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We investigate the erbium flip-flop dynamics as a limiting factor of the electron spin lifetime and more generally as an indirect source of decoherence in rare-earth doped insulators. Despite the random isotropic arrangement of dopants in the host crystal, the dipolar interaction strongly depends on the magnetic field orientation following the strong anisotropy of the $g$-factor. In Er$^{3+}$:Y$_2$SiO$_5$, we observe by transient optical spectroscopy a three orders of magnitude variation of the erbium flip-flop rate (10ppm dopant concentration). The measurements in two different samples, with 10ppm and 50ppm concentrations, are well-supported by our analytic modeling of the dipolar coupling between identical spins with an anisotropic $g$-tensor. The model can be applied to other rare-earth doped materials. We extrapolate the calculation to Er$^{3+}$:CaWO$_4$, Er$^{3+}$:LiNbO$_3$ and Nd$^{3+}$:Y$_2$SiO$_5$ at different concentrations.

Optical coherence lifetimes and decoherence processes in erbium-doped lithium niobate ( Er 3 + :LiNbO3) crystalline powders are investigated for materials that underwent different mechanical and thermal treatments. Several complimentary methods are used to assess the coherence lifetimes for these highly scattering media. Direct intensity or heterodyne detection of two-pulse photon echo techniques was employed for samples with longer coherence lifetimes and larger signal strengths, while time-delayed optical free induction decays were found to work well for shorter coherence lifetimes and weaker signal strengths. Spectral hole burning techniques were also used to characterize samples with very rapid dephasing processes. The results on powders are compared to the properties of a bulk crystal, with observed differences explained by the random orientation of the particles in the powders combined with new decoherence mechanisms introduced by the powder fabrication. Modeling of the coherence decay shows that paramagnetic materials such as Er 3 + :LiNbO3 that have highly anisotropic interactions with an applied magnetic field can still exhibit long coherence lifetimes and relatively simple decay shapes even for a powder of randomly oriented particles. We find that coherence properties degrade rapidly from mechanical treatment when grinding powders from bulk samples, leading to the appearance of amorphous-like behavior and a broadening of up to three orders of magnitude for the homogeneous linewidth even when low-energy grinding methods are employed. Annealing at high temperatures can improve the properties in some samples, with homogeneous linewidths reduced to less than 10 kHz, approaching the bulk crystal linewidth of 3 kHz under the same experimental conditions.

With their optical wavelength in the near infrared (790-800nm) and their unique spectroscopic properties at cryogenic temperatures, thulium-doped crystals are at the center of many architectures linked to classical signal processing and quantum information. In this work, we focus on Tm-doped YSO, a compound that was left aside in the mid-1990s due to its rather short optical coherence lifetime. By means of time-resolved hole-burning spectroscopy, we investigate the anisotropic enhanced nuclear Zeeman effect and demonstrate deep, sub-MHz, persistent spectral hole burning under specific magnetic field orientation and magnitude. By estimating the experimental parameters corresponding to a real-scale ultrasound optical tomography setup using Tm:YSO as a spectral filter, we validate Tm:YSO as a promising compound for medical imaging in the human body., Comment: 8 pages, 11 figures

High-quality rare-earth-ion (REI) doped materials are a prerequisite for many applications such as quantum memories, ultra-high-resolution optical spectrum analyzers and information processing. Compared to bulk materials, REI doped powders offer low-cost fabrication and a greater range of accessible material systems. Here we show that crystal properties, such as nuclear spin lifetime, are strongly affected by mechanical treatment, and that spectral hole burning can serve as a sensitive method to characterize the quality of REI doped powders. We focus on the specific case of thulium doped Y3AI5O12 (Tm:YAG). Different methods for obtaining the powders are compared and the influence of annealing on the spectroscopic quality of powders is investigated on a few examples. We conclude that annealing can reverse some detrimental effects of powder fabrication and, in certain cases, the properties of the bulk material can be reached. Our results may be applicable to other impurities and other crystals, including color centers in nano-structured diamond., Graphical Abstract

