We propose and analyze a high fidelity readout scheme for a single instance approach to quantum computing in rare-earth-ion-doped crystals. The scheme is based on using different species of qubit and readout ions, and it is shown that by allowing the closest qubit ion to act as a readout buffer, the readout error can be reduced by more than an order of magnitude. The scheme is shown to be robust against certain experimental variations, such as varying detection efficiencies, and we use the scheme to predict the expected quantum fidelity of a CNOT gate in these solid state systems. In addition, we discuss the potential scalability of the protocol to larger qubit systems. The results are based on parameters which we believed are experimentally feasible with current technology, and which can be simultaneously realized.
Owing to their long excited state lifetimes, rare-earth ions in crystals are widely used in quantum applications. To allow optical readout of the qubit state of individual ions, we propose to dope the crystal with an additional nearby ancilla ion with a shorter radiative lifetime. We show how a Bayesian analysis exhausts the information about the state of the qubit from the optical signal of the ancilla ion. We study the effects of incoherent processes and propose ways to reduce their effect on the readout. Finally, we extend the architecture to ions residing in two remote cavities, and we sho…
Quantum networks based on optically addressable spin qubits promise to enable secure communication, distributed quantum computing, and tests of fundamental physics. Scaling up quantum networks based on solid-state luminescent centers requires coherent spin and optical transitions coupled to photonic resonators. Here we investigate single $\mathrm{{}^{171}Yb^{3+}}$ ions in yttrium orthovanadate coupled to a nanophotonic cavity. These ions possess optical and spin transitions that are first-order insensitive to magnetic field fluctuations, enabling optical linewidths less than 1 MHz and spin coh…
We discuss the issues surrounding the implementation of quantum computation in rare-earth-ion doped solids. We describe a practical scheme for two qubit gate operations which utilise experimentally available interactions between the qubits. Possibilities for a scalable quantum computer are discussed.
We explore spin-orbit thermal entanglement in rare-earth ions, based on a witness obtained from mean energies. The entanglement temperature $T_{E}$, below which entanglement emerges, is found to be thousands of kelvin above room temperature for all light rare earths. This demonstrate the robustness to environmental fluctuations of entanglement between internal degrees of freedom of a single ion.
Spontaneous Raman emission in atomic gases provides an attractive source of photon pairs with a controllable delay. We show how this technique can be implemented in solid state systems by appropriately shaping the inhomogeneous broadening. Our proposal is eminently feasible with current technology and provides a realistic solution to entangle remote rare-earth doped solids in a heralded way.
We propose a scheme for universal quantum computing based on Kramers rare-earth ions. Their nuclear spins in the presence of a Zeeman-split electronic crystal field ground state act as 'passive' qubits which store quantum information. The qubits can be activated optically by fast coherent transitions to excited crystal field states with a magnetic moment. The dipole interaction between these states is used to implement CNOT gates. We compare our proposal with a similar one based on phosphorus donor atoms in silicon and discuss the significantly improved CNOT gate time as compared to rare-earth…
We study the possibility of using single rare-earth ions coupled to a photonic cavity with high cooperativity for performing non-destructive measurements of photons, which would be useful for global quantum networks and photonic quantum computing. We calculate the achievable fidelity as a function of the parameters of the rare-earth ion and photonic cavity, which include the ion's optical and spin dephasing rates, the cavity linewidth, the single photon coupling to the cavity, and the detection efficiency. We suggest a promising experimental realization using current state of the art technolog…
We propose a scheme to couple short single photon pulses to superconducting qubits. An optical photon is first absorbed into an inhomogeneously broadened rare-earth doped crystal using controlled reversible inhomogeneous broadening. The optical excitation is then mapped into a spin state using a series of $π$-pulses and subsequently transferred to a superconducting qubit via a microwave cavity. To overcome the intrinsic and engineered inhomogeneous broadening of the optical and spin transitions in rare earth doped crystals, we make use of a special transfer protocol using staggered $π$-pulses.…
