Single-photon detectors are an essential part of the toolbox of modern quantum optics for implementing quantum technologies and enabling tests of fundamental physics. The low energy of microwave photons, the natural signal path for superconducting quantum devices, makes their detection much harder than for visible light. Despite impressive progress in recent years and the proposal and realization of a number of different detector architectures, the reliable detection of a single itinerant microwave photon remains an open topic.
Here, we investigate and simulate a detailed protocol for single-photon multiplication and subsequent amplification and detection. At its heart lies a Josephson-photonics device which uses inelastic Cooper-pair tunneling driven by a dc bias in combination with the energy of an incoming photon to create multiple photons, thus compensating for the low-energy problem. Our analysis provides clear design guidelines for utilizing such devices, which have previously been operated in an amplifier mode with a continuous wave input, for counting photons. Combining a formalism recently developed by Mølmer to describe the full quantum state of in- and outgoing photon pulses with stochastic Schrödinger equations, we can describe the full multiplication and detection protocol and calculate performance parameters, such as detection probabilities and dark count rates. With optimized parameters, a high population of a single output mode can be achieved that can then be easily distinguished from vacuum noise in heterodyne measurements of quadratures with a conventional linear amplifier. Realistic devices with two multiplication stages with multiplication of $16$ reach for an impinging Gaussian pulse of length $T$ a detection probability of $84.5\%$ with a dark count rate of $10^{-3}/T$, and promise to outperform competing schemes.
A wide range of experiments studying microwave photons localized in superconducting cavities have made important contributions to our understanding of the quantum properties of radiation. Propagating microwave photons, however, have so far been studied much less intensely. Here we present measurements in which we reconstruct the Wigner function of itinerant single photon Fock states and their superposition with the vacuum using linear amplifiers and quadrature amplitude detectors. We have developed efficient methods to separate the detected single photon signal from the noise added by the ampl…
Continuous variable entanglement between two modes of a radiation field is usually studied at optical frequencies. As an important step towards the observation of entanglement between propagating microwave photons we demonstrate the experimental state reconstruction of two field modes in the microwave domain. In particular, we generate two-mode correlated states with a Josephson parametric amplifier and detect all four quadrature components simultaneously in a two-channel heterodyne setup using amplitude detectors. Analyzing two-dimensional phase space histograms for all possible pairs of quad…
A localized qubit entangled with a propagating quantum field is well suited to study non-local aspects of quantum mechanics and may also provide a channel to communicate between spatially separated nodes in a quantum network. Here, we report the on demand generation and characterization of Bell-type entangled states between a superconducting qubit and propagating microwave fields composed of zero, one and two-photon Fock states. Using low noise linear amplification and efficient data acquisition we extract all relevant correlations between the qubit and the photon states and demonstrate entang…
Single-photon detection is an essential component in many experiments in quantum optics, but remains challenging in the microwave domain. We realize a quantum non-demolition detector for propagating microwave photons and characterize its performance using a single-photon source. To this aim we implement a cavity-assisted conditional phase gate between the incoming photon and a superconducting artificial atom. By reading out the state of this atom in single shot, we reach an internal photon detection fidelity of 71%, limited by the coherence properties of the qubit. By characterizing the cohere…
Single photon detection is a key resource for sensing at the quantum limit and the enabling technology for measurement based quantum computing. Photon detection at optical frequencies relies on irreversible photo-assisted ionization of various natural materials. However, microwave photons have energies 5 orders of magnitude lower than optical photons, and are therefore ineffective at triggering measurable phenomena at macroscopic scales. Here, we report the observation of a new type of interaction between a single two level system (qubit) and a microwave resonator. These two quantum systems do…
