We develop and demonstrate a spectroscopic method for Rydberg-Rydberg transitions using a phase-controlled and -modulated, standing-wave laser field focused on a cloud of cold ^{85}Rb Rydberg atoms. The method is based on the ponderomotive (A^{2}) interaction of the Rydberg electron, which has less-restrictive selection rules than electric-dipole couplings, allowing us to probe both nS_{1/2}→nP_{1/2} and nS_{1/2}→(n+1)S_{1/2} transitions in first order. Without increase in laser power, third- and fourth-order subharmonic drives are employed to access Rydberg transitions in the 40 to 70 GHz frequency range using widely available optical phase modulators in the Ku band (12 to 18 GHz). Measurements agree well with simulations based on the model we develop. The spectra have prominent Doppler-free components with linewidths ≲200 kHz. The method paves the way for optical Doppler-free high-precision spectroscopy of Rydberg-Rydberg transitions and for spatially selective qubit manipulation with μm-scale resolution in Rydberg-based simulators and quantum computers, provided that magic states are chosen and that the atoms are sufficiently cold.
In ponderomotive spectroscopy an amplitude-modulated optical standing wave is employed to probe Rydberg-atom transitions, utilizing a ponderomotive rather than a dipole-field interaction. Here, we engage nonlinearities in the modulation to drive dipole-forbidden transitions up to the fifth order. We reach transition frequencies approaching the sub-THz regime. We also demonstrate magic-wavelength conditions, which result in symmetric spectral lines with a Fourier-limited peak at the line center. Applicability to precision measurement is discussed.
Using cold atoms, I probe the energy-level intervals between Rydberg states to high spectroscopic precision. The focus of this work is to lay the groundwork for an updated, highly-controlled measurement of the Rydberg constant using circular-state Rydberg atoms, needed to resolve a recent conflict in proton-radius values that arose in 2010 (the so-called 'proton radius puzzle'). Toward this end, I have demonstrated a fundamentally-new mechanism with which to drive atomic (Rydberg-Rydberg) transitions, utilizing an inelastic (state-changing) ponderomotive interaction. Until now, the multipole-field interaction has been the sole mechanism on which spectroscopy of atomic transitions has been based. In this work, the state-changing ponderomotive interaction ('ponderomotive spectroscopy') is demonstrated by amplitude-modulating an optical standing wave at a transition resonance of a Rydberg atom. At the core of this new spectroscopic technique is the requirement that the light intensity must be modulated in space within the atomic volume, and in time at the desired atomic transition frequency. A Rydberg atom in a modulated optical lattice is very well-suited for a demonstration of this novel type of spectroscopy. Magic-wavelength conditions of this interaction are also identified, as well as a method to drive transitions at harmonics of the modulation. Both of these features of ponderomotive spectroscopy will be utilized to simultaneously trap and probe Rydberg atoms to perform the Rydberg constant measurement. I also present a high-precision measurement of the quantum defect of a high-angular-momentum state of rubidium, the atomic species that will be used in the Rydberg constant measurement. The quantum defects of high-angular-momentum states are needed to determine the effect of the rubidium core polarizability on the Rydberg constant measurement, which is anticipated to be a leading uncertainty. Finally, I present the background and design work for a measurement of the Rydberg constant specifically tailored to help resolve the proton radius puzzle, thereby completing the major preliminary work needed for the performance of that high-precision measurement.
In ponderomotive spectroscopy an amplitude-modulated optical standing wave is employed to probe Rydberg-atom transitions, utilizing a ponderomotive rather than a dipole-field interaction. Here, we engage nonlinearities in the modulation to drive dipole-forbidden transitions up to the fifth order. We reach transition frequencies approaching the sub-THz regime. We also demonstrate magic-wavelength conditions, which result in symmetric spectral lines with a Fourier-limited feature at the line center. Applicability to precision measurement is discussed.
