We present a light-storage experiment in a praseodymium-doped crystal where the light is mapped onto an inhomogeneously broadened optical transition shaped into an atomic frequency comb. After absorption of the light the optical excitation is converted into a spin-wave excitation by a control pulse. A second control pulse reads the memory (on-demand) by reconverting the spin-wave excitation to an optical one, where the comb structure causes a photon-echo type rephasing of the dipole moments and directional retrieval of the light. This combination of photon echo and spin-wave storage allows us to store sub-microsecond (450ns) pulses for up to 20 µs. The scheme has a high potential for storing multiple temporal modes in the single photon regime, which is an important resource for future long-distance quantum communication based on quantum repeaters.A quantum memory (QM) for photons is a light-matter interface that can achieve a coherent and reversible transfer of quantum information between a light field and a material system [1]. A QM should enable efficient, highfidelity storage of non-classical states of light, which is a key resource for future quantum networks, particularly in quantum repeaters [2][3][4][5][6] that have the potential for distributing entangled states over long distances for quantum communication tasks. In order to achieve reasonable entanglement distribution rates, it has been shown that some type of multiplexing is required [4,5], using for instance independent frequency, spatial or temporal modes (multimode QM).Several types of light-matter interactions have been proposed for building a QM, for instance electromagnetically induced transparency [7][8][9][10], Raman interactions [11][12][13][14], or photon-echo techniques [15][16][17][18][19][20][21][22]. Photon echo techniques in rare-earth-ion doped crystals have an especially high multimode capacity for storing classical light [23]. Classical photon echoes are not useful, however, for single-photon storage due to inherent noise problems due to unwanted spontaneous and stimulated emission processes when storing light on a single photon level [24]. The photon-echo QM based on controlled reversible inhomogeneous broadening [15][16][17][18][19] is free of these noise problems. But this technique has a lower time-multiplexing capacity than classical photon echoes, for a given optical depth, due to loss of storage efficiency as the controlled frequency bandwidth is increased [20,25]. Some of us recently proposed a photon-echo type QM based on an atomic frequency comb (AFC) [20] that has a storage efficiency independent of the bandwidth, allowing optimal use of the inhomogeneous broadening of rare-earthdoped crystals. An AFC memory has the potential for providing multimode storage capacity [20,25] crucial to quantum repeaters. In a first experiment [21] based on this scheme we performed a light-matter interface at the single-photon level. However, the light was retrieved after a predetermined storage time, while for quantum repeaters it is crucia...

We realize fast transport of ions in a segmented micro-structured Paul trap. The ion is shuttled over a distance of more than 10 4 times its groundstate wavefunction size during only 5 motional cycles of the trap (280 µm in 3.6 µs). Starting from a ground-state-cooled ion, we find an optimized transport such that the energy increase is as low as 0.10±0.01 motional quanta. In addition, we demonstrate that quantum information stored in a spin-motion entangled state is preserved throughout the transport. Shuttling operations are concatenated, as a proof-of-principle for the shuttling-based architecture to scalable ion trap quantum computing. . Scalable information processing in a multiplexed ion trap can be accomplished by having fixed processing sites where logic operations are performed, and ion qubits will be moved in and out of these regions by shuttling operations. The duration of such shuttling has to be much faster than the relevant decoherence times [4]. Furthermore, it is desirable to reduce the total time consumption of all relevant operations, where shuttling will contribute a considerable amount [5], and aim for the performance of the naturally fast solid state architectures [6]. So far, ion shuttling in a multiplexed trap has been demonstrated together with additional sympathetic cooling [7], and in the adiabatic regime, where the transient displacement of the ion is smaller than the size of the its wavepacket [8,9]. Transport of neutral atoms have also been performed using magnetic [10] or optical [11] techniques.Because quantum gate operations require ions close to the motional ground state and fast transport inherently creates motional excitation, the challenge is to develop transport protocols that guarantee sufficiency small energy transfer. In this work we demonstrate shuttling operations that are highly non-adiabatic while the final state of the ion is close to the motional groundstate. We also show that quantum information stored in both the motional and the spin degree of freedom is preserved through the shuttling.During a shuttling operation, the ion motion in the harmonic trapping potential is excited when the acceleration is sufficiently strong. This motional excitation is a harmonic oscillation, characterized by a well defined phase, thus allowing it to be canceled out by proper management of the forces involved during or after the transport. We experimentally demonstrate two methods of canceling the acquired motional excitation. One method uses two shuttles, where the transport to the destination generates the same net momentum transfer as the transport back, but is applied 180 • out of phase with respect to the secular oscillation of the ion (Fig. 1b). We refer to this as the pairwise energy-neutral transport. For the second scheme, the self-neutral transport we apply a sharp counter-"kick" to the ion at the end of a single transport operation, stopping its motion (Fig. 1c). This case of single-sided transport allows even faster shuttling and can be sequentially repeated since it is ener...