Nanostructured rare-earth-ion-doped materials are increasingly being investigated for on-chip implementations of quantum information processing protocols as well as commercial applications such as fluorescent lighting. However, achieving high-quality and optimized materials at the nanoscale is still challenging. Here we present a detailed study into the restriction of phonon processes in the transition from bulk crystals to small ($\ensuremath{\le}40$-nm) nanocrystals by observing the relaxation dynamics between crystal-field levels of ${\mathrm{Tb}}^{3+}:{\mathrm{Y}}_{3}{\mathrm{Al}}_{5}{\mathrm{O}}_{12}$. We find that the population relaxation dynamics are modified as the particle size is reduced, consistent with our simulations of inhibited relaxation through a modified vibrational density of states and hence modified phonon emission. However, our experiments also indicate that nonradiative processes not driven by phonons are also present in the smaller particles, causing transitions and rapid thermalization between the levels on a time scale of $l100\phantom{\rule{0.16em}{0ex}}\mathrm{ns}$.

In Er$^{3+}$:Y$_2$SiO$_5$, we demonstrate the selective optical addressing of the $^{89}$Y$^{3+}$ nuclear spins through their superhyperfine coupling with the Er$^{3+}$ electronic spins possessing large Land\'e $g$-factors. We experimentally probe the electron-nuclear spin mixing with photon echo techniques and validate our model. The site-selective optical addressing of the Y$^{3+}$ nuclear spins is designed by adjusting the magnetic field strength and orientation. This constitutes an important step towards the realization of long-lived solid-state qubits optically addressed by telecom photons., Comment: 5 pages, 4 figures, supplementary material (3 pages)

Anisotropy of the quadratic Zeeman effect for the $^{3}\mathrm{H}_{6}\ensuremath{\rightarrow}^{3}\mathrm{H}_{4}$ transition at 793 nm wavelength in $^{169}\mathrm{Tm}^{3+}\text{-doped} {\mathrm{Y}}_{3}{\mathrm{Al}}_{5}{\mathrm{O}}_{12}$ is studied, revealing shifts ranging from near zero up to $+4.69\phantom{\rule{0.28em}{0ex}}{\mathrm{GHz}/\mathrm{T}}^{2}$ for ions in magnetically inequivalent sites. This large range of shifts is used to spectrally resolve different subsets of ions and study nuclear spin relaxation as a function of temperature, magnetic field strength, and orientation in a site-selective manner. A rapid decrease in spin lifetime is found at large magnetic fields, revealing the weak contribution of direct phonon absorption and emission to the nuclear spin-lattice relaxation rate. We furthermore confirm theoretical predictions for the phonon coupling strength, finding much smaller values than those estimated in the limited number of past studies of thulium in similar crystals. Finally, we observe a significant---and unexpected---magnetic field dependence of the two-phonon Orbach spin relaxation process at higher field strengths, which we explain through changes in the electronic energy-level splitting arising from the quadratic Zeeman effect.

Understanding decoherence in cryogenically-cooled rare-earth-ion doped glass fibers is of fundamental interest and a prerequisite for applications of these material in quantum information applications. Here we study the coherence properties in a weakly doped erbium silica glass fiber motivated by our recent observation of efficient and long-lived Zeeman sublevel storage in this material and by its potential for applications at telecommunication wavelengths. We analyze photon echo decays as well as the potential mechanisms of spectral diffusion that can be caused by coupling with dynamic disorder modes that are characteristic for glassy hosts, and by the magnetic dipole-dipole interactions between $Er^{3+}$ ions. We also investigate the effective linewidth as a function of magnetic field, temperature and time, and then present a model that describes these experimental observations. We highlight that the operating conditions (0.6 K and 0.05 T) at which we previously observed efficient spectral hole burning coincide with those for narrow linewidths (1 MHz) { an important property for applications that has not been reported before for a rare-earth-ion doped glass., Comment: 6 pages and 5 figures

