Efficient three-photon excitation of quasi-one-dimensional strontium Rydberg atoms with $n\sim 300$

The efficient production of very-high-$n$, $n\sim 300$, quasi-one-dimensional (quasi-1D) strontium Rydberg atoms through three-photon excitation of extreme Stark states in the presence of a weak dc field is demonstrated using a crossed laser-atom beam geometry. Strongly polarized quasi-1D states with large permanent dipole moments $\sim 1.2n^2$ a.u. can be created in the beam at densities ($\sim {10}^6$ cm${}^{-3}$) where dipole blockade effects should become important. A further advantage of three-photon excitation is that the product $F$ states are sensitive to the presence of external fields, allowing stray fields to be reduced to very small values. The experimental data are analyzed using quantum calculations based on a two-active-electron model together with classical trajectory Monte Carlo simulations. These allow determination of the atomic dipole moments and confirm that stray fields can be reduced to $\le 25\mu$V cm${}^{-1}$.

Figure 1

Schematic diagram of the apparatus. The inset in the lower right corner shows the three-photon excitation scheme employed.

Figure 2

(a) Evolution of the Stark energy levels for strontium $\left|M\right|=1$ states in the vicinity of $n=50$ (black lines) calculated using a two-active-electron model. The thick blue (gray) lines show the calculated spectrum for excitation of “$nF$” states, the red (dark gray) lines show the measured excitation spectrum at $n\sim 306$. The applied dc field is normalized to the crossing field (see text). The energy axis is scaled such that a scaled energy of one corresponds to the energy separation between neighboring $n$ and ($n-1$) states. The inset shows an expanded view in the low-field region (indicated by the dashed square). (b) Applied field dependence of the calculated average dipole moment of several states including “$nF$” states.

Figure 3

The average number of 306$F$ Rydberg atoms excited during a 0.6-$\mu$s-duration laser pulse as a function of the oven temperature. The solid symbols show the results of measurements in which the production rate was limited by reducing the intensity of the 893 nm beam by the factors indicated. The open squares show the excitation probabilities expected (in the absence of dipole blockade) when using the full laser intensity. The calculated results (solid lines) employ a four-level model multiplied by the number of atoms within the interaction volume derived from the vapor pressure [27].

Figure 4

Measured ionization probabilities for “306$F$” states excited in the dc fields indicated as a function of the scaled amplitude of a probe field, $F_{\mathrm{step}}{n}^4$, of 10 ns duration, $T_p\sim 2.3T_n$. Solid (open) circles denote data points recorded with the probe field applied parallel (antiparallel) to the dc electric field $F_{\mathrm{dc}}$. The solid (dashed) lines show the ionization probabilities calculated with the probe field parallel (anti-parallel) to $F_{\mathrm{dc}}$. As the initial state, the CTMC calculations employ (a) a microcanonical ensemble restricted to $\ell =1$ and $m=1$ and (b)–(d) an ensemble of 13 parabolic states with an average $k$ of (b) $k=166$, (c) $k=212$, and (d) $k=244$.

Figure 5

(a)–(c) Measured ionization probabilities for $n\sim 306$ states excited in a dc field $F_{\mathrm{dc}}\sim 0.4F_{\mathrm{cross}}$ with the laser tuned to the points (A–C) indicated in the spectrum in the inset as a function of the scaled amplitude of a 10 ns probe field, $F_{\mathrm{step}}$. Solid (open) circles denote data points recorded with the probe field applied parallel (anti-parallel) to $F_{\mathrm{dc}}$. Measured ionization probabilities [(d) and (e)] for “309$P$” states and [(f) and (g)] for “308$D$” states excited in the dc fields $F_{\mathrm{dc}}$ indicated. The CTMC simulations employ, as the initial state, an ensemble of 13 parabolic states with an average $k$ of (a) $k=244$, (b) $k=0$, and (c) $k=-$195 and (d)–(g) a distribution derived from the quantum TAE calculations [19]. The probe field amplitude is indicated in scaled units, $F_{\mathrm{step}}{n}^4$.

Figure 6

Survival probabilities measured (black lines) for “309$F$” states produced in a field $F_{\mathrm{dc}}\sim 0.3F_{\mathrm{cross}}$ and subject to a 5 mV cm${}^{-1}$ 80-ns-long pump pulse, $F_{\mathrm{pump}}$, as a function of the time delay between the end of $F_{\mathrm{pump}}$ and the application of a 6-ns-long probe pulse $F_{\mathrm{step}}\sim 100$ mV cm${}^{-1}$. The blue (gray) lines show the result of CTMC simulations in which the initial state is represented by an ensemble of 13 parabolic states with an average $k\simeq 224$ and $m=2$. In (a) the probe pulse is parallel to $F_{\mathrm{dc}}$, in (b) parallel to $F_{\mathrm{pump}}$.

Figure 7

(a) Measured and (b) calculated survival probabilities for “306$F$” states as a function of the time delay, $t_d$, between turn-off of the pump field $F_{\mathrm{pump}}$ and application of the probe pulse $F_{\mathrm{step}}\sim 120$ mV cm${}^{-1}$ in the $z$ direction. Shown is the envelope of the unresolved fast quantum beats with period $T_n\simeq 4.3$ ns (see Fig. 6).