Imagine that you are blindfolded inside an unknown room. You snap your fingers and listen to the room's response. Can you hear the shape of the room? Some people can do it naturally, but can we design computer algorithms that hear rooms? We show how to compute the shape of a convex polyhedral room from its response to a known sound, recorded by a few microphones. Geometric relationships between the arrival times of echoes enable us to "blindfoldedly" estimate the room geometry. This is achieved by exploiting the properties of Euclidean distance matrices. Furthermore, we show that under mild conditions, first-order echoes provide a unique description of convex polyhedral rooms. Our algorithm starts from the recorded impulse responses and proceeds by learning the correct assignment of echoes to walls. In contrast to earlier methods, the proposed algorithm reconstructs the full 3D geometry of the room from a single sound emission, and with an arbitrary geometry of the microphone array. As long as the microphones can hear the echoes, we can position them as we want. Besides answering a basic question about the inverse problem of room acoustics, our results find applications in areas such as architectural acoustics, indoor localization, virtual reality, and audio forensics. room geometry | geometry reconstruction | echo sorting | image sources I n a famous paper (1), Mark Kac asks the question "Can one hear the shape of a drum?" More concretely, he asks whether two membranes of different shapes necessarily resonate at different frequencies.* This problem is related to a question in astrophysics (2), and the answer turns out to be negative: Using tools from group representation theory, Gordon et al. (3,4) presented several elegantly constructed counterexamples, including the two polygonal drum shapes shown in Fig. 1. Although geometrically distinct, the two drums have the same resonant frequencies. † In this work, we ask a similar question about rooms. Assume you are blindfolded inside a room; you snap your fingers and listen to echoes. Can you hear the shape of the room? Intuitively, and for simple room shapes, we know that this is possible. A shoebox room, for example, has well-defined modes, from which we can derive its size. However, the question is challenging in more general cases, even if we presume that the room impulse response (RIR) contains an arbitrarily long set of echoes (assuming an ideal, noiseless measurement) that should specify the room geometry.It might appear that Kac's problem and the question we pose are equivalent. This is not the case, for the sound of a drum depends on more than its set of resonant frequencies (eigenvalues)-it also depends on its resonant modes (eigenvectors). In the paper "Drums that sound the same" (5), Chapman explains how to construct drums of different shapes with matching resonant frequencies. Still, these drums would hardly sound the same if hit with a drumstick. They share the resonant frequencies, but the impulse responses are different. Even a single drum struck at ...

