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 quadratures allows us to determine the full covariance matrix and reconstruct the four-dimensional Wigner function. We demonstrate strong correlations between the quadrature amplitude noise in the two modes. Under ideal conditions two-mode squeezing below the standard quantum limit should be observable in future experiments.
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…
We perform state tomography of an itinerant squeezed state of the microwave field prepared by a Josephson parametric amplifier (JPA). We use a second JPA as a pre-amplifier to improve the quantum efficiency of the field quadrature measurement (QM) from 2% to 36 +/- 4%. Without correcting for the detection inefficiency we observe a minimum quadrature variance which is 69 +/- 8% of the variance of the vacuum. We reconstruct the state's density matrix by a maximum likelihood method and infer that the squeezed state has a minimum variance less than 40% of the vacuum, with uncertainty mostly caused…
Detecting an itinerant microwave photon with high efficiency is an outstanding problem in microwave photonics and its applications. We present a scheme to detect an itinerant microwave photon in a transmission line via the nonlinearity provided by a transmon in a driven microwave resonator. With a single transmon we achieve 84% distinguishability between zero and one microwave photons and 90% distinguishability with two cascaded transmons by performing continuous measurements on the output field of the resonator. We also show how the measurement diminishes coherence in the photon number basis …
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…
We propose a scheme for continuous detection of itinerant microwave photons in circuit quantum electrodynamics. In the proposed device, a superconducting qubit is coupled dispersively to two resonators: one is used to form an impedance-matched $Λ$ system that deterministically captures incoming photons, and the other is used for continuous monitoring of the event. The present scheme enables efficient photon detection: for realistic system parameters, the detection efficiency reaches 0.9 with a bandwidth of about ten megahertz.
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…
Microwave photonics is a remarkably powerful system for quantum simulation and technologies, but its integration in superconducting circuits, superior in many aspects, is constrained by the long wavelengths and impedance mismatches in this platform. We introduce a solution to these difficulties via compact networks of high-kinetic inductance microstrip waveguides and coupling wires with strongly reduced phase velocities. We demonstrate broadband capabilities for superconducting microwave photonics in terms of routing, emulation and generalized linear and nonlinear networks.
We theoretically demonstrate dynamically selective bidirectional emission and absorption of a single itinerant microwave photon in a waveguide. The proposed device is an artificial molecule composed of two qubits coupled to a waveguide a quarter-wavelength apart. By using simulations based on the input--output theory, we show that upon preparing an appropriate entangled state of the two qubits, a photon is emitted directionally as a result of the destructive interference occurring either at the right or left of the qubits. Moreover, we demonstrate that this artificial molecule possesses the ca…
By combining a squeezed propagating microwave field and an unsqueezed vacuum field on a hybrid (microwave beam-splitter), we generate entanglement between the two output modes. We verify that we have generated entangled states by making independent and efficient single-quadrature measurements of the two output modes. We observe the entanglement witness $E_\mathrm{W}=-0.263^{+0.001}_{-0.036}$ and the negativity $N=0.0824^{+0.01}_{-0.0004}$ with measurement efficiencies at least $26\pm{0.1}\%$ and $41\pm{0.2}\%$ for channel~1 and 2 respectively. These measurements show that the output two-mode s…
Single photon detectors are fundamental tools of investigation in quantum optics and play a central role in measurement theory and quantum informatics. Photodetectors based on different technologies exist at optical frequencies and much effort is currently being spent on pushing their efficiencies to meet the demands coming from the quantum computing and quantum communication proposals. In the microwave regime however, a single photon detector has remained elusive although several theoretical proposals have been put forth. In this article, we review these recent proposals, especially focusing …
Generalized cat states represent arbitrary superpositions of coherent states, which are of great importance in various quantum information processing protocols. Here we demonstrate a versatile approach to creating generalized itinerant cat states in the microwave domain, by reflecting coherent state photons from a microwave cavity containing a superconducting qubit. We show that, with a coherent control of the qubit state, a full control over the coherent state superposition can be realized. The prepared cat states are verified through quantum state tomography of the qubit state dependent refl…
