Waveguide Quantum Memory

We study Erbium doped LiNbO3 waveguides for their suitability to store quantum information encoded into single photons, as required for a quantum repeater. Specifically, we perform stimulated photon-echo experiments for storage and readout of (classical) light pulses, which yield important information about the storage of single photon states. Furthermore, we investigate Stark-shift based line-shifts of the 1.53 μm transition, as required for a highly efficient quantum state storage protocol. Our findings demonstrate the potential of Er:LiNbO3 waveguides for quantum state storage. Introduction The last years have seen a remarkable advance of experimental quantum communication, in particular of quantum cryptography that promises informationtheoretic secure communication [1]. Yet, many problems still have to be overcome before a quantum secured communication network will be available. A major challenge concerns the increase of the transmission distance, which is, among others, limited through the combination of absorption in the transmission channel and detector noise. In contrast to classical telecommunications, a direct amplification of a single-photon quantum state is impossible. The concept of a quantum repeater [2] is based on several key elements, which are the creation and distribution of entangled pairs of photons over sub-sections of the complete link, swapping to extend the entanglement over the whole channel, and quantum memories that allow increasing the efficiency of the overall process. The entanglement can then be used for any kind of quantum communication task, for instance for quantum cryptography. Many schemes for storage of non-classical light have been proposed. However, only a few experiments can be mentioned in the context of quantum memory [3], and efficient, reversible transfer of quantum information between different species has not yet been accomplished. An original protocol for a quantum, as well as classical, memory in solid state material is based on controlled reversible inhomogeneous broadening (CRIB) of a single atomic absorption line [4]. It requires an atomic ensemble with a large optical depth and a long optical coherence time. It also relies on the possibilities to prepare, through optical pumping, a narrow absorption line on a nonabsorbing background, to broaden this line in a controlled and reversible way, and to apply a position dependent phase shift. Erbium doped crystalline waveguides are interesting candidates for the realization of CRIB, as interaction lengths of many centimeters can be achieved, allowing for large absorption even at low doping concenration. In addition, the 1.53 μm, I15/2→I13/2 transition in Erbium can feature coherence times in the ms range [5], and is well matched to standard telecommunication fibre, which allows future interfacing of such a memory with the standard telecommunication fibre network. In this paper we report on the storage, recall and measurement of classical optical pulses via stimulated photon echoes [6], which provides an important test-bed for future quantum state storage based on CRIB. Furthermore, we present investigations of the linear dc-Stark effect for controlled broadening [7]. The experiments took advantage of Er doped LiNbO3 crystals with waveguiding structures, cooled to a temperature of around 3.5 Kelvin. While LiNbO3 waveguides are extensively used in integrated optics, these are, to the best of our knowledge, the first studies in the context of all optical data storage. Photon-echo based storage of classical light pulses A common approach to storage and retrieval of light is based on three-pulse photon echo (3PE), also known as stimulated photon echo [6]. In this process a first, strong, optical write pulse excites the medium, creating an atomic coherence. The data pulses, a sequence of pulses encoding the information to be stored, are sent into the medium some time after the write pulse, which transfer the coherence into a frequency-dependent population grating in the ground and excited states. In order to retrieve the information, a third, strong, read pulse is used, which scatters off the grating and causes a photon echo to be emitted a time after the read pulse, which is equal to the time separation between write and data pulse [8]. If certain conditions for excitation energy and absorption depths are met, the echo is, to a high degree, an amplitude and phase replica of the stored data pulses. Now, consider a data field consisting of two pulses (D1 and D2) with an amplitude ratio R and relative phase φ (see Fig. 1). The 3PEs appear at times te = tr + tDi tw (i = 1, 2), where tr is the arrival time of the readout, tDi