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Deep and Periodically Driven Optical Lattices for Fundamental Physics

Ryan Cardman

Published Jan 1, 2023• 0 citations
Publisher

Abstract

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 $textbf{A}cdottextbf{p}$ 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 $A^2$ term. Leading problems in the field of fundamental physics include the commercialization of optical frequency standards with short-term stabilities beating $10^{-11}/sqrt{tau}$ 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 $ket{5S}rightarrowket{5D}$ 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 $ket{5D_{3/2}}$ AC polarizability and photoionization cross section is performed using a cavity-enhanced optical lattice with an ultra-deep depth on the order of $sim10^{5}$ single-photon recoils. The lattice wavelength is $lambda=1.064~mu$m, which induces shifts on $ket{5D_{3/2}}$ that can be characterized by the measured scalar polarizability of $alpha^{S}_{5D_{3/2}}=-524(17)$~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 $sigma_{PI}=44(1)$~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 $ket{46S_{1/2}}rightarrowket{46P_{1/2}}$ and $ket{48S_{1/2}}rightarrowket{49S_{1/2}}$ 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.

DOI
10.7302/8387

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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 textbfAcdottextbfptextbf{A}cdottextbf{p}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 A2A^2A2 term. Leading problems in the field of fundamental physics include the commercialization of optical frequency standards with short-term stabilities beating 10−11/sqrttau10^{-11}/sqrt{tau}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 778778778-nm laser in order to obtain the ket5Srightarrowket5Dket{5S}rightarrowket{5D}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 (10−1210^{-12}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 ket5D3/2ket{5D_{3/2}}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 sim105sim10^{5}sim105 single-photon recoils. The lattice wavelength is lambda=1.064 mulambda=1.064~mulambda=1.064 mum, which induces shifts on ket5D3/2ket{5D_{3/2}}ket5D3/2​ that can be characterized by the measured scalar polarizability of alpha5D3/2S=−524(17)alpha^{S}_{5D_{3/2}}=-524(17)alpha5D3/2​S​=−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)sigma_{PI}=44(1)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 ket46S1/2rightarrowket46P1/2ket{46S_{1/2}}rightarrowket{46P_{1/2}}ket46S1/2​rightarrowket46P1/2​ and ket48S1/2rightarrowket49S1/2ket{48S_{1/2}}rightarrowket{49S_{1/2}}ket48S1/2​rightarrowket49S1/2​ 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.
In this dissertation, I explore several aspects of Rydberg physics with laser spectroscopy. The experiments center around the use of a very deep, cavity-generated, one-dimensional optical lattice in a cold atom sample. The optical lattice produces elongated clouds of dense, cold atoms via dipole trapping and is able to generate extreme light shifts in the atoms due to its high intensity. I describe experiments which may be divided into two main classes. In the first, I use the dipole trap to prepare a dense sample of atoms for photoassociation of Rb atom pairs into diatomic Rydberg molecules. The Rydberg molecules are formed by low-energy scattering of the Rydberg electron of one atom from the other atom, which is a ground-state atom. This novel binding mechanism also has relevance for chemical physics. I present binding energy measurements for eight different cases of Rydberg molecules. The binding energies reveal information about electron-atom collisions, such as their scattering lengths, and about the spin couplings present within the molecular system. In the second class of experiments, I introduce two proposed measurements in which the optical lattice is ramped to very high intensity during the laser excitation, creating AC Stark shifts in the transition frequencies. In one measurement, low-lying atomic states are probed. Measurements of the light shifts are expected to yield data on the dynamic polarizability and the photoionization cross section of the 5D3/2D_{3/2}D3/2​-state in rubidium in a 1064-nm light field. I show corresponding preliminary experimental data. The polarizability and photo-ionization cross-section measurements will provide tests of atomic structure theory, which is important both at a fundamental level and for applications such as atomic clocks. In another proposed measurement, Rydberg atoms in the lattice experience ponderomotive shifts and strong mixing of their angular-momentum states, allowing direct optical excitation of the lattice-mixed high-angular-momentum states. I describe the theoretical basis and experimental preparation for spectroscopically characterizing the lattice-mixed states. The ability to optically excite selected high-angular-momentum states without the use of static or RF fields may be useful for quantum information processing and simulation.
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.
