In this letter we present a method for increasing the coherence time of praseodymium hyperfine ground state transitions in Pr^3+:Y_2SiO_5 by the application of a specific external magnetic field. The magnitude and angle of the external field is applied such that the Zeeman splitting of a hyperfine transition is at a critical point in three dimensions, making the first order Zeeman shift vanishingly small for the transition. This reduces the influence of the magnetic interactions between the praseodymium ions and the spins in the host lattice on the transition frequency. Using this method a phase memory time of 82ms was observed, a value two orders of magnitude greater than previously reported. It is shown that the residual dephasing is amenable quantum error correction.
The spin coherence time of $^{151}$Eu$^{3+}$ which substitutes the yttrium at site 1 in Y$_2$SiO$_5$ crystal has been extended to 6 hours in a recent work [\textit{Nature} \textbf{517}, 177 (2015)]. To make this long-lived spin coherence useful for optical quantum memory applications, we experimentally characterize the hyperfine interaction of the optically-excited state $^5$D$_0$ using Raman-heterodyne-detected nuclear magnetic resonance. The effective spin Hamiltonians for excited and ground state are fitted based on the experimental spectra obtained in 200 magnetic fields with various orien…
High-resolution Zeeman spectroscopy of electronic-nuclear hyperfine levels of ${^5\mathrm{I}_8}\rightarrow{^5\mathrm{I}_7}$ transitions in Ho$^{3+}$:Y$_2$SiO$_5$ is reported. Crystal-field parameters determined for the two $C_1$ symmetry sites in Er$^{3+}$:Y$_2$SiO$_5$ are successfully used to model the Zeeman-hyperfine data, including the prediction of avoided crossings between hyperfine levels under the influence of an external magnetic field. The two six- and seven-coordinate substitutional sites may be distinguished by comparing the spectra with crystal-field calculations.
We characterize the Europium (Eu$^{3+}$) hyperfine interaction of the excited state ($^5$D$_0$) and determine its effective spin Hamiltonian parameters for the Zeeman and quadrupole tensors. An optical free induction decay method is used to measure all hyperfine splittings under weak external magnetic field (up to 10 mT) for various field orientations. On the basis of the determined Hamiltonian we discuss the possibility to predict optical transition probabilities between hyperfine levels for the $^7$F$_{0} \longleftrightarrow ^5$D$_{0}$ transition. The obtained results provide necessary infor…
Praseodymium (Pr$^{3+}$) ions doped in the site 1 of yttrium orthosilicate (Y$_2$SiO$_5$) has been widely employed as the photonic quantum memory due to their excellent optical coherence and spin coherence. While praseodymium ions occupying the site 2 in Y$_2$SiO$_5$ crystal have better optical coherence as compared with those at site 1, which may enable better performance in quantum memory. Here we experimentally characterize the hyperfine interactions of the ground state $^3$H$_4$ and excited state $^1$D$_2$ of Pr$^{3+}$ at site 2 in Y$_2$SiO$_5$ using Raman heterodyne detected nuclear magne…
We report on the development and application of a parametrized crystal-field model for both C$_{1}$ symmetry centers in trivalent erbium-doped Y$_{2}$SiO$_{5}$. High resolution Zeeman and temperature dependent absorption spectroscopy was performed to acquire the necessary experimental data. The obtained data, in addition to the ground ($^{4}$I$_{15/2}$Z$_{1}$) state and exited ($^{4}$I$_{13/2}$Y$_{1}$) state Zeeman and hyperfine structure, was simultaneously fitted in order to refine an existing crystal-field interpretation of the Er$^{3+}$:Y$_{2}$SiO$_{5}$ system. We demonstrate that it is po…
We show that crystal-field calculations for $C_1$ point-group symmetry are possible, and that such calculations can be performed with sufficient accuracy to have substantial utility for rare-earth based quantum information applications. In particular, we perform crystal-field fitting for a C$_1$-symmetry site in $^{167}$Er$^{3+}$:Y$_2$SiO$_5$. The calculation simultaneously includes site-selective spectroscopic data up to 20,000 cm$^{-1}$, rotational Zeeman data, and ground- and excited-state hyperfine structure determined from high-resolution Raman-heterodyne spectroscopy on the 1.5 $μ$m tele…
Rare-earth ion doped crystals are promising systems for quantum communication and quantum information processing. In particular, paramagnetic rare-earth centres can be utilized to realize quantum coherent interfaces simultaneously for optical and microwave photons. In this article, we study hyperfine and magnetic properties of a Y$_2$SiO$_5$ crystal doped with $^{171}$Yb$^{3+}$ ions. This isotope is particularly interesting since it is the only rare--earth ion having electronic spin $S=\frac{1}{2}$ and nuclear spin $I=\frac{1}{2}$, which results in the simplest possible hyperfine level structu…
The coherence of a hyperfine-state superposition of a trapped $^{9}$Be$^+$ ion in the presence of off-resonant light is experimentally studied. It is shown that Rayleigh elastic scattering of photons that does not change state populations also does not affect coherence. Coherence times exceeding the average scattering time of 19 photons are observed. This result implies that, with sufficient control over its parameters, laser light can be used to manipulate hyperfine-state superpositions with very little decoherence.