The realization of a high-efficiency microwave single photon detector is a long-standing problem in the field of microwave quantum optics. Here we propose a quantum non-demolition, high-efficiency photon detector that can readily be implemented in present state-of-the-art circuit quantum electrodynamics. This scheme works in a continuous fashion, gaining information about the arrival time of the photon as well as about its presence. The key insight that allows to circumvent the usual limitations imposed by measurement back-action is the use of long-lived dark states in a small ensemble of inho…
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…
Photon detectors are an elementary tool to measure electromagnetic waves at the quantum limit and are heavily demanded in the emerging quantum technologies such as communication, sensing, and computing. Of particular interest is a quantum non-demolition (QND) type detector, which projects the quantum state of a photonic mode onto the photon-number basis without affecting the temporal or spatial properties. This is in stark contrast to conventional photon detectors which absorb a photon to trigger a `click' and thus inevitably destroy the photon. The long-sought QND detection of a flying photon…
Recently, macroscopic mechanical oscillators have been coaxed into a regime of quantum behavior, by direct refrigeration [1] or a combination of refrigeration and laser-like cooling [2, 3]. This exciting result has encouraged notions that mechanical oscillators may perform useful functions in the processing of quantum information with superconducting circuits [1, 4-7], either by serving as a quantum memory for the ephemeral state of a microwave field or by providing a quantum interface between otherwise incompatible systems [8, 9]. As yet, the transfer of an itinerant state or propagating mode…
We experimentally study the phase space distribution (PSD) of a mechanical resonator that is simultaneously coupled to two electromagnetic cavities. The first one, operating in the microwave band, is employed for inducing either cooling or self-excited oscillation, whereas the second one, operating in the optical band, is used for displacement detection. A tomography technique is employed for extracting the PSD from the signal reflected by the optical cavity. Measurements of PSD are performed in steady state near the threshold of self-excited oscillation while sweeping the microwave cavity det…
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…
Superconducting circuits offer a scalable platform for the construction of large-scale quantum networks where information can be encoded in multiple temporal modes of propagating microwaves. Characterization of such microwave signals with a method extendable to an arbitrary number of temporal modes with a single detector and demonstration of their phase-robust nature are of great interest. Here we show the on-demand generation and Wigner tomography of a microwave time-bin qubit with superconducting circuit quantum electrodynamics architecture. We perform the tomography with a single heterodyne…
The protocol of measurement the probability density of a rotated quadrature of microwave mode in an arbitrary quantum state is presented and numerically investigated. The protocol is adapted to the measuring procedure used in the CQED experiments. The method is based on measurement of integrated probability of detection of atoms - probes in the top working state from atoms flying via the cavity. Connection of random variables and is found, when is a qudrature phase. Connection of the tomogram and the tomogram is found. The protocol prescribes the rule of choice of problem parameters, such as i…
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…
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 state tomography is an important tool in quantum information science for complete characterization of multi-qubit states and their correlations. Here we report a method to perform a joint simultaneous read-out of two superconducting qubits dispersively coupled to the same mode of a microwave transmission line resonator. The non-linear dependence of the resonator transmission on the qubit state dependent cavity frequency allows us to extract the full two-qubit correlations without the need for single shot read-out of individual qubits. We employ standard tomographic techniques to recons…
We demonstrate an all-microwave two-qubit gate on superconducting qubits which are fixed in frequency at optimal bias points. The gate requires no additional subcircuitry and is tunable via the amplitude of microwave irradiation on one qubit at the transition frequency of the other. We use the gate to generate entangled states with a maximal extracted concurrence of 0.88 and quantum process tomography reveals a gate fidelity of 81%.
