The quest for a quantum system best satisfying the stringent requirements of a quantum information processor has made tremendous progress in many fields of physics. In the last decade, trapped ions have been established as one of the most promising architectures to accomplish the task. Internal states of an ion which can have extremely long coherence time can be used to store a quantum bit, and therefore allow many gate operations before the coherence is lost. Entanglement between multiple ions can be established via Coulomb interactions mediated by appropriate laser fields. Entangling schemes usually require the ions to be initialized to near their motional ground state. The interaction of fluctuating electric fields with the motional state of the ion leads to heating and thus to decoherence for entanglement generation limiting the fidelity of quantum logic gates. Effective ground state cooling of trapped ion motion and suppression of motional heating are thus crucial to many applications of trapped ions in quantum information science. In this thesis, I describe the implementation and study of several components of a Cadmium-ion-based quantum information processor, with special emphasis on the control and decoherence of trapped ion motion. I first discuss the building and design of various ion traps that were used in this work. I also report on the use of ultrafast laser pulses to photoionize and load cadmium ions in a variety of rf Paul trap geometries. A detailed analysis of the photoionization scheme is presented, along with its dependence on controlled experimental parameters. I then describe the implementation of Raman sideband cooling on a single trapped 111 Cd + ion to the ground state of motion, where a ground state population of 97% was achieved. The efficacy of this cooling technique is discussed with respect to different initial motional state distributions and its sensitivity to the presence of motional heating. I also present an experiment where the motion of a single trapped 112 Cd + ion is sympathetically cooled by directly Doppler cooling a 114 Cd + ion in the same trap. The implications of this result are relevant to the scaling of a trapped ion quantum computer, where the unwanted motion of an ion crystal can be quenched while not affecting the internal states of the qubit ions. (Abstract shortened by UMI.)
The quest for a quantum system best satisfying the stringent requirements of a quantum information processor has made tremendous progress in many fields of physics. In the last decade, trapped ions have been established as one of the most promising architectures to accomplish the task. Internal states of an ion which can have extremely long coherence time can be used to store a quantum bit, and therefore allow many gate operations before the coherence is lost. Entanglement between multiple ions can be established via Coulomb interactions mediated by appropriate laser fields. Entangling schemes usually require the ions to be initialized to near their motional ground state. The interaction of fluctuating electric fields with the motional state of the ion leads to heating and thus to decoherence for entanglement generation limiting the fidelity of quantum logic gates. Effective ground state cooling of trapped ion motion and suppression of motional heating are thus crucial to many applications of trapped ions in quantum information science. In this thesis, I describe the implementation and study of several components of a Cadmium-ion-based quantum information processor, with special emphasis on the control and decoherence of trapped ion motion. I first discuss the building and design of various ion traps that were used in this work. I also report on the use of ultrafast laser pulses to photoionize and load cadmium ions in a variety of rf Paul trap geometries. A detailed analysis of the photoionization scheme is presented, along with its dependence on controlled experimental parameters. I then describe the implementation of Raman sideband cooling on a single trapped 111 Cd + ion to the ground state of motion, where a ground state population of 97% was achieved. The efficacy of this cooling technique is discussed with respect to different initial motional state distributions and its sensitivity to the presence of motional heating. I also present an experiment where the motion of a single trapped 112 Cd + ion is sympathetically cooled by directly Doppler cooling a 114 Cd + ion in the same trap. The implications of this result are relevant to the scaling of a trapped ion quantum computer, where the unwanted motion of an ion crystal can be quenched while not affecting the internal states of the qubit ions. (Abstract shortened by UMI.)
Over the past decade, the field of trapped ion quantum computing has emerged as one of the leaders in quantum information processing due the level of manipulation available and the long coherence times possible in the system. As this thesis will demonstrate, all of the necessary building blocks for a quantum computer have been exhibited in ion traps and small scale quantum algorithms have been implemented. In this trapped ion system, quantum bits consist of the first order magnetic field insensitive ground state hyperfine levels of 111Cd+. The qubits are manipulated via resonant and off-resonant coherent laser interactions. We experimentally realize Grover's quantum search algorithm over a 4 element database with n=2 trapped 111Cd+ ion qubits. One of the four states is marked, and with a single query it is recovered, on average, with 60% probability. This exceeds the performance of any possible classical search, which can only succeed with 50% probability following a single query. The algorithm consists of two Molmer-Sorensen entangling gates, that utilize bichromatic stimulated Raman transitions to create a spin dependent force, paired with several single-qubit rotations and near-perfect qubit measurements. The spectral arrangement of the Raman beams is tailored to suppress phase noise accumulation between gates. This suppression is critical for reliably performing consecutive operations during the algorithm. Additionally, this thesis discusses the possibility of combining trapped ions with trapped neutral atoms for the purpose studying ultra-cold charge exchange interactions. It may be possible to conceal quantum information, initially prepared in an ionic qubit, inside a pure nuclear spin qubit for the purpose of transportation and storage. As a first step, we present the laser-cooling and confinement of Cd atoms in a magneto-optical trap, and characterize the loading process from the background Cd vapor. The trapping laser drives the 1S0~rightarrow~1P1 transition at 229 nm in this two valence electron atom and also photoionizes atoms directly from the 1P1 state. This photoionization dominates other loss mechanisms and allows a direct measurement of the photoionization cross section.