the arrival time of data pulse Di (i = 1, 2), and tw the arrival time of the write pulse. The echoes will thus be dt = tD2 tD1 apart. Because the efficiency of the 3PE is at best a few percent [9], much of the frequency-dependent population grating is preserved in the atomic ensemble after the read pulse. Therefore more echoes can be produced by sending in several read pulses. In our experiment, two subsequent read pulses were used to produce two copies of the data pulse. If we chose the distance between the read pulses to be dt, the same as the distance between the two data pulses D1 and D2, the echo of the second data pulse read out by the first read pulse (D2|R1), and the echo of the first data pulse read out by the second read pulse (D1|R2), will overlap and interfere (Fig. 1 c). The intensity of the echo in the central time interval (time-bin) is thus controlled by the phases of the write, the data and the read pulses, i.e. α1, α2/3, and α4/5, respectively. This is true provided that the phase coherence or amplitude ratio is not perturbed partially or totally during storage and retrieval. The sequence of two data pulses above is related to what is known in quantum communication as a timebin qubit [10]. A time-bin qubit is a coherent superposition of a photon being in two time-bins, separated by a time difference long compared to the coherence time of the photon. It can be written as: |ψ〉= c0 |1,0〉+ c1e |0,1〉, (1) where |1,0〉 (|0,1〉) represents a photon in the first (the second, respectively) time-bin, and φ=α2-α3 denotes their relative phase. In the present experiment, classical (strong) coherent pulses were used, with width smaller than the temporal spacing dt between the two pulses; the state of light is thus described by a Poisson distribution of photons (n~10), each of which is in the state described by Eq.1. Note that one could also describe our experiment as a setup containing two interferometers, as used for phase-coding quantum cryptography [1]: one interferometer prepares the time-bin qubits, i.e. here our two data pulses, while the second allows the projection measurement, i.e. our two read pulses. Let us now describe the experimental setup. The output from an external-cavity cw diode laser was gated by a combined phase and intensity modulator, followed by an intensity modulator (both fibre optic). The first modulator was used to create the five excitation pulses and to apply phase shifts to some of the pulses, depending on the particular experiment. The second modulator was synchronized to the first one and used to improve the peak-to-background intensity ratio. The pulses were then amplified by an Erbium Doped Fiber Amplifier (EDFA). In order to obtain a good background suppression (>70 dB), the EDFA was followed by an acousto-optical modulator, which opened only for the series of pulses and suppressed light for all other times. The resulting pulses had durations of tpulse=15 ns, with peak powers of around 5 mW for the write pulses, and around 1 mW for the other pulses. The first data pulse was created at tD1 = 0.6μs, the time between the data pulses was typically dt = 60ns and the read-out pulses were delayed with respect to the data pulses by 1 to 2 μs. The light was then coupled into an Er-doped LiNbO3 crystal (with waveguide, see below), which was cooled to 3.4 K by means of a pulse tube cooler. A magnetic field of about 0.2 Tesla was applied parallel to the C3 axis. This reduces decoherence due to spectral diffusion [11], resulting in a coherence time T2 of about 6 μs. Finally, the photon echoes were detected by a fast photo detector and displayed on an oscilloscope. The clock frequency was of 30 Hz, which ensured that all atomic excitations (featurig radiative a lifetime of 10 ms) had decayed between two subsequent storage/recall sequences. The z-cut LiNbO3 crystal was Erbium doped over a length of 10 mm by indiffusion of an evaporated 8 μm thick Er-layer at 1130°C for 150 h, leading to a Gaussian concentration profile of 8,2 μm 1/e penetration depth and 3.6x10cm surface concentration. The guiding channel was fabricated by indiffusion of a 7 μm wide, 98 nm thick Titanium-stripe at 1060°C for 8.5 h, resulting in a mono-mode guide with a mode size of 4.5x 3 μm FWHM intensity distribution [12]. The light was injected and collected with stanFig. 1: Illustration of the sequence of pulses for the interference of photon echoes. The data is read out twice and the phase between the data (or read) pulses is changed to produce interference in the central time bin. -100 -50 0 50 100 destructive interference constructive interference Ec ho In te ns ity (a rb .u ni ts ) time (ns) -2 -1 0 1 2 3 4 5 6 7 0.0 PE Ar ea (a rb .u ni ts )