We introduce a new entangling gate between two fixed-frequency qubits statically coupled via a microwave resonator bus which combines the following desirable qualities: all-microwave control, appreciable qubit separation for reduction of crosstalk and leakage errors, and the ability to function as a two-qubit conditional-phase gate. A fixed, always-on interaction is explicitly designed between higher energy (non-computational) states of two transmon qubits, and then a conditional-phase gate is `activated' on the otherwise unperturbed qubit subspace via a microwave drive. We implement this micr…
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…
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…
Quantum entanglement, one of the defining features of quantum mechanics, has been demonstrated in a variety of nonlinear spin-like systems. Quantum entanglement in linear systems has proven significantly more challenging, as the intrinsic energy level degeneracy associated with linearity makes quantum control more difficult. Here we demonstrate the quantum entanglement of photon states in two independent linear microwave resonators, creating N-photon NOON states as a benchmark demonstration. We use a superconducting quantum circuit that includes Josephson qubits to control and measure the two …
By properly driving a qubit-resonator system in the strong dispersive regime, we implement an "impedance-matched" $Λ$ system in the dressed states, where a resonant single photon deterministically induces a Raman transition and excites the qubit. Combining this effect and a fast dispersive readout of the qubit, we realize a detector of itinerant microwave photons. We theoretically analyze the single-photon response of the $Λ$ system and evaluate its performance as a detector. We achieve a high detection efficiency close to unity without relying on precise temporal control of the input pulse sh…
Encoding quantum states in complex multiphoton fields can overcome loss during signal transmission in a quantum network. Transmitting quantum information encoded in this way requires that locally stored states can be converted to propagating fields. Here we experimentally show the controlled conversion of multiphoton quantum states, like "Schrödinger cat" states, from a microwave cavity quantum memory into propagating modes. By parametric conversion using the nonlinearity of a single Josephson junction, we can release the cavity state in ~500 ns, about 3 orders of magnitude faster than its int…
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…
While a propagating state of light can be generated with arbitrary squeezing by pumping a parametric resonator, the intra-resonator state is limited to 3 dB of squeezing. Here, we implement a reservoir engineering method to surpass this limit using superconducting circuits. Two-tone pumping of a three-wave-mixing element implements an effective coupling to a squeezed bath which stabilizes a squeezed state inside the resonator. Using an ancillary superconducting qubit as a probe allows us to perform a direct Wigner tomography of the intra-resonator state. The raw measurement provides a lower bo…
The parity of the number of elementary excitations present in a quantum system provides important insights into its physical properties. Parity measurements are used, for example, to tomographically reconstruct quantum states or to determine if a decay of an excitation has occurred, information which can be used for quantum error correction in computation or communication protocols. Here we demonstrate a versatile parity detector for propagating microwaves, which distinguishes between radiation fields containing an even or odd number n of photons, both in a single-shot measurement and without …
Photons at telecom wavelength are the ideal choice for high density interconnects while solid state qubits in the microwave domain offer strong interactions for fast quantum logic. Here we present a general purpose, quantum-enabled interface between itinerant microwave and optical light. We use a pulsed electro-optic transducer at millikelvin temperatures to demonstrate nanosecond timescale control of the converted complex mode amplitude with an input added noise of $N^{oe}_\textrm{in} = 0.16^{+0.02}_{-0.01}$ ($N^{eo}_\textrm{in} = 1.11^{+0.15}_{-0.07}$) quanta for the microwave-to-optics (rev…
In this letter we introduce a novel approach to Hamiltonian tomography of non-interacting tight-binding photonic lattices. To begin with, we prove that the matrix element of the low-energy effective Hamiltonian between sites $i$ and $j$ may be obtained directly from $S_{ij}(ω)$, the (suitably normalized) two-port measurement between sites $i$ and $j$ at frequency $ω$. This general result enables complete characterization of both on-site energies and tunneling matrix elements in arbitrary lattice networks by spectroscopy, and suggests that coupling between lattice sites is actually a topologica…
A most intuitive realization of a qubit is a single electron charge sitting at two well-defined positions, such as the left and right sides of a double quantum dot. This qubit is not just simple but also has the potential for high-speed operation, because of the strong coupling of electric fields to the electron. However, charge noise also couples strongly to this qubit, resulting in rapid dephasing at nearly all operating points, with the exception of one special 'sweet spot'. Fast dc voltage pulses have been used to manipulate semiconductor charge qubits, but these previous experiments did n…
