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.
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.
We study the deterministic entanglement of a pair of neutral atoms trapped in an optical lattice by coupling to excited-state molecular hyperfine potentials. Information can be encoded in the ground-state hyperfine levels and processed by bringing atoms together pair-wise to perform quantum logical operations through induced electric dipole-dipole interactions. The possibility of executing both diagonal and exchange type entangling gates is demonstrated for two three-level atoms and a figure of merit is derived for the fidelity of entanglement. The fidelity for executing a CPHASE gate is calcu…
We propose the implementation of a geometric-phase gate on magnetic-field-insensitive qubits with $\hatσ^z$-dependent forces for trapped ion quantum computing. The force is exerted by two laser beams in a Raman configuration. Qubit-state dependency is achieved by a small frequency detuning from the virtually-excited state. Ion species with excited states of long radiative lifetimes are used to reduce the chance of a spontaneous photon emission to less than 10$^{-8}$ per gate-run. This eliminates the main source of gate infidelity of previous implementations. With this scheme it seems possible …
Many systems used for quantum computing possess additional states beyond those defining the qubit. Leakage out of the qubit subspace must be considered when designing quantum error correction codes. Here we consider trapped ion qubits manipulated by Raman transitions. Zeeman qubits do not suffer from leakage errors but are sensitive to magnetic fields to first-order. Hyperfine qubits can be encoded in clock states that are insensitive to magnetic fields to first-order, but spontaneous scattering during the Raman transition can lead to leakage. Here we compare a Zeeman qubit ($^{174}$Yb$^+$) to…
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…
We analyze the effects of hyperfine interactions on coherent control experiments in triple quantum dots. By exploiting Hamiltonian symmetries and the SU(3) structure of the triple-dot system under pseudo-exchange and longitudinal hyperfine couplings, we provide analytic formulae for the hyperfine decay of triple-dot Rabi and dephasing experiments.
We analyze the error in trapped-ion, hyperfine qubit, quantum gates due to spontaneous scattering of photons from the gate laser beams. We investigate single-qubit rotations that are based on stimulated Raman transitions and two-qubit entangling phase-gates that are based on spin-dependent optical dipole forces. This error is compared between different ion species currently being investigated as possible quantum information carriers. For both gate types we show that with realistic laser powers the scattering error can be reduced to below current estimates of the fault-tolerance error threshold…
We propose an architecture and methodology for large-scale quantum simulations using hyperfine states of trapped-ions in an arbitrary-layout microtrap array with laserless interactions. An ion is trapped at each site, and the electrode structure provides for the application of single and pairwise evolution operators using only locally created microwave and radio-frequency fields. The avoidance of short-lived atomic levels during evolution effectively eliminates errors due to spontaneous scattering; this may allow scaling of quantum simulators based on trapped ions to much larger systems than c…
We propose an efficient quantum measurement protocol for the hyperfine interaction between the electron spin and the $^{15}$N nuclear spin of a diamond nitrogen-vacancy center. In this protocol, a sequence of quantum operations of successively increasing duration is utilized to estimate the hyperfine interaction with successively higher precision approaching the quantum metrology limit. This protocol does not need the preparation of the nuclear spin state. In the presence of realistic operation errors and electron spin decoherence, the overall precision of our protocol still surpasses the stan…
