Hole-spins localized in semiconductor structures, such as quantum dots or defects, serve to the realization of efficient gate-tunable solid-state quantum bits. Here we study two electrically driven spin $3/2$ holes coupled to the electromagnetic field of a microwave cavity. We show that the interplay between the non-Abelian Berry phases generated by local time-dependent electrical fields and the shared cavity photons allows for fast manipulation, detection, and long-range entanglement of the hole-spin qubits in the absence of any external magnetic field. Owing to its geometrical structure, such a scheme is more robust against external noises than the conventional hole-spin qubit implementations. These results suggest that hole-spins are favorable qubits for scalable quantum computing by purely electrical means.
We report a technique that can noninvasively add multiple DC wires into a 3D superconducting microwave cavity for electronic devices that require DC electrical terminals. We studied the influence of our DC lines on the cavity performance systematically. We found that the quality factor of the cavity is reduced if any of the components of the electrical wires cross the cavity equipotential planes. Using this technique, we were able to incorporate a quantum dot (QD) device into a 3D cavity. We then controlled and measured the QD transport signal using the DC lines. We have also studied the heati…
We report a technique for applying a dc bias in a 3d microwave cavity. This is achieved by isolating the two halves of the cavity with a dielectric and directly using them as dc electrodes. By embedding a variable capacitance diode in the cavity, we tune the resonant frequency with a dc voltage at room temperature, demonstrating the introduction of a dc bias into the 3d cavity without compromising its high quality factor.
We report on a technique for applying a DC bias in a 3D microwave cavity. We achieve this by isolating the two halves of the cavity with a dielectric and directly using them as DC electrodes. As a proof of concept, we embed a variable capacitance diode in the cavity and tune the resonant frequency with a DC voltage, demonstrating the incorporation of a DC bias into the 3D cavity with no measurable change in its quality factor at room temperature. We also characterize the architecture at millikelvin temperatures and show that the split cavity design maintains a quality factor $Q_\text{i} \sim 8…
We realize scattering states in a lossy and chaotic two-dimensional microwave cavity which follow bundles of classical particle trajectories. To generate such particlelike scattering states we measure the system's transmission matrix and apply an adapted Wigner-Smith time-delay formalism to it. The necessary shaping of the incident wave is achieved in situ using phase and amplitude regulated microwave antennas. Our experimental findings pave the way for establishing spatially confined communication channels that avoid possible intruders or obstacles in wave-based communication systems.
We realize a cavity magnon-microwave photon system in which magnetic dipole interaction mediates strong coupling between collective motion of large number of spins in a ferrimagnet and the microwave field in a three-dimensional cavity. By scaling down the cavity size and increasing number of spins, an ultrastrong coupling regime is achieved with a cooperativity reaching 12600. Interesting dynamic features including classical Rabi oscillation, magnetically induced transparency, and Purcell effect are demonstrated in this highly versatile platform, highlighting its great potential for coherent i…
We present a technique for addressing single NV$^{-}$ center spins in diamond over macroscopic distances using a tunable dielectric microwave cavity. We demonstrate optically detected magnetic resonance (ODMR) for a single NV$^{-}$ center in a nanodiamond (ND) located directly under the macroscopic microwave cavity. By moving the cavity relative to the ND, we record the ODMR signal as a function of position, mapping out the distribution of the cavity magnetic field along one axis. In addition, we argue that our system could be used to determine the orientation of the NV$^{-}$ major axis in a s…
Nanomechanical resonators with increasingly high quality factors are enabled following recent insights into energy storage and loss mechanisms in nanoelectromechanical systems (NEMS). Consequently, efficient, non-dissipative transduction schemes are required to avoid the dominating influence of coupling losses. We present an integrated NEMS transducer based on a microwave cavity dielectrically coupled to an array of doubly-clamped pre-stressed silicon nitride beam resonators. This cavity-enhanced detection scheme allows resolving the resonators' Brownian motion at room temperature while preser…
We propose a scheme able to entangle at the steady state a nanomechanical resonator with a microwave cavity mode of a driven superconducting coplanar waveguide. The nanomechanical resonator is capacitively coupled with the central conductor of the waveguide and stationary entanglement is achievable up to temperatures of tens of milliKelvin.