We propose a solid-state based superradiance laser which is almost insensitive to the cavity mirror vibration. Therefore, it can compete with the best frequency-stable local oscillators. The long coherence time and the large optical density of rare-earth-ions (REIs) doped solids are employed to find a regime to demonstrate a steady-state laser emission with linewidth smaller than the atomic decay rate. The experimental parameters are discussed and intracavity photon number and laser linewidth are calculated based on the mean-field theory. A procedure for measuring absolute laser linewidth is p…
We investigate the possibility of achieving the strong coupling regime of cavity quantum electrodynamics using rare earth ions as impurities in monolithic optical resonators. We conclude that due to the weak oscillator strengths of the rare earths, it may be possible but difficult, to reach the regime where the single photon Rabi frequency is large compared to both the cavity and atom decay rates. However reaching the regime where the saturation photon and atom numbers are less than one should be much more achievable. We show that in this `bad cavity' regime, transfer of quantum states and an …
We describe a method for creating small quantum processors in a crystal stoichiometric in an optically active rare earth ion. The crystal is doped with another rare earth, creating an ensemble of identical clusters of surrounding ions, whose optical and hyperfine frequencies are uniquely determined by their spatial position in the cluster. Ensembles of ions in each unique position around the dopant serve as qubits, with strong local interactions between ions in different qubits. These ensemble qubits can each be used as a quantum memory for light, and we show how the interactions between qubit…
Probing collective spin dynamics is a current challenge in the field of magnetic resonance spectroscopy and has important applications in material analysis and quantum information protocols. Recently, the rare-earth ion doped crystals are an attractive candidate for making long-lived quantum memory. Further enhancement of its performance would benefit from the direct knowledge on the dynamics of nuclear-spin bath in the crystal. Here we detect the collective dynamics of nuclear-spin bath located around the rare-earth ions in a crystal using dynamical decoupling spectroscopy method. From the me…
We demonstrate optical probing of spectrally resolved single Nd rare-earth ions in yttrium orthovanadate. The ions are coupled to a photonic crystal resonator and show strong enhancement of the optical emission rate via the Purcell effect, resulting in near radiatively limited single photon emission. The measured high coupling cooperativity between a single photon and the ion allows for the observation of coherent optical Rabi oscillations. This could enable optically controlled spin qubits, quantum logic gates, and spin-photon interfaces for future quantum networks.
Most investigations of rare earth ions in solids for quantum information have used rare earth ion doped crystals. Here we analyse the conversion of quantum information from microwave photons to optical frequencies using crystals where the rare earth ions, rather than being dopants, are part of the host crystal. The potential of large ion densities and small linewidths makes such systems very attractive in this application. We show that, as well as high efficiency, large bandwidth conversion is possible. In fact, the collective coupling between the rare earth ions and the optical and microwave …
Three orders of magnitude cavity-linewidth narrowing in a rare-earth-ion-doped crystal cavity, induced by strong intra-cavity dispersion caused by off-resonant interaction with dopant ions is demonstrated. The strong dispersion is created by semi-permanent but rapidly reprogrammable changes of the rare earth absorption profiles using optical pumping techniques. Several cavity modes are shown within the spectral transmission window. Potential applications are discussed.
Fluoride crystals doped with rare-earth ions (REI) and pair centers in diamond for fast ($10^{-9}\rm{s}$) quantum computers (FQC) are proposed. As specific systems for REI doping, we propose $Ca_{1-x}Sr_{x}F_{2}$ crystals and their analogues. The $^{4}f$-states with different total orbital angular moments of these ions serve as two-level systems (qubits). Suitable REIs are proposed as well. It is established that the pair $SiV$ and $GeV$ centers in diamond are promising systems for fast optical quantum computers operating at elevated temperatures.
