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Circuit Quantum Electrodynamics with Electrons on Helium

Ge Yang

Published Mar 1, 2020• 0 citations
Publisher

Abstract

The quest towards precise measurement and control of quantum mechanical systems is behind many if not most of the advances in mesoscopic physics in the recent years. This thesis follows that tradition, and describes the first realization of a hybrid circuit integrating electrons on helium (EonHe) with the circuit quantum electrodynamics (cQED) architecture. In this hybrid architecture, the quantized lateral motion of the electrons strongly couples with the transverse electric field inside a high-Q superconducting resonator, enabling sensitive detection and manipulation of the electron's in-plane motion degree of freedom. Such architecture also provide a plausible road map towards using the spin degrees of freedom of the electrons as a quantum memory. Our hope is to establish a novel model system for quantum control and manipulation, where the uncanny similarity between the electron hamiltonian and the strong coulomb interactions could give rise to unparallelly rich quantum phenomena. In our first experiment towards this goal, we demonstrate strong dispersive coupling between $\sim 10^5$ electrons and a superconducting co-planar waveguide resonator. The effort of the second experiment focuses on bringing down this number to just a few electrons in an isolated trap. The CPW resonator was replaced by a quarter-wavelength strip-line resonator with one side terminated by a short (``the tuning fork"). This design changes the microwave mode that is visible to the electron dipole interaction, improves the coupling strength, and opens up the geometry for more sophisticated DC controls isolating an individual electron. The third experiment implements such DC control scheme, and manages to trap just a single electron in a small trap. This small electron trap is defined by multiple DC electrodes near the open-end of the tuning fork. The overall circuit design resembles those seen in the quantum dot community. Much effort was spent on hitting the tight space between the dispersive constraints of the cQED measurement scheme and the increasing complication of the sample. Single or few electron spectra are measured, and we provided an upper estimate on the acoustically broadened electron line-width, together with design changes that reduce the line-width of the electron states.

