We report on experiments dealing with feedback-controlled pulse shaping to optimize the efficiency of light storage by electromagnetically induced transparency (EIT) in a Pr${}^{3+}$:Y${}_{2}$SiO${}_{5}$ crystal. A learning loop in combination with an evolutionary algorithm permits the automatic determination of optimal temporal profiles of intensities and frequencies in the driving laser pulses (i.e., the probe and coupling pulses). As a main advantage, the technique finds optimal solutions even in the complicated multilevel excitation scheme of a doped solid, involving large inhomogeneous broadening. The learning loop experimentally determines optimal temporal intensity profiles of the coupling pulses for a given probe pulse. The optimized intensity pulse shapes enhance the light-storage efficiency in the doped solid by a factor of $2$. The learning loop also determines a fast and efficient preparation pulse sequence, which serves to optically prepare the crystal prior to light-storage experiments. The optimized preparation sequence is 5 times faster than standard preparation sequences. Moreover, the optimized preparation sequence enhances the optical depth in the medium by a factor of $5$. As a consequence, the efficiency of light storage also increases by another factor of $3$. Our experimental data clearly demonstrate the considerable potential of feedback-controlled pulse shaping, applied to EIT-driven light storage in solid media.
We report on experiments dealing with feedback-controlled pulse shaping to optimize the efficiency of light storage by electromagnetically induced transparency (EIT) in a Pr3+:Y2SiO5 crystal. A learning loop in combination with an evolutionary algorithm permits the automatic determination of optimal temporal profiles of intensities and frequencies in the driving laser pulses (i.e., the probe and coupling pulses). As a main advantage, the technique finds optimal solutions even in the complicated multilevel excitation scheme of a doped solid, involving large inhomogeneous broadening. The learning loop experimentally determines optimal temporal intensity profiles of the coupling pulses for a given probe pulse. The optimized intensity pulse shapes enhance the light-storage efficiency in the doped solid by a factor of 2. The learning loop also determines a fast and efficient preparation pulse sequence, which serves to optically prepare the crystal prior to light-storage experiments. The optimized preparation sequence is 5 times faster than standard preparation sequences. Moreover, the optimized preparation sequence enhances the optical depth in the medium by a factor of 5. As a consequence, the efficiency of light storage also increases by another factor of 3. Our experimental data clearly demonstrate the considerable potential of feedback-controlled pulse shaping, applied to EIT-driven light storage in solid media.
We demonstrate efficient storage and retrieval of light pulses by electromagnetically induced transparency (EIT) in a Pr^{3+}:Y_{2}SiO_{5} crystal. Using a ring-type multipass configuration, we increase the optical depth (OD) of the medium up to a factor of 16 towards OD≈96. Combining the large optical depth with optimized conditions for EIT, we reach a light storage efficiency of (76.3±3.5)%. In addition, we perform extended systematic measurements of the storage efficiency versus optical depth, control Rabi frequency, and probe pulse duration. The data confirm the theoretically expected behavior of an EIT-driven solid-state memory.
The maximal storage duration is an important benchmark for memories. In quantized media, storage times are typically limited due to stochastic interactions with the environment. Also, optical memories based on electromagnetically induced transparency (EIT) suffer strongly from such decoherent effects. External magnetic control fields may reduce decoherence and increase EIT storage times considerably but also lead to complicated multilevel structures. These are hard to prepare perfectly in order to push storage times toward the theoretical limit, i.e., the population lifetime T(1). We present a self-learning evolutionary strategy to efficiently drive an EIT-based memory. By combination of the self-learning loop for optimized optical preparation and improved dynamical decoupling, we extend EIT storage times in a doped solid above 40 s. Moreover, we demonstrate storage of images by EIT for 1 min. These ultralong storage times set a new benchmark for EIT-based memories. The concepts are also applicable to other storage protocols.
