From coherent collective excitation to Rydberg blockade on an atom chip

Using time-resolved measurements, we demonstrate coherent collective Rydberg excitation crossing over into Rydberg blockade in a dense and ultracold gas trapped at a distance of 100 $\mu \mathrm{m}$ from a room-temperature atom chip. We perform Ramsey-type measurements to characterize the coherence. The experimental data are in good agreement with numerical results from a master equation using a mean-field approximation and with results from a super-atom-based Hamiltonian. This represents significant progress in exploring a strongly interacting driven Rydberg gas on an atom chip.

Figure 1

Demonstration of Rydberg blockade on an atom chip. (a) Illustration of our mounted chip trapping a cloud of atoms containing Rydberg excitations (black) in blockade spheres (blue). The two counterpropagating excitation beams are drawn as well. (b) Rydberg excitation of the $|28D_{5/2},m_J=5/2\rangle$ state with two different pulse configurations with the same total pulse time, excited at a constant Rabi frequency of $\mathrm{\Omega }/2\pi =140\mathrm{kHz}$. This data set was obtained using $21\times {10}^3$ atoms at a temperature of $T=0.7\mu \mathrm{K}$. The open squares are a loss spectrum measured with 75 pulses of $500\mathrm{ns}$ sent every $30\mu \mathrm{s}$; the solid circles are a loss spectrum measured with a single $37.5\mu \mathrm{s}$ pulse. Each point is the average of four measurements; the error bars denote one standard error of the mean. The solid lines are solutions to the mean-field master equation model (see the main text). Inset: schematic pulse shapes used for obtaining the spectra.

Figure 2

Regimes of collective Rydberg excitation observed in atom loss. Time evolution of the relative losses per pulse when exciting the $|28D_{5/2},m_J=5/2\rangle$ (red circles, top data set) and $|30S_{1/2},m_J=1/2\rangle$ (blue squares, bottom data set) states resonantly. Using $N=2\times {10}^4$ atoms at $T=2\mu \mathrm{K}$ with two-photon, single-atom Rabi frequencies of $\mathrm{\Omega }/2\pi \approx 210\mathrm{kHz}$ and $40\mathrm{kHz}$ for the $28D_{5/2}$ and $30S_{1/2}$ states, respectively. The error bars denote one standard error of the mean of three measurements. The solid and dotted lines are the result of the mean-field master equation model and the superatom Hamiltonian evolution, respectively. The solid, gray line indicates a linear relation, and serves to show deviations from this in both the coherent and in the blockaded regime.

Figure 3

Ramsey fringes measured both in (a) the frequency and (b) time domain to assess the coherence of the excitation of the $|30S_{1/2},m_J=1/2\rangle$ state. In both measurements (blue circles) we used multiple pair pulses sent at intervals longer than the Rydberg lifetime. The pairs consisted of two 250 $\mathrm{ns}$ pulses, either at a variable detuning [(a) time between pulses fixed to $250\mathrm{ns}$, measured using $13\times {10}^3$ atoms at $T=2\mu \mathrm{K}]$ or using a variable time between the pulses [(b) detuning fixed to $\mathrm{\Delta }/2\pi =-2\mathrm{MHz}$, measured using $N={10}^4$ atoms at $T=1\mu \mathrm{K}]$. The orange, solid lines are the results of the mean-field master equation. The gray, dotted lines are the populations in the Rydberg state obtained by evolving the Hamiltonian as described in the main text; this is either convolved with a Gaussian (a) or given an offset and an exponentially decaying envelope (b) to approximate the effects of decoherence (dash-dotted, red lines). The bottom figure also contains a fit to an exponentially decaying sine (dashed, green line), from which we extract a coherence time of $1/\gamma =0.44\mu \mathrm{s}$.