We present an investigation of the effects of constant but random shifts of the ground hyperfine qubit states in the setting of quantum computing with ion doped crystals. Complex hyperbolic secant pulses can be used to transfer ions reliably to electronically excited states, and a perturbative approach is used to analyse the effect of ground state hyperfine shifts. This analysis shows that the errors due to the hyperfine shift are dynamically supressed during gate operation, a fact we attribute to the AC Stark shift. Furthermore we present an implementation of a controlled phase gate which is …
Precise characterization of a hyperfine interaction is a prerequisite for high fidelity manipulations of electron and nuclear spins belonging to a hybrid qubit register in diamond. Here, we demonstrate a novel scheme for determining a hyperfine interaction, using single-quantum and zero-quantum Ramsey fringes, by applying it to the system of a Nitrogen Vacancy (NV) center and a $^{13}$C nuclear spin in the 1$^{\mathrm{st}}$ shell. The zero-quantum Ramsey fringe, analogous to the quantum beat in a $Λ$-type level structure, particularly enhances the measurement precision for non-secular hyperfin…
We studied the recall efficiency as a function of optical depth of rephased amplified spontaneous emission (RASE), a protocol for generating entangled light. The experiments were performed on the $^{3}\! H_{4}$ $\rightarrow$ $^{1}\! D_{2}$ transition in the rare-earth doped crystal Pr$^{3+}$:Y$_{2}$SiO$_{5}$, using a four-level echo sequence between four hyperfine levels to rephase the emission. Rephased emission was observed for optical depths in the range of $αL$ = 0.8 to 2.0 with a maximum rephasing efficiency of 14 % observed while incorporating spin storage. This efficiency is a significa…
We describe a quantum memory spectral preparation strategy that maximises memory efficiency and bandwidth in materials such as 167 Er3+:Y2SiO5 in a high field regime, where the hyperfine structure is resolved. We demonstrate the method in 167 Er3+:Y2SiO5 by preparing spectrally isolated 18 dB-absorbing features on a < 1 dB background. Using these features we create an atomic frequency comb and show quantum storage of 200 ns pulses with 22% efficiency, limited by the background absorption which arises from laser instability. We describe the experimental improvements needed to reach the material…
We demonstrate quantum control of a large spin-angular momentum associated with the F=3 hyperfine ground state of 133Cs. A combination of time dependent magnetic fields and a static tensor light shift is used to implement near-optimal controls and map a fiducial state to a broad range of target states, with yields in the range 0.8-0.9. Squeezed states are produced also by an adiabatic scheme that is more robust against errors. Universal control facilitates the encoding and manipulation of qubits and qudits in atomic ground states, and may lead to improvement of some precision measurements.
Hybrid interfaces between distinct quantum systems play a major role in the implementation of quantum networks. Quantum states have to be stored in memories to synchronize the photon arrival times for entanglement swapping by projective measurements in quantum repeaters or for entanglement purification. Here, we analyze the distortion of a single photon wave packet propagating through a dispersive and absorptive medium with high spectral resolution. Single photons are generated from a single In(Ga)As quantum dot with its excitonic transition precisely set relative to the Cesium D1 transition. …
We demonstrate the use of trapped ytterbium ions as quantum bits for quantum information processing. We implement fast, efficient state preparation and state detection of the first-order magnetic field-insensitive hyperfine levels of 171Yb+, with a measured coherence time of 2.5 seconds. The high efficiency and high fidelity of these operations is accomplished through the stabilization and frequency modulation of relevant laser sources.
We demonstrate laser-driven two-qubit and single-qubit logic gates with fidelities 99.9(1)% and 99.9934(3)% respectively, significantly above the approximately 99% minimum threshold level required for fault-tolerant quantum computation, using qubits stored in hyperfine ground states of calcium-43 ions held in a room-temperature trap. We study the speed/fidelity trade-off for the two-qubit gate, for gate times between 3.8$μ$s and 520$μ$s, and develop a theoretical error model which is consistent with the data and which allows us to identify the principal technical sources of infidelity.