Quantum information processing combines information theory with laws of quantum mechanics to provide an interesting new study that promises significant technological advances in the field of computation. The quest for a physical quantum information processor not only tests the limits of quantum mechanics but also motivates the development of new control techniques for quantum systems. This thesis documents the implementation of the necessary components of a quantum computer in a new atomic ion species, while demonstrating an entangling procedure that is uniquely insensitive to certain types of phase noise. Quantum bits are stored in the ground state hyperfine levels of individual trapped cadmium ions, and the collective vibration of the ions in the trap potential form a quantum databus through which information can be transferred. Quantum state measurements and initialization processes are accomplished through optical pumping, and quantum logic operations are performed through interactions with applied electromagnetic fields. The spin-dependent force, which is the underlying principle of many entanglement schemes for trapped ions, is investigated in detail in a series of Schrodinger cat experiments that generates entangled wavepackets well separated in the momentum-position phase space (alpha = 6). Phase control of the interaction in the gate scheme proposed by Molmer and Sorensen results in phase coherence between single-qubit rotations and a robust two-qubit entangling logic gate that can operate on magnetic-field insensitive clock qubits at finite temperature. The coherence time of the clock qubit (∼ 1s) is long compared to the gate time (∼ 100mus). Finally, quantum state tomography is performed on two ions, featuring a set of universal quantum logic gates that is sufficient for any quantum computation, with an entangling gate fidelity of 0.83. The combination of the tools developed here is sufficient to perform universal quantum computation. With the advent of scalable, multi-zone ion trap structures, the concept of a quantum computation device may become reality in the not so distant future.
For 35 years, laser-cooled trapped ions have been at the frontier of progress in quantum computing, quantum simulation and precision measurement, and remain one of the most valuable tools in these fields to this day. Most of these experiments are predicated upon or benefit from the ability to place ions in the motional quantum ground state, a technique that was first demonstrated in radiofrequency ion traps 25 years ago. For a range of crucial experiments that are impossible to conduct in radiofrequency traps or are not well suited to this architecture, Penning traps provide an important alternative. However, the performance of Penning traps had been limited by the fact that ground-state cooling was yet to be achieved in such a system. This thesis reports the first demonstration of resolved-sideband cooling in a Penning trap, for 40Ca+ions cooled with light at 729-nm, achieving a ground state occupation of 99% in one dimension. Demonstrations of the coherent manipulations possible at this level of confinement are presented. The ion heating rate is measured and although higher than might be expected given the unusually large ion-electrode distance remains amongst the lowest reported in any trap to date. Achieving this result required the development of a number of new experimental systems and major upgrades to the stability and reliability of the experiment, the details of which are also given. The thesis also presents theoretical work into the use of two-dimensional Coulomb crystals in a Penning trap as a resource for quantum information. Using the symmetries of the crystal, we find that it is possible to engineer complex entangled states, specifically two small quantum error correcting codes, using a very small number of global entangling pulses. Efficient entanglement protocols such as these are vital for the implementation of useful quantum error correction.
Since the dawn of quantum information science, laser-cooled trapped atomic ions have been one of the most compelling systems for the physical realization of a quantum computer. By applying qubit state dependent forces to the ions, their collective motional modes can be used as a bus to realize entangling quantum gates. Ultrafast state-dependent kicks [1] can provide a universal set of quantum logic operations, in conjunction with ultrafast single qubit rotations [2], which uses only ultrafast laser pulses. This may present a clearer route to scaling a trapped ion processor [3]. In addition to the role that spin-dependent kicks (SDKs) play in quantum computation, their utility in fundamental quantum mechanics research is also apparent. In this thesis, we present a set of experiments which demonstrate some of the principle properties of SDKs including ion motion independence (we demonstrate single ion thermometry from the ground state to near room temperature and the largest Schrodinger cat state ever created in an oscillator), high speed operations (compared with conventional atom-laser interactions), and multi-qubit entanglement operations with speed that is not fundamentally limited by the trap oscillation frequency. We also present a method to provide higher stability in the radial mode ion oscillation frequencies of a linear radiofrequency (rf) Paul trap--a crucial factor when performing operations on the rf-sensitive modes. Finally, we present the highest atomic position sensitivity measurement of an isolated atom to date of ~0.5 nm Hz^(-1/2) with a minimum uncertainty of 1.7 nm using a 0.6 numerical aperature (NA) lens system, along with a method to correct aberrations and a direct position measurement of ion micromotion (the inherent oscillations of an ion trapped in an oscillating rf field). This development could be used to directly image atom motion in the quantum regime, along with sensing forces at the yoctonewton [10^(-24) N)] scale for gravity sensing, and 3D imaging of atoms from static to higher frequency motion. These ultrafast atomic qubit manipulation tools demonstrate inherent advantages over conventional techniques, offering a fundamentally distinct regime of control and speed not previously achievable.