Coherent conversion from microwave to optical wave opens new research avenues towards long distant quantum network covering quantum communication, computing, and sensing out of the laboratory. Especially multi-mode enabled system is essential for practical applications. Here we experimentally demonstrate coherent multi-mode conversion from the microwave to optical wave via collective spin excitation in a single crystal yttrium iron garnet (YIG, Y3Fe5O12) which is strongly coupled to a microwave cavity mode in a three-dimensional rectangular cavity. Expanding collective spin excitation mode of …
We consider a strongly correlated quantum dot, tunnel coupled to two superconducting leads and capacitively coupled to a single mode microwave cavity. When the superconducting gap is the largest energy scale, multiple Shiba states are formed inside the gap. The competition of these states for the ground state signals a quantum phase transition. We demonstrate that photonic measurements can be used to probe such localized Shiba states. Moreover, the quantum phase transition can be pinpointed exactly from the sudden change in the transmission signal. Calculations were performed using the numeric…
We study the spectrum of a one-dimensional Kitaev chain placed in a microwave cavity. In the off-resonant regime, the frequency shift of the cavity can be used to identify the topological phase transition of the coupled system. In the resonant regime, the topology of the system can be controlled via the microwave cavity occupation and, moreover, for a large number of photons (classical limit), the physics becomes similar to that of periodically-driven systems (Floquet insulators). We also analyze numerically a finite chain and show the existence of a degenerate subspace in the presence of the …
Microwave to optical transduction has received a great deal of interest from the cavity optomechanics community as a landmark application for electro-optomechanical systems. In this Letter, we demonstrate a novel transducer that combines high-frequency mechanical motion and a microwave cavity for the first time. The system consists of a 3D microwave cavity and a gallium arsenide optomechanical crystal, which has been placed in the microwave electric field maximum. This allows the microwave cavity to actuate the gigahertz-frequency mechanical breathing mode in the optomechanical crystal through…
We study spin-photon coupling in cavity in the presence of relative phase shift between two ferromagnetic resonance driving forces. We show that the anticrossing gap can be manipulated by varying the relative phase. Increasing the phase difference leads to narrowing the anticrossing gap of hybridized modes and eventually to phase locked coupling at the value of relative phase of π: The FMR and cavity modes become phase locked and oscillate at the same frequency near the resonance frequency. Characteristic linewidth drop and transmission amplitude enhancement are demonstrated. The phase resolve…
We theoretically study a one dimensional p-wave superconducting mesoscopic ring interrupted by a weak link and coupled inductively to a microwave cavity. We establish an input-output description for the cavity field in the presence of the ring, and identify the electronic contributions to the cavity response and their dependence on various parameters, such as the magnetic flux, chemical potential, and cavity frequency. We show that the cavity response is $4π$ periodic as a function of the magnetic flux in the topological region, stemming from the so called fractional Josephson current carried …
An extended Josephson junction intrinsically couples the superconducting current to the microwave cavity in the insulating barrier. We demonstrate that this coupling produces sidebands in the microwave cavity resonances of the junction. By measuring the switching current distribution, we show that microwave radiation at sidebands brings the Josephson phase out of equilibrium. In particular, the effective phase temperature is reduced or enhanced through anti-Stokes and Stokes scattering, respectively. Phase cooling and heating both increase with microwave power.
We present a cavity piezo-optomechanical system where microwave and optical degrees of freedom are coupled through an ultra-high frequency mechanical resonator. By utilizing the coherence among the three interacting modes, we demonstrate optical amplification, coherent absorption and a more general asymmetric Fano resonance. The strong piezoelectric drive further allows access to the large-amplitude-induced optomechanical nonlinearity, with which optical transparency at higher harmonics through multi-phonon scattering is demonstrated.
