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arXiv:1702.07129 · Quantum Science and Technology

Enhanced quantum sensing with multi-level structures of trapped ions

N. Aharon, Michael Drewsen, Alex Retzker

Published Jul 7, 2017• 5 citations
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Abstract

Abstract We present a method of enhanced sensing of AC magnetic fields. The method is based on the construction of a robust qubit by the application of continuous driving fields. Specifically, magnetic noise and power fluctuations of the driving fields do not operate within the robust qubit subspace, hence robustness to both external and controller noise is achieved. The scheme is applicable to either a single ion or an ensemble of ions. We consider trapped-ion based implementation via the dipole transitions, which is relevant for several types of ions, such as the 40 Ca + , 88 Sr + and the 138 Ba + ions. Taking experimental errors into account, we conclude that the coherence time of the robust qubit can be improved by up to ∼4 orders of magnitude compared to the coherence time of the bare states. We show how the robust qubit can be utilised for the task of sensing AC magnetic fields in the range ∼ 0.1 − 100 MHz with an improvement of ∼2 orders of magnitude of the sensitivity. In addition, we present a microwave-based sensing scheme that is suitable for ions with a hyperfine structure, such as the 9 Be + , 25 Mg + , 43 Ca + , 87 Sr + , 137 Ba + , 111 Cd + ,

