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Building A Magnesium Ion Trap For Quantum Computation

Jiajia Zhou

Published Aug 1, 2007• 0 citations
Publisher

Abstract

Trapped ions are one of the best candidate systems to realize quantum computation. In our laboratory, we are trying to implement quantum computing and information processing: two hyperfine ground-states of magnesium-25 ions will serve as the two-level system to store quantum information. The ions are confined in a linear radio-frequency trap under ultra-high vacuum conditions and will be cooled down to their motional ground-states. By illuminating the ions with frequency-stabilized lasers we will be able to initialize, manipulate, and read out their internal electronic quantum states in a well-controlled way and with high fidelity. In addition, the ions can be made to interact with each other by coupling their internal electronic states to a collective vibrational mode of motion along the trap axis. In this thesis, the focus will be on the process of building a trapped-magnesium-ion quantum information processor.

DOI
10.71548/6907

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Trapped ions are one of the best candidate systems to realize quantum computation. In our laboratory, we are trying to implement quantum computing and information processing: two hyperfine ground-states of magnesium-25 ions will serve as the two-level system to store quantum information. The ions are confined in a linear radio-frequency trap under ultra-high vacuum conditions and will be cooled down to their motional ground-states. By illuminating the ions with frequency-stabilized lasers we will be able to initialize, manipulate, and read out their internal electronic quantum states in a well-controlled way and with high fidelity. In addition, the ions can be made to interact with each other by coupling their internal electronic states to a collective vibrational mode of motion along the trap axis. In this thesis, the focus will be on the process of building a trapped-magnesium-ion quantum information processor.
This thesis provides an overview of an approach to quantum simulations using magnesium-25 ions stored in a linear Paul trap as the carriers of quantum information. Their quantum state is manipulated and read out using ultraviolet laser beams. Several important steps towards realising the first experiments have been undertaken, the most striking of which is cooling the ions to their motional ground state. We describe a first experiment simulating cosmological particle creation in the Early Universe and discuss the expected results.
With all the key elements of quantum computing in ion traps demonstrated by the research community, the focus is now placed on building more sophisticated traps with larger numbers of ions to allow practical scale information processing. One promising avenue is to store ions in and shuttle them between many independent traps which serve as potential interaction sites. The core of the work described in this thesis is the experimental evaluation of a microfabricated segmented ion trap, built by Sandia National Laboratories ("Sandia trap"). These experiments required construction of a wholly new optical setup including laser and detection systems, a vacuum system and control electronics. Among our experimental achievements were: successful loading of single and pairs of ions in the microscale trap, measurement of ion storage lifetime, measurement of the motional heating rate with a time-resolved Doppler-cooling method — which showed above than average heating, and implemented a single-ion shuttling method — which reliably transferred the ion through a distance of 360 μm (two DC electrode widths away) and back. These results have been used to improve the next version of the Sandia trap design. We also used computer modelling to study several aspects of ion traps: a mesoscopic ion trap designed for fast ion separation, simulated ion loading to quantify requirements for successful trapping in small and shallow traps, and analyzed a precise shuttling method — where the time dependence of the trapping potential is engineered such that there is minimal motional heating. The results show that ion trap arrays at the 100 μm distance scale are feasible and suggests that such multiple trap designs merit further study.
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.
An experimental realization of quantum computers is composed of two or more calcium ions trapped in a magnetic quadripole. Information is transferred to and read from the ions by means of structured lasers that interact with the ions’ vibration pattern, causing changes of energy distribution in their electronic structure. Departing from an initial state when the ions are cooled, the use of lasers modifies the internal state of one ion that is entangled with the others, then changing the collective states. In such quantum computers, some of the physically possible electronic states are avoided or not taken into consideration, to force the system to work as a binary device. In this essay, we discuss the dynamics that the ions could spontaneously display and its possible implications for the principles of computational logics.
This dissertation describes a prototype experiment aiming at the realization of scalable quantum information. The essential feature is the usage of a novel microstructured ion trap derived from the Paul trap. It allows for storing and manipulating a large number of ions, as compared to conventional linear Paul traps. This thesis describes how the way is paved towards the realization of quantum information experiments in this ion trap. An analysis of the electrostatic properties of the ion trap is presented, which is laying the foundation for understanding the limits of confinement stability and effects beyond standard Paul trap behavior. The focus of this work lies on the realization and characterization of single and dual qubit operations, which are achieved by means of (semiclassical) atom-light interaction. In our experiment, the qubit is implemented in the Zeeman sublevels of the ion’s ground state, i.e. in the spin of the bright electron of a 40Ca+ ion. The main body of this thesis then describes the realization of the necessary steps of preparation, manipulation and readout of this qubit. The preparation includes optical pumping and cooling close to the motional quantum ground state by means of sideband cooling. Several possible techniques for these steps are tested and analyzed. Coherent manipulations are carried out by means of stimulated Raman transitions. Here, a strong emphasis is put on the characterization of the various decoherence mechanisms, which are dominated by the motional excitation of the ion due to thermalization of the ion with the trap electrodes, and by imperfections in the ion-laser interactions. As by-product of the latter investigation, a new measurement scheme for the experimental determination of atomic dipole matrix elements is presented.
An experimental realization of quantum computers is composed of two or more calcium ions trapped in a magnetic quadripole. Information is transferred to and read from the ions by means of structured lasers that interact with the ions’ vibration pattern, causing changes of energy distribution in their electronic structure. Departing from an initial state when the ions are cooled, the use of lasers modifies the internal state of one ion that is entangled with the others, then changing the collective states. In such quantum computers, some of the physically possible electronic states are avoided or not taken into consideration, to force the system to work as a binary device. In this essay, we discuss the dynamics that the ions could spontaneously display and its possible implications for the principles of computational logics.