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 waveforms that generate an arbitrary target state from an initial fiducial state. We develop a generalized Wigner function representation for this space consisting of the direct sum of two irreducible representation of SU(2), allowing us to visualize these states. The performance of different control scenarios is evaluated based on the ability to generate high-fidelity operation in an allotted time with the available resources. We find good operating points commensurate with modest laboratory requirements.
We consider the Autler-Townes effect when a strong coupling field is applied in the hyperfine manifold of an alkali atom. Explicit solution is obtained in the case of the D1-line. We show how the hyperfine interaction modifies the dressing effects associated with the strong field as well as the sample susceptibility with respect to the probe mode. Particularly, if the strong field is far detuned from the atomic resonance line the Autler-Townes structure differs significantly from the prediction of the Lambda-type approximation. We also find that tuning the strong field in between the upper sta…
The spins of gaseous alkali atoms are commonly assumed to oscillate at a constant hyperfine frequency, which for many years has been used to define the Second. Indeed, under standard experimental conditions, the spins oscillate independently, only weakly perturbed and slowly decaying due to random spin-spin collisions. Here we consider a different, unexplored regime of very dense gas, where collisions, more frequent than the hyperfine frequency, dominate the dynamics. Counter-intuitively, we find that the hyperfine oscillations become significantly longer-lived, and their frequency becomes dep…
This dissertation studies spin squeezing, entanglement and decoherence in large ensembles of cold, trapped alkali atoms with hyperfine spin f interacting with optical fields. Restricting the state of each atom to a qutrit embedded in the 2f+1 dimensional hyperfine spin enables us to efficiently model the coherent and dissipative dynamics of the ensemble. This formalism also allows us to explore the effects of local control on the internal hyperfine spins of the atoms. State preparation using such control increases the entangling power of the atom-light interface for f>1/2. Subsequent control o…
We calculate the bound state spectrum of the highly excited valence electron in the heavy alkali atoms solving the radial Schrödinger eigenvalue problem numerically with an accurate spectral collocation algorithm that applies also for a large principal quantum number $n\gg1$. As an effective single-particle potential we favor the reputable potential of Marinescu \emph{et al}., {[}Phys. Rev.A \textbf{49}, 982(1994){]}. Recent quasiclassical calculations of the quantum defect of the valence electron agree for orbital angular momentum $l=0,1,2,...$ overall remarkably well with the results of the …
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…
Alkali-metal atomic magnetometers suffer from heading errors in geomagnetic fields as the measured magnetic field depends on the orientation of the sensor with respect to the field. In addition to the nonlinear Zeeman splitting, the difference between Zeeman resonances in the two hyperfine ground states can also generate heading errors depending on initial spin polarization. We examine heading errors in an all-optical scalar magnetometer that uses free precession of polarized $^{87}\text{Rb}$ atoms by varying the direction and magnitude of the magnetic field at different spin polarization regi…
We show that nuclear spin subsystems can be completely controlled via microwave irradiation of resolved anisotropic hyperfine interactions with a nearby electron spin. Such indirect addressing of the nuclear spins via coupling to an electron allows us to create nuclear spin gates whose operational time is significantly faster than conventional direct addressing methods. We experimentally demonstrate the feasibility of this method on a solid-state ensemble system consisting of one electron and one nuclear spin.
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 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.
In this dissertation I analyze Hamiltonian control of $d$-dimensional quantum systems as realized in alkali atomic spins. Alkali atoms provide an ideal platform for studies of quantum control due to the extreme precision with which the control fields are characterized as well as their isolation from their environment. In chapter 2, I review some background material on open-loop quantum control theory. Chapter 3 provides a derivation of the Hamiltonians arising from electromagnetic fields that we use to control our alkali atomic spins. In chapter 4, I develop an algorithm for state preparation,…
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.
