The quantum states of trapped atomic ions can be highly isolated from external perturbation, and precisely manipulated with applied laser fields. This makes them an excellent medium for quantum-limited experiments such as quantum information processing and precision spectroscopy. A relatively small number of ion species have been used for these types of experiments because most species are difficult to laser cool and detect directly. This thesis demonstrates a way to overcome this limitation by use of sympathetic cooling and state detection based on quantum logic. We apply these techniques to mixed-species arrays of Al+ and Be+ ions. A mathematical model for the motion of such a two-species array is presented in order to explore some features of the ion dynamics that are relevant for the experiments. Repetitive quantum nondemolition measurements of the electronic states of a Al+ ion show detection fidelities as high as 99.94 %. We also demonstrate the simultaneous detection of two Al+ ions and observe a detection fidelity of 99.8 %. The basic ideas behind the detection strategy are extended to potentially enable similar experiments on a more general class of atomic and molecular ions.\nWe have also investigated, theoretically and experimentally, a method for preparing entangled Dicke states in trapped atomic ions. We consider a linear chain of N ion qubits that is prepared in a particular Fock state of motion. The m phonons are removed by applying a laser pulse globally to the N qubits, and converting the motional excitation to m flipped spins. The global nature of this pulse ensures that the m flipped spins are shared by all the target ions in a state that is a close approximation to the Dicke state.\nWe calculate numerically the fidelity limits of the protocol and find small deviations from the ideal state for m = 1 and m = 2. We have demonstrated the basic features of this protocol by preparing the Bell state in two Mg+ target ions trapped simultaneously with an Al+ ancillary ion.
The quantum states of trapped atomic ions can be highly isolated from external perturbation, and precisely manipulated with applied laser fields. This makes them an excellent medium for quantum-limited experiments such as quantum information processing and precision spectroscopy. A relatively small number of ion species have been used for these types of experiments because most species are difficult to laser cool and detect directly. This thesis demonstrates a way to overcome this limitation by use of sympathetic cooling and state detection based on quantum logic. We apply these techniques to mixed-species arrays of Al+ and Be+ ions. A mathematical model for the motion of such a two-species array is presented in order to explore some features of the ion dynamics that are relevant for the experiments. Repetitive quantum nondemolition measurements of the electronic states of a Al+ ion show detection fidelities as high as 99.94 %. We also demonstrate the simultaneous detection of two Al+ ions and observe a detection fidelity of 99.8 %. The basic ideas behind the detection strategy are extended to potentially enable similar experiments on a more general class of atomic and molecular ions.\nWe have also investigated, theoretically and experimentally, a method for preparing entangled Dicke states in trapped atomic ions. We consider a linear chain of N ion qubits that is prepared in a particular Fock state of motion. The m phonons are removed by applying a laser pulse globally to the N qubits, and converting the motional excitation to m flipped spins. The global nature of this pulse ensures that the m flipped spins are shared by all the target ions in a state that is a close approximation to the Dicke state.\nWe calculate numerically the fidelity limits of the protocol and find small deviations from the ideal state for m = 1 and m = 2. We have demonstrated the basic features of this protocol by preparing the Bell state in two Mg+ target ions trapped simultaneously with an Al+ ancillary ion.