Recently, de Visser and Blaauboer [Phys. Rev. Lett. {\bf 96}, 246801 (2006)] proposed the most efficient deterministic teleportation protocol $\cal T$ for electron spins in a semiconductor nanostructure consisting of a single and a double quantum dot. However, it is as yet unknown if $\cal T$ can be completed before decoherence sets in. In this paper we analyze the detrimental effect of nuclear spin baths, the main source of decoherence, on $\cal T$. We show that nonclassical teleportation fidelity can be achieved with $\cal T$ provided certain conditions are met. Our study indicates that real…
Hyperfine atomic states are among the most promising candidates for qubit encoding in quantum information processing. In atomic systems, hyperfine transitions are typically driven through a two-photon Raman process by a laser field which is amplitude modulated at the hyperfine qubit frequency. Here, we introduce a new method for generating amplitude modulation by phase modulating a laser and reflecting it from a highly dispersive optical element known as a chirped Bragg grating (CBG). This approach is passively stable, offers high efficiency, and is compatible with high-power laser sources, en…
Fast and efficient detection of the qubit state in trapped ion quantum information processing is critical for implementing quantum error correction and performing fundamental tests such as a loophole-free Bell test. In this work we present a simple qubit state detection protocol for a $^{171}$Yb$^+$ hyperfine atomic qubit trapped in a microfabricated surface trap, enabled by high collection efficiency of the scattered photons and low background photon count rate. We demonstrate average detection times of 10.5, 28.1 and 99.8\,$\upmu$s, corresponding to state detection fidelities of 99%, 99.85(1…
We report measurements of electron spin echo envelope modulation (ESEEM) performed at millikelvin temperatures in a custom-built high-sensitivity spectrometer based on superconducting micro-resonators. The high quality factor and small mode volume (down to 0.2pL) of the resonator allow to probe a small number of spins, down to $5\cdot 10^2$. We measure 2-pulse ESEEM on two systems: erbium ions coupled to $^{183}$W nuclei in a natural-abundance $\text{CaWO}_4$ crystal, and bismuth donors coupled to residual $^{29}$Si nuclei in a silicon substrate that was isotopically enriched in the $^{28}$Si …
We introduce a technique to store and manipulate single x-ray photons which relies on dynamically controlled absorption via nuclear hyperfine magnetic splitting. This scheme is inherently suitable for storage, on-demand generation and dynamical manipulation of single x-ray photons, for instance, the manipulation of the temporal shape, temporal splitting, the interference between x-ray photons and the control of the polarization. Our approach opens up new paths in x-ray quantum information.
Precise knowledge of a quantum system's Hamiltonian is a critical pre-requisite for its use in many quantum information technologies. Here, we report a method for the precise characterization of the non-secular part of the excited-state Hamiltonian of an electronic-nuclear spin system in diamond. The method relies on the investigation of the dynamic nuclear polarization mediated by the electronic spin, which is currently exploited as a primary tool for initializing nuclear qubits and performing enhanced nuclear magnetic resonance. By measuring the temporal evolution of the population of the gr…
We study quantum control of the full hyperfine manifold in the ground-electronic state of alkali atoms based on applied radio frequency and microwave fields. Such interactions should allow essentially decoherence-free dynamics and the application of techniques for robust control developed for NMR spectroscopy. We establish the conditions under which the system is controllable in the sense that one can generate an arbitrary unitary on the system. We apply this to the case of $^{133}$Cs with its $d=16$ dimensional Hilbert space of magnetic sublevels in the $6S_{1/2}$ state, and design control wa…
Hole spin qubits are frontrunner platforms for scalable quantum computers, but state-of-the-art devices suffer from noise originating from the hyperfine interactions with nuclear defects. We show that these interactions have a highly tunable anisotropy that is controlled by device design and external electric fields. This tunability enables sweet spots where the hyperfine noise is suppressed by an order of magnitude and is comparable to isotopically purified materials. We identify surprisingly simple designs where the qubits are highly coherent and are largely unaffected by both charge and hyp…
Measurements of hyperfine polarization quantum beats are used determine the magnetic dipole (A) and electric quadrupole (B) coupling constants in the excited atomic Cs 8p level. The experimental approach is a novel combination of pulsed optical pumping and time-delayed stimulated emission probing of the excited level. From the measured evolution of the atomic linear polarization degree as a function of probe delay time, we determine the hyperfine coupling constants A = 7.42(6) MHz and B = 0.14(29) MHz.
