We examine quantum statistics of optical photons emitted from atomic ensembles which are classically driven and simultaneously coupled to a two-level atom via microwave photon exchange. Quantum statistics and correlations are analyzed by calculating second order coherence degree, von Neumann entropy, spin squeezing for multi-particle entanglement, as well as genuine two and three-mode entanglement parameters for steady state and non-equilibrium situations. Coherent transfer of population between the radiation modes and quantum state mapping between the two-level atom and the optical modes are discussed. A potential experimental realization of the theoretical results in a superconducting coplanar waveguide resonator containing diamond crystals with Nitrogen-Vacancy color centers and a superconducting artificial two-level atom is discussed.
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…
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 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…
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 …
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 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 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 …
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…
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…
We theoretically propose a biphoton entanglement-enhanced multidimensional spectroscopic technique as a probe for the dissipative polariton dynamics in the ultrafast regime. It is applied to the cavity-confined monomeric photosynthetic complex that represents a prototypical multi-site excitonic quantum aggregate. The proposed technique is shown to be particularly sensitive to inter-manifold polariton coherence between the two and one-excitation subspaces. It is demonstrated to be able to monitor the dynamical role of cavity-mediated excitonic correlations, and dephasing in the presence of phon…
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 propose a scheme able to generate stationary continuous variable entanglement between an optical and a microwave cavity mode by means of their common interaction with a micro-mechanical resonator. We show that when both cavities are intensely driven one can generate bipartite entanglement between any pair of the tripartite system, and that, due to entanglement sharing, optical-microwave entanglement is efficiently generated at the expense of microwave-mechanical and opto-mechanical entanglement.
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 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…
We consider the problem of quantum decoherence in cavity QED devices and investigate the possibility to preserve a Schroedinger cat as a coherent superposition along the time.
Quantum coherence and non-Markovianity of an atom in dissipative cavity under weak measurement are investigated in this work. We find that, the quantum coherence obviously depends on the atomic initial state, the strength of the weak measurement and its reversal, the atom-cavity coupling constant and the non-Markovian effecct. The more obvious the weak measurement effect is, the better the protection of coherence is. The quantum coherence is preserved more efficiently for lager the atom-cavity coupling. The stronger the non-Markovian effect, the more slowly the coherence reduces. This is, the …
The low energy losses in the superconducting magnetic levitation make it attractive for exciting applications in physics. Recently, superconducting magnetic levitation has been realized as novel mechanical transduction for the individual spin qubit in the nitrogen-vacancy center [1]. Furthermore, the Meissner has been proposed for the study of modified gravitational wave detection [2]. Meissner levitation within the microwave cavity could open avenues for the novel cavity optomechanical system, readout for quantum object such as the transmon, and magnon, gravitational wave detection, and magne…
We propose a method to create superpositions of two macroscopic quantum states of a single-mode microwave cavity field interacting with a superconducting charge qubit. The decoherence of such superpositions can be determined by measuring either the Wigner function of the cavity field or the charge qubit states. Then the quality factor Q of the cavity can be inferred from the decoherence of the superposed states. The proposed method is experimentally realizable within current technology even when the $Q$ value is relatively low, and the interaction between the qubit and the cavity field is weak…
We propose a new scheme to realize holonomic quantum computation with rf-SQUID qubits in a microwave cavity. In this scheme associated with the non-Abelian holonomies, the single-qubit gates and a two-qubit control-Phase gate as well as a control-NOT gate can be easily constructed by tuning adiabatically the Rabi frequencies of classical microwave pulses coupled to the SQUIDs. The fidelity of these gates is estimated to be possibly higher than 90 % with the current technology.
We propose an implementation of a universal quantum gate between pairs of spatially separated atoms in a microwave cavity at finite temperature. The gate results from reversible laser excitation of Rydberg states of atoms interacting with each other via exchange of virtual photons through a common cavity mode. Quantum interference of different transition paths between the two-atom ground and double-excited Rydberg states makes both the transition amplitude and resonance largely insensitive to the excitations in the microwave cavity "quantum bus" which can therefore be in any superposition or m…
We theoretically study the transmission of a weak probe field under the influence of a strong pump field in a coupled nanomechanical resonator-superconducting microwave cavity system. Using the standard input-output theory, we find that both pulse delay (slow light effect) and advancement (fast light effect) of the probe field can appear in this coupled system provided that we choose the suitable detuning of the pump field from cavity resonance. The magnitude of the delay (advancement) can be tuned continuously by adjusting the power of the pump field. This technique demonstrates great potenti…
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…
The rigorous resource framework of quantum coherence has been set up recently and excited a wide variety of interests. Here we show that a quantum cavity optomechanical system, as an emerging platform, can behave with a certain value of quantum coherence at a macroscopic scale. We also find that the difference between the total optomechanical coherence and the sum of the optical and the mechanical coherence just equals their mutual information. Motivated by the detection of the optomechanical entanglement, an experimentally feasible scheme to probe the optomechanical coherence is proposed.
