Linear Stark effect in ${\mathrm{Y}}_3{\mathrm{Al}}_5{\mathrm{O}}_{12}:{\mathrm{Tm}}^{3+}$ crystal and its application in the addressable quantum memory protocol

We report an observation of the linear Stark effect in a ${\mathrm{Tm}}^{3+}:{\mathrm{Y}}_3{\mathrm{Al}}_5{\mathrm{O}}_{12}$ crystal with the distribution of the Stark coefficient over the ion ensemble. We associate this effect with local lattice distortions near the positions of ${\mathrm{Tm}}^{3+}$ ions. Using this effect, the addressable storage of a series of weak light pulses in a cavity-assisted scheme of the revival of silenced echo quantum memory protocol is implemented. In this memory scheme, we also demonstrate storage of a light pulse on the few photon level. The application of an optical resonator makes it possible to increase the memory efficiency in this crystal and to reduce the minimal number of photons in the input signal pulse to 5.6 for the signal-to-noise ratio of 1 in the retrieved echo pulse. The results are in good agreement with the theoretical analysis. The possible ways of the further improvement of the implemented memory scheme are also discussed.

Figure 1

Simplified sketch of the experimental setup: ${\mathrm{R}}_1$ and ${\mathrm{R}}_2$ denote front and back mirror of the concentric resonator; P, Glan-Taylor polarizer; D, diaphragm; A, neutral density filter; BS, 50:50 beam splitter; F, fluorescence bandpass filter; MM, multimode fiber; SM, single mode fiber; SPCM, single photon counting module; APD, avalanche photodetector; TDC, time to digital converter; C, cylindrical lens; f, spherical lens; GTH, Gauss to top hat beam shaping lens.

Figure 2

Sequence of light pulses that were used to study the Stark effect in the ${\mathrm{Tm}}^{3+}:{\mathrm{Y}}_3{\mathrm{Al}}_5{\mathrm{O}}_{12}$ crystal using (a) two-pulse photon echo, (b) spectral hole burning, and (c) ROSE protocol with the multipulse signal field using control Stark pulses of opposite polarities. Orange rectangles show the applied pulses of the external electric field. The pulses propagating in the control beam are shown in green and in the signal beam are shown by blue (as in Fig. 1).

Figure 3

Dependence of the two-pulse photon echo intensity on the Stark pulse area with different durations in the ${\mathrm{Tm}}^{3+}:{\mathrm{Y}}_3{\mathrm{Al}}_5{\mathrm{O}}_{12}$ crystal on the ${}^3\mathrm{H}_6\left(0\right)\to {}^3\mathrm{H}_4\left(0\right)$ transition at 3.7 K. $E_{\mathrm{laser}}\parallel E_{St}\parallel \left[110\right]$ the crystal axes. Squares, circles, and diamonds correspond to the Stark pulse duration of 5, 15, and $25\mu \mathrm{s}$, respectively. The orange curve is the theoretical fitting of the echo decay by the Lorentzian distribution of dipole moments characterized by the parameters $\delta p_{0,L}=65.2\mathrm{Hz}\text{cm}{\text{V}}^{-1}$ corresponding to the full linewidth on half maximum.

Figure 4

Dependence of the width of the spectral hole $\delta {\nu }_{\mathrm{hom}}\left(\mathrm{kHz}\right)$ on the ${}^3\mathrm{H}_6\left(0\right)\to {}^3\mathrm{H}_4\left(0\right)$ transition of the ${\mathrm{Tm}}^{3+}:{\mathrm{Y}}_3{\mathrm{Al}}_5{\mathrm{O}}_{12}$ crystal versus the external electric field strength $E_{St}(\mathrm{kV}/\mathrm{cm})$. The crystal was cooled down to $T=3.7\mathrm{K}$, $E_{\mathrm{laser}}\parallel E_{St}\parallel \left[110\right]$ crystal axis. The red line is the linear fit of the experimental data according to the equation $\delta {\nu }_{\mathrm{hom}}=49.4+61.6E_{St}$. Inset: spectral hole broadening with the increase of the Stark field

Figure 5

Lower panel demonstrates four ROSE signals in the case of four input pulses in the ${\mathrm{Tm}}^{3+}:{\mathrm{Y}}_3{\mathrm{Al}}_5{\mathrm{O}}_{12}$ crystal on the ${}^3\mathrm{H}_6\left(0\right)\to {}^3\mathrm{H}_4\left(0\right)$ transition at 3.7 K. The upper panel shows the applied voltage during the revival of second and third silenced echo pulses. The second and third pulses are partially suppressed by the external electric field pulses with the opposite polarity (blue line), but the fourth pulse has approximately the same amplitude (blue solid line) as the echo pulse in the absence of the external electric field (black solid line). The red solid line demonstrates the suppression of all echo pulses after $70\mu \mathrm{s}$.

Figure 6

Addressable readout of the input optical signals by using Stark pulses in the ROSE memory scheme in the ${\mathrm{Tm}}^{3+}:{\mathrm{Y}}_3{\mathrm{Al}}_5{\mathrm{O}}_{12}$ crystal placed into an optical cavity. In all cases, three groups of the input pulses are sent to the memory cell. The incident signal light pulses before the cavity, which are reduced by a factor of 100, are shown at $t=0$. Signals from the second detector are plotted for $t>25$ $\mu \text{s}$. Signals from the control pulses can be seen at $t=30\mu \text{s}$ and $t=80\mu \text{s}$. The lower (gray) curve shows the recovery of all the input pulses without the external electrical field pulses. The remaining curves correspond to the suppression of all the reading signals, individual signals, pairs of signals, and recovery of all the recorded light pulses. Red curves show the external electric field pulses for each series.

Figure 7

Experimental results on recall of light sequence with (a) reversed and (b) original temporal order (black curves). The reflected part of the input pulse (about $\sim 8\%$) from the cavity due to mismatching is shown at $t=0\mu \text{s}$. The chosen recall order is controlled by the number and polarities of external electric field pulses (red curves). Optical rephasing pulses (control beam) are shown by blue. Different intensities of the recalled ROSE pulses in our experiments were determined mainly by the phase relaxation $T_M$ of atomic transition.

Figure 8

Laser beam profile of the control field in the case of (a) Gaussian beam and (b) so-called top hat shape, after the GTH lens.

Figure 9

Storage and retrieval of few photon signals in the ROSE scheme with the ${\mathrm{Tm}}^{3+}:{\mathrm{Y}}_3{\mathrm{Al}}_5{\mathrm{O}}_{12}$ crystal placed into the impedance-matched optical cavity. Input pulse (blue curve at $t=0\mu \mathrm{s}$) contains $\overline{n}=5.6$ photons on average. At the time $t=36\mu \mathrm{s}$ the violet curve represents the ROSE signal with the retrieval efficiency of $\eta =27\pm 2\%$. The orange curve represents the signal after applying only one rephasing pulse at $t=9\mu \mathrm{s}$ and the red curve represents the signal after applying two rephasing pulses at $t=9\mu \mathrm{s}$ and $t=27\mu \mathrm{s}$ without the input pulse.

Figure 10

Experimental (black squares) and theoretical (blue solid curve) dependence of the ROSE echo efficiency versus the pulse area of the two identical rephasing laser pulses. The theoretical curve corresponds to Eq. (5). Values on the $x$ axis correspond to the weakly interacting group of atoms so $\theta ={\mathrm{\Theta }}_1$ (see text for details).