Long-lived population storage in optically pumped levels of rare-earth ions doped into solids, referred to as persistent spectral hole burning, is of significant fundamental and technological interest. However, the demonstration of deep and persistent holes in rare-earth ion doped amorphous hosts, e.g. glasses, has remained an open challenge since many decades -- a fact that motivates our work towards a better understanding of the interaction between impurities and vibrational modes in glasses. Here we report the first observation and detailed characterization of such holes in an erbium-doped silica glass fiber cooled to below 1 K. We demonstrate population storage in electronic Zeeman-sublevels of the erbium ground state with lifetimes up to 30 seconds and 80\% spin polarization. In addition to its fundamental aspect, our investigation reveals a potential technological application of rare-earth ion doped amorphous materials, including at telecommunication wavelength., 5 pages, 5 figures, 1 table

We report the storage of qubits encoded in the orbital angular momentum of the light at the single photon level with a fidelity larger than 90 % inside a cold atomic ensemble.

Nano-structuring impurity-doped crystals affects the phonon density of states and thereby modifies the atomic dynamics induced by interaction with phonons. We propose the use of nano-structured materials in the form of powders or phononic bandgap crystals to enable or improve persistent spectral hole-burning and coherence for inhomogeneously broadened absorption lines in rare-earth-ion-doped crystals. This is crucial for applications such as ultra-precise radio-frequency spectrum analyzers and optical quantum memories. As an example, we discuss how phonon engineering can enable spectral hole burning in erbium-doped materials operating in the convenient telecommunication band, and present simulations for density of states of nano-sized powders and phononic crystals for the case of Y2SiO5, a widely-used material in current quantum memory research., 6 pages, 4 figures

While measuring the orbital angular momentum state of bright light beams can be performed using imaging techniques, a full characterization at the single-photon level is challenging. For applications to quantum optics and quantum information science, such characterization is an essential capability. Here, we present a setup to perform the quantum state tomography of photonic qubits encoded in this degree of freedom. The method is based on a projective technique using spatial mode projection via fork holograms and single-mode fibers inserted into an interferometer. The alignment and calibration of the device is detailed as well as the measurement sequence to reconstruct the associated density matrix. Possible extensions to higher-dimensional spaces are discussed.

We implement a quantum memory for photonic qubits encoded in orbital angular momentum states of light and characterize it by performing a full tomography on stored and retrieved states, proving the quantumness of the process.

Summary form only given. If in general the transparency of an initially absorbing medium for a probe field is increased by the presence of a control field on an adjacent transition, two very different processes can be invoked to explain it. One of them is a quantum Fano interference between two paths in the three-level system, which occurs even at low control intensity and gives rise to electromagnetically-induced transparency (EIT), the other one is the appearance of two dressed states in the excited level at higher control intensity, corresponding to the Autler-Townes splitting (ATS). This distinction is particularly critical for instance for the implementation of slow light or optical quantum memories. In a recent paper, P. M. Anisimov, J. P. Dowling and B. C. Sanders proposed a quantitative test to objectively discerning ATS from EIT. We experimentally investigated this test with cold atoms and demonstrated that it is very sensitive to the specific properties of the medium. In this study, we use an ensemble of cold Cesium atoms trapped in a MOT, interacting with light via a Λ-type scheme on the D2 line. Absorption profiles are obtained for various values of the control Rabi frequency Ω between 0.1Γ and 4Γ, where Γ is the natural linewidth.

Among the optical degrees of freedom, the orbital angular momentum of light1 provides unique properties2, including mechanical torque action, which has applications for light manipulation3, enhanced sensitivity in imaging techniques4 and potential high-density information coding for optical communication systems5. Recent years have also seen a tremendous interest in exploiting orbital angular momentum at the single-photon level in quantum information technologies6,7. In pursuing this endeavour, we demonstrate here the implementation of a quantum memory8 for quantum bits encoded in this optical degree of freedom. We generate various qubits with computer-controlled holograms, store and retrieve them on demand using a dynamic electromagnetically induced transparency protocol. We further analyse the retrieved states by quantum tomography and thereby demonstrate fidelities exceeding the classical benchmark, confirming the quantum functioning of our storage process. Our results provide an essential capability for future networks9 exploring the promises of orbital angular momentum of photons for quantum information applications. A quantum memory for orbital angular momentum qubits is demonstrated in the single-photon regime. It is based on cold cesium atoms and the dynamic electromagnetically induced transparency protocol. Retrieved states were analysed by quantum tomography, and fidelities after readout of over 92% were obtained, confirming the quantum functionality of the storage process.