We report on frequency- and angle-multiplexed image storage by electromagnetically induced transparency (EIT) in a Pr3+:Y2SiO5 crystal. Frequency multiplexing by EIT relies on simultaneous storage of light pulses in atomic coherences, driven in different frequency ensembles of the inhomogeneously broadened solid medium. Angular multiplexing by EIT relies on phase matching of the driving laser beams, which permits simultaneous storage of light pulses propagating under different angles into the crystal. We apply the multiplexing techniques to increase the storage capacity of the EIT-driven optical memory, in particular to implement multiplexed storage of larger two-dimensional amounts of data (images). We demonstrate selective storage and readout of images by frequency-multiplexed EIT and angular-multiplexed EIT, as well as the potential to combine both multiplexing approaches towards further enhanced storage capacities.
The present work deals with techniques to improve the EIT-based light storage in an all solid-state memory, i.e. a rare-earth ion-doped PrYSO crystal. The performance of such a memory can be defined by its capability to store light pulses with high efficiency and for long storage durations. In general, the storage efficiency is theoretically limited by the EIT-LS protocol efficiency, while the storage duration is limited by decoherence processes in the solid-state memory. Thus, we first optimized the EIT-LS efficiency at short storage durations. We then investigated the performance of composite and adiabatic techniques for efficient and robust rephasing and finally applied composite techniques for DDC to extend the coherence lifetime in our storage medium. Optimization of the EIT Light Storage Efficiency: In order to optimize the EIT-LS protocol we performed systematic measurements of the EIT-LS efficiency in a PrYSO crystal featuring an optical depth d of 6. The optical depth sets the theoretical limit of the EIT-LS protocol efficiency. We experimentally optimized the efficiency by systematic variations of the control pulse power and the probe pulse duration. Furthermore, we applied an iterative algorithm, to optimize the temporal shape of the probe pulse. We found a maximal protocol efficiency 36 %, comparable to the theoretical limit. In order to increase the optical depth d, we developed a multipass setup for the probe beam, consisting of a ringlike arrangement, which is compatible with the geometrical constraints given by the existing setup. This multipass setup allows the simple variation of the number of probe passes N through the crystal and thus enables a flexible change of the effective optical depth. With this setup we achieved up to 16 probe passes through the PrYSO crystal, which corresponds to an increase of the effective optical depth from 6 to 96. We experimentally optimized the EIT-LS efficiency at variable optical depths. At N=14, i.e. an effective optical depth of about 84, we achieved an EIT-LS efficiency of 76.3 % in forward retrieval configuration, reaching previous values in an EIT-driven memory of cold atoms and achieving the highest ever obtained EIT-LS efficiency in a solid-state memory. However, due to losses at the optical components, the setup efficiency was limited to about 25.2 % at N=2. As future work will focus on the storage of few photons, it will thus be necessary to improve the optical components, to achieve adequate detection efficiencies. It might also be useful, to further investigate possibilities for backward readout configurations combined with a multipass probe setup. Composite and Adiabatic Rephasing of Atomic Coherences: In order to extend the EIT-LS duration of our memory towards the coherence lifetime, we implemented composite and adiabatic rephasing techniques, exhibiting an improved robustness regarding variations and fluctuations of experimental parameters. We investigated their performance regarding experimental variations, in an application for rephasing of atomic coherences in the inhomogeneously broadened hyperfine transition of PrYSO. First, we applied universal composite pulses (UCP). UCP were originally designed for robust and high-fidelity population inversion in a two-state system, compensating simultaneous variations in any type of experimental parameter. We have experimentally shown that UCP exhibit an enhanced robustness to variations in several experimental parameters. Using UCP we could increase the higher rephasing efficiency about 25 %, compared to diabatic π pulses. UCP can be useful whenever significant unknown experimental variations or fluctuations prevent the application of diabatic π pulses. Second, we demonstrated a first experimental implementation of composite adiabatic passage (CAP). Essentially, CAP is a composite version of RAP, consisting of a sequence of RAP pulses with appropriately chosen relative phases. CAP was proposed to improve RAP in situations of fairly fulfilled adiabaticity. We compared the performance of CAP and RAP at different degrees of adiabaticity. In particular, we systematically investigated their performance with respect to