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arXiv:2204.07957 · Physical Review Research

Feasibility study on ground-state cooling and single-phonon readout of trapped electrons using hybrid quantum systems

Alto Osada, Kento Taniguchi, Masato Shigefuji, Atsushi Noguchi

Published Sep 29, 2022• 12 citations
arXivHTMLPDF

Abstract

Qubits of long coherence time and fast quantum operations are long-sought objectives toward the realization of high-fidelity quantum operations and their applications to quantum technologies. An electron levitated in a vacuum by a Paul trap is expected to be a good candidate, for its light mass and hence the high secular frequency which allows for faster gate operations than those in trapped ions. Controlling the motional state of the trapped electron is a crucial issue, for it mediates an interaction between electron spins, intrinsic qubits embedded in electrons, and its decoherence results in degraded fidelity of two-qubit gates. In addition, an efficient readout of the motional state is important, regarding the possibility of detecting spin state by using it. Despite such importance, how to achieve the motional ground state and how to efficiently detect it are not reported so far. Here we propose methods addressing these issues by utilizing hybrid quantum systems involving an electron-superconducting circuit and electron-ion coupled systems and analyze the feasibility of our schemes. In both systems, we show that ground-state cooling and single-phonon readout of the motional state of the trapped electron are possible. Our work sheds light on a way to precisely control the motional states of the trapped electrons, that provides an interesting playground for the development of quantum technologies.

DOI
10.1103/physrevresearch.4.033245

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Qubits of long coherence time and fast quantum operations are long-sought objectives toward the realization of high-fidelity quantum operations and their applications to quantum technologies. An electron levitated in a vacuum by a Paul trap is expected to be a good candidate, for its light mass and hence the high secular frequency which allows for faster gate operations than those in trapped ions. Controlling the motional state of the trapped electron is a crucial issue, for it mediates an interaction between electron spins, intrinsic qubits embedded in electrons, and its decoherence results in degraded fidelity of two-qubit gates. In addition, an efficient readout of the motional state is important, regarding the possibility of detecting spin state by using it. Despite such importance, how to achieve the motional ground state and how to efficiently detect it are not reported so far. Here we propose methods addressing these issues by utilizing hybrid quantum systems involving an electron-superconducting circuit and electron-ion coupled systems and analyze the feasibility of our schemes. In both systems, we show that ground-state cooling and single-phonon readout of the motional state of the trapped electron are possible. Our work sheds light on a way to precisely control the motional states of the trapped electrons, that provides an interesting playground for the development of quantum technologies.
Trapped charged particles have been at the forefront of quantum information processing (QIP) for a few decades now, with deterministic two-qubit logic gates reaching record fidelities of 99.999.9%99.9 and single-qubit operations of much higher fidelity. In a hybrid system involving trapped charges, quantum degrees of freedom of macroscopic objects such as bulk acoustic resonators, superconducting circuits, or nanomechanical membranes, couple to the trapped charges and ideally inherit the coherent properties of the charges. The hybrid system therefore implements a ``quantum transducer,'' where the quantum reality (i.e., superpositions and entanglement) of small objects is extended to include the larger object. Although a hybrid quantum system with trapped charges could be valuable both for fundamental research and for QIP applications, no such system exists today. Here we study theoretically the possibilities of coupling the quantum-mechanical motion of a trapped charged particle (e.g., an ion or electron) to the quantum degrees of freedom of superconducting devices, nanomechanical resonators, and quartz bulk acoustic wave resonators. For each case, we estimate the coupling rate between the charged particle and its macroscopic counterpart and compare it to the decoherence rate, i.e., the rate at which quantum superposition decays. A hybrid system can only be considered quantum if the coupling rate significantly exceeds all decoherence rates. Our approach is to examine specific examples by using parameters that are experimentally attainable in the foreseeable future. We conclude that hybrid quantum systems involving a single atomic ion are unfavorable compared with the use of a single electron because the coupling rates between the ion and its counterpart are slower than the expected decoherence rates. A system based on trapped electrons, on the other hand, might have coupling rates that significantly exceed decoherence rates. Moreover, it might have appealing properties such as fast entangling gates, long coherence, and flexible topology that is fully electronic in nature. Realizing such a system, however, is technologically challenging because it requires accommodating both a trapping technology and superconducting circuitry in a compatible manner. We review some of the challenges involved, such as the required trap parameters, electron sources, electrical circuitry, and cooling schemes in order to promote further investigations towards the realization of such a hybrid system.
The promise of quantum computing has driven a persistent quest for new qubit platforms with long coherence, fast operation, and large scalability. Electrons, ubiquitous elementary particles of nonzero charge, spin, and mass, have commonly been perceived as paradigmatic local quantum information carriers. Despite superior controllability and configurability, their practical performance as qubits via either motional or spin states depends critically on their material environment. Here we report our experimental realization of a new qubit platform based upon isolated single electrons trapped on an ultraclean solid neon surface in vacuum. By integrating an electron trap in a circuit quantum electrodynamics architecture, we achieve strong coupling between the motional states of a single electron and a single microwave photon in an on-chip superconducting resonator. Qubit gate operations and dispersive readout are implemented to measure the energy relaxation time T1T_1T1​ of 15μ\muμs and phase coherence time T2T_2T2​ over 200ns. These results indicate that the electron-on-solid-neon qubit already performs near the state of the art as a charge qubit.
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.
The promise of quantum computing has driven a persistent quest for new qubit platforms with long coherence, fast operation, and large scalability. Electrons, ubiquitous elementary particles of nonzero charge, spin, and mass, have commonly been perceived as paradigmatic local quantum information carriers. Despite superior controllability and configurability, their practical performance as qubits via either motional or spin states depends critically on their material environment. Here we report our experimental realization of a new qubit platform based upon isolated single electrons trapped on an ultraclean solid neon surface in vacuum. By integrating an electron trap in a circuit quantum electrodynamics architecture, we achieve strong coupling between the motional states of a single electron and microwave photons in an on-chip superconducting resonator. Qubit gate operations and dispersive readout are used to measure the energy relaxation time T1T_1T1​ of 15 μ15~\mu15 μs and phase coherence time T2T_2T2​ over 200 ns, indicating that the electron-on-solid-neon qubit already performs near the state of the art as a charge qubit.
We propose a scheme to read out the spin of a single electron quantum bit in a surface Paul trap using oscillating magnetic-field gradients. The readout sequence is composed of cooling, driving, amplification, and detection of the electron's motion. We study the scheme in the presence of noise and trap anharmonicities at liquid-helium temperatures. An analysis of the four procedures shows short measurement times ($25\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{s}$) and high fidelities (99.799.7%99.7) are achievable with realistic experimental parameters. Our scheme performs the function of fluorescence detection in ion trapping schemes, highlighting the potential to build all-electric quantum computers based on trapped electron-spin qubits.