Summary form only given. The orbital angular momentum (OAM) of light has raised a great deal of applications [1], ranging from the trapping of particles, the driving of optical micromachines to applications in astrophysics studies. In quantum optics, twisted single-photons have also been identified as promising carriers for the implementation of various quantum information protocols. They indeed offer the possibility to encode and process information in high-dimensional Hilbert spaces and could enable to reach higher efficiencies and enhanced information capacity. For further applications in quantum networks involving light-matter interfaces, a critical capability is the ability to reversibly map OAM into and out of atomic memories. While the storage of bright beams of light in Laguerre-Gaussian modes has been reported in the past few years [2, 3], we report here the first demonstration of storage in the single-photon regime [4]. The experimental realization proceeds in the following way. First, LG modes are generated using a spatial light modulator. These modes, which are weak coherent states at the single-photon level, are then mapped into an ensemble of cold cesium atoms in a magneto-optical trap using the dynamic electromagnetically-induced transparency (EIT) protocol. The signal quantum properties, including its OAM, are expected to be transferred to the atomic medium and can be stored for a programmable time, limited by the lifetime of the atomic coherence. After this reversible storage, unlike for bright beams, the detection of twisted single-photons cannot be performed by imaging on a CCD camera. Here we have chosen to work with a combination of a computergenerated hologram, which adds or subtracts one unity of OAM, and a single-mode fiber to implement a mode discriminator. In our experiment, the output mode is actually split on a 50/50 beam splitter and one discriminator is installed in each of the two output paths so that we can quantify both the LG+1 and LG-1 components of the retrieved light. We stored and retrieved LG+1 and LG-1 modes. As can be seen in fig. 1, detection events in the detection path with l opposite to the one of the incoming mode are negligible, within the distinction ratio. For both modes, the overall storage and retrieval efficiency is (16 ± 2%). We thus demonstrated that such pulses carrying OAM can be stored in the single-photon regime into and out the ensemble with preserved handedness of the helical phase structure. Mapping of a TEM10 mode, i.e. an equal-weight superposition of LG+1 and LG-1 modes was also performed. Within our experimental precision, the achieved storage and retrieval efficiency is the same here each LG components than for the individual storage presented previously. Further works should include reconstruction of a full density matrix, including coherences not measured here, and the calculation of process fidelity. We implemented a sophisticated detection technique based on a Mach-Zehnder interferometer. Preliminary results will be reported. Extensions to higher alphabets for the realization of high-dimensional quantum information networks is also work for future.

Storage and read-out of quantum states of light based on EIT is studied in atomic ensembles. We compare storage schemes in Cs atomic vapors at room temperature and in cold atomic clouds.

In this paper, an optical memory based on an ensemble of cold Cesium atoms interacting with light in the electromagnetically induced transparency (EIT) regime is studied in view of spatially multimode quantum storage. The interfacing protocol involves a control field, generating EIT for the very weak field that carries the quantum signal to be stored and enabling its mapping into the collective hyperfine coherence of the cold atomic ensemble. For the demonstration of multimode storage, the signal pulse at the single photon level is prepared in a mode with (OAM), while the control field is in a TEM00 mode. After the writing process, the information is kept in the memory register. In the retrieval phase, the information is read back from atoms to light and we show that these pulses at the single photon level with OAM can be stored and retrieved with a preserved spatial phase and a good efficiency.

We investigated a method that allows for objectively discerning between the Autler-Townes splitting and the electromagnetically-induced transparency models. We demonstrated the suitability of the test and additionally show its sensitivity to the medium properties.