Compared to electrons, holes in InAs quantum dots have a significantly weaker hyperfine interaction that leads to less dephasing from nuclear spins. Thus many recent studies have suggested that nuclear spins are unimportant for hole spin dynamics compared to electric field fluctuations. We show that the hole hyperfine interaction can have a strong effect on hole spin coherence measurements through a nuclear feedback effect. The nuclear polarization is generated through a unique process that is dependent on the anisotropy of the hole hyperfine interaction and the coherent precession of nuclear …
We investigate hyperfine induced electron spin and entanglement dynamics in a system of two quantum dot spin qubits. We focus on the situation of zero external magnetic field and concentrate on approximation-free theoretical methods. We give an exact solution of the model for homogeneous hyperfine coupling constants (with all coupling coefficients being equal) and varying exchange coupling, and we derive the dynamics therefrom. After describing and explaining the basic dynamical properties, the decoherence time is calculated from the results of a detailed investigation of the short time electr…
We implement a 4-level semiclassical model of a single pulse interacting with the hyperfine structure in ultracold rubidium aimed at control of population dynamics and quantum state preparation. We discuss a method based on pulse chirping to achieve population inversion between hyperfine states of the 5S shell. The results may prove useful for quantum operations with ultracold atoms.
We investigate the electric manipulation of a single electron spin in a single gate-defined quantum dot. We observe that so-far neglected differences between the hyperfine and spin-orbit mediated electric dipole spin resonance conditions have important consequences at high magnetic fields. In experiments using adiabatic rapid passage to invert the electron spin, we observe an unusually wide and asymmetric response as a function of magnetic field. Simulations support the interpretation of the lineshape in terms of four different resonance conditions. These findings may lead to isotope-selective…
We present an all-electron calculation of the hyperfine parameters for conduction electrons in Si, showing that: (i) all parameters scale linearly with the spin density at a $^{29}$Si site; (ii) the isotropic term is over 30 times larger than the anisotropic part; (iii) conduction electron charge density at a Si nucleus is consistent with experimental estimates; (iv) Overhauser fields in natural Si quantum dots (QDs) are two orders of magnitude smaller than in GaAs QDs. This reinforces the outstanding performance of Si in keeping spin coherence and opens access to reliable quantitative informa…
Understanding (and controlling) hyperfine interactions in semiconductor nanostructures is important for fundamental studies of material properties as well as for quantum information processing with electron, hole, and nuclear-spin states. Through a combination of first-principles density-functional theory (DFT) and $\mathbf{k}\cdot\mathbf{p}$ theory, we have calculated hyperfine tensors for electrons and holes in GaAs and crystalline silicon. Accounting for relativistic effects near the nuclear core, we find contact hyperfine interactions for electrons in GaAs that are consistent with Knight-s…
On the basis of quasipotential approach to the bound state problem in quantum electrodynamics we calculate hyperfine structure intervals Delta E^{hfs}(2P_{1/2}) and Delta E^{hfs}(2P_{3/2}) for P-states in muonic deuterium. The tensor method of projection operators for the calculation of the hyperfine structure of P-states with definite quantum numbers of total atomic momentum F and total muon momentum j in muonic deuterium is formulated. We take into account vacuum polarization, relativistic, quadrupole and structure corrections of orders alpha^4, alpha^5 and alpha^6. The obtained numerical va…
On the basis of quasipotential method in quantum electrodynamics we calculate corrections of order $α^5$ and $α^6$ to hyperfine structure of S-wave energy levels of muonic deuterium. Relativistic corrections, effects of vacuum polarization in first, second and third orders of perturbation theory, nuclear structure and recoil corrections are taken into account. The obtained numerical values of hyperfine splitting $ΔE^{hfs}(1S)=50.2814$ meV (1S state) and $ΔE^{hfs}(2S)=6.2804$ meV (2S state) represent reliable estimate for a comparison with forthcoming experimental data of CREMA collaboration. T…
We numerically study the hyperfine induced nuclear spin dynamics in a system of two coupled quantum dots in zero magnetic field. Each of the electron spins is considered to interact with an individual bath of nuclear spins via homogeneous coupling constants (all coupling coefficients being equal). In order to lower the dimension of the problem, the two baths are approximated by two single long spins. We demonstrate that the hyperfine interaction enables to utilize the nuclear baths for quantum information purposes. In particular, we show that it is possible to swap the nuclear ensembles on tim…
Transition metal (TM) defects in silicon carbide (SiC) are a promising platform in quantum technology, especially because some TM defects emit in the telecom band. We develop a theory for the interaction of an active electron in the $D$-shell of a TM defect in SiC with the TM nuclear spin and derive the effective hyperfine tensor within the Kramers doublets formed by the spin-orbit coupling. Based on our theory we discuss the possibility to exchange the nuclear and electron states with potential applications for nuclear spin manipulation and long-lived nunclear-spin based quantum memories.