variations in pulse duration and static detuning. We found CAP to be able to compensate for weak adiabaticity, leading to constant and high rephasing efficiency, irrespectively of the exact choice of the experimental parameters. These properties of CAP can be of interest whenever robust state manipulations are required, while sufficient adiabaticity cannot be provided, e.g. due to experimental restrictions. Third, we performed a first experimental demonstration of single-shot shaped pulses (SSSP), derived from techniques on shortcuts to adiabaticity. We demonstrated the capability of SSSP for efficient and robust rephasing and compared our results with diabatic π pulses. A further comparison with other adiabatic techniques might be necessary to provide a broader insight on SSSP. All three presented techniques can be used to improve the robustness of an population inversion or rephasing process. However, different requirements on the control of the experimental parameters have to be fulfilled. UCP, and CAP rely on identical pulses and a precise relative phase control, i.e. within a few degrees. CAP in addition needs a simple control of the time-dependent detuning. The complex time-dependent Rabi frequency and detuning of SSSP require a much more sophisticate control of experimental parameters. Thus, the choice of an adequate technique strongly depends on the actual experimental situation, i.e. on the experimentally controllable parameters. Composite Pulses for Dynamic Decoherence Control: We investigated the performance of UCP and universal robust (UR) sequences for DDC of directly RF-prepared coherences. We compared our results with well known CPMG DD and KDD sequences. We performed systematic measurements with respect to the cycling time, the phase of the coherence and the order of UCP and UR DD sequence. We found time separated UR DD sequences to be robust with respect to the phase of the coherence. We applied these DD sequences on EIT-LS coherences and compared with CPMG DD and KDD in XY4. Our experiments showed that our UR DD sequences can outperform the often considered state-of-the-art KDD in XY4 sequence, yielding about a factor of 2 longer coherence lifetimes. Combining our results on optimized EIT-LS with advanced composite DD sequences and static decoherence control by ZEFOZ might provide a major step towards the development of an all solid-state quantum memory.
Abstract We present the experimental demonstration of light storage towards the single photon level at a long storage time by electromagnetically induced transparency in a rare-earth ion-doped Pr3+:Y2SiO5 crystal. We apply decoherence control by static magnetic fields and appropriately designed radio-frequency composite pulse sequences to prolong the storage time in the memory. A rare-earth ion-doped filter crystal prepared by optical pumping serves to efficiently separate the signal at the single photon level from optical noise. Multipass setups around the memory and the filter crystal improve the storage efficiency and filter selectivity. Already without decoherence control, the setup permits storage of single photons in the microsecond regime at a storage efficiency of 42%. With decoherence control we demonstrate storage of weak coherent pulses containing some 10 photons for up to 10 s at a storage efficiency of several percent. The experimental data clearly demonstrate the applicability of EIT light storage to implement a true quantum memory in Pr3+:Y2SiO5 at long storage times. The scientific findings and technical developments are of relevance also to other protocols and media for quantum information storage.
The present work deals with techniques to improve the EIT-based light storage in an all solid-state memory, i.e. a rare-earth ion-doped PrYSO crystal. The performance of such a memory can be defined by its capability to store light pulses with high efficiency and for long storage durations. In general, the storage efficiency is theoretically limited by the EIT-LS protocol efficiency, while the storage duration is limited by decoherence processes in the solid-state memory. Thus, we first optimized the EIT-LS efficiency at short storage durations. We then investigated the performance of composite and adiabatic techniques for efficient and robust rephasing and finally applied composite techniques for DDC to extend the coherence lifetime in our storage medium. Optimization of the EIT Light Storage Efficiency: In order to optimize the EIT-LS protocol we performed systematic measurements of the EIT-LS efficiency in a PrYSO crystal featuring an optical depth d of 6. The optical depth sets the theoretical limit of the EIT-LS protocol efficiency. We experimentally optimized the efficiency by systematic variations of the control pulse power and the probe pulse duration. Furthermore, we applied an iterative algorithm, to optimize the temporal shape of the probe pulse. We found a maximal protocol efficiency 36 %, comparable to the theoretical limit. In order to increase the optical depth d, we developed a multipass setup for the probe beam, consisting of a ringlike