Quantum illumination (QI) is a quantum sensing protocol mainly for target detection which uses entangled signal-idler photon pairs to enhance the detection efficiency of low-reflectivity objects immersed in thermal noisy environments. Especially, due to the naturally occurring background radiation, the photon emitted toward potential targets more appropriately lies in the microwave region. Here, we propose a hybrid quantum source based on cavity magnonics for microwave QI, where the medium that bridges the optical and the microwave modes is magnon, the quanta of spin wave. Within experimentall…
We propose a scheme that can generate tunable magnomechanically induced amplification in a double-cavity parity-time-(PT -) symmetric-like magnomechanical system under a strong control and weak probe field. The system consists of a ferromagnetic-material yttrium iron garnet (YIG) sphere placed in a passive microwave cavity which is connected with another active cavity. We reveal that ideally induced amplification of the microwave probe signal may reach the maximum value 1000000 when cavity-cavity, cavity-magnon and magnomechanical coupling strengths are nonzero simultaneously. The phenomenon m…
Coherence has been remaining a key resource for numerous applications of quantum physics ranging from quantum metrology to quantum information. Here, we report a theoretical work on how maximally created coherence results in the squeezing of cavity field coupled to a coherently driven single quantum dot. We employ a recently developed polaron master equation theory for accurately incorporating the impact of exciton-phonon coupling on squeezing.
We theoretically and experimentally demonstrate coherence phenomena in optical parametric amplification inside a cavity. The mode splitting in transmission spectra of phase-sensitive optical parametric amplifier is observed. Especially, we show a very narrow dip and peak, which are the shape of $δ$ function, appear in the transmission profile. The origin of the coherence phenomenon in this system is the interference between the harmonic pump field and the subharmonic seed field in cooperation with dissipation of the cavity.
We study the entanglement of the superconducting charge qubit with the quantized electromagnetic field in a microwave cavity. It can be controlled dynamically by a classical external field threading the SQUID within the charge qubit. Utilizing the controllable quantum entanglement, we can demonstrate the dynamic process of the quantum storage of information carried by charge qubit. On the other hand, based on this engineered quantum entanglement, we can also demonstrate a progressive decoherence of charge qubit with quantum jump due to the coupling with the cavity field in quasi-classical stat…
Atomic vapors offer many opportunities for manipulating electromagnetic signals across a broad range of the electromagnetic spectrum. Here, a microwave signal with an audio-frequency modulation encodes information in an optical signal by exploiting an atomic microwave-to-optical double resonance, and magnetic-field coupling that is amplified by a resonant high-Q microwave cavity. Using this approach, audio signals are encoded as amplitude or frequency modulations in a GHz carrier, transmitted through a cable or over free space, demodulated through cavity-enhanced atom-microwave interactions, a…
We have created a quantum three-level ladder system with the cavity dispersive energy level in a superconducting circuit quantum electrodynamics system consisting of a transmon qubit and a cavity, and have directly observed the Autler-Townes splitting effect instead of representing it by the probability of the qubit being at each level. A coupler tone is applied on the transition between the second excited state of transmon and cavity dispersive level, while the cavity spectrum is probed. A doublet transmission and anormalous dispersion spectrum of the cavity level is clearly shown. The invers…
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…
We propose a scheme for entangling the optical and microwave output modes of the respective cavities by using a micro mechanical resonator. The micro-mechanical resonator on one side is capacitively coupled to the microwave cavity and on the other side is coupled to a high finesses optical cavity. We then show how this continuous variable entanglement can be profitably used to teleport the non-Gaussian number state |1> and the superposition (|0>+|1>)/\surd2 from the microwave cavity output mode onto an output of optical cavity mode with fidelity much larger than the no-cloning limit.
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 construct a model for the detection of one atom maser in the context of cavity Quantum Electrodynamics (QED) used to study coherence properties of superpositions of electromagnetic modes. Analytic expressions for the atomic ionization are obtained, considering the imperfections of the measurement process due to the probabilistic nature of the interactions between the ionization field and the atoms. Limited efficiency and false counting rates are considered in a dynamical context, and consequent results on the information about the state of the cavity modes are obtained.
