Population-resolved measurement of an avoided crossing of light-dressed states

TL;DR

This work addresses measuring both the energies and the eigenvector amplitudes of an avoided crossing in a two-level system driven by a near-resonant field. By spectroscopically mapping the dressed energies $E_+$ and $E_-$ while resolving the populations in |g> and |e> via selective field ionization, the authors extract the eigenvector components as functions of detuning. They also perform Landau-Zener sweeps to observe diabatic versus adiabatic transitions, obtaining a Landau-Zener probability $P_D = \exp(-2\pi (\Omega/2)^2 / |d\Delta/dt|)$ and an Omega of about $2\pi\ times 0.54$ MHz. The results demonstrate selective field ionization as a precise readout of the full 2x2 dressed-state eigensystem in RF-dressed Rydberg atoms with potential applications in metrology and quantum control.

Abstract

A two-level system coupled by a coherent field is a ubiquitous system in atomic and molecular physics. In the rotating wave approximation, the light-dressed states are well described by a simple 2x2 Hamiltonian which can be easily solved analytically and is thus used in quantum mechanics education and as a basis for intuition for more complicated systems. The solution to the Hamiltonian is an avoided crossing between the light-dressed ground and excited states. In experiments, the avoided crossing is probed spectroscopically, meaning only the energies, or eigenvalues of the Hamiltonian, are measured. Here, we present a measurement of the avoided crossing which also resolves population, thus indicating the amplitude coefficients of the eigenvectors of the Hamiltonian. We perform the measurement in Rydberg states of cold rubidium atoms, resolving the energies spectroscopically with our pump lasers and the populations of each state using selective field ionization.

Figures (4)

• Figure 1: The avoided crossing described by equations \ref{['eq:evals']} and \ref{['eq:evecs']} for a Rabi rate of $\Omega = 2\pi \cdot 1$ MHz. The color represents the projection of each state onto the atomic basis states.
• Figure 2: Experimental scheme for measuring the dressed states. a The energy level scheme for the optical pumping and light dressing. b The state readout scheme. As the electric field is ramped, the states ionize at different times, resulting in an ionization signal with peaks for each state. c The timing of the experiment.
• Figure 3: Experimental (top) and theoretical (bottom) mappings of the avoided crossings at various RF powers. The theoretical curves are calculated from Eqs. \ref{['eq:evals']} and \ref{['eq:evecs']} using a Rabi frequency inferred from a measured calibration between the square root of the power emitted by the source and the Autler-Townes splitting observed.
• Figure 4: Landau-Zener transition rate mapping. a The timing of the experiment. b The transition in the dressed state picture. c Experimental mapping of the populations and the associated diabatic transition probability $P_D$ for various sweep rates. Each point represents 10 measurements. Here the solid lines represent Landau-Zener theory with a fit offset and contrast (Eq. \ref{['eq:LZfit']}).