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…
Directional transmission or amplification of microwave signals is indispensable in various applications involving sensitive measurements. In this work we show in experiment how to use a generic cavity optomechanical setup to non-reciprocally amplify microwave signals above 3 GHz in one direction by 9 decibels, and simultaneously attenuate the transmission in the opposite direction by 21 decibels. We use a device including two on-chip superconducting resonators and two metallic drumhead mechanical oscillators. Application of four microwave pump tone frequencies allows for designing constructive…
Sensitive measurement of electrical signals is at the heart of modern science and technology. According to quantum mechanics, any detector or amplifier is required to add a certain amount of noise to the signal, equaling at best the energy of quantum fluctuations. The quantum limit of added noise has nearly been reached with superconducting devices which take advantage of nonlinearities in Josephson junctions. Here, we introduce a new paradigm of amplification of microwave signals with the help of a mechanical oscillator. By relying on the radiation pressure force on a nanomechanical resonator…
High-gain amplifiers of electromagnetic signals operating near the quantum limit are crucial for quantum information systems and ultrasensitive quantum measurements. However, the existing techniques have a limited gain-bandwidth product and only operate with weak input signals. Here we demonstrate a two-port optomechanical scheme for amplification and routing of microwave signals, a system that simultaneously performs high-gain amplification and frequency conversion in the quantum regime. Our amplifier, implemented in a two-cavity microwave optomechanical device, shows 41 dB of gain and has a …
The low-noise amplification of weak microwave signals is crucial for countless protocols in quantum information processing. Quantum mechanics sets an ultimate lower limit of half a photon to the added input noise for phase-preserving amplification of narrowband signals, also known as the standard quantum limit (SQL). This limit, which is equivalent to a maximum quantum efficiency of $0.5$, can be overcome by employing nondegenerate parametric amplification of broadband signals. We show that, in principle, a maximum quantum efficiency of 1 can be reached. Experimentally, we find a quantum effic…
Nature sets fundamental limits regarding how accurate the amplification of analog signals may be. For instance, a linear amplifier unavoidably adds some noise which amounts to half a photon at best. While for most applications much higher noise levels are acceptable, the readout of microwave quantum systems, such as spin or superconducting qubits, requires noise as close as possible to this ultimate limit. To date, it is approached only by parametric amplifiers exploiting non-linearities in superconducting circuits and driven by a strong microwave pump tone. However, this microwave drive makes…
The interaction between propagating microwave fields and Cooper-pair tunneling across a DC voltage-biased Josephson junction can be highly nonlinear. We show theoretically that this nonlinearity can be used to convert an incoming single microwave photon into an outgoing $n$-photon Fock state in a different mode. In this process, the electrostatic energy released in a Cooper-pair tunneling event is transferred to the outgoing Fock state, providing energy gain. The created multi-photon Fock state is frequency entangled and highly bunched. The conversion can be made reflectionless (impedance-matc…
A process which strongly amplifies both quadrature amplitudes of an oscillatory signal necessarily adds noise. Alternatively, if the information in one quadrature is lost in phase-sensitive amplification, it is possible to completely reconstruct the other quadrature. Here we demonstrate such a nearly perfect phase-sensitive measurement using a cavity optomechanical scheme, characterized by an extremely small noise less than 0.2 quanta. We also observe microwave radiation strongly squeezed by 8 dB below vacuum. A source of bright squeezed microwaves opens up applications in manipulations of qua…
We report the parametric amplification of a microwave signal in a Kerr medium formed from superconducting qubits. Two mutually coupled flux qubits, embedded in the current antinode of a superconducting coplanar waveguide resonator, are used as a nonlinear element. Shared Josephson junctions provide the qubit-resonator coupling, resulting in a device with a measured gain of about 20 dB. We argue, that this arrangement represents a unit cell which can be straightforwardly extended to a quasi one-dimensional quantum metamaterial with a large tunable Kerr nonlinearity.
