Excitation of a Single Atom with Exponentially Rising Light Pulses

We investigate the interaction between a single atom and optical pulses in a coherent state with a controlled temporal envelope. In a comparison between a rising exponential and a square envelope, we show that the rising exponential envelope leads to a higher excitation probability for fixed low average photon numbers, in accordance with a time-reversed Weisskopf-Wigner model. We characterize the atomic transition dynamics for a wide range of the average photon numbers and are able to saturate the optical transition of a single atom with $\approx 50$ photons in a pulse by a strong focusing technique.

Figure 1

Top: Preparation of pulses with controllable waveform. Bottom: Setup for transmission and reflection measurement of light by a single atom. UHV: ultra high vacuum chamber, AL: aspheric lenses with full $\mathrm{NA}=0.55$ and focal length $f=4.51\mathrm{mm}$; PBS, polarizing beam splitter; ND1,2, stacks of neutral density filters; $\lambda /2$, $\lambda /4$, wave plates; DM, dichroic mirrors; IF, interference bandpass filters centered at 780 nm.

Figure 2

Histograms of detection times with respect to a pulse edge for $1.5\times {10}^7$ excitation pulses in time bins of 1 ns. Top: exponentially rising pulse with $\tau =15\mathrm{ns}$ and mean photon number $⟨N⟩=110\pm 6$, with an exponential fit (dashed line). Bottom: Reference pulse with $\tau =15\mathrm{ns}$ and $⟨N⟩=104\pm 5$.

Figure 3

Exponentially rising excitation pulse (a) and atomic fluorescence detected in backward direction (b). The left-hand axis depicts the histogrammed photoevents in a 1 ns wide time bin, the right-hand axis on the fluorescence plot the excitation probability derived from it (see text for details). Error bars indicate Poissonian counting statistics. The solid lines indicate exponential fits with time constants of $\tau =15.4\mathrm{ns}$ for the excitation pulse and $\tau =26.2\mathrm{ns}$ for the decay in the fluorescence.

Figure 4

Time-dependent atomic excitation probability $P_e$ for pulses with a large average photon number $⟨N⟩$, leading to Rabi oscillations. Solid lines represent simulations according to the model in 10.

Figure 5

Maximal atomic excitation probability during a single pulse for different average photon numbers $⟨N⟩$ and characteristic pulse times $\tau$. Filled circles represent experimental data for exponential, open circles for square excitation pulses. Solid lines represent simulations using a time-dependent coupling strength of Eq. (4) [10], according to which the advantage of the exponential pulse compared to the square pulses decreases with $⟨N⟩$.

Figure 6

Excitation dynamics for an exponential pulse (filled circles) with ${\tau }_e=25\mathrm{ns}$ and a square pulse (open circles) with ${\tau }_{\mathrm{sq}}=60\mathrm{ns}$ optimized for the same experimental parameter $\eta =0.027$, and comparable $⟨N_e⟩=2.75\pm 0.06$ and $⟨N_s⟩=2.10\pm 0.08$, respectively. Solid lines show theoretical predictions for those cases.