Er$^{3+}$$:$Y$_2$SiO$_5$ is a material of particular interest due to its suitability for telecom-band quantum memories and quantum transducers interfacing optical communication with quantum computers working in the microwave regime. Extending the coherence lifetimes of the electron spins and the nuclear spins is essential for implementing efficient quantum information processing based on such hybrid electron-nuclear spin systems. The electron spin coherence time of Er$^{3+}$$:$Y$_2$SiO$_5$ is so far limited to several microseconds, and there are significant challenges in optimizing coherence l…
We investigate the single qubit transformations under several typical coherence-free operations, such as, incoherent operation (IO), strictly incoherent operation (SIO), physically incoherent operation (PIO), and coherence preserving operation (CPO). Quantitative connection has been built between IO and SIO in single qubit systems. Moreover, these coherence-free operations have a clear hierarchical relationship in single qubit systems: CPO $\subset$ PIO $\subset$ SIO=IO. A new and explicit proof for the necessary and sufficient condition of single qubit transformation via IO or SIO has been pr…
Efficient optical pumping is an important tool for state initialization in quantum technologies, such as optical quantum memories. In crystals doped with Kramers rare-earth ions, such as erbium and neodymium, efficient optical pumping is challenging due to the relatively short population lifetimes of the electronic Zeeman levels, of the order of 100 ms at around 4 K. In this article we show that optical pumping of the hyperfine levels in isotopically enriched $^{145}$Nd$^{3+}$:Y$_2$SiO$_5$ crystals is more efficient, owing to the longer population relaxation times of hyperfine levels. By optic…
The goal of this short note is to show that the formulas I derived originally in [Phys. Rev. A 65, 022308 (2002)] regarding the errors introduced in quantum logical operations by the quantum nature of the control fields apply even in the situation discussed recently by Ozeri et al. in quant-ph/0502063, where the decoherence-inducing spontaneous Raman scattering is considerably suppressed.