We experimentally constructed an all-microwave scheme for the controlled-NOT (cNOT) gate between two superconducting transmon qubits in a three dimensional cavity. Our cNOT gate is based on the microwave-activated phase (MAP) gate, which requires an additional procedure to compensate the accumulated phases during the operation of the MAP gate. We applied Z-axis phase gates using microwave hyperbolic secant pulse on both qubits with adequate rotation angles systematically calibrated by separate measurements.We evaluated the gate performance of the constructed cNOT gate by performing two-qubit q…
Electromagnetic signals in circuits consist of discrete photons, though conventional voltage sources can only generate classical fields with a coherent superposition of many different photon numbers. While these classical signals can control and measure bits in a quantum computer (qubits), single photons can carry quantum information, enabling non-local quantum interactions, an important resource for scalable quantum computing. Here, we demonstrate an on-chip single photon source in a circuit quantum electrodynamics (QED) architecture, with a microwave transmission line cavity that collects th…
A switch capable of routing microwave signals at cryogenic temperatures is a desirable component for state-of-the-art experiments in many fields of applied physics, including but not limited to quantum information processing, communication and basic research in engineered quantum systems. Conventional mechanical switches provide low insertion loss but disturb operation of dilution cryostats and the associated experiments by heat dissipation. Switches based on semiconductors or microelectromechanical systems have a lower thermal budget but are not readily integrated with current superconducting…
Precisely engineered mechanical oscillators keep time, filter signals, and sense motion, making them an indispensable part of today's technological landscape. These unique capabilities motivate bringing mechanical devices into the quantum domain by interfacing them with engineered quantum circuits. Proposals to combine microwave-frequency mechanical resonators with superconducting devices suggest the possibility of powerful quantum acoustic processors. Meanwhile, experiments in several mechanical systems have demonstrated quantum state control and readout, phonon number resolution, and phonon-…
Mechanical resonators are macroscopic quantum objects with great potential. They couple to many different quantum systems such as spins, optical photons, cold atoms, and Bose Einstein condensates. It is however difficult to measure and manipulate the phonon state due to the tiny motion in the quantum regime. On the other hand, microwave resonators are powerful quantum devices since arbitrary photon state can be synthesized and measured with a quantum tomography. We show that a linear coupling, strong and controlled with a gate voltage, between the mechanical and the microwave resonators enable…
We demonstrate and evaluate an on-demand source of single itinerant microwave photons. Photons are generated using a highly coherent, fixed-frequency qubit-cavity system, and a protocol where the microwave control field is far detuned from the photon emission frequency. By using a Josephson parametric amplifier (JPA), we perform efficient single-quadrature detection of the state emerging from the cavity. We characterize the imperfections of the photon generation and detection, including detection inefficiency and state infidelity caused by measurement backaction over a range of JPA gains from …
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…
Interfacing between various elements of a computer - from memory to processors to long range communication - will be as critical for quantum computers as it is for classical computers today. Paramagnetic rare earth doped crystals, such as Nd$^{3+}$:Y$_2$SiO$_5$ (YSO), are excellent candidates for such a quantum interface: they are known to exhibit long optical coherence lifetimes (for communication via optical photons), possess a nuclear spin (memory) and have in addition an electron spin that can offer hybrid coupling with superconducting qubits (processing). Here we study two of these three …
A superconducting qutrit link beyond the qubit limit
Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所凝聚态物理国家实验室）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；Hefei National Laboratory（合肥国家实验室）；Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）
We describe the back action of microwave-photon detection via a Josephson photomultiplier (JPM), a superconducting qubit coupled strongly to a high-quality microwave cavity. The back action operator depends qualitatively on the duration of the measurement interval, resembling the regular photon annihilation operator at short interaction times and approaching a variant of the photon subtraction operator at long times. The optimal operating conditions of the JPM differ from those considered optimal for processing and storing of quantum information, in that a short $T_2$ of the JPM suppresses the…