Quantum magnonics is a new and active research field, leveraging the strong collective coupling between microwaves and magnetically ordered spin systems. To date work in quantum magnonics has focused on transition metals and almost entirely on ferromagnetic resonances in yttrium iron garnet (YIG). Antiferromagnetic systems have gained interest as they produce no stray field, and are therefore robust to magnetic perturbations and have narrow, shape independent resonant linewidths. Here we show the first experimental evidence of ultrastrong-coupling between a microwave cavity and collective anti…
Interfacing photonic and solid-state qubits within a hybrid quantum architecture offers a promising route towards large scale distributed quantum computing. Ideal candidates for coherent qubit interconversion are optically active spins magnetically coupled to a superconducting resonator. We report on a cavity QED experiment with magnetically anisotropic Er3+:Y2SiO5 crystals and demonstrate strong coupling of rare-earth spins to a lumped element resonator. In addition, the electron spin resonance and relaxation dynamics of the erbium spins are detected via direct microwave absorption, without a…
We perform an investigation into the properties of Pr3+:Y2SiO5 whispering gallery mode resonators as a first step towards achieving the strong coupling regime of cavity QED with rare-earth-ion doped crystals. Direct measurement of cavity QED parameters are made using photon echoes, giving good agreement with theoretical predictions. By comparing the ions at the surface of the resonator to those in the center it is determined that the physical process of making the resonator does not negatively affect the properties of the ions. Coupling between the ions and resonator is analyzed through the ob…
In this work the inhomogeneous (zero-phonon line) and homogeneous line widths, and one projection of the permanent electric dipole moment change for the Ce 4f-5d transition in Y_2SiO_5 were measured in order to investigate the possibility for using Ce as a sensor to detect the hyperfine state of a spatially close-lying Pr or Eu ion. The experiments were carried out on Ce doped or Ce-Pr co-doped single Y_2SiO_5 crystals. The homogeneous line width was measured to be about 3 MHz, which is essentially limited by the excited state lifetime. Based on the line width measurements, the oscillator stre…
Rare-earth ion ensembles doped in single crystals are a promising materials system with widespread applications in optical signal processing, lasing, and quantum information processing. Incorporating rare-earth ions into integrated photonic devices could enable compact lasers and modulators, as well as on-chip optical quantum memories for classical and quantum optical applications. To this end, a thin film single crystalline wafer structure that is compatible with planar fabrication of integrated photonic devices would be highly desirable. However, incorporating rare-earth ions into a thin fil…
We demonstrate the coupling of rare-earth ions locally implanted in a substrate (Gd$^{3+}$ in Al$_{2}$O$_{3}$) to a superconducting NbN lumped-element micro-resonator. The hybrid device is fabricated by a controlled ion implantation of rare-earth ions in well-defined micron-sized areas, aligned to lithographically defined micro-resonators. The technique does not degrade the internal quality factor of the resonators which remain above $10^{5}$. Using microwave absorption spectroscopy we observe electron-spin resonances in good agreement with numerical modelling and extract corresponding couplin…
We present cavity QED experiments with an Er:YSO crystal magnetically coupled to a 3D cylindrical sapphire loaded copper resonator. Such waveguide cavities are promising for the realization of a superconducting quantum processor. Here, we demonstrate the coherent integration of a rare-earth spin ensemble with the 3D architecture. The collective coupling strength of the Er$^{3+}$ spins to the 3D cavity is 21 MHz. The cylindrical sapphire loaded resonator allowed us to explore the anisotropic collective coupling between the rare-earth doped crystal and the cavity. This work shows the potential o…
Interfacing superconducting quantum processors, working in the GHz frequency range, with optical quantum networks and atomic qubits is a challenging task for the implementation of distributed quantum information processing as well as for quantum communication. Using spin ensembles of rare earth ions provide an excellent opportunity to bridge microwave and optical domains at the quantum level. In this letter, we demonstrate magnetic coupling of Er$^{3+}$ spins doped in Y$_{2}$SiO$_{5}$ crystal to a high-Q coplanar superconducting resonator.
We demonstrate that experiments measuring the transition energies of rare-earth ions doped in crystalline lattices are sensitive to violations of Local Lorentz Invariance and Einstein's Equivalence Principle. Using the crystal field of LaCl$_{3}$ as an example, we calculate the frame-dependent energy shifts of the transition frequencies between low-lying states of Ce$^{3+}$, Nd$^{3+}$, and Er$^{3+}$ dopants in the context of the Standard Model Extension, and show that they have high sensitivity to electron anomalies that break rotational invariance.
The possibility of using mixed crystals highly doped with rare earth ions (REIs) as physical systems for creating fast quantum computers with a sampling time of nanoseconds is discussed. The electronic 4f states of rare earth ions with small values of the diagonal elements of the Judd-Ofelt matrix U(2) are proposed as optical frequency qubit levels. CNOT and other conditional gate operations are performed by exciting the rare earth ion into the 4f state with a large diagonal element of U(2), causing a Stark blockade. It is found that the main interaction responsible for this blockade is the qu…
We have demonstrated electron-electron and electron-nuclear spin manipulations of Gd3+ ion in CaWO4 crystal. The results suggest that the studied system is perspective for multiqubit implementation in quantum computing.