Spins in solids are an ideal candidate to act as a memory and interface with superconducting qubits due to their long coherence times. We spectroscopically investigate erbium-167-doped yttrium orthosilicate as a possible microwave-addressed memory employing its microwave frequency transitions that occur without applying an external magnetic field. We obtain coherence times of 380 $μ$s in a ground state spin transition and 1.48 ms in an excited state spin transition. This is 28 times longer compared to previous zero field measurements, as well as 200 times longer than a previous microwave memor…
Theoretical studies indicating the presence of long-lived coherence in the radical pair system have engendered questions about the utilitarian role of sustained coherence in the avian compass. In this manuscript, we investigate this for a realistic multi-nuclear radical pair system, along with the related question of its sensitivity to the geomagnetic field. Firstly, we find that sustenance of long-lived coherence is unlikely in a realistic hyperfine environment. Secondly, probing the role of the hyperfine interactions on the compass sensitivity, we establish the hyperfine anisotropy as an ess…
We demonstrate the preparation and probing of the coherence between the hyperfine ground states |5S_{1/2}, F=1> and |5S_{1/2}, F=2> of the Rubidium 87 isotope. The effect of various coherence control techniques, i.e. fractional Stimulated Raman Adiabatic Passage and Coherent Population Return on the coherence are investigated. These techniques are implemented using nearly degenerate pump and Stokes lasers at 795nm (Rubidium D1 transition) which couple the two hyperfine ground states via the excited state |5P_{1/2}, F=1> through a resonant two-photon process, in which a coherent superposition o…
Rare-earth ions in dielectric crystals are interesting candidates for storing quantum states of photons. A limiting factor on the optical density and thus the conversion efficiency is the distortion introduced in the crystal by doping elements of one type into a crystal matrix of another type. Here, we investigate the system Pr3+:La2(WO4)3, where the similarity of the ionic radii of Pr and La minimizes distortions due to doping. We characterize the praseodymium hyperfine interaction of the ground state (3H4) and one excited state (1D2) and determine the spin Hamiltonian parameters by numerical…
We complete the task of optimal probabilistic coherence distillation protocol, whose aim is to transform a general state into a set of n-level maximally coherent states via strictly incoherent operations (SIO). Specifically, we present the necessary and sufficient condition for the transformation from a mixed state into a pure-state ensemble via SIO. With the aid of this condition and the simplex algorithm, we can accomplish the probabilistic distillation protocol by presenting an analytical expression of the maximal average distillable coherence of a general state and constructing the corresp…
We compute analytically the maximal rates of distillation of quantum coherence under strictly incoherent operations (SIO) and physically incoherent operations (PIO), showing that they coincide for all states, and providing a complete description of the phenomenon of bound coherence. In particular, we establish a simple, analytically computable necessary and sufficient criterion for the asymptotic distillability under SIO and PIO. We use this result to show that almost every quantum state is undistillable --- only pure states as well as states whose density matrix contains a rank-one submatrix …
Er$^{3+}$:Y$_2$SiO$_5$ crystal is a promising candidate with a great variety of its potential applications in quantum information processing and quantum communications ranging from optical/microwave quantum memories to circuit QED and microwave-to-optics frequency converters. Some of the above listed applications require ultra-low temperature environment, i.e., temperatures $T\lesssim0.1~$K. Most of the experiments with erbium doped crystals have been so far carried out at temperatures above 1.5~K. Therefore, only little information is known about Er$^{3+}$:Y$_2$SiO$_5$ coherence properties at…
We demonstrate coherent control of two nuclear spins mediated by the magnetic resonance of a hyperfine-coupled electron spin. This control is used to create a double nuclear coherence in one of the two electron spin manifolds, starting from an initial thermal state, in direct analogy to the creation of an entangled (Bell) state from an initially pure unentangled state. We identify challenges and potential solutions to obtaining experimental gate fidelities useful for quantum information processing in this type of system.
We investigate the decoherence of Er$^{3+}$ in Y$_2$SiO$_5$ at low magnetic fields using the photon-echo technique. We reproduce accurately a variety of the decay curves with a unique coherence time by considering the so-called superhyperfine modulation induced by a large number of neighbouring spins. There is no need to invoke any characteristic time of the spin fluctuations to reproduce very different decay curves. The number of involved nuclei increases when the magnetic is lowered. The experiment is compared with a model associating 100 surrounding ions with their exact positions in the cr…
Multiple quantum experiments are used to resolve broad peaks in nuclear magnetic resonance spectra of quadrupolar nuclei. In this work, we study phase cycling of radio frequency pulses in a single quantum satellite transition magic angle spinning experiment. The particular pulse sequence is a shifted echo sequence where phases of the pulses are varied in accordance with coherence selection rules. Experiments were performed on a $^{17}$O enriched sample of SiO$_2$. Results show that certain phase sequences may decrease the full width at half maximum of spectral peaks.