We consider a system of two strongly coupled electron spins in zero magnetic field, each of which is interacting with an individual bath of nuclear spins via the hyperfine interaction. Applying the long spin approximation (LSA) introduced in Europhys. Lett. 95, 47009 (here each bath is replaced by a single long spin), we numerically study the electron spin and entanglement dynamics. We demonstrate that the decoherence time is scaling with the bath size according to a power law. As expected, the decaying part of the dynamics decreases with increasing bath polarization. However, surprisingly it …
Nuclear spins of dopant atoms in semiconductors are promising candidates as quantum bits, due to the long lifetime of their quantum states. Conventionally, coherent control of nuclear spins is done using ac magnetic fields. Using the example of a phosphorus atom in silicon, we theoretically demonstrate that hyperfine interaction can enhance the speed of magnetic control: the electron on the donor amplifies the ac magnetic field felt by the nuclear spin. Based on that result, we show that hyperfine interaction also provides a means to control the nuclear spin efficiently using an ac electric fi…
Precise characterization of a system's Hamiltonian is crucial to its high-fidelity control that would enable many quantum technologies, ranging from quantum computation to communication and sensing. In particular, non-secular parts of the Hamiltonian are usually more difficult to characterize, even if they can give rise to subtle but non-negligible effects. Here we present a strategy for the precise estimation of the transverse hyperfine coupling between an electronic and a nuclear spin, exploiting effects due to forbidden transitions during the Rabi driving of the nuclear spin. We applied the…
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…
On the basis of quasipotential approach in quantum electrodynamics we calculate vacuum polarization and quadrupole corrections in first and second orders of perturbation theory in hyperfine structure of P-states in muonic deuterium. All corrections are presented in integral form and evaluated analytically and numerically. The obtained results can be used for the improvement of the transition frequencies between levels 2P and 2S.
We discuss the use of a region of uniform and constant magnetic field in order to implement a two-state atomic polarizer for an H(2S) beam. We have observed that a device with such field configuration is capable of achieving an efficient polarization for a wide range of magnetic field intensities and atomic velocities. In addition, we establish a criterion that must be met to confirm a successful polarization. That is possible due to a specific beating pattern for the Lyman-$α$ radiation expected for the outgoing two-state atomic beam.
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…
We consider two qubits interacting by means of an optical cavity, where each qubit is represented by a single electron spin confined to a quantum dot. It is known that electron spins in III-V semiconductor quantum dots are affected by the decoherence due to the hyperfine interaction with nuclear spins. Here we show that the interaction between two qubits is influenced by the Overhauser field as well. Starting from an unpolarizied nuclear ensemble, we investigate the dependance of the fidelities for two-qubit gates on the Overhauser field. We include the hyperfine interaction perturbatively to …
The time-dependent Schrodinger equation of a many particle spin system consisting of an electron in a quantum dot interacting with the spins of the nuclei (N) in the dot due to hyperfine interaction is solved exactly for a given arbitrary initial state. The electron spin dynamics is then expressed in terms of the reduced density matrix of the composite system by computing the marginal density matrix of the electron. This is accomplished by classifying states of the system by the total spin of the coupled electron and nuclear system that commutes with the system Hamiltonian. These states are us…
Interference between different energy eigenstates in a quantum system results in an oscillation with a frequency which is proportional to the difference in energy between the states. Such an oscillation is observable in polarized positronium when it is placed in a magnetic field. In order to measure the hyperfine splitting of positronium, we perform the precise measurement of this oscillation using a high quality superconducting magnet and fast photon-detectors. A result of $203.324 \pm 0.039\rm{~(stat.)} \pm 0.015\rm{(~sys.)}$~GHz is obtained which is consistent with both theoretical calculat…