DOI
10.6082/mk0yz-n7z15

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•Jan 27, 2021•0 citations
The quest towards precise measurement and control of quantum mechanical systems is behind many if not most of the advances in mesoscopic physics in the recent years. This thesis follows that tradition, and describes the first realization of a hybrid circuit integrating electrons on helium (EonHe) with the circuit quantum electrodynamics (cQED) architecture. In this hybrid architecture, the quantized lateral motion of the electrons strongly couples with the transverse electric field inside a high-Q superconducting resonator, enabling sensitive detection and manipulation of the electron's in-plane motion degree of freedom. Such architecture also provide a plausible road map towards using the spin degrees of freedom of the electrons as a quantum memory. Our hope is to establish a novel model system for quantum control and manipulation, where the uncanny similarity between the electron hamiltonian and the strong coulomb interactions could give rise to unparallelly rich quantum phenomena. In our first experiment towards this goal, we demonstrate strong dispersive coupling between ∼105\sim 10^5∼105 electrons and a superconducting co-planar waveguide resonator. The effort of the second experiment focuses on bringing down this number to just a few electrons in an isolated trap. The CPW resonator was replaced by a quarter-wavelength strip-line resonator with one side terminated by a short (``the tuning fork"). This design changes the microwave mode that is visible to the electron dipole interaction, improves the coupling strength, and opens up the geometry for more sophisticated DC controls isolating an individual electron. The third experiment implements such DC control scheme, and manages to trap just a single electron in a small trap. This small electron trap is defined by multiple DC electrodes near the open-end of the tuning fork. The overall circuit design resembles those seen in the quantum dot community. Much effort was spent on hitting the tight space between the dispersive constraints of the cQED measurement scheme and the increasing complication of the sample. Single or few electron spectra are measured, and we provided an upper estimate on the acoustically broadened electron line-width, together with design changes that reduce the line-width of the electron states.
The quantized lateral motional states and the spin states of electrons trapped on the surface of superfluid helium have been proposed as basic building blocks of a scalable quantum computer.Circuit quantum electrodynamics allows strong dipole coupling between electrons and a high-Q superconducting microwave resonator, enabling such sensitive detection and manipulation of electron degrees of freedom.Here, we present the first realization of a hybrid circuit in which a large number of electrons are trapped on the surface of superfluid helium inside a coplanar waveguide resonator.The high finesse of the resonator allows us to observe large dispersive shifts that are many times the linewidth and make fast and sensitive measurements on the collective vibrational modes of the electron ensemble, as well as the superfluid helium film underneath.Furthermore, a large ensemble coupling is observed in the dispersive regime during experiment, and it shows excellent agreement with our numeric model.The coupling strength of the ensemble to the cavity is found to be ≈1 MHz per electron, indicating the feasibility of achieving single electron strong coupling.
The quantized lateral motional states and the spin states of electrons trapped on the surface of superfluid helium have been proposed as basic building blocks of a scalable quantum computer.Circuit quantum electrodynamics allows strong dipole coupling between electrons and a high-Q superconducting microwave resonator, enabling such sensitive detection and manipulation of electron degrees of freedom.Here, we present the first realization of a hybrid circuit in which a large number of electrons are trapped on the surface of superfluid helium inside a coplanar waveguide resonator.The high finesse of the resonator allows us to observe large dispersive shifts that are many times the linewidth and make fast and sensitive measurements on the collective vibrational modes of the electron ensemble, as well as the superfluid helium film underneath.Furthermore, a large ensemble coupling is observed in the dispersive regime during experiment, and it shows excellent agreement with our numeric model.The coupling strength of the ensemble to the cavity is found to be ≈1 MHz per electron, indicating the feasibility of achieving single electron strong coupling.
Electrons on helium form a unique two-dimensional system on the interface of liquid helium and vacuum. A small number of trapped electrons on helium exhibits strong interactions in the absence of disorder, and can be used as a qubit. Trapped electrons typically have orbital frequencies in the microwave regime and can therefore be integrated with circuit quantum electrodynamics (cQED), which studies light-matter interactions using microwave photons. Here, we experimentally realize a cQED platform with the orbitals of single electrons on helium. We deterministically trap one to four electrons in a dot integrated with a microwave resonator, allowing us to study the electrons' response to microwaves. Furthermore, we find a single-electron-photon coupling strength of [Formula: see text] MHz, greatly exceeding the resonator linewidth [Formula: see text] MHz. These results pave the way towards microwave studies of Wigner molecules and coherent control of the orbital and spin state of a single electron on helium.
Semiconductor qubits rely on the control of charge and spin degrees of freedom of electrons or holes confined in quantum dots (QDs). Typically, semiconductor qubit-qubit coupling is short range, effectively limiting qubit distance to the spatial extent of the wavefunction of the confined particle (a few hundred nanometers). This is a significant constraint towards scaling of QD-based architectures to realize dense 1D or 2D arrays of QDs. Inspired by techniques originally developed for circuit QED, we recently demonstrated the strong coupling of individual electrons confined in GaAs quantum dots to individual microwave photons, making use of the enhanced electric component of the vacuum fluctuations of a resonator with impedance beyond the typical 50 Ohm of standard coplanar waveguides. In this hybrid technology, we recently realized a proof of concept experiment, where the coupling between a transmon and a double QD (DQD) is mediated by virtual microwave photon excitations in a high impedance SQUID array resonator, which acts as a quantum bus enabling long-range coupling between dissimilar qubits. Similarly, we achieved coherent coupling between two DQD charge qubits separated by approximately 50 um. In the dispersive regime, we spectroscopically observed qubit-qubit coupling as an avoided-crossing in the energy spectrum of the DQD charge qubits. The methods and techniques developed in this work are transferable to QD devices based on other material systems and can be beneficial for spin based hybrid systems.
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.
This dissertation describes a set of experiments with the goal of creating a super-conductor-semiconductor hybrid circuit quantum electrodynamics architecture with single electron spins. Single spins in silicon quantum dots have emerged as attractive qubits for quantum computation. However, how to scale up spin qubit systems remains an open question. The hybrid architecture considered here could provide a route to realizing large networks of quantum dot–based spin qubit registers. The first experiment in this thesis is aimed at achieving strong coupling between a single electron spin and a single microwave photon. The electron is trapped in a gate-defined double quantum dot in a Si/SiGe heterostructure and the photon is stored in an on-chip superconducting high-impedance NbTiN cavity. The photon is coupled directly to the electron charge, and indirectly to the electron spin, mediated through a synthetic spin-orbit field. We observe a vacuum Rabi splitting that depends on the spin-charge hybridization. The ratio of spin-photon coupling strength to decoherence rates of the spin and cavity combined is larger than unity, confirming the strong coupling regime has been reached. In addition, we find an optimal degree of spin-charge hybridization for which this ratio is maximized. The demonstration of strong spin-photon coupling not only opens a new range of physics experiments, but fulfills also a crucial requirement for coupling spin qubits at a distance via a cavity. The second experiment is focused on spin readout with the on-chip cavity. Instead of the direct dispersive readout of a single spin, we use the cavity to detect whether the electron is allowed to tunnel between the two dots or not. We benchmark the charge sensitivity and bandwidth of the detector and find that rapid detection of the electron charge with high SNR is possible. In the two-electron regime, electron tunneling is contingent on the total spin state (Pauli spin blockade). This spin-to-charge conversion scheme enables single-shot detection of singlet states with high-fidelity. The demonstration of single-shot spin readout with a cavity is an essential step towards readout in dense spin qubit arrays, such as the crossbar network, where it is not possible to integrate electrometers and accompanying reservoirs adjacent to the qubit dots. In the third experiment, we develop on-chip microwave filters to suppress microwave photon leakage from the cavity through the gate electrodes that are necessary to form quantum dots. We introduce a new cavity design that is compatible with long-distance connectivity between spins, but is also more susceptible to microwave leakage. We test and compare two low-pass filter variations in terms of performance, footprint and integrability. They use the same nanowire inductor, but different implementations of the capacitor: one with a planar interdigitated capacitor and one novel design with an overlapping thin-film capacitor. We find that both approaches are effective against microwave leakage. However, the large footprint of the interdigitated capacitor makes this solution inconvenient as the number of gate lines increases. The thin-film capacitor, with its much smaller footprint, is better suited for our devices. The final part of this dissertation contains concluding remarks and possible future directions are proposed.