Surface acoustic waves are commonly used in classical electronics applications, and their use in quantum systems is beginning to be explored, as evidenced by recent experiments using acoustic Fabry-Pérot resonators. Here we explore their use for quantum communication, where we demonstrate a single-phonon surface acoustic wave transmission line, which links two physically-separated qubit nodes. Each node comprises a microwave phonon transducer, an externally-controlled superconducting variable coupler, and a superconducting qubit. Using this system, precisely-shaped individual itinerant phonons…
We propose a method to couple metastable flux-based qubits to superconductive resonators based on a quantum-optical Raman excitation scheme that allows for the deterministic generation of stationary and propagating microwave Fock states and other weak quantum fields. Moreover, we introduce a suitable microwave quantum homodyne technique, with no optical counterpart, that enables the measurement of relevant field observables, even in the presence of noisy amplification devices.
Josephson junctions (JJ) and their tunable properties, including their nonlinearities, form the core of superconducting circuit quantum electrodynamics (cQED). In quantum circuits, low-noise amplification of feeble microwave signals is essential and the Josephson parametric amplifiers (JPA) are the widely used devices. The existing JPAs are based on Al-AlOx-Al tunnel junctions realized in a superconducting quantum interference device geometry, where magnetic flux is the knob for tuning the frequency. Recent experimental realizations of 2D van der Waals JJs provide an opportunity to implement v…
We present the driven response at T=30mK of 6 GHz superconducting resonators constructed from capacitively-shunted three dimensional (3D) aluminum nanobridge superconducting quantum interference devices (nanoSQUIDs). We observe flux modulation of the resonant frequency in quantitative agreement with numerical calculation and characteristic of near-ideal short weak link junctions. Under strong microwave excitation, we observe stable bifurcation in devices with coupled quality factor (Q) ranging from ~30-3500. Near this bias point, parametric amplification with > 20dB gain, 40 MHz bandwidth, and…
An excited emitter decays by radiating a photon into a quantized mode of the electromagnetic field, a process known as spontaneous emission. If the emitter is driven to a higher excited state, it radiates multiple photons in a cascade decay. Atomic and biexciton cascades have been exploited as sources of polarization-entangled photon pairs. Because the photons are emitted sequentially, their intensities are strongly correlated in time, as measured in a double-beam coincidence experiment. Perhaps less intuitively, their phases can also be correlated, provided a single emitter is deterministical…
We describe a new kind of phase-preserving quantum amplifier which utilizes dissipative interactions in a parametrically-coupled three-mode bosonic system. The use of dissipative interactions provides a fundamental advantage over standard cavity-based parametric amplifiers: large photon number gains are possible with quantum-limited added noise, with no limitation on the gain-bandwidth product. We show that the scheme is simple enough to be implemented both in optomechanical systems and in superconducting microwave circuits.
This short and opinionated review starts with a concept of quantum signals at microwave frequencies and focuses on the principle of linear parametric amplification. The amplification process arises from the dispersive nonlinearity of Josephson junctions driven with appropriate tones. We discuss two defining characteristics of these amplifiers: the number of modes receiving the signal, idler and pump waves and the number of independent ports through which these waves enter into the circuit.
