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Physical Review Letters

Optical Mixing of Rydberg Angular Momenta

John D. Corless, Carlos R. Stroud

Published Jul 28, 1997• 35 citations
Publisher

Abstract

When optical frequency fields are used to couple a ground state to a Rydberg state, the resonant dipole coupling is to a low angular momentum state. Higher angular momentum states are typically thought not to play a role in the excitation. The extremely large dipole matrix elements coupling Rydberg states of the same $n$ but differing $l$, however, allow optical fields of modest strengths to produce Rabi frequencies larger than optical frequencies. We demonstrate that these optical fields can therefore readily excite the higher angular momentum states, and we examine the consequences of this coupling.

DOI
10.1103/physrevlett.79.637

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When optical frequency fields are used to couple a ground state to a Rydberg state, the resonant dipole coupling is to a low angular momentum state. Higher angular momentum states are typically thought not to play a role in the excitation. The extremely large dipole matrix elements coupling Rydberg states of the same nnn but differing lll, however, allow optical fields of modest strengths to produce Rabi frequencies larger than optical frequencies. We demonstrate that these optical fields can therefore readily excite the higher angular momentum states, and we examine the consequences of this coupling.
Numerical integration of the Schr\"odinger equation for the resonant single-photon excitation from the 1s1s1s to 10p10p10p state in atomic hydrogen has been used to produce solutions converged to a precision of a few parts per million. At all intensities investigated (in the range 10−−100TW/cm2),10--100{\mathrm{T}\mathrm{W}/\mathrm{c}\mathrm{m}}^{2}),10−−100TW/cm2), the population in the states having angular momentum higher than l=1\mathcal{l}=1l=1 after a narrowband (500 fs) laser pulse are found to be neglible. This shows that off-resonant states can effectively suppress Raman-like transitions to degenerate states of higher angular momentum. Instead of such mixing, strong Rabi-like oscillations between 1s1s1s and the np\mathrm{np}np Rydberg series are observed.
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 consider the excitation of Rydberg states through photons carrying an intrinsic orbital angular momentum degree of freedom. Laguerre–Gauss modes, with a helical wave-front structure, correspond to such a set of laser beams, which carry units of orbital angular momentum in their propagation direction, with ℓ 0 the winding number. We demonstrate that, in a proper geometry setting, this orbital angular momentum can be transferred to the internal degrees of freedom of the atoms, thus violating the standard dipole selection rules. Higher orbital angular momentum states become accessible through a single photon excitation process. We investigate how the spacial structure of the Laguerre–Gauss beam affects the radial coupling strength, assuming the simplest case of hydrogen-like wavefunctions. Finally we discuss a generalization of the angular momentum coupling, in order to include the effects of the fine and hyperfine splitting, in the context of the Wigner–Eckart theorem.
We report efficient microwave-optical two photon excitation of Rb Rydberg atoms in a magneto-optical trap. This approach allows the excitation of normally inaccessible states and provides a path toward excitation of high-angular-momentum states. The efficiency stems from the elimination of the Doppler width, the use of a narrow-band pulsed laser, and the enormous electric-dipole matrix element connecting the intermediate and final states of the transition. The excitation is efficient in spite of the low optical and microwave powers, of order 1 kW and 1 mW, respectively. This is an application of the large dipole coupling strengths between Rydberg states to achieve two-photon excitation of Rydberg atoms.
We demonstrate the coherent excitation of a mesoscopic ensemble of about 100 ultracold atoms to Rydberg states by driving Rabi oscillations from the atomic ground state. We employ a dedicated beam shaping and optical pumping scheme to compensate for the small transition matrix element. We study the excitation in a weakly interacting regime and in the regime of strong interactions. When increasing the interaction strength by pair state resonances, we observe an increased excitation rate through coupling to high angular momentum states. This effect is in contrast to the proposed and previously observed interaction-induced suppression of excitation, the so-called dipole blockade.
The authors describe and analyse an RF-optical technique for exciting alkali atoms in an atomic beam to a specific high angular momentum Rydberg state. In the procedure the Rydberg states are dressed by an RF field and two optical photons are used to excite the dressed state that goes adiabatically into the desired Rydberg state as the RF field is turned off. They describe in detail the excitation of the aligned-circular-orbit states. The states have the maximum angular momentum quantum numbers for a given principal quantum number, and thus are the most nearly classical of all eigenstates. It is shown that in excess of 90% of the excited state population can be put into the aligned-circular-orbit state.