We observe the emission of bunches of k⩾1 photons by a circuit made of a microwave resonator in series with a voltage-biased tunable Josephson junction. The bunches are emitted atspecific values Vk of the bias voltage, for which each Cooper pair tunneling across the junction creates exactly k photons in the resonator. The latter is a micro-fabricated spiral coil which resonates and leaks photons at 4.4~GHz in a measurement line. Its characteristic impedance of 1.97~kΩ is high enough to reach a strong junction-resonator coupling and a bright emission of the k-photon bunches. We show that a RWA treatment of the system accounts quantitatively for the observed radiation intensity, from k=1 to 6, and over three orders of magnitude when varying the Josephson energy EJ. We also measure the second order correlation function of the radiated microwave to determine its Fano factor Fk, which in the low EJ limit, confirms with Fk=k the emission of k photon bunches. At larger EJ, a more complex behavior is observed in quantitative agreement with numerical simulations.
We show experimentally that a dc-biased Josephson junction in series with two microwave resonators emits entangled beams of microwaves leaking out of the resonators. In the absenceof a stationary phase reference for characterizing the entanglement of the outgoing beams, we measure second-order coherence functions for proving entanglement up to an emission rate of 2.5 billion photon pairs per second. The experimental results are found in quantitative agreement with theory, proving that the low frequency noise of the dc bias is the main limitation for the coherence time of the entangled beams. This agreement allows us to evaluate the entropy of entanglement of the resonators, and to identify the improvements that could bring this device closer to a useful bright source of entangled microwaves for quantum-technological applications.
A long-lived multi-mode qubit register is an enabling technology for modular quantum computing architectures. For interfacing with superconducting qubits, such a quantum memory shouldbe able to store incoming quantum microwave fields at the single-photon level for long periods of time, and retrieve them on-demand. Here, we demonstrate the partial absorption of a train of weak microwave fields in an ensemble of bismuth donor spins in silicon, their storage for 100 ms, and their retrieval, using a Hahn-echo-like protocol. The long storage time is obtained by biasing the bismuth donors at a clock transition. Phase coherence and quantum statistics are preserved in the storage.
We show experimentally that a dc biased Josephson junction in series with a high-enough impedance microwave resonator emits antibunched photons. Our resonator is made of a simple micro-fabricatedspiral coil that resonates at 4.4 GHz and reaches a 1.97 kΩ characteristic impedance. The second order correlation function of the power leaking out of the resonator drops down to 0.3 at zero delay, which demonstrates the antibunching of the photons emitted by the circuit at a rate of 6 10^7 photons per second. Results are found in quantitative agreement with our theoretical predictions. This simple scheme could offer an efficient and bright single-photon source in the microwave domain.
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 halfa 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 them much more difficult to implement and operate than conventional DC powered amplifiers, which, so far suffer from much higher noise. Here we present the first experimental proof that a simple DC-powered setup allows for amplification close to the quantum limit. Our amplification scheme is based on the stimulated microwave photon emission accompanying inelastic Cooper pair tunneling through a DC-biased Josephson junction, with the key to low noise lying in the separation of nonlinear and dissipative elements, in analogy to parametric amplifiers.
Although vacuum fluctuations appear to represent a fundamental limit to the sensitivity of electromagnetic field measurements, it is possible to overcome them by using so-called squeezedstates. In such states, the noise in one field quadrature is reduced below the vacuum level while the other quadrature becomes correspondingly more noisy, as required by Heisenberg’s uncertainty principle. Squeezed optical fields have been proposed and demonstrated to enhance the sensitivity of interferometric measurements beyond the photon shot-noise limit, with applications in gravitational wave detection. They have also been used to increase the sensitivity of atomic absorption spectroscopy, imaging, atom-based magnetometry, and particle tracking in biological systems. At microwave frequencies, cryogenic temperatures are required for the electromagnetic field to be in its vacuum state. Squeezed microwaves have been produced, used for fundamental studies of light-matter interaction and for enhanced sensing of a mechanical resonator, and proposed to enhance the sensitivity of the readout of superconducting qubits. Here we report the use of squeezed microwave fields to enhance the sensitivity of magnetic resonance spectroscopy of an ensemble of electronic spins. Our scheme consists in sending a squeezed vacuum state to the input of a cavity containing the spins while they are emitting an echo, with the phase of the squeezed quadrature aligned with the phase of the echo. We demonstrate a total noise reduction of 1.2\,dB at the spectrometer output due to the squeezing. These results provide a motivation to examine the application of the full arsenal of quantum metrology to magnetic resonance detection.
This article reviews efforts to build a new type of quantum device, which combines an ensemble of electronic spins with long coherence times, and a small-scale superconducting quantumprocessor. The goal is to store over long times arbitrary qubit states in orthogonal collective modes of the spin-ensemble, and to retrieve them on-demand. We first present the protocol devised for such a multi-mode quantum memory. We then describe a series of experimental results using NV center spins in diamond, which demonstrate its main building blocks: the transfer of arbitrary quantum states from a qubit into the spin ensemble, and the multi-mode retrieval of classical microwave pulses down to the single-photon level with a Hahn-echo like sequence. A reset of the spin memory is implemented in-between two successive sequences using optical repumping of the spins.
We report the storage of microwave pulses at the single-photon level in a spin-ensemble memory consisting of 1010 NV centers in a diamond crystal coupled to a superconducting LC resonator.The energy of the signal