Recent progress in the development of superconducting circuits has enabled the realization of interesting sources of nonclassical radiation at microwave frequencies. Here, we discuss field quadrature detection schemes for the experimental characterization of itinerant microwave photon fields and their entanglement correlations with stationary qubits. In particular, we present joint state tomography methods of a radiation field mode and a two-level system. Including the case of finite quantum detection efficiency, we relate measured photon field statistics to generalized quasi-probability distr…
Quantum-limited microwave parametric amplifiers are genuine key pillars for rising quantum technologies and in general for applications that rely on the successful readout of weak microwave signals by adding only the minimum amount of noise allowed by quantum mechanics. In this perspective, after providing a brief overview on the different families of parametric microwave amplifiers, we focus on traveling wave parametric amplifiers (TWPAs), underlining the key achievements of the last years and the present open challenges. We discuss also possible new research directions beyond amplification s…
It has recently become possible to encode the quantum state of superconducting qubits and the position of nanomechanical oscillators into the states of microwave fields. However, to make an ideal measurement of the state of a qubit, or to detect the position of a mechanical oscillator with quantum-limited sensitivity requires an amplifier that adds no noise. If an amplifier adds less than half a quantum of noise, it can also squeeze the quantum noise of the electromagnetic vacuum. Highly squeezed states of the vacuum serve as an important quantum information resource. They can be used to gener…
Cavity optomechanical phenomena, such as cooling, amplification or optomechanically induced transparency, emerge due to a strong imbalance in the dissipation rates of the parametrically coupled electromagnetic and mechanical resonators. Here we analyze the reversed dissipation regime where the mechanical energy relaxation rate exceeds the energy decay rate of the electromagnetic cavity. We demonstrate that this regime allows for mechanically-induced amplification (or cooling) of the electromagnetic mode. Gain, bandwidth, and added noise of this electromagnetic amplifier are derived and compare…
Quantum state reconstruction involves measurement devices that are usually described by idealized models, but not known in full detail in experiments. For weak propagating microwaves, the detection process requires linear amplifiers which obscure the signal with random noise. Here, we introduce a theory which nevertheless allows one to use these devices for measuring all quadrature moments of propagating quantum microwaves based on cross-correlations from a dual-path amplification setup. Simultaneously, the detector noise properties are determined, allowing for tomography. We demonstrate the f…
Various applications of quantum devices call for an accurate calibration of cryogenic amplification chains. To this end, we present a convenient calibration scheme and use it to accurately measure the total gain and noise temperature of an amplification chain by employing normal-metal--insulator--superconductor (NIS) junctions. Our method is based on the radiation emitted by inelastic electron tunneling across voltage-biased NIS junctions. We derive an analytical equation that relates the generated power to the applied bias voltage which is the only control parameter of the device. After the s…
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…
Coherent conversion of microwave and optical photons in the single-quantum level can significantly expand our ability to process signals in various fields. Efficient up-conversion of a feeble signal in the microwave domain to the optical domain will lead to quantum-noise-limited microwave amplifiers. Coherent exchange between optical photons and microwave photons will also be a stepping stone to realize long-distance quantum communication. Here we demonstrate bidirectional and coherent conversion between microwave and light using collective spin excitations in a ferromagnet. The converter cons…
The investigation of the ultimate limits imposed by quantum mechanics on amplification represents an important topic both on a fundamental level and from the perspective of potential applications. We propose here a novel setup for an optomechanical amplifier, constituted by a mechanical resonator dispersively coupled to an optomechanical cavity asymmetrically driven around both mechanical sidebands. We show that, on general grounds, the present amplifier operates in a novel regime-- which we here call phase-mixing amplification. At the same time, for a suitable choice of parameters, the amplif…
Single photon detectors are key for time-correlated photon counting applications [1] and enable a host of emerging optical quantum information technologies [2]. So far, the leading approach for continuous and efficient single-photon detection in the optical domain has been based on semiconductor photodiodes [3]. However, there is a paucity of efficient and continuous single-photon detectors in the microwave regime, because photon energies are four to five orders of magnitude lower therein and conventional photodiodes do not have that sensitivity. Here we tackle this gap and demonstrate how iti…