Laser spectroscopy is a versatile tool to investigate the internal structure of atoms, molecules and nuclei.High precision spectroscopy requires laser cooling to reduce Doppler broadening and Doppler shifts.Sympathetic cooling extends these advantages to species which do not have an appropriate transition for laser cooling and allows precision spectroscopy of previously inaccessible species using the quantum logic technique.The original implementation of quantum logic spectroscopy relies on the long lifetime of the excited spectroscopy state to realize a transfer sequence.Precision spectroscopy of transitions with a short-lived excited state is typically performed using laser induced uorescence or laser absorption spectroscopy.Neither of these methods has reached the fundamental quantum projection noise limit and are rather limited by photon shot noise.For these situations, we develop the technique of photon recoil spectroscopy as an extension of quantum logic spectroscopy to broad transitions.The common motion of a sideband-cooled two-ion crystal is excited by photon recoil during photon absorption on the spectroscopically investigated ion.This motional excitation is transferred to an internal state excitation on the co-trapped ion of a dierent species and detected with high eciency.We demonstrate the technique on the 2 S 1/2 ↔ 2 P 1/2 transition of the 40 Ca + ion and resolve the line center to 1/300 of its observed linewidth.The simplicity and versatility of the technique promises applications to other previously inaccessible species.A variation of the technique is proposed for rotational state preparation of molecular ions.A moving optical lattice is employed to exert a state-dependent force on the molecule.This would allow the detection of the rotational state of the molecular ion and therefore enable precision spectroscopy of specic rovibrational transitions in the molecule.
We have investigated theoretically and experimentally a method for preparing Dicke states in trapped atomic ions. We consider a linear chain of N ion qubits that is prepared in a particular Fock state of motion ∣m⟩. The m phonons are removed by applying a laser pulse globally to the N qubits and converting the motional excitation to m flipped spins. The global nature of this pulse ensures that the m flipped spins are shared by all the target ions in a state that is a close approximation to the Dicke state ∣DN(m)⟩. We calculate numerically the fidelity limits of the protocol and find small deviations from the ideal state for m=1 and m=2. We have demonstrated the basic features of this protocol by preparing the Bell state ∣D2(1)⟩ in two 25Mg+ target ions trapped simultaneously with an 27Al+ ancillary ion.
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.
In quantum logic spectroscopy (QLS), one species of trapped ion is used as a sensor to detect the state of an otherwise inaccessible ion species. This extends precision measurements to a broader class of atomic and molecular systems for applications like atomic clocks and tests of fundamental physics. Here, we develop a new technique based on a Schrödinger cat interferometer to address the problem of scaling QLS to larger ion numbers. We demonstrate the basic features of this method using various combinations of ^{25}Mg^{+} logic ions and ^{27}Al^{+} spectroscopy ions. We observe higher detection efficiency by increasing the number of ^{25}Mg^{+} ions. Applied to multiple ^{27}Al^{+}, this method will improve the stability of high-accuracy optical clocks and could enable Heisenberg-limited QLS.
Scaling trapped-ion quantum sensors from single ions to large ensembles is a key challenge for next-generation precision measurements. At the same time, many ion species of interest for optical clocks and tests of fundamental physics lack closed cycling transitions required for direct laser cooling and state detection. Collective quantum logic spectroscopy addresses both limitations by coupling an ensemble of sensor, or spectroscopy, ions to one or more logic ions that provide sympathetic cooling and state readout. Here, we establish the fundamental performance limits and operating regimes of this protocol, identifying how the interaction strength, interrogation time, and logic-ensemble size govern sensitivity, dynamic range, and robustness to experimental imperfections. We show that quantum-limited sensitivity can be retained even with a single logic ion, while increasing the number of logic ions substantially improves readout efficiency and robustness. Beyond precision metrology, the same collective interface enables many-body measurements relevant to quantum information processing, including parity measurements and stabilizer-like syndrome extraction. Our results establish collective quantum logic spectroscopy as a scalable framework for optical clocks, quantum-enhanced sensing, and trapped-ion quantum information processing.
We present a general technique for precision spectroscopy of atoms that lack suitable transitions for efficient laser cooling, internal state preparation, and detection. In our implementation with trapped atomic ions, an auxiliary "logic" ion provides sympathetic laser cooling, state initialization, and detection for a simultaneously trapped "spectroscopy" ion. Detection is achieved by applying a mapping operation to each ion, which results in a coherent transfer of the spectroscopy ion's internal state onto the logic ion, where it is then measured with high efficiency. Experimental realization, by using 9Be+ as the logic ion and 27Al+ as the spectroscopy ion, indicates the feasibility of applying this technique to make accurate optical clocks based on single ions.