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.

arXiv:1508.04847Physical Review XMar 21, 201653 citations

Circuit Quantum Electrodynamics with Electrons on Helium

Ge Yang

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.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.

Mar 1, 20200 citations

Proposal for Manipulating and Detecting Spin and Orbital States of Trapped Electrons on Helium Using Cavity Quantum Electrodynamics

David Schuster, A. Fragner, M. I. Dykman +2 more

We propose a hybrid architecture in which an on-chip high finesse superconducting cavity is coupled to the lateral motion and spin state of a single electron trapped on the surface of superfluid helium. We estimate the motional coherence times to exceed 15 μs, while energy will be coherently exchanged with the cavity photons in less than 10 ns for charge states and faster than 1 μs for spin states, making the system attractive for quantum information processing and strong coupling cavity quantum electrodynamics experiments. The cavity is used for nondestructive readout and as a quantum bus mediating interactions between distant electrons or an electron and a superconducting qubit.We propose a hybrid architecture in which an on-chip high finesse superconducting cavity is coupled to the lateral motion and spin state of a single electron trapped on the surface of superfluid helium. We estimate the motional coherence times to exceed 15 μs, while energy will be coherently exchanged with the cavity photons in less than 10 ns for charge states and faster than 1 μs for spin states, making the system attractive for quantum information processing and strong coupling cavity quantum electrodynamics experiments. The cavity is used for nondestructive readout and as a quantum bus mediating interactions between distant electrons or an electron and a superconducting qubit.

arXiv:0912.1406Physical Review LettersJul 23, 2010114 citations

Circuit Quantum Electrodynamics with Electrons on Helium

A. Fragner

We propose to couple an on-chip high finesse superconducting cavity to the lateral-motion and spin state of a single electron trapped on the surface of superfluid helium. We estimate the motional coherence times to exceed 15 microseconds, while energy will be coherently exchanged with the cavity photons in less than 10 nanoseconds for charge states and faster than 1 microsecond for spin states, making the system attractive for quantum information processing and cavity quantum electrodynamics experiments. Strong interaction with cavity photons will provide the means for both nondestructive readout and coupling of distant electrons.We propose to couple an on-chip high finesse superconducting cavity to the lateral-motion and spin state of a single electron trapped on the surface of superfluid helium. We estimate the motional coherence times to exceed 15 microseconds, while energy will be coherently exchanged with the cavity photons in less than 10 nanoseconds for charge states and faster than 1 microsecond for spin states, making the system attractive for quantum information processing and cavity quantum electrodynamics experiments. Strong interaction with cavity photons will provide the means for both nondestructive readout and coupling of distant electrons.

Jan 1, 20133 citations

Coupling a single electron on superfluid helium to a superconducting resonator

Gerwin Koolstra, Ge Yang, David Schuster

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.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.

arXiv:1902.04190Nature CommunicationsNov 22, 201979 citations

Trapping a Single Electron on Superfluid Helium Using a Superconducting Resonator

Gerwin Koolstra

Electrons on helium form a unique two-dimensional system on the interface of superfluid $^4$ He and vacuum. At low temperatures and weak confinement, trapped electrons can arrange into strongly correlated states known as Wigner molecules, which can be used to study electron interactions in the absence of disorder, or as a promising resource for quantum computation. Wigner molecules have orbital frequencies in the microwave regime and can therefore be integrated with circuit quantum electrodynamics, which would allow rapid detection and manipulation of such a molecule's orbital state. In this thesis, we demonstrate deterministic preparation of one to four-electron Wigner molecules in an electron-on-helium quantum dot located at the tip of an on-chip microwave resonator. The Wigner molecule dipole coupling to the resonator allows us to measure spectral features of Wigner molecules in the microwave regime. We find that different-sized Wigner molecules have strikingly different spectra, and each spectrum serves as a fingerprint for the molecule's internal structure and its surroundings. By modeling the electron-cavity system, we extract each molecule's orbital frequency and electron configuration. For a single electron, the orbital frequency crosses the cavity resonance and we measure a large coherent electron-photon coupling rate of $g/2\pi = 4.8$ MHz, which exceeds the incoherent cavity decay rate by ten times. These results provide a solid base for the development of an electron-on-helium qubit. Looking forward, our platform allows for new microwave studies of strongly correlated electron states and can be used to couple a single microwave photon to a single electron spin.Electrons on helium form a unique two-dimensional system on the interface of superfluid $^4$He and vacuum. At low temperatures and weak confinement, trapped electrons can arrange into strongly correlated states known as Wigner molecules, which can be used to study electron interactions in the absence of disorder, or as a promising resource for quantum computation. Wigner molecules have orbital frequencies in the microwave regime and can therefore be integrated with circuit quantum electrodynamics, which would allow rapid detection and manipulation of such a molecule's orbital state. In this thesis, we demonstrate deterministic preparation of one to four-electron Wigner molecules in an electron-on-helium quantum dot located at the tip of an on-chip microwave resonator. The Wigner molecule dipole coupling to the resonator allows us to measure spectral features of Wigner molecules in the microwave regime. We find that different-sized Wigner molecules have strikingly different spectra, and each spectrum serves as a fingerprint for the molecule's internal structure and its surroundings. By modeling the electron-cavity system, we extract each molecule's orbital frequency and electron configuration. For a single electron, the orbital frequency crosses the cavity resonance and we measure a large coherent electron-photon coupling rate of $g/2\pi = 4.8$ MHz, which exceeds the incoherent cavity decay rate by ten times. These results provide a solid base for the development of an electron-on-helium qubit. Looking forward, our platform allows for new microwave studies of strongly correlated electron states and can be used to couple a single microwave photon to a single electron spin.

Dec 1, 20191 citation

\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.

Electrons on helium form a unique two-dimensional system on the interface of superfluid

^4

He and vacuum. At low temperatures and weak confinement, trapped electrons can arrange into strongly correlated states known as Wigner molecules, which can be used to study electron interactions in the absence of disorder, or as a promising resource for quantum computation. Wigner molecules have orbital frequencies in the microwave regime and can therefore be integrated with circuit quantum electrodynamics, which would allow rapid detection and manipulation of such a molecule's orbital state. In this thesis, we demonstrate deterministic preparation of one to four-electron Wigner molecules in an electron-on-helium quantum dot located at the tip of an on-chip microwave resonator. The Wigner molecule dipole coupling to the resonator allows us to measure spectral features of Wigner molecules in the microwave regime. We find that different-sized Wigner molecules have strikingly different spectra, and each spectrum serves as a fingerprint for the molecule's internal structure and its surroundings. By modeling the electron-cavity system, we extract each molecule's orbital frequency and electron configuration. For a single electron, the orbital frequency crosses the cavity resonance and we measure a large coherent electron-photon coupling rate of

g/2\pi = 4.8

MHz, which exceeds the incoherent cavity decay rate by ten times. These results provide a solid base for the development of an electron-on-helium qubit. Looking forward, our platform allows for new microwave studies of strongly correlated electron states and can be used to couple a single microwave photon to a single electron spin.