detection of Rydberg states . . . . . . . . . . . 36 2.5 Converting between and triggering of the CPmmW and PFI experiments 37 2.6 PFI detection of Rydberg–Rydberg transitions: Diagnostic tools . . . 40 2.6.1 PFID-OOmmTR measurement of Rydberg–Rydberg transitions 42 2.6.2 Location of Rydberg–Rydberg transitions by purely optical PFI 43 9 2.7 Excitation methods and Rydberg–Rydberg FID spectra . . . . . . . . 45 2.7.1 Notation for Rydberg–Rydberg transitions . . . . . . . . . . . 45 2.7.2 Single-frequency versus chirped excitation pulses . . . . . . . . 46 2.7.3 Characteristics of Rydberg–Rydberg FID spectra . . . . . . . 48 3 Transient nutations and transition phases in Rydberg states 51 3.1 Transient nutations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.1.1 Transient nutations of absorptive versus emissive transitions . 52 3.1.2 Transient nutations of different excitation pulse areas . . . . . 53 3.1.3 Information from transient nutations . . . . . . . . . . . . . . 57 3.1.4 Transient nutations in chirped-pulse excitation . . . . . . . . . 58 3.2 Principles of transition phases . . . . . . . . . . . . . . . . . . . . . . 60 3.2.1 High accuracy of phase information . . . . . . . . . . . . . . . 60 3.2.2 Transition phases for single-frequency excitation . . . . . . . . 61 3.2.3 Transition phases for chirped-pulse excitation . . . . . . . . . 62 3.3 Extraction of transition phases . . . . . . . . . . . . . . . . . . . . . . 63 3.3.1 Overview of the phase extraction procedure . . . . . . . . . . 64 3.3.2 Digital filtering . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3.3.3 Phase extraction for a single-frequency . . . . . . . . . . . . . 65 3.3.4 Phase extraction for a chirped pulse . . . . . . . . . . . . . . . 66 4 Manipulations of Rydberg quantum states and cooperative dynam- ics in Rydberg ensembles 69 4.1 Manipulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 4.1.1 Populating high-(cid:96) states with pulse sequences . . . . . . . . . 69 4.1.2 Photon echoes of Rydberg–Rydberg transitions . . . . . . . . 71 4.2 Cooperative effects and superradiance . . . . . . . . . . . . . . . . . . 73 4.2.1 Superradiant decay of photon echoes . . . . . . . . . . . . . . 75 4.2.2 Direct observation of superradiance in FID . . . . . . . . . . . 79 4.2.3 Further consequences of cooperative effects . . . . . . . . . . . 81 10