Approaches for a quantum memory at telecommunication wavelengths

We report experimental storage and retrieval of weak coherent states of light at telecommunication wavelengths using erbium ions doped into a solid. We use two photon-echo-based quantum storage protocols. The first one is based on controlled reversible inhomogeneous broadening (CRIB). It allows the retrieval of the light on demand by controlling the collective atomic coherence with an external electric field, via the linear Stark effect. We study how atoms in the excited state affect the signal-to-noise ratio of the CRIB memory. Additionally we show how CRIB can be used to modify the temporal width of the retrieved light pulse. The second protocol is based on atomic frequency combs. Using this protocol we verify that the reversible mapping is phase preserving by performing an interference experiment with a local oscillator. These measurements are enabling steps toward solid-state quantum memories at telecommunication wavelengths. We also give an outlook on possible improvements.

Figure 1

(a) Level scheme of the material. $Z_1$ and $Z_2$ denote the first and second crystal field level of the ground state, and $Y_1$ denotes the first crystal field level of the excited state. (b) Experimental setup. Both lasers are amplified using erbium-doped fiber amplifiers (EDFA). The pump laser (1536 nm) is split into two paths. For state preparation (path 1) it is combined with the stimulation laser (1545 nm) using a wave division multiplexer (WDM). In path 2 it is attenuated to produce the weak optical pulses to store in the medium. An optical switch allows either of them to be sent into the sample. The strong path is blocked before the cryostat during the measurement sequence and after the cryostat during state preparation, respectively, in order to protect the superconducting single photon detector (SSPD) and to avoid noise from a leakage in the optical switch. Pulses are created with acousto-optical modulators (AOMs). Two AOMs were necessary for the laser at 1536 nm in order to obtain a sufficient extinction ratio. The polarizing beam splitter (PBS) is set parallel to the $D_2$ axis to achieve maximal optical depth and polarization is adjusted before to maximize the power arriving at the sample. Inset: Illustration of the crystal with electrodes, magnetic field, and direction of light propagation indicated.

Figure 2

Pulse sequences used in the experiments. During state preparation ions are pumped from one to the other ground-state Zeeman level via the excited state as described in the text and illustrated in Fig. 1a. The stimulation laser is still left on for 23.5 ms after the optical pumping in order to deplete the excited state. After state preparation the switch is set to the attenuated path 2 and a series of measurements is carried out. A number of $N$ (typically $N=8000$) consecutive weak optical pulses is sent into the sample. For each of these trials the time-to-analog-converter is triggered and in the case of a detection a count is added to the measured time bin in a histogram. The sequence is repeated at a rate of 3 Hz.

Figure 3

Pulse sequences used for the preparation. To create a spectral pit the pump laser is repeatedly swept. To create the central peak required for the CRIB protocol it is turned off each time it passes the central frequency (a). To create a comb structure it is turned off periodically (b). The trigger delay $\tau$ between sweep sequence and pulse sequence allows one to create combs that are shifted in frequency and was used to perform the measurements that show the preservation of coherence during storage (see Sec. 5 and Fig. 10).

Figure 4

Noise measurement: Number of counts as function of the delay after state preparation for different powers of the stimulation laser (logarithmic plot). An exponential fit to the data gave a decay time of 11 ms which confirms that the noise is due to ions left in the excited state. Application of the stimulation laser yields a strong reduction of this noise. Integration time was 100 s and $N=8000$ for each data point. $T_{\mathrm{extra}}=10$ ms for all measurements. The power of the stimulation laser was measured before the cryostat.

Figure 5

Efficiency of the memory and signal to noise ratio as a function of waiting time after state preparation with and without stimulation laser. For these measurements $N=2000$ consecutive pulses with a temporal width of 200 ns were sent into the sample. The distance between the pulses was 5 $\mu$s. The number of incident photons per pulse was $\mathrm{n̄}=27$. Note that the signal to noise ratio is a linear function of $\mathrm{n̄}$ and the efficiency is independent of the number of input photons in this regime [27]. The gray box labeled MEASUREMENT indicates the time interval in which storage experiments were carried out in the rest of this work.

Figure 6

CRIB echoes for two different switching times of the electric field. The number of photons per incident pulse was $\mathrm{n̄}=0.9$. Input pulse duration was 100 ns. The integration time was $2.5\times {10}^4$ s. Dark counts of 10 Hz have been subtracted from the data. The voltage applied on the electrodes was $\pm 70$ V. The enlargement of the echo with respect to the incident pulse can be explained by a spectral mismatch between pulse and absorption line. $A$ and $B$ indicate the time windows used to calculate the signal to noise ratio (see text).

Figure 7

Efficiency of the CRIB memory as a function of temperature. At temperatures significantly above 3 K there can be no contribution to the tailored absorption profile from population transferred between ground-state Zeeman levels [56]. The existence of very long-lived (persistent) holes and their contribution to the absorption profile allows the observation of a CRIB echo at temperatures up to 4.5 K. The number of incident photons per pulse was $\mathrm{n̄}=10$; the integration time for each measurement was 200 s. For the positive and the negative electrical pulses a voltage of $\pm 50$ V was applied to the electrodes.

Figure 8

Full width at half maximum (FWHM) of the CRIB echo for three different voltages $U_2$ applied to the sample after switching the polarity of the electrical field as sketched in the inset. Before switching, voltages of $U_1=95$ V (green triangles) and $U_1=65$ V (blue circles), respectively, were applied. One can see that using this method, the FWHM of the echo can be changed.

Figure 9

AFC echoes at the single photon level. The graph shows a histogram of $8.64\times {10}^8$ trials (10-h integration time) with a mean photon number of $\mathrm{n̄}=0.5$ per incident pulse. The peak on the left is the transmitted part of the incident photons. On the right one can see the echoes at the first and the second time (360 and 720 ns) the atomic dipoles get back into phase.

Figure 10

Results of the interference experiments described in the text. (a) Atomic frequency combs (zoom) for two different delays $\tau$ [see Fig. 3b] are shifted by ${\Delta }_0$. (b) Constructive (delay 1) and destructive (delay 2) interference of the AFC echo with the transmitted part of a second pulse send into the sample for the two cases shown in panel (a). (c) Interference fringes: Successively shifting the comb by changing the delay $\tau$ [Fig. 3b] allows one to observe a phase shift range of $2\pi$. The visibility is $89\pm 3\%$. (d) The same experiment with the second AFC echo. One can see that twice the phase is accumulated. This also explains the lower visibility of $66\pm 3\%$ (see text). Dark counts have been subtracted from the data. $\mathrm{n̄}\approx 0.9$ for (c) and $\mathrm{n̄}\approx 9$ for (d).

Figure 11

Here we show control of AFC echoes using the CRIB effect. The dashed line (in blue) is a reference measurement where no CRIB effect was used. The short-dashed line (red) shows how the first echo can be suppressed by applying an electric field gradient to the sample. In practice a small echo can still be seen since we could not apply a large enough broadening with respect to the comb peak separation. Note that since the applied field is not reversed here, also the second echo is suppressed. The solid line (black) shows the results if the broadening is reversed at $t=1/\Delta$, such that the initial coherence is recovered at $t=2/\Delta$, resulting in a recovery of the second echo. Here $\mathrm{n̄}\approx 8$ and dark counts have been subtracted from the data.