We study a parametrically-driven nanomechanical resonator capacitively coupled to a microwave cavity. If the nanoresonator can be cooled to near its quantum ground state then quantum squeezing of a quadrature of the nanoresonator motion becomes feasible. We consider the adiabatic limit in which the cavity mode is slaved to the nanoresonator mode. By driving the cavity on its red-detuned sideband, the squeezing can be coupled into the microwave field at the cavity resonance. The red-detuned sideband drive is also compatible with the goal of ground state cooling. Squeezing of the output microwav…
The ability to achieve strong-coupling has made cavity-magnon systems an exciting platform for the development of hybrid quantum systems and the investigation of fundamental problems in physics. Unfortunately, current experimental realizations are constrained to operate at a single frequency, defined by the geometry of the microwave cavity. In this article we realize a highly-tunable, cryogenic, microwave cavity strongly coupled to magnetic spins. The cavity can be tuned in situ by up to 1.5 GHz, approximately 15% of its original 10 GHz resonance frequency. Moreover, this system remains within…
We introduce the concept of Berry's phase in Josephson junctions and consider how this geometric phase arises due to applied oscillating electric fields. The electromagnetic field excites topological quasi-particles from the junction vacuum which affect Cooper-pair tunneling across the Josephson junction barrier. A finite Berry's phase can be detected by its renormalization of the electric field amplitude absorbed by the junction. This has implications for the designing of accurate Josephson junction microwave detectors.
Cavity optomagnonics has emerged as a promising platform for studying coherent photon-spin interactions as well as tunable microwave-to-optical conversion. However, current implementation of cavity optomagnonics in ferrimagnetic crystals remains orders of magnitude larger in volume than state-of-the-art cavity optomechanical devices, resulting in very limited magneto-optical interaction strength. Here, we demonstrate a cavity optomagnonic device based on integrated waveguides and its application for microwave-to-optical conversion. By designing a ferrimagnetic rib waveguide to support multiple…
We investigate theoretically the properties of the photon state and the electronic transport in a system consisting of a metallic quantum dot strongly coupled to a superconducting microwave transmission line cavity. Within the framework of circuit quantum electrodynamics we derive a Hamiltonian for arbitrary strong capacitive coupling between the dot and the cavity. The dynamics of the system is described by a quantum master equation, accounting for the electronic transport as well as the coherent, non-equilibrium properties of the photon state. The photon state is investigated, focusing on, f…
An ensemble of N identical noninteracting spins being in thermal equilibrium and coupled to the resonant mode of a lossless microwave cavity is studied at arbitrary temperature T. Near T = 0 the system is known to be in a coupled spin-photon state that manifests itself by the splitting of the cavity mode (vacuum Rabi splitting). The cavity emission spectrum is simulated for arbitrary T. It is shown that the spin-photon coherence can be partially preserved for T < w sqrt{N}/2, where w is the spin excitation energy, even in case when the spins are randomly directed. The calculations corroborate …
We have developed a novel architecture for room temperature microwave cavity optomechanics, which is based on the coupling of a 3D microwave reentrant cavity to a compliant membrane. Devices parameters have enabled resolving the thermomechanical motion of the membrane, and observing optomechanically induced transparency/absorption in the linear regime, for the first time in a microwave optomechanical system operated at room temperature. We have extracted the single photon coupling rate (g0) using four independent measurement techniques, and hence obtain a full characterization of the proposed …
Quantum confinement leads to the formation of discrete electronic states in quantum dots. Here we probe electron-phonon interactions in a suspended InAs nanowire double quantum dot (DQD) that is electric-dipole coupled to a microwave cavity. We apply a finite bias across the wire to drive a steady state population in the DQD excited state, enabling a direct measurement of the electron-phonon coupling strength at the DQD transition energy. The amplitude and phase response of the cavity field exhibit features that are periodic in the DQD energy level detuning due to the phonon modes of the nanow…