Single ions in Paul traps are investigated for quantum information processing. Superpositions of the S1/2 and the D5/2 states are used to implement a qubit. The ions are optically cooled and fluorescence light at 397 nm on the S1/2-P1/2 transition is monitored for a state measurement by the “electron shelving” technique. The S1/2-D5/2 quadrupole transition at 729 nm is excited for sideband cooling and for quantum state preparation and manipulation. Individual ions in a linear string are addressed by a tightly focused 729 nm laser beam. A single Ca+ ion has been cooled in the spherical Paul trap to the ground state of vibration with up to 99.9% probability. Cooling is achieved in all three dimensions simultaneously as well as ground state cooling of two ions. Starting from a Fock state |n=0> coherent quantum state manipulation on the S1/2-D5/2 transition is achieved. The data show that decoherence is negligible on the time scale of a few oscillations, i.e. during the time required for a quantum gate operation. The measured several decoherence time of a few ms is attributed to residual laser and magnetic field fluctuations. Heating of the motional degrees of freedom has been measured directly and appears at a rate of 1 phonon per 190 ms (70 ms) at the secular frequencies ωaxial (ωradial). A novel type of ground state laser cooling of a single trapped ion is achieved using a technique which tailors the absorption profile for the cooling laser by exploiting electromagnetically induced transparency in the Zeeman structure of the S1/2–P1/2 dipole transition. This new method is robust, easy to implement and proves particularly useful for cooling several motional degrees of freedom simultaneously, which is of great practical importance for the implementation of quantum logic schemes with trapped ions.
Laser-cooled atomic ions have led to an unprecedented amount of control over the quantum states of matter. The Coulombic interaction allows for information to be transferred between neighboring ions, and this interaction can be used to entangle qubits for logic operations in quantum information processors. The same procedure for logic operations can be used for high resolution atomic spectroscopy, and is the basis for the most accurate atomic optical clocks to date. This thesis describes how laser-cooled atomic ions can impact physical chemistry through the development of molecular ion spectroscopy techniques and the simulation of magnetic systems by ion trap quantum computers. \n\t \n\tA new technique developed for spectroscopy, Sympathetic Heating Spectroscopy (SHS), takes advantage of the Coulombic interaction between two trapped ions: the control ion and a spectroscopy ion. SHS uses the back action of the interrogating laser to map spectroscopy ion information onto the Doppler shift of the control ion for measurement. SHS only requires Doppler cooling of the ions and fluorescence measurement and represents a simplification of quantum logic spectroscopy. This technique is demonstrated on two individual isotopes of calcium: Ca-40(+) for cooling and Ca-44(+) as the spectroscopy ion. \n \n\tHaving demonstrated SHS with atomic ions, the next step was to extend the technique by loading and characterizing molecular ions. The identification of an unknown molecular ion is necessary and can be achieved by monitoring the change in motion of the two ion crystal, which is dependent on the molecular ion mass. The motion of two trapped ions is described by their normal modes, which can be accurately measured by performing resolved sideband spectroscopy of the S(1/2)-D(5/2) transition of calcium. The resolved sidebands can be used to identify unknown ions (atomic and molecular) by calculating the mass based on the observed value in axial normal mode frequencies. Again, the trapped molecular ion is sympathetically cooled via the Coulombic interaction between the Ca-40(+) and the unknown molecular ion. The sensitivity of SHS could be improved by implementing sympathetic sideband cooling and determining the heating by measuring single quanta of motion. \n\t \n\tThe ultimate limit of control would be the development of an ion trap quantum computer. Many theoretical quantum computing researchers have made bold claims of the exponential improvement a quantum computer would have over a classical computer for the simulation of physical systems such as molecules. These claims are true in principle for ideal systems, but given non-ideal components it is necessary to consider the scaling due to error correction. An estimate of the resource requirements, the total number of physical qubits and computational time, required to compute the ground state energy of a 1-D quantum Transverse Ising Model (TIM) of N spin-1/2 particles, as a function of the system size and the numerical precision, is presented. This estimate is based on analyzing the impact of fault-tolerant quantum error correction in the context of the quantum logic array architecture. The results show that a significant amount of error correction is required to implement the TIM problem due to the exponential scaling of the computational time with the desired precision of the energy. Comparison of this result to the resource requirements for a fault-tolerant implementation of Shor's quantum factoring algorithm reveals that the required logical qubit reliability is similar for both the TIM problem and the factoring problem.