Although a nuclear spin is weakly coupled to its environment, due to its small gyromagnetic ratio, its coherence time is limited by the hyperfine coupling to a nearby noisy electron. Here, we propose to utilize continuous dynamical decoupling to refocus the coupling to the electron. If the random phase accumulated by the nuclear spin through the reduced coupling terms is sufficient small, we can increase the nuclear coherence time. Initially, we demonstrate this on a simple case with a two-level electron spin, while taking all relevant hyperfine coupling terms and noise terms into account. We …
We present the full magnetic g tensors of the $^{6}$H$_{5/2}$Z$_{1}$ and $^{4}$G$_{5/2}$A$_{1}$ electronic states for both crystallographic sites in Sm$^{3+}$:Y$_{2}$SiO$_{5}$, deduced through the use of Raman heterodyne spectroscopy performed along 9 different crystallographic directions. The maximum principle g values were determined to be 0.447 (site 1) and 0.523 (site 2) for the ground state and 2.490 (site 1) and 3.319 (site 2) for the excited state. The determination of these g tensors provide essential spin Hamiltonian parameters that can be utilized in future magnetic and hyperfine stu…
We study in detail the mechanisms causing dephasing of hyperfine coherences of cesium atoms confined by a far off-resonant standing wave optical dipole trap [S. Kuhr et al., Phys. Rev. Lett. 91, 213002 (2003)]. Using Ramsey spectroscopy and spin echo techniques, we measure the reversible and irreversible dephasing times of the ground state coherences. We present an analytical model to interpret the experimental data and identify the homogeneous and inhomogeneous dephasing mechanisms. Our scheme to prepare and detect the atomic hyperfine state is applied at the level of a single atom as well as…
Quantum memories for light will be essential elements in future long-range quantum communication networks. These memories operate by reversibly mapping the quantum state of light onto the quantum transitions of a material system. For networks, the quantum coherence times of these transitions must be long compared to the network transmission times, approximately 100 ms for a global communication network. Due to a lack of a suitable storage material, a quantum memory that operates in the 1550 nm optical fiber communication band with a storage time greater than 1 us has not been demonstrated. Her…
Progress with quantum technology has for a large part been realized with the nitrogen-vacancy centre in diamond. Part of its properties, however, are nonideal and this drives research into other spin-active crystal defects. Several of these come with much stronger energy scales for spin-orbit and hyperfine coupling, but how this affects their spin coherence is little explored. Vanadium in silicon carbide is such a system, with technological interest for its optical emission at a telecom wavelength and compatibility with semiconductor industry. Here we show coherent spin dynamics of an ensemble…
In contrast to the traditional Spontaneous Generated Coherence (SGC), Field Generated Coherence (FGC)-based atomic scheme is presented for spontaneous emission cancellation. It is easy to achieve externally controllable experimental trapping condition in this 4-field-driven 5-level atomic system. Consequently, due to the FGC the decay from the central dressed \emph{bare-energy-state} of the set of upper three closely spaced hyperfine decaying states of Sodium D2 line is completely cancelled under the trapping condition, exhibiting a novel phenomenon of a \textit{dark bare-energy-state}% . Exte…
For quantum information processing (QIP) with trapped ions, the isotope 43Ca+ offers the combined advantages of a quantum memory with long coherence time, a high fidelity read out and the possibility of performing two qubit gates on a quadrupole transition with a narrow-band laser. Compared to other ions used for quantum computing, 43Ca+ has a relatively complicated level structure. In this paper we discuss how to meet the basic requirements for QIP and demonstrate ground state cooling, robust state initialization and efficient read out for the hyperfine qubit with a single 43Ca+ ion. A microw…
Nuclear-spin qubits have long coherence time and are desirably applied into quantum information processing. However, the existing methods either fail to address single nucleus (such as nuclear magnetic resonance), or severely affect nuclear coherence time (such as electrical nuclear manipulation based on hyperfine stark effect, ENMHSE). Here we propose an electrical nuclear manipulation called nuclear electric resonance which can on the one hand address the single nuclear qubit, and on the other keep the long coherence time. Applying this, we construct universal quantum gates with external ele…