We have observed the dynamical bistability of a microwave superconducting Fabry-Perot cavity incorporating a non-linear element in the form of Josephson tunnel junction. The effect, which is the analog of optical bistability, manifests itself in the transmission and reflection characteristics of the cavity and is governed by a competition between the wave amplitude dependence of the resonant frequency and the finite residence time of the field energy inside the cavity. This finite residence time is solely due to extraction of radiation from the cavity by the measurement process. The tight quan…
Recent experimental progress in coupling nanoscale conductors to superconducting microwave cavities has opened up for transport investigations of the deep quantum limit of light-matter interactions, with tunneling electrons strongly coupled to individual cavity photons. We have investigated theoretically the most basic cavity-conductor system with strong, single photon induced non-local transport effects; two spatially separated double quantum dots (DQD:s) resonantly coupled to the fundamental cavity mode. The system, described by a generalized Tavis-Cummings model, is investigated within a qu…
We propose and analyze the use of hybrid microwave cavities as quantum heat engines. A possible realization consists of two macroscopically separated quantum dot conductors coupled capacitively to the fundamental mode of a microwave cavity. We demonstrate that an electrical current can be induced in one conductor through cavity-mediated processes by heating up the other conductor. The heat engine can reach Carnot efficiency with optimal conversion of heat to work. When the system delivers the maximum power, the efficiency can be a large fraction of the Carnot efficiency. The heat engine functi…
We discuss various microscopic mechanisms for level attraction in a hybridized magnon-photon system of a ferromagnet in a microwave cavity. The discussion is based upon the electromagnetic theory of continuous media where the effects of the internal magnetization dynamics of the ferromagnet are described using dynamical response functions. This approach is in agreement with quantized multi-oscillator models of coupled photon-magnon dynamics. We demonstrate that to provide the attractive interaction between the modes, the effective response functions should be diamagnetic. Magneto-optical coupl…
The combination of low mass density, high frequency, and high quality-factor of mechanical resonators made of two-dimensional crystals such as graphene make them attractive for applications in force sensing/mass sensing, and exploring the quantum regime of mechanical motion. Microwave optomechanics with superconducting cavities offers exquisite position sensitivity and enables the preparation and detection of mechanical systems in the quantum ground state. Here, we demonstrate coupling between a multilayer graphene resonator with quality factors up to 220,000 and a high-$\textit{Q}$ supercondu…
We demonstrate how heating of an environment can invert the line shape of a driven cavity. We consider a superconducting coplanar cavity coupled to multiple artificial atoms. The measured cavity transmission is characterized by Fano-type resonances with a shape that is continuously tunable by bias current through nearby (magnetic flux) control lines. In particular, the same dispersive shift of the microwave cavity can be observed as a peak or a dip. We find that this Fano-peak inversion is possible due to a tunable interference between a microwave transmission through a background, with reacti…
Distinguishing Majorana bound states from accidental zero-energy modes with a microwave cavity
International Research Centre MagTop, Institute of Physics, Polish Academy of Sciences（波兰科学院物理研究所马格托国际研究中心）；CPHT, CNRS, École polytechnique, Institut Polytechnique de Paris（巴黎理工学院综合理工学院中心）；Department of Physics, University of Basel（巴塞尔大学物理系）
We investigate spin states of few electrons in a double quantum dot by coupling them weakly to a magnetic field resilient NbTiN microwave resonator. We observe a reduced resonator transmission if resonator photons and spin singlet states interact. This response vanishes in a magnetic field once the quantum dot ground state changes from a spin singlet into a spin triplet state. Based on this observation, we map the two-electron singlet-triplet crossover by resonant spectroscopy. By measuring the resonator only, we observe Pauli spin blockade known from transport experiments at finite source-dra…
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-particle motion. We present a complete description of this phenomenon based on classi…
We demonstrate a hybrid architecture consisting of a quantum dot circuit coupled to a single mode of the electromagnetic field. We use single wall carbon nanotube based circuits inserted in superconducting microwave cavities. By probing the nanotube-dot using a dispersive read-out in the Coulomb blockade and the Kondo regime, we determine an electron-photon coupling strength which should enable circuit QED experiments with more complex quantum dot circuits.