Full quantum state tomography is used to characterize the state of an ensemble based qubit implemented through two hyperfine levels in Pr 3+ ions, doped into a Y2SiO5 crystal. We experimentally verify that single-qubit rotation errors due to inhomogeneities of the ensemble can be suppressed using the Roos-Mølmer dark state scheme [1]. Fidelities above > 90%, presumably limited by excited state decoherence, were achieved. Although not explicitly taken care of in the Roos-Mølmer scheme, it appears that also decoherence due to inhomogeneous broadening on the hyperfine transition is largely suppressed.A large variety of systems are presently investigated in order to find out whether they can be used as hardware for quantum computers. The present work is carried out on a solid state based system, rare earth ions doped into inorganic crystals. As in several other solid state systems the qubits are encoded in nuclear spin states, which for rare earths can have coherence times of seconds and where much longer coherence times are predicted [2]. For being a solid state system the rare earth ions are unusual because their optical transitions can have coherence times as long as several ms [3,4]. Quantum state tomography have previously been carried out to characterize the fidelity by which superpositions on an optical transition can be manipulated [5]. However, since coherence times for the hyperfine states are several orders of magnitude longer, it is highly relevant to also investigate the fidelity of arbitrary qubit rotations using hyperfine qubits. Multi-qubit gate operations can readily be implemented in the system, because optical excitation of an ion will induce frequency shifts >100 MHz (>10 4 line widths) of the optical transitions of nearby ions [6]. The large frequency shift of the optical transition makes it possible to entangle two nearby ions using operations with a duration of just a few ns [7]. A scalable implementation of the rare earth ion scheme can e.g. be achieved using a short lifetime readout ion, acting as a state sensitive probe for the local environment [7] in a manner similar to how the electronic spin of an NV center can probe the nuclear spin states of surrounding C 13 ions [8]. However, because of the hour-long lifetimes of the rare earth spin states [9,10], it is possible to also create qubits consisting of an ensemble of ions, all in a specific quantum state. Each such qubit can be selectively manipulated by optical pulses [6,11,12]. These ensemble qubits, which give strong readout signals, can be used to investigate general properties of the system. In this work ensemble qubits * present address: Research Center COM, DTU, DK-2800, Lyngby, Denmark are used to experimentally carry out arbitrary rotations on the qubit Bloch sphere and the results are characterized by full quantum state tomography. The relevant part of the Pr 3+ :Y 2 SiO 5 energy level diay z x 1 0 B D (b) 17.3 MHz 10.2 MHz 4.6 MHz 4.8 MHz (a) 0 0 , 1 1 , aux 0 e z x y 1 2 (c) B e 1 FIG. 1: (color online) a) energy level diagram,...

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We experimentally demonstrate fast separation of a two-ion crystal in a microstructured segmented Paul trap. By the use of spectroscopic calibration routines for the electrostatic trap potentials, we achieve the required precise control of the ion trajectories near the \textit{critical point}, where the harmonic confinement by the external potential vanishes. The separation procedure can be controlled by three parameters: A static potential tilt, a voltage offset at the critical point, and the total duration of the process. We show how to optimize the control parameters by measurements of ion distances, trap frequencies and the final motional excitation. At a separation duration of $80 \mu$s, we achieve a minimum mean excitation of $\bar{n} = 4.16(0.16)$ vibrational quanta per ion, which is consistent with the adiabatic limit given by our particular trap. We show that for fast separation times, oscillatory motion is excited, while a predominantly thermal state is obtained for long times. The presented technique does not rely on specific trap geometry parameters and can therefore be adopted for different segmented traps

We present an efficient photon-echo experiment based on atomic frequency combs [Phys. Rev. A 79, 052329 (2009)]. Echoes containing an energy of up to 35% of that of the input pulse are observed in a Pr 3+ -doped Y 2 SiO 5 crystal. This material allows for the precise spectral holeburning needed to make a sharp and highly absorbing comb structure. We compare our results with a simple theoretical model with satisfactory agreement. Our results show that atomic frequency combs has the potential for high-efficiency storage of single photons as required in future long-distance communication based on quantum repeaters.

We demonstrate experimentally a quantum memory scheme for the storage of weak coherent light pulses in an inhomogeneously broadened optical transition in a Pr 3+ : YSO crystal at 2.1 K. Precise optical pumping using a frequency stable (≈1kHz linewidth) laser is employed to create a highly controllable Atomic Frequency Comb (AFC) structure. We report single photon storage and retrieval efficiencies of 25%, based on coherent photon echo type re-emission in the forward direction. The coherence property of the quantum memory is proved through interference between a super Gaussian pulse and the emitted echo. Backward retrieval of the photon echo emission has potential for increasing storage and recall efficiency.