Dynamic nuclear polarisation (DNP) refers to a class of techniques used to increase the signal in nuclear magnetic resonance measurements by transferring spin polarisation from ensembles of highly polarised electrons to target nuclear analytes. These techniques, however, require the application of strong magnetic fields to maximise electron spin polarisation, limiting pathways for electron-nuclear (hyperfine) spin coupling and transfer. In this work we show that, for systems of electronic spin $S\geq1$ possessing an intrinsic zero-field splitting, a separate class of stronger hyperfine interac…
We show that Ramsey spectroscopy of fermionic alkaline-earth atoms in a square-well trap provides an efficient and accurate estimate for the eigenspectrum of a density matrix whose $n$ copies are stored in the nuclear spins of $n$ such atoms. This spectrum estimation is enabled by the high symmetry of the interaction Hamiltonian, dictated, in turn, by the decoupling of the nuclear spin from the electrons and by the shape of the square-well trap. Practical performance of this procedure and its potential applications to quantum computing, quantum simulation, and time-keeping with alkaline-earth …
As the deepest group V donor in Si, Bi has by far the largest hyperfine interaction, and also a large I=9/2 nuclear spin. At zero field this splits the donor ground state into states having total spin 5 and 4, which are fully resolved in the photoluminescence spectrum of Bi donor bound excitons. Under a magnetic field, the 60 expected allowed transitions cannot be individually resolved, but the effects of the nuclear spin distribution, -9/2 <= I_z <= 9/2, are clearly observed. A strong hyperpolarization of the nuclear spin, with sign opposite to the expected equilibrium polarization, is observ…
An experimental platform of ultralow-temperature pulsed ENDOR (electron-nuclear double resonance) spectroscopy is constructed for the bulk materials. Coherent property of the coupled electron and nuclear spins of the rare-earth (RE) dopants in a crystal (143Nd3+:Y2SiO5) is investigated from 100 mK to 6 K. At the lowest working temperatures, two-pulse-echo coherence time exceeding 2 ms and 40 ms are achieved for the electron and nuclear spins, while the electronic Zeeman and hyperfine population lifetimes are more than 15 s and 10 min. With the aid of the near-unity electron spin polarization a…
Using 201Hg+ contained within a linear quadrupole rf ion trap that is part of an atomic clock, we report the first high-resolution spectroscopy on the hyperfine structure of 201Hg+. We measure the absolute ground state hyperfine interval to be 29.954365821130(171)(62)(10) GHz, more than 8 orders of magnitude improvement over the previous measurement. The first error estimate in parentheses is the statistical error in the shifted line center measurement, the second is systematic uncertainty, and the third is calibration uncertainty in the hydrogen maser reference standard. By comparison to the …
We experimentally demonstrate hyperfine optical pumping of rubidium atoms probed by an evanescent electromagnetic field at a dielectric-vapor interface. This light-atom interaction at the nanoscale is investigated using a right angle prism integrated with a vapor cell and excited by evanescent wave under total internal reflection. An efficient hyperfine optical pumping, leading to a complete suppression of absorption on the probed evanescent signal, is observed when a pump laser beam is sent at normal incidence to the interface. In contrast, when the pump and probe beams are co-propagating in …
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 …
The Nitrogen-Vacancy (NV) center in diamond has attractive properties for a number of quantum technologies that rely on the spin angular momentum of the electron and the nuclei adjacent to the center. The nucleus with the strongest interaction is the $^{13}$C nuclear spin of the first shell. Using this degree of freedom effectively hinges on precise data on the hyperfine interaction between the electronic and the nuclear spin. Here, we present detailed experimental data on this interaction, together with an analysis that yields all parameters of the hyperfine tensor, as well as its orientation…
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…
We investigate pure dephasing decoherence (free induction decay and spin echo) of a spin qubit interacting with a nuclear spin bath. While for infinite magnetic field B the only decoherence mechanism is spectral diffusion due to dipolar flip-flops of nuclear spins, with decreasing B the hyperfine-mediated interactions between the nuclear spins become important. We give a theory of decoherence due to these interactions which takes advantage of their long-range nature. For a thermal uncorrelated bath we show that our theory is applicable down to B~10 mT, allowing for comparison with recent exper…