The development of microwave photon detectors is paving the way for a wide range of quantum technologies and fundamental discoveries involving single photons. Here, we investigate the photon emission from a microwave cavity and find that distribution of photon waiting times contains information about few-photon processes, which cannot easily be extracted from standard correlation measurements. The factorial cumulants of the photon counting statistics are positive at all times, which may be intimately linked with the bosonic quantum nature of the photons. We obtain a simple expression for the r…
High-gain and low-noise signal amplification is a valuable tool in various cryogenic microwave experiments. A microwave optomechanical device, in which a vibrating capacitor modulates the frequency of a microwave cavity, is one technique that is able to amplify microwave signals with high gain and large dynamical range. Such optomechanical amplifiers typically rely on strong backaction of microwave photons on the mechanical mode achieved in the sideband-resolved limit of optomechanics. Here, we observe microwave amplification in an optomechanical cavity in the extremely unresolved sideband lim…
We report the observation of strong coupling of a macroscopic ensemble of ~10^{16} Fe_8 molecular nanomagnets to the resonant mode of a microwave cavity. We use millimeter-wave spectroscopy to measure the splitting of the system's resonant frequency induced by the coupling between the spins and the cavity mode. The magnitude of this splitting is found to scale with Sqrt[N], where N is the number of collectively coupled spins. We control N by changing the system's temperature and, thereby, the populations of the relevant spin energy levels. Strong coupling is observed for two distinct transitio…
This work discusses theoretically the behavior of a microwave cavity and a Cooper pair beam splitter (CPS) coupled non-resonantly. The cavity frequency pull is modified when the CPS is resonant with a microwave excitation. This provides a direct way to probe the coherence of the Cooper pair splitting process. More precisely, the cavity frequency pull displays an anticrossing whose specificities can be attributed unambiguously to coherent Cooper pair injection. This work illustrates that microwave cavities represent a powerful tool to investigate current transport in complex nanocircuits.
Microwave optomechanical circuits have been demonstrated in the past years to be extremely powerfool tools for both, exploring fundamental physics of macroscopic mechanical oscillators as well as being promising candidates for novel on-chip quantum limited microwave devices. In most experiments so far, the mechanical oscillator is either used as a passive device element and its displacement is detected using the superconducting cavity or manipulated by intracavity fields. Here, we explore the possibility to directly and parametrically manipulate the mechanical nanobeam resonator of a cavity el…
We demonstrate the dispersive measurement of ferromagnetic resonance in a yttrium iron garnet sphere embedded within a microwave cavity. The reduction in the longitudinal magnetization at resonance is measured as a frequency shift in the cavity mode coupled to the sphere. This measurement is a result of the intrinsic non-linearity in magnetization dynamics, indicating a promising route towards experiments in magnon cavity quantum electro-dynamics.