arrangement, which is compatible with the geometrical constraints given by the existing setup. This multipass setup allows the simple variation of the number of probe passes N through the crystal and thus enables a flexible change of the effective optical depth. With this setup we achieved up to 16 probe passes through the PrYSO crystal, which corresponds to an increase of the effective optical depth from 6 to 96. We experimentally optimized the EIT-LS efficiency at variable optical depths. At N=14, i.e. an effective optical depth of about 84, we achieved an EIT-LS efficiency of 76.3 % in forward retrieval configuration, reaching previous values in an EIT-driven memory of cold atoms and achieving the highest ever obtained EIT-LS efficiency in a solid-state memory. However, due to losses at the optical components, the setup efficiency was limited to about 25.2 % at N=2. As future work will focus on the storage of few photons, it will thus be necessary to improve the optical components, to achieve adequate detection efficiencies. It might also be useful, to further investigate possibilities for backward readout configurations combined with a multipass probe setup. Composite and Adiabatic Rephasing of Atomic Coherences: In order to extend the EIT-LS duration of our memory towards the coherence lifetime, we implemented composite and adiabatic rephasing techniques, exhibiting an improved robustness regarding variations and fluctuations of experimental parameters. We investigated their performance regarding experimental variations, in an application for rephasing of atomic coherences in the inhomogeneously broadened hyperfine transition of PrYSO. First, we applied universal composite pulses (UCP). UCP were originally designed for robust and high-fidelity population inversion in a two-state system, compensating simultaneous variations in any type of experimental parameter. We have experimentally shown that UCP exhibit an enhanced robustness to variations in several experimental parameters. Using UCP we could increase the higher rephasing efficiency about 25 %, compared to diabatic π pulses. UCP can be useful whenever significant unknown experimental variations or fluctuations prevent the application of diabatic π pulses. Second, we demonstrated a first experimental implementation of composite adiabatic passage (CAP). Essentially, CAP is a composite version of RAP, consisting of a sequence of RAP pulses with appropriately chosen relative phases. CAP was proposed to improve RAP in situations of fairly fulfilled adiabaticity. We compared the performance of CAP and RAP at different degrees of adiabaticity. In particular, we systematically investigated their performance with respect to variations in pulse duration and static detuning. We found CAP to be able to compensate for weak adiabaticity, leading to constant and high rephasing efficiency, irrespectively of the exact choice of the experimental parameters. These properties of CAP can be of interest whenever robust state manipulations are required, while sufficient adiabaticity cannot be provided, e.g. due to experimental restrictions. Third, we performed a first experimental demonstration of single-shot shaped pulses (SSSP), derived from techniques on shortcuts to adiabaticity. We demonstrated the capability of SSSP for efficient and robust rephasing and compared our results with diabatic π pulses. A further comparison with other adiabatic techniques might be necessary to provide a broader insight on SSSP. All three presented techniques can be used to improve the robustness of an population inversion or rephasing process. However, different requirements on the control of the experimental parameters have to be fulfilled. UCP, and CAP rely on identical pulses and a precise relative phase control, i.e. within a few degrees. CAP in addition needs a simple control of the time-dependent detuning. The complex time-dependent Rabi frequency and detuning of SSSP require a much more sophisticate control of experimental parameters. Thus, the choice of an adequate technique strongly depends on the actual experimental situation, i.e. on the experimentally controllable parameters. Composite Pulses for Dynamic Decoherence Control: We investigated the performance of UCP and universal robust (UR) sequences for DDC of directly RF-prepared coherences. We compared our results with well known CPMG DD and KDD sequences. We performed systematic measurements with respect to the cycling time, the phase of the coherence and the order of UCP and UR DD sequence. We found time separated UR DD sequences to be robust with respect to the phase of the coherence. We applied these DD sequences on EIT-LS coherences and compared with CPMG DD and KDD in XY4. Our experiments showed that our UR DD sequences can outperform the often considered state-of-the-art KDD in XY4 sequence, yielding about a factor of 2 longer coherence lifetimes. Combining our results on optimized EIT-LS with advanced composite DD sequences and static decoherence control by ZEFOZ might provide a major step towards the development of an all solid-state quantum memory.