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…
The study of hyperfine interactions in optically excited fullerenes has recently acquired importance within the context of nuclear spin entanglement for quantum information technology. We here report a first-principles pseudopotential study of the hyperfine coupling parameters of optically excited fullerene derivatives as well as small organic radicals. The calculations are performed within the gauge-invariant projector-augmented wave method [C. Pickard and F. Mauri, Phys. Rev. B. 63, 245101 (2001)]. In order to establish the accuracy of this methodology we compare our results with all-electro…
Nuclear spins in the solid state environment of diamond are highly coherent, but difficult to rapidly control due to the small nuclear gyromagnetic ratio. Here we demonstrate a more than 50-fold enhancement of the effective nuclear gyromagnetic ratio by coupling the nuclear spin to an electronic spin of a nitrogen-vacancy (NV) center in diamond. The enhancement allows for faster nuclear spin rotations and is in good agreement with second-order perturbation theory. The method may be applied to other systems with similar electron-nuclear spin interactions, such as phosphorous donors in silicon, …
On the basis of quasipotential method in quantum electrodynamics we calculate nuclear finite size radiative corrections of order $α(Zα)^5$ to the hyperfine structure of S-wave energy levels in muonic hydrogen and muonic deuterium. For the construction of the particle interaction operator we employ the projection operators on the particle bound states with definite spins. The calculation is performed in the infrared safe Fried-Yennie gauge. Modern experimental data on the electromagnetic form factors of the proton and deuteron are used.
We report the operation of a dual Rb/Cs atomic fountain clock. 133Cs and 87Rb atoms are cooled, launched, and detected simultaneously in LNE-SYRTE's FO2 double fountain. The dual clock operation occurs with no degradation of either the stability or the accuracy. We describe the key features for achieving such a simultaneous operation. We also report on the results of the first Rb/Cs frequency measurement campaign performed with FO2 in this dual atom clock configuration, including a new determination of the absolute 87Rb hyperfine frequency.
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 find specific polarizations of components of a bichromatic field, which allow one to prepare pure superposition states of atoms, using the coherent population trapping effect. These $m$$-$$m$ states are prepared in the system of Zeeman substates of the ground-state hyperfine levels with arbitrary angular momenta $F_1$ and $F_2$. It is established that, in general case $m\ne 0$, the use of waves with elliptical polarizations ($ε_1$$\perp$$ε_2$ field configuration for alkali metal atoms) is necessary for the pure state preparation. We analytically show an unique advantage of the D1 line of al…
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…
We study the zero-field optical spin noise spectra (OSN) for a thermal state hot 87Rb vapor with strong spin exchange coupling. Our main findings are: (1) The OSN spectrum consists of two components representing a positive and a negative hyperfine spin correlation (HSC), the relative power of which varies dramatically with the detuning frequency of the probe. (2) There exist two polar frequencies at which the OSN spectrum is completely polarized with one type of HSC. (3) At the limit of far detuning, the power ratio of the positive and negative HSC component of the OSN is 4:5. (4) The total po…
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.
Nuclear slowing-down factors in alkali-metal vapors
Institute of Electronic Structure and Laser, Foundation for Research and Technology（电子结构与激光研究所，研究与技术基金会）；Department of Physics, Princeton University（普林斯顿大学物理系）
Nuclear spin levels play an important role in understanding magnetization dynamics and implementation and control of quantum bits in lanthanide-based single-molecule magnets. We investigate the hyperfine and nuclear quadrupole interactions for $^{161}$Dy and $^{163}$Dy nucleus in anionic DyPc$_2$ (Pc=phthalocyanine) single-molecule magnets, using multiconfigurational ab-initio methods (beyond density-functional theory) including spin-orbit interaction. The two isotopes of Dy are chosen because the others have zero nuclear spin. Both isotopes have the nuclear spin $I=5/2$, although the magnitud…