The geometric or Berry phase, a characteristic of quasiparticles, is fundamental to the underlying quantum materials. The discoveries of new materials at a rapid pace nowadays call for efficient detection of the Berry phase. Utilizing $α$-T$_3$ lattice as a paradigm, we find that, in the Dirac electron optics regime, the semiclassical decay of the quasiparticles from a chaotic cavity can be effectively exploited for detecting the Berry phase. In particular, we demonstrate a one-to-one correspondence between the exponential decay rate and the geometric phase for the entire family of $α$-T$_3$ m…
We present a scalable architecture for the exploration of interacting topological phases of photons in arrays of microwave cavities, using established techniques from cavity and circuit quantum electrodynamics. A time-reversal symmetry breaking (non-reciprocal) flux is induced by coupling the microwave cavities to ferrites, allowing for the production of a variety of topological band structures including the $α=1/4$ Hofstadter model. Effective photon-photon interactions are included by coupling the cavities to superconducting qubits, and are sufficient to produce a $ν=1/2$ bosonic Laughlin pud…
We report observation of the nonlinear Meissner effect (NLME) in Nb films by measuring the resonance frequency of a planar superconducting cavity as a function of the magnitude and the orientation of a parallel magnetic field. Use of low power rf probing in films thinner than the London penetration depth, significantly increases the field for the vortex penetration onset and enables NLME detection under true equilibrium conditions. The data agree very well with calculations based on the Usadel equations. We propose to use NLME angular spectroscopy to probe unconventional pairing symmetries in …
We discuss the problem of magnetic-dipolar oscillations combined with microwave resonators. The energy density of magnetic-dipolar or magnetostatic (MS) oscillations in ferrite resonators is not the electromagnetic-wave density of the energy and not the exchange energy density as well. This fact reveals very special behaviors of the geometrical effects. Compared to other geometries, thin-film ferrite disk resonators exhibit very unique interactions of MS oscillations with the cavity electromagnetic fields. MS modes in a flat ferrite disk are characterized by a complete discrete spectrum of ene…
We report strong coupling between an ensemble of N impurity (P1) centres in diamond and microwave photons using a unique double post re-entrant cavity. The cavity is designed so that the magnetic component of the cavity field is spatially separated from the electric component and focused into the small volume in which the diamond sample is mounted. The novelty of the structure simultaneously allows high magnetic filling factor (38.4\%) and low frequencies necessary to interact, at low magnetic field, with transitions in diamond such as those in NV$^{-}$ and P1 centres. Coupling strength (or no…
Nonlinear phenomena in superconducting resonator circuits are of great significance in the field of quantum technology. We observe thermal self-oscillations in a monolayer graphene flake coupled to Molybdenum-Rhenium superconducting resonator. The graphene flake forms a SINIS junction coupled to the resonator with strong temperature dependent resistance. In certain conditions of pump power and frequency, this nonlinearity leads to thermal self-oscillations appearing as sidebands in cavity transmission measurements with strong temperature dependence and gate tunability. The experimental observa…
We assess experimentally the suitability of coupled transmission line resonators for studies of quantum phase transitions of light. We have measured devices with low photon hopping rates t/2pi = 0.8MHz to quantify disorder in individual cavity frequencies. The observed disorder is consistent with small imperfections in fabrication. We studied the dependence of the disorder on transmission line geometry and used our results to fabricate devices with disorder less than two parts in 10^4. The normal mode spectrum of devices with a high photon hopping rate t/2pi = 31MHz shows little effect of diso…
Electrically actuated optomechanical resonators provide a route to quantum-coherent, bidirectional conversion of microwave and optical photons. Such devices could enable optical interconnection of quantum computers based on qubits operating at microwave frequencies. Here we present a novel platform for microwave-to-optical conversion comprising a photonic crystal cavity made of single-crystal, piezoelectric gallium phosphide integrated on pre-fabricated niobium circuits on an intrinsic silicon substrate. The devices exploit spatially extended, sideband-resolved mechanical breathing modes at $\…
We experimentally study an optomechanical cavity consisting of an oscillating mechanical resonator embedded in a superconducting microwave transmission line cavity. Tunable optomechanical coupling between the mechanical resonator and the microwave cavity is introduced by positioning a niobium-coated single mode optical fiber above the mechanical resonator. The capacitance between the mechanical resonator and the coated fiber gives rise to optomechanical coupling, which can be controlled by varying the fiber-resonator distance. We study radiation pressure induced self-excited oscillations as a …
We carry out a quantum analysis of a dc SQUID mechanical displacement detector, comprising a SQUID with mechanically compliant loop segment, which is embedded in a microwave transmission line resonator. The SQUID is approximated as a nonlinear, current dependent inductance, inducing an external flux tunable, nonlinear Duffing self-interaction term in the microwave resonator mode equation. Motion of the compliant SQUID loop segment is transduced inductively through changes in the external flux threading SQUID loop, giving a ponderomotive, radiation pressure type coupling between the microwave a…