I examine the trapping of Rydberg atoms in an optical standing wave. This trap, called an optical lattice, offers a platform for utilizing Rydberg atoms and their unique properties in applications such as atomic spectroscopy and quantum computing. Toward this end, I demonstrate the capability to trap rubidium 85 Rydberg atoms in a one-dimensional 1064 nm wavelength optical lattice with high efficiency. I have achieved a 90% trapping efficiency by inverting the lattice immediately after Rydberg-atom excitation, using an electro-optic technique. In addition, I investigate the dependence of optical-lattice trapping potentials for Rydberg atoms on the angular portion of the atomic wavefunction. While ground-state atoms are point-like in relation to an optical-lattice field, Rydberg-atom wavefunctions extend over a substantial fraction of the lattice period, leading to an angular dependence of the lattice trapping potentials. I measure the potentials using various angular sublevels of Rydberg nD states prepared in the optical lattice with a superimposed transverse DC electric field. This unique angular dependence of Rydberg-atom optical lattices may be exploited to tailor the trapping potentials as needed for spectroscopy or quantum computing. Further, atom loss due to lattice-induced photoionization of Rydberg atoms must be characterized for applications. I investigate the photoionization process as a function of position within the volume of a Rydberg atom. Since Rydberg-atom sizes approximately equal the lattice period, the lattice intensity varies maximally within the atomic volume. I find that photoionization rates are higher for lattice intensity maxima located near the nucleus than within the lobes of the electronic probability distribution. Photoionization therefore occurs near the Rydberg-atom nucleus. Finally, I calculate photoionization rates for Rydberg atoms in optical fields and investigate how these rates relate to the validity of the electric dipole approximation. This approximation is usually central to matter-field interactions, and Rydberg atoms in optical fields present a system for studying the approximation in a limiting case. I further apply the photoionization calculations to experimentally-relevant conditions. With these advances, this thesis lays essential groundwork for the employment of Rydberg-atom optical lattices in applications.
Accurate time keeping is critical to the function and advancement of many human endeavours. Atomic clocks based on a microwave transition in atomic Cs have served as primary frequency standards to realise the SI second since their formal adoption in 1967. State-of-the-art, laser cooled, Cs fountains now routinely operate with fractional frequency uncertainties below the 10⁻¹⁵ level in laboratories throughout the world. Over the last decade, efforts to build frequency standards based on optical transitions have come to fruition and potential inaccuracies below the 10⁻¹⁷ level have been demonstrated. Such standards point to the future of time keeping and much development is being pursued to realise the potential of these 'next generation' optical clocks. One such approach, on which this work focusses, relies on a 'magic' wavelength optical lattice trap to provide (almost) Doppler- and recoil-free confinement of atoms during clock interrogation. At this 'magic' wavelength, light induced perturbation of the clock states is equal and so cancels precisely. This thesis describes the design and implementation of an optical lattice frequency standard apparatus based on 88Sr held in a 1D optical lattice. A review of the development of atomic frequency metrology is given from a historical viewpoint and the technology and limitations of current methods discussed. To tackle the blackbody radiation shift, which currently presents the greatest limitation to the Sr lattice clock, imposing at the 10⁻¹⁶ level, a scheme to measure the blackbody radiation shift coefficient at the 10⁻¹⁷ level is developed. Techniques to laser cool and trap atomic strontium are described and the implementation detailed. All laser systems required for clock operation are described including the design and implementation of extended-cavity diode lasers for precision spectroscopy. Details relevant to the eventual operation of the apparatus are discussed.
Rydberg atoms are highly excited atoms that have large sensitivities to external fields, lending these atoms extraordinary characteristics for fundamental high-precision spectroscopy as well as for electromagnetic-field sensing applications. Recent results on high-precision spectroscopy with cold Rydberg atoms in modulated optical lattices are presented. The discussed approach can serve as a platform for fundamental-physics studies, which include a model-insensitive measurement of the Rydberg constant and a search for wave-like dark matter. As an example for the utility of Rydberg atoms in field sensing applications, an experiment is presented in which the linear Stark effect of cold Rydberg atoms is employed to measure electric fields in cold ion clouds, demonstrating that Rydberg laser spectroscopy allows electrode-free, non-invasive plasma diagnostics.
— Modern capabilities in quantum state engineering of ultracold matter and precise control of light fields now permit accurate control of interactions between matter and field to suit applications for precision tests of fundamental physics. We report on our recent development of a highly stable and accurate optical atomic clock based on ultracold neutral Sr atoms confined in an optical lattice. We discuss precision tools for the lattice clock, including stabilized lasers with sub-Hz linewidth, femtosecond-comb based technology allowing accurate clock comparison in both microwave and optical domains, and clock transfer over optical fibers. With microkelvin Sr atoms confined in an optical lattice that provide a zero differential a.c. Stark shift between two clock states, we achieve a resonance quality factor >2×10 on the S0 − P0 doubly forbidden Sr clock transition at 698 nm. High resolution spectroscopy of spin-polarized atoms is used for both high-performance clock operations and accurate atomic structure measurement. The overall systematic uncertainty of the clock has been evaluated at the 10−16 level, while the stability approaches low 10−15 at 1 s. These developments in precise engineering of lightatom interactions can be extended to the field of ultracold molecules, bringing new prospects for precision measurements, quantum control, and determinations of the constancy of the fundamental constants.