We discuss a general method for constructing nonreciprocal, cavity-based photonic devices, based on matching a given coherent interaction with its corresponding dissipative counterpart; our method generalizes the basic structure used in the theory of cascaded quantum systems, and can render an extremely wide class of interactions directional. In contrast to standard interference-based schemes, our approach allows directional behavior over a wide bandwidth. We show how it can be used to devise isolators and directional, quantum-limited amplifiers. We discuss in detail how this general method al…
Josephson meta-materials have recently emerged as very promising platform for superconducting quantum science and technologies. Their distinguishing potential resides in ability to engineer them at sub-wavelength scales, which allows complete control over wave dispersion and nonlinear interaction. In this article we report a versatile Josephson transmission line with strong third order nonlinearity which can be tuned from positive to negative values, and suppressed second order non linearity. As an initial implementation of this multipurpose meta-material, we operate it to demonstrate reversed…
Recent progress in solid state quantum information processing has stimulated the search for ultra-low-noise amplifiers and frequency converters in the microwave frequency range, which could attain the ultimate limit imposed by quantum mechanics. In this article, we report the first realization of an intrinsically phase-preserving, non-degenerate superconducting parametric amplifier, a so far missing component. It is based on the Josephson ring modulator, which consists of four junctions in a Wheatstone bridge configuration. The device symmetry greatly enhances the purity of the amplification p…
We explore amplification and cross-Kerr nonlinearity by a three-level emitter (3LE) embedded in a waveguide and driven by two light beams. The coherent amplification and cross-Kerr nonlinearity were demonstrated in recent experiments, respectively, with a V and a ladder-type 3LE coupled to an open superconducting transmission line carrying two microwave fields. Here, we consider $Λ$, V, and ladder-type 3LE, and compare the efficiency of coherent and incoherent amplification as well as the magnitude of the cross-Kerr phase shift in all three emitters. We apply the Heisenberg-Langevin equations …
Motivated by recent experiments on the generation of coherent light in engineered hybrid quantum systems, we investigate gain in a microwave photonic cavity coupled to quantum dot structures, and develop concrete directions for achieving a giant amplification in photon transmission. We propose two architectures for scaling up the electronic gain medium: (i) $N$ double quantum dot systems (N-DQD), (ii) $M$ quantum dots arranged in series akin to a quantum cascade laser setup. In both setups, the fermionic reservoirs are voltage biased, and the quantum dots are coupled to a single-mode cavity. O…
Detection of single, itinerant microwave photons is an important functionality for emerging quantum technology applications as well as of fundamental interest in quantum thermodynamics experiments on heat transport. In a recent experiment [W. Khan et al., Nat. Commun. 12, 5130 (2021)], it was demonstrated that a double quantum dot (DQD) coupled to a microwave resonator can act as an efficient and continuous photodetector by converting an incoming stream of photons to an electrical photocurrent. In the experiment, average photon and electron flows were analyzed. Here we theoretically investigat…
We demonstrate a lumped-element Josephson parametric amplifier, using a single-ended design that includes an on-chip, high-bandwidth flux bias line. The amplifier can be pumped into its region of parametric gain through either the input port or through the flux bias line. Broadband amplification is achieved at a tunable frequency $ω/2 π$ between 5 to 7 GHz with quantum-limited noise performance, a gain-bandwidth product greater than 500 MHz, and an input saturation power in excess of -120 dBm. The bias line allows fast frequency tuning of the amplifier, with variations of hundreds of MHz over …
Photons are fundamental excitations of the electromagnetic field and can be captured in cavities. For a given cavity with a certain size, the fundamental mode has a fixed frequency {\it f} which gives the photons a specific "color". The cavity also has a typical lifetime $τ$, which results in a finite linewidth $δ${\it f}. If the size of the cavity is changed fast compared to $τ$, and so that the frequency change $Δ${\it f} $\gg δ${\it f}, then it is possible to change the "color" of the captured photons. Here we demonstrate superconducting microwave cavities, with tunable effective lengths. T…
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…
Sharing information coherently between nodes of a quantum network is at the foundation of distributed quantum information processing. In this scheme, the computation is divided into subroutines and performed on several smaller quantum registers connected by classical and quantum channels. A direct quantum channel, which connects nodes deterministically, rather than probabilistically, is advantageous for fault-tolerant quantum computation because it reduces the threshold requirements and can achieve larger entanglement rates. Here, we implement deterministic state transfer and entanglement prot…
Low-noise amplification atmicrowave frequencies has become increasingly important for the research related to superconducting qubits and nanoelectromechanical systems. The fundamental limit of added noise by a phase-preserving amplifier is the standard quantum limit, often expressed as noise temperature $T_{q} = \hbar ω/2k_{B}$. Towards the goal of the quantum limit, we have developed an amplifier based on intrinsic negative resistance of a selectively damped Josephson junction. Here we present measurement results on previously proposed wide-band microwave amplification and discuss the challen…