Fundamental physics is concerned with the problems of defining fundamental constants, units of measurement, and searching for new forces and aspects of matter. Usually, the best way to resolve these inquiries is to have a precise knowledge of atomic energy levels and the transition frequencies in order for their quantum states to be manipulated. Spectroscopy is a tool that probes these atomic energy levels by observing the atom's response as the energy of the applied radiation is varied. Over the past century, spectroscopy using electromagnetic radiation has involved direct interactions with the atom's electric and magnetic multipole moments via the
textbfAcdottextbfp term of the minimal coupling Hamiltonian. The work presented in this thesis utilizes such interactions with laser fields and goes a step further by exploring a novel light-matter interaction via the
A2 term. Leading problems in the field of fundamental physics include the commercialization of optical frequency standards with short-term stabilities beating
10−11/sqrttau and the discovery of new science arising from competitive precision measurements of the Rydberg constant and the detection of axion dark matter. Ultracold rubidium atoms subject to periodic optical potentials in standing waves of light known as optical lattices offer solutions to these problems. Rubidium atoms contained in miniaturized, glass vapor cells can be probed with a
778-nm laser in order to obtain the
ket5Srightarrowket5D transition frequency as a portable optical frequency standard. Optical traps can induce shifts that compensate those incurred by the probing lasers and confine the atoms to prevent residual Doppler effects, both of which would otherwise hamper the clock stability. Addressing the other two problems mentioned, circular-state Rydberg atoms that are able to be manipulated with optical lattices introduce a platform for high-resolution spectroscopy of their electronic transitions using very weak microwave fields. The long lifetimes of circular states, which approach 1~s, extend the probing times for a measurement of the Rydberg constant (
10−12 uncertainty) insensitive to the proton charge radius, and the existence of microwaves generated by axion couplings to the electromagnetic field. This dissertation explores the functionality of optical lattices as a tool that can contribute to the advancement of these aforementioned endeavors. In the first implementation of optical lattices for these goals, a measurement of the Rb
ket5D3/2 AC polarizability and photoionization cross section is performed using a cavity-enhanced optical lattice with an ultra-deep depth on the order of
sim105 single-photon recoils. The lattice wavelength is
lambda=1.064 mum, which induces shifts on
ket5D3/2 that can be characterized by the measured scalar polarizability of
alpha5D3/2S=−524(17)~atomic units. I choose this wavelength because it is commonly available as a narrow-linewidth, high-powered laser. At this wavelength, photoionization induces decay of this energy level and broadening of spectral lines as evidence of the significant measured cross section
sigmaPI=44(1)~Mb. The secondary use of lattices as a tool for fundamental physics concerns periodically driven ponderomotive potentials for the effort of initializing the circular states required for a Rydberg constant measurement and dark-matter detection. Experimentally, the principles are discussed in a newly developed lattice phase-modulation technique, where the
ket46S1/2rightarrowket46P1/2 and
ket48S1/2rightarrowket49S1/2 transitions were spectrocscopically measured with this driving mechanism. Additionally, the importance of cancelling stray electric and magnetic fields for this mechanism to be efficient is also demonstrated. The applicability of ponderomotive light-matter interactions for obtaining circular states is discussed in a theoretical proposal of all-optical circularization techniques.
We develop and study quantum and semiclassical models of Rydberg-atom spectroscopy in amplitude-modulated optical lattices. Both initial- and target-state Rydberg atoms are trapped in the lattice. Unlike in other spectroscopic schemes, the modulation-induced ponderomotive coupling between the Rydberg states is spatially periodic and perfectly phase-locked to the lattice trapping potentials. This leads to a type of sub-Doppler mechanism which we explain in detail. In our exact quantum model, we solve the time-dependent Schr\"odinger equation in the product space of center-of-mass (COM) momentum states and the internal-state space. We also develop a perturbative model based on the band structure in the lattice and Fermi's golden rule, as well as a semiclassical trajectory model in which the COM is treated classically and the internal-state dynamics quantum-mechanically. In all models we obtain the spectrum of the target Rydberg-state population versus the lattice modulation frequency, averaged over the initial thermal COM momentum distribution of the atoms. We investigate the quantum-classical correspondence of the problem in several parameter regimes and exhibit spectral features that arise from vibrational COM coherences and rotary-echo effects. Applications in Rydberg-atom spectroscopy are discussed.