Magnetic-field gradients are important for single-site addressability and electric-dipole spin resonance of spin qubits in semiconductor devices. We show that these advantages are offset by a potential reduction in coherence time due to the non-uniformity of the magnetic field experienced by a nuclear-spin bath interacting with the spin qubit. We theoretically study spins confined to quantum dots or at single donor impurities, considering both free-induction and spin-echo decay. For quantum dots in GaAs, we find that, in a realistic setting, a magnetic-field gradient can reduce the Hahn-echo c…
Theoretical prediction of antilocalization of light in ultracold atomic gas samples, in the weak localization regime, is reported. Calculations and Monte-Carlo simulations show that, for selected spectral ranges in the vicinity of atomic 85Rb hyperfine transitions, quantum coherence in optical transitions through nondegenerate hyperfine levels in multiple light scattering generates destructive interference in otherwise reciprocal scattering paths. This effect leads to enhancement factors less than unity in a coherent backscattering geometry, and suggests the possibility of enhanced diffusion o…
We report microwave spectroscopy of co-trapped $^9\text{Be}^+$ and $^{40}\text{Ca}^+$ within a compact permanent-magnet-based Penning ion trap. The trap is constructed with a reconfigurable array of NdFeB rings providing a 0.654 T magnetic field that is near the 0.6774-T magnetic-field-insensitive hyperfine transition in $^9\text{Be}^+$. Performing Ramsey spectroscopy on this hyperfine transition, we demonstrate nuclear spin coherence with a contrast decay time of >1 s. The $^9\text{Be}^+$ is sympathetically cooled by a Coulomb crystal of $^{40}\text{Ca}^+$, which minimizes $^9\text{Be}^+$ ill…
We demonstrate a coherence time of 2.1(1)~s for electron spin superposition states of a single trapped $^{40}$Ca$^+$ ion. The coherence time, measured with a spin-echo experiment, corresponds to residual rms magnetic field fluctuations $\leq$~2.7$\times$10$^{-12}$~T. The suppression of decoherence induced by fluctuating magnetic fields is achieved by combining a two-layer $μ$-metal shield, which reduces external magnetic noise by 20 to 30~dB for frequencies of 50~Hz to 100~kHz, with Sm$_2$Co$_{17}$ permanent magnets for generating a quantizing magnetic field of 0.37~mT. Our results extend the …
We experimentally demonstrate coherent amplification of probe field in a tripod-type atoms driven by strong coupling, signal and weak probe fields. We suppress linear and nonlinear atomic absorptions for resonant and near resonant probe via double electromagnetically induced transparency (DEIT). Combining these advantages of suppressed absorption along with temperature- or atomic-density-controlled transfer of population(ToP) between hyperfine ground states, we can induce near-resonant amplification of probe through stimulated Raman scattering(SRS) pumped by low-intensity signal field. The inc…
Hole spins in semiconductors are a potential qubit alternative to electron spins. In nuclear-spin-rich host crystals like GaAs, the hyperfine interaction of hole spins with nuclei is considerably weaker than that for electrons, leading to potentially longer coherence times. Here we demonstrate optical pumping and coherent population trapping for acceptor-bound holes in a strained GaAs epitaxial layer. We find $μ$s-scale longitudinal spin relaxation time T$_1$ and an inhomogeneous dephasing time T$_2^*$ of $\sim$7~ns. We attribute the spin relaxation mechanism to a combination effect of a hole-…
We experimentally investigate the coherence properties of a qubit stored in the Zeeman substates of the 5S1/2, F=1 hyperfine ground level of a single optically trapped Rb-87 atom. Larmor precession of a single atomic spin-1 system is observed by preparing the atom in a defined initial spin-state and then measuring the resulting state after a programmable period of free evolution. Additionally, by performing quantum state tomography, maximum knowledge about the spin coherence is gathered. By using an active magnetic field stabilization and without application of a magnetic guiding field we achi…
The spectrum of atomic hydrogen has long been viewed as a Rosetta stone that bears the key to decode the writings of quantum mechanics in a vast variety of physical, chemical, and biological systems. Here, we show that, in addition to its role as a basic model of quantum mechanics, the hydrogen atom provides a fundamental building block of quantum information. Through its electron and nuclear spin degrees of freedom, the hydrogen atom is shown to lend a physically meaningful frame and a suitable Hilbert space for bipartite entanglement, whose two-qubit concurrence and quantum coherence can be …
Coherence-Based Identification of Carbon-Based Spin Qubits in Hexagonal Boron Nitride from First Principles
