Abstract:We investigate the regime of strong coupling of an ensemble of two-dimensional electrons to a single-mode cavity resonator. In particular, we realized such a regime of light-matter interaction by coupling the cyclotron motion of a collection of electrons on the surface of liquid helium to the microwave field in a semi-confocal Fabry-Perot resonator. For the co-rotating component of the microwave field, the strong coupling is pronouncedly manifested by the normal-mode splitting in the spectrum of coupled field-… Show more
“…Reducing the linewidth and increasing the coupling strength offers a path toward the strong coupling regime, which has recently been achieved for the cyclotron motion of large electron ensembles on liquid helium 35 . In the strong coupling regime, direct measurement of the electron orbital frequencies using two-tone spectroscopy 36 may bring to light new microwave features of strongly correlated electron states 37 .…”
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 MHz, greatly exceeding the resonator linewidth 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.
“…Reducing the linewidth and increasing the coupling strength offers a path toward the strong coupling regime, which has recently been achieved for the cyclotron motion of large electron ensembles on liquid helium 35 . In the strong coupling regime, direct measurement of the electron orbital frequencies using two-tone spectroscopy 36 may bring to light new microwave features of strongly correlated electron states 37 .…”
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 MHz, greatly exceeding the resonator linewidth 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.
“…This presents an opportunity for anther interesting CQED-type experiment with a many-electron ensemble on liquid helium coupled to a single-mode cavity resonator. Recently, the strong coupling of such an ensemble to a highquality single-mode Fabry-Perot resonator has been demonstrated [56]. In this experiment, the resonator geometry favors the polarization of the microwave electric field being parallel to the surface, therefore the cyclotron motion of SE in a perpendicular magnetic field was excited.…”
Section: Discussionmentioning
confidence: 99%
“…In this experiment, the resonator geometry favors the polarization of the microwave electric field being parallel to the surface, therefore the cyclotron motion of SE in a perpendicular magnetic field was excited. However, the linearity of such a coupled system precludes to observe differences between purely classical behaviour and any predictions based on quantum mechanics [56]. By introducing the parallel component of magnetic field, the strong coupling between an ensemble of the highly nonlinear two-level systems and a single mode of a cavity field can be readily realized and studied.…”
The Jaynes-Cummings model (JCM), one of the paradigms of quantum electrodynamics, was introduced to describe interaction between light and a fictitious two-level atom. Recently it was suggested that the JCM Hamiltonian can be invoked to describe the motional states of electrons trapped on the surface of liquid helium and subjected to a constant uniform magnetic field tilted with respect to the surface [Yunusova et al. Phys. Rev. Lett. 122, 176802 (2019)]. In this case, the surface-bound (Rydberg) states of an electron are coupled to the electron cyclotron motion by the in-plane component of tilted field. Here we investigate, both theoretically and experimentally, the spectroscopic properties of surface electrons in a tilted magnetic field and demonstrate that such a system exhibits a variety of phenomena common to the light dressed states of atomic and molecular systems. This shows that electrons on helium realize a prototypical atomic system where interaction between components can be engineered and controlled by simple means and with high accuracy, and which therefore can be potentially used as a new flexible platform for quantum experiments. Our work introduces a pure condensedmatter system of electrons on helium into the context of atomic, molecular and optical physics.
“…The SE can be manipulated by the circuit QED architecture [51,52] or the microchannel devices [53][54][55][56][57][58][59] with high transport efficiency [60,61]. With a static magnetic field perpendicular to the surface, the motion parallel to the surface is quantized as orbital states [62], which is similar to the Landau levels. In addition, the spin state of the SE is also an important quantum resource owing to its long relaxation time that exceeds 100 s [63].…”
The nonadiabatic holonomic quantum computation based on the geometric phase is robust against the built-in noise and decoherence. In this work, we theoretically propose a scheme to realize nonadiabatic holonomic quantum gates in a surface electron system, which is a promising two-dimensional platform for quantum computation. The holonomic gate is realized by a three-level structure that combines the Rydberg states and spin states via an inhomogeneous magnetic field. After a cyclic evolution, the computation bases pick up different geometric phases and thus perform a holonomic gate. Only the electron with spin up experiences the holonomic gate, while the electron with spin down is decoupled from the state-selective driving fields. The arbitrary controlled-U gate encoded on the Rydberg states and spin states can then be realized. The fidelity of the output state exceeds 0.99 with experimentally achievable parameters.
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