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New Journal of Physics

Adiabatic potentials for Rydberg atoms in a ponderomotive optical lattice

Kelly Cooper Younge, Sarah Elizabeth Anderson, Georg A. Raithel

Published Feb 22, 2010• 28 citations
Publisher

Abstract

We calculate the adiabatic potentials and adiabatic wavefunctions of Rydberg atoms in a one-dimensional ponderomotive optical lattice. All lattice-induced couplings between the degenerate high-angular-momentum Rydberg states are taken into account. To obtain insight into the underlying physics, we analyze the numerical results in terms of effective electric and magnetic fields produced by the lattice. Near the inflection points of the lattice potential and for sufficiently low principal quantum numbers ( n ≲35 in the cases studied), the adiabatic level structure resembles that of the dc Stark effect, and an effective electric-field model can be used to model the lattice-induced perturbation. Near the nodes and anti-nodes of the lattice field, the adiabatic level structure exhibits a combination of adjacent rotational and vibrational energy level sequences. Here, an analogy between the ponderomotive optical lattice and the diamagnetic problem works well to interpret the lattice-induced perturbation in terms of an effective magnetic field.

DOI
10.1088/1367-2630/12/2/023031

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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.

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We study Rydberg atoms in ponderomotive optical lattices. Unlike for ground-state atoms, for Rydberg atoms in an optical lattice the extent of the electronic wave-function can approach the lattice period. This leads to state-dependent adiabatic trapping potentials that are unique to Rydberg atoms. We first discuss a theoretical model of adiabatic lattice potentials of Rydberg atoms. Then, we use microwave spectroscopy to experimentally demonstrate and investigate the state-dependence of the adiabatic potentials of S1/2 Rydberg states of rubidium. The observed microwave spectra depend strongly on both the principal quantum number and the depth of the lattice. A semi-classical simulation is used to explain the features seen in the spectra. Based on the results, we estimate the trapping efficiency of the ponderomotive optical lattice.

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We calculate the adiabatic potentials and adiabatic wavefunctions of Rydberg atoms in a one-dimensional ponderomotive optical lattice. All lattice-induced couplings between the degenerate high-angular-momentum Rydberg states are taken into account. To obtain insight into the underlying physics, we analyze the numerical results in terms of effective electric and magnetic fields produced by the lattice. Near the inflection points of the lattice potential and for sufficiently low principal quantum numbers ( n ≲35 in the cases studied), the adiabatic level structure resembles that of the dc Stark effect, and an effective electric-field model can be used to model the lattice-induced perturbation. Near the nodes and anti-nodes of the lattice field, the adiabatic level structure exhibits a combination of adjacent rotational and vibrational energy level sequences. Here, an analogy between the ponderomotive optical lattice and the diamagnetic problem works well to interpret the lattice-induced perturbation in terms of an effective magnetic field.
We study Rydberg atoms in ponderomotive optical lattices. Unlike for ground-state atoms, for Rydberg atoms in an optical lattice, the extent of the electronic wave-function can approach the lattice period. This leads to state-dependent adiabatic trapping potentials that are unique to Rydberg atoms. We use microwave spectroscopy to experimentally demonstrate and investigate the state-dependence of the adiabatic potentials of S1/2 Rydberg states of rubidium. The observed microwave spectra depend strongly on both the principal quantum number and the depth of the lattice. A semi-classical simulation is used to interpret the features seen in the microwave spectra. A large fraction of the Rydberg atoms can be trapped in the ponderomotive optical lattice.
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.
We study Rydberg atoms in ponderomotive optical lattices. Unlike for ground-state atoms, for Rydberg atoms in an optical lattice the extent of the electronic wave-function can approach the lattice period. This leads to state-dependent adiabatic trapping potentials that are unique to Rydberg atoms. We first discuss a theoretical model of adiabatic lattice potentials of Rydberg atoms. Then, we use microwave spectroscopy to experimentally demonstrate and investigate the state-dependence of the adiabatic potentials of S1/2 Rydberg states of rubidium. The observed microwave spectra depend strongly on both the principal quantum number and the depth of the lattice. A semi-classical simulation is used to explain the features seen in the spectra. Based on the results, we estimate the trapping efficiency of the ponderomotive optical lattice.
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.
Abstract We present a degenerate perturbation analysis in the spin–orbit coupled basis for Rydberg atoms in an optical trap. The perturbation matrix is found to be nearly the same for two states with the same total angular momentum j , and orbital angular momentum number l differing by 1, The same perturbation matrices result in the same state-mixing and energy shift. We also study the dependence of state mixing and energy shift on the periodicity and symmetry of the ponderomotive potentials induced by different optical traps. State mixing in a one-dimensional lattice formed with two counterpropagating Gaussian beams is studied and yields a state-dependent trap depth. We also calculate the state-mixing in an optical trap formed by four parallel, separated and highly focused Gaussian beams.
We discuss three proposed schemes of initializing circular-state Rydberg atoms via optical couplings provided by the ponderomotive effect in contrast to the current circularization methods that utilize electric-dipole interactions. In our first proposed method, a radial optical trap consisting of two Laguerre-Gaussian beams of opposite winding numbers transfers orbital angular momentum to the Rydberg atom, providing a first-order coherent coupling between an F state and a circular state. Additionally, we propose a one-dimensional ponderomotive optical lattice modulated at rf frequencies, providing quadrupolelike couplings in the hydrogenic manifold for rapid adiabatic passage through a series of intermediate Rydberg states into the circular state. For the third proposed scheme, a two-dimensional ponderomotive optical lattice with a time-orbiting trap center induces effectively the same coupling as a ${\ensuremath{\sigma}}^{+}$- or ${\ensuremath{\sigma}}^{\ensuremath{-}}$-polarized rf field of tunable purity for all-optical rapid adiabatic passage into the circular state.