SKKU Advanced Institute of Nanotechnology, Sungkyunkwan University（成均馆大学 SKKU 纳米技术高级研究所）；Department of Quantum Information Engineering, Sungkyunkwan University（成均馆大学量子信息工程系）
Solid-state electronic spins are extensively studied in quantum information science, as their large magnetic moments offer fast operations for computing and communication, and high sensitivity for sensing. However, electronic spins are more sensitive to magnetic noise, but engineering of their spectroscopic properties, e.g. using clock transitions and isotopic engineering, can yield remarkable spin coherence times, as for electronic spins in GaAs, donors in silicon and vacancy centres in diamond. Here we demonstrate simultaneously induced clock transitions for both microwave and optical domain…
The possibility of performing single spin measurements in Si-based quantum computers through electric field control of electrons bound to double donors near a barrier interface is assessed. We find that both the required electric fields and the tunneling times involved are probably too large for practical implementations. On the other hand, operations with double donors in their first excited state require smaller fields and faster tunneling times, and are therefore suitable for spin-to-charge conversion measurements. We also propose a measurement scheme that would render statistical (ensemble…
We demonstrate experimentally a robust quantum memory using a magnetic-field-independent hyperfine transition in 9Be+ atomic ion qubits at a magnetic field B ~= 0.01194 T. We observe that the single physical qubit memory coherence time is greater than 10 seconds, an improvement of approximately five orders of magnitude from previous experiments with 9Be+. We also observe long coherence times of decoherence-free subspace logical qubits comprising two entangled physical qubits and discuss the merits of each type of qubit.
The temperature dependence of the coherence time of hole spins confined in self-assembled (In,Ga)As/GaAs quantum dots is studied by spin mode-locking and spin echo techniques. Coherence times limited to about a μs are measured for temperatures below 8 K. For higher temperatures a fast drop occurs down to a few ns over a 10 K range. The hole-nuclear hyperfine interaction appears too weak to account for these limitations. We suggest that spin-orbit related interactions are the decisive sources for hole spin decoherence.
The quantum state of the emitted light from the cascade recombination of a biexciton in a quantum dot is theoretically investigated including exciton fine structure splitting (FSS) and electron-nuclear spin hyperfine interactions. In an ideal situation, the emitted photons are entangled in polarization making the biexciton recombination process a candidate source of entangled photons necessary for the growing field of quantum communication and computation. The coherence of the exciton states in real quantum dots is affected by a finite FSS and the hyperfine interactions via the effective magne…
We study Landau-Zener dynamics in a double quantum dot filled with two electrons, where the spin states can become correlated with charge states and the level velocity can be tuned in a time-dependent fashion. We show that a correct interpretation of experimental data is only possible when finite-time effects are taken into account. In addition, our formalism allows the study of partial adiabatic dynamics in the presence of phonon-mediated hyperfine relaxation and charge-noise-induced dephasing. Our findings demonstrate that charge noise severely impacts the visibility of Landau-Zener-Stückelb…
This work introduces the so-called synchrosqueezed wavelet transform, to shed light on the dipolar fluctuations of a thermal ensemble of nuclear spins in a diamond crystal structure, hyperfine-coupled to a central spin. The raw time series of the nuclear spin bath coherent dynamics is acquired through the two-point correlation function computed using the cluster correlation expansion method. The dynamics can be conveniently analyzed according to zero-, single-, and double-quantum transitions derived from the dipolar pairwise spin flips. We show that in the early-time behavior when the coherenc…
The coherent interaction of solid-state spins with both optical and microwave fields provides a platform for a range of quantum technologies, such as quantum sensing, microwave-to-optical quantum transduction and optical quantum memories. Rare-earth ions with electronic spins are interesting in this context, but it is challenging to simultaneously and efficiently drive both optical and microwave transitions over a long crystal. In this work, we use a loop-gap microwave resonator to coherently drive optical and microwave clock transitions in $^{171}$Yb$^{3+}$:Y$_2$SiO$_5$, at close to zero exte…