DOI
10.1088/2058-9565/aa771a

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Abstract We present a method of enhanced sensing of AC magnetic fields. The method is based on the construction of a robust qubit by the application of continuous driving fields. Specifically, magnetic noise and power fluctuations of the driving fields do not operate within the robust qubit subspace, hence robustness to both external and controller noise is achieved. The scheme is applicable to either a single ion or an ensemble of ions. We consider trapped-ion based implementation via the dipole transitions, which is relevant for several types of ions, such as the 40 Ca + , 88 Sr + and the 138 Ba + ions. Taking experimental errors into account, we conclude that the coherence time of the robust qubit can be improved by up to ∼4 orders of magnitude compared to the coherence time of the bare states. We show how the robust qubit can be utilised for the task of sensing AC magnetic fields in the range ∼ 0.1 − 100 MHz with an improvement of ∼2 orders of magnitude of the sensitivity. In addition, we present a microwave-based sensing scheme that is suitable for ions with a hyperfine structure, such as the 9 Be + , 25 Mg + , 43 Ca + , 87 Sr + , 137 Ba + , 111 Cd + ,
We present a new method of constructing a fully robust qubit in a three-level system. By the application of continuous driving fields, robustness to both external and controller noise is achieved. Specifically, magnetic noise and power fluctuations do not operate within the robust qubit subspace. Whereas all the continuous driving based constructions of such a fully robust qubit considered so far have required at least four levels, we show that in fact only three levels are necessary. This paves the way for simple constructions of a fully robust qubit in many atomic and solid state systems that are controlled by either microwave or optical fields. We focus on the NV-center in diamond and analyze the implementation of the scheme, by utilizing the electronic spin sub-levels of its ground state. In current state-of-the-art experimental setups the scheme leads to improvement of more than two orders of magnitude in coherence time, pushing it towards the lifetime limit. We show how the fully robust qubit can be used to implement quantum sensing, and in particular, the sensing of high frequency signals.
We present a new method of constructing a fully robust qubit in a three-level system. By the application of continuous driving fields, robustness to both external and controller noise is achieved. Whereas all the continuous driving based constructions of such a fully robust qubit considered so far have required at least four levels, we show that in fact only three levels are necessary. This paves the way for simple constructions of a fully robust qubit in many atomic and solid state systems that are controlled by either microwave or optical fields. We focus on the NV-center in diamond and analyze the implementation of the scheme, by utilizing the electronic spin sub-levels of its ground state. In current state-of-the-art experimental setups the scheme leads to improvement of more than two orders of magnitude in coherence time, pushing it towards the lifetime limit. We show how the fully robust qubit can be used to implement quantum sensing, and in particular, the sensing of high frequency signals.
Scalability is a challenging yet key aspect required for large scale quantum computing and simulation using ions trapped in radio-frequency (rf) Paul traps. In this thesis 171Yb+ ions are used to demonstrate a magnetic field insensitive qubit which has a measured coherence time of 1.5 s, making it an ideal candidate to use for storing quantum information. A magnetic field sensitive qubit is also characterised which can be used for the implementation of multi-qubit gates using a potentially very scalable scheme based on microwaves in conjunction with a static magnetic field gradient instead of using lasers. However, the measured coherence time is limited by magnetic field fluctuations and will prohibit high fidelity gate operations from being performed. To address this issue, the preparation of a dressed-state qubit using a microwave based stimulated rapid adiabatic passage (STIRAP) pulse sequence will be presented. This qubit is protected against the noisy environment making it less sensitive to magnetic field fluctuations. The lifetime of this qubit is measured to demonstrate its suitability for storing quantum information. A powerful method for manipulating the dressed-state qubit will be presented and is used to measure a coherence time of the qubit of 500 ms which is two orders of magnitude longer compared to the magnetic field sensitive qubit. It will also be shown that our method allows for the implementation of arbitrary rotations of the dressed-state qubit on the Bloch sphere using only a single rf field. This substantially simplifies the experimental setup for single and multi-qubit gates. Furthermore, this thesis will present a experimental setup capable of successfully operating microfabricated surface ion traps. This setup is then used to operate and characterise the first two-dimensional (2D) lattice of ion traps on a microchip. A unique feature of the microfabrication technique used for this device is the extremely large voltage that can be applied which allows long ion lifetimes along with large secular frequencies to be measured, demonstrating the robustness of this device. Rudimentary shuttling between neighbouring lattice sites will be shown which could be used as part of a efficient scheme to load a large lattice of ions. One of the many applications of a 2D lattice of ions lies in the field of quantum simulations where many-body systems such as quantum magnetism, high temperature superconductivity, the fractional quantum hall effect and synthetic gauge fields can be simulated. It will be shown how making only minor modifications to the microchip the ion-ion separation can be reduced sufficiently to offer an exciting platform for the successful implementation of 2D quantum simulations. A theoretical investigation on the optimal 2D ion trap lattice geometry will also be presented with the aim to maximise the ratio of ion-ion coupling strength to decoherence from motional heating of the ions and to laser induced off-resonant coupling.
This thesis describes experimental work on implementing single and two qubit gates in ¹7¹Yb+ ions using methods suitable for a large scale quantum computer. By combining a magnetic field gradient with microwave and radiofrequency radiation, the spin and motional states of the ions are coupled which allows multi-qubit operations to be performed, as well as providing individual addressing of ions in frequency space. A dressed state qubit is used which exhibits an increase of over two orders of magnitude in the coherence time for a qubit that it is sensitive to the magnetic field gradient. Using this system, single qubit gates are characterised using the technique of randomised benchmarking, resulting in a measured average error per gate of 9(3)x10¯4. A new type of two qubit gate is experimentally demonstrated, which in comparison to a standard two qubit gate shows significantly increased resilience to two major sources of gate infidelity: heating of the motional mode of the ions during gate operations, and incorrectly set gate field frequencies. These types of errors are expected to become increasingly important with the move towards quantum processors with large numbers of qubits. Using this same technique, a two qubit gate is also demonstrated at a higher initial temperature with a significantly improved fidelity compared to standard methods. These gate techniques are used to demonstrate work towards implementing positiondependent quantum logic, a method which could remove the correlation between the number of ions and the number of gate fields required in a large scale quantum computing architecture. A method to move the dressed state qubit through a magnetic field gradient while preserving quantum information is demonstrated, as well as a method to optimise the phase of a two qubit gate of unknown phase in order to implement a CNOT logic gate. This provides a path forwards to demonstrating a CNOT gate using position-dependent quantum logic.
We introduce a scheme that combines phonon-mediated quantum logic gates in trapped ions with the benefits of continuous dynamical decoupling. We demonstrate theoretically that a strong driving of the qubit decouples it from external magnetic-field noise, enhancing the fidelity of two-qubit quantum gates. Moreover, the scheme does not require ground-state cooling, and is inherently robust to undesired ac Stark shifts. The underlying mechanism can be extended to a variety of other systems where a strong driving protects the quantum coherence of the qubits without compromising the two-qubit couplings.
This thesis describes an ion trap magnetometer, in which experimental hardware and theory for trapped ion magnetometry has been developed and demonstrated. Quantum magnetometry has been a fast expanding field in recent years due to the plethora of military, medical and security applications. The current quantum magnetometer literature has shown great improvements on the standard magnetometer success metrics such as sensitivity, spacial resolution, frequency tuneability, noise shielding and vector field resolution. Ion trap magnetometry could potentially boast several advantages over some of the better established methods such as, nano-meter spatial resolution, broadband tuneability over radio-frequency (RF) and microwave frequencies, and magnetic field noise shielding and sensitivity improvements through dynamic decoupling methods; all in room temperature environments. The experimental setup discussed uses a micro-fabricated Paul trap for ion confinement due to the scalability of this technology. The method for sensing that was demonstrated utilises long-wavelength radiation dressed states to extend the coherence time of a single 171Yb+ ion beyond the bare states and to allow for a high level of frequency tuneability. The coherence times measured were T2 = 0:645 s for RF field sensing at 15.616 MHz and T2 = 1.153 s for microwave field sensing at 12.658466 GHz. Sensitivities of SB = 125.857 ± 26.155 pT/ vHz for RF magnetic fields and SB = 102.054 ± 11.046 pT/ vHz for microwave magnetic fields were achieved experimentally. A novel micro-fabricated Paul trap for trapping multiple ion clusters was developed to improve sensitivity values by increasing the total number of trapped ions. The design confines ions over a two-dimensional surface spanning 0.65 x 1.00 mm which would also allow for magnetic field gradient measurements. Efforts have been made to miniaturise certain experimental hardware to further the development of portable trapped ion experiments. For this, a miniaturised RF resonator that could be used for radial confinement of ions within Paul traps has been developed. At the current stage of development it is capable of applying a peak RF voltage of 114.9 V with a Q value of 70 at a resonant frequency of O/2p = 12.65 MHz.