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…
We analyze cavity-assisted cooling schemes for polar molecules in the microwave domain, where molecules are excited on a rotational transition and energy is dissipated via strong interactions with a lossy stripline cavity, as recently proposed by A. Andre et al., Nature Physics 2, 636 (2006). We identify the dominant cooling and heating mechanisms in this setup and study cooling rates and final temperatures in various parameter regimes. In particular we analyze the effects of a finite environment temperature on the cooling efficiency, and find minimal temperature and optimized cooling rate in …
An electro-optomechanical device capable of microwave-to-optics conversion has recently been demonstrated, with the vision of enabling optical networks of superconducting qubits. Here we present an improved converter design that uses a three-dimensional (3D) microwave cavity for coupling between the microwave transmission line and an integrated LC resonator on the converter chip. The new design simplifies the optical assembly and decouples it from the microwave part of the setup. Experimental demonstrations show that the modular device assembly allows us to flexibly tune the microwave coupling…
The strong coupling regime is observed in a system of two-dimensional electrons whose cyclotron motion is coupled to an electro-magnetic mode in a Fabry-Perot cavity resonator. The Rabi splitting of eigenfrequencies of coupled motion is observed both in the cavity reflection spectrum and ac current of electrons, the latter probed by measuring their bolometric photoresponse. Despite the fact that similar observations of the Rabi splitting in many-particle systems have been described as a quantum-mechanical effect, we show that the observed splitting can be explained completely by a model based …
We evaluate the distributed cavity phase and microwave lensing frequency shifts, which were the two largest sources of uncertainty for the NPL-CsF2 cesium fountain clock. We report measurements that confirm a detailed theoretical model of the microwave cavity fields and the frequency shifts of the clock that they produce. The model and measurements significantly reduce the distributed cavity phase uncertainty to $1.1 \times 10^{-16}$. We derive the microwave lensing frequency shift for a cylindrical cavity with circular apertures. An analytic result with reasonable approximations is given, in …
Raman heterodyne spectroscopy is a powerful tool for characterizing the energy and dynamics of spins. The technique uses an optical pump to transfer coherence from a spin transition to an optical transition where the coherent emission is more easily detected. Here Raman heterodyne spectroscopy is used to probe an isotopically purified ensemble of erbium dopants, in a yttrium orthosilicate (Y$_2$SiO$_5$) crystal coupled to a microwave cavity. Because the erbium electron spin transition is strongly coupled to the microwave cavity, we observed Raman heterodyne signals at the resonant frequencies …
We propose a scheme that is able to generate the microwave controlled optical double optome-chanical induced transparency (OMIT) in a hybrid piezo-optomechanical cavity system, which a piezoelectric optomechanical crystal AlN-nanobeam resonator is placed in a superconducting microwave cavity, and the AlN-nanobeam resonator can be simultaneously driven by both the optical field via the radiation pressure and the microwave field via the piezoelectric interaction. We show that in the presence of a strong pumped optical field applied to the optomechanical crystal cavity through the optical wavegui…
Recent experiments on Josephson junction arrays (JJAs) in microwave cavities have opened up a new avenue for investigating the properties of these devices while minimising the amount of external noise coming from the measurement apparatus itself. These experiments have already shown promise for probing many-body quantum effects in JJAs. In this work, we develop a general theoretical description of such experiments by deriving a quantum phase model for planar JJAs containing quantized vortices. The dynamical susceptibility of this model is calculated for some simple circuits, and signatures of …
In this work, we investigate quantum Fisher information(QFI) and quantum coherence(QC) of an atom in dissipative cavity. In zero temperature reservior and with one excitation number, we obtain the analytical solutions of QFI and QC as well as their relationship for Ohmic and Lorentzian reservoir, respectively. The results show that both of the atom-cavity coupling and the cavity-reservoir coupling can effectively protect QFI and QC. Especially, QFI and QC will tend to their stable values when the atom-cavity coupling or the cavity-reservoir coupling is larger than a certain value. QC can augme…
The role of spontaneous emission in the interaction between a two-level atom and a pumped micro-cavity in the strong coupling regime is discussed in this paper. Especially, using a quantum Monte-Carlo simulation, we investigate atomic spatial coherence. It is found that atomic spontaneous emission destroys the coherence between neighboring lattice sites, while the cavity decay does not. Furthermore, our computation of the spatial coherence function shows that the in-site locality is little affected by the cavity decay, but greatly depends on the cavity pump amplitude.
Multiple-post reentrant 3D lumped cavity modes have been realized to design the concept of discrete Whispering Gallery and Fabry-Perot-like Modes for multimode microwave Quantum Electrodynamics experiments. Using a magnon spin-wave resonance of a submillimeter-sized Yttrium-Iron-Garnet sphere at milliKelvin temperatures and a four-post cavity, we demonstrate the ultra-strong coupling regime between discrete Whispering Gallery Modes and a magnon resonance with strength of 1.84 GHz. By increasing the number of posts to eight and arranging them in a D$_4$ symmetry pattern, we expand the mode stru…
We study the dynamical Casimir effect in the presence of a finite coherence time, which is associated with a finite quality factor of the optical cavity. We use the time refraction model, where a fixed cavity with a modulated optical medium, replaces the empty cavity with a vibrating mirror. Temporal coherence is described with the help of cavity quasi-mode operators. Asymptotic expressions for the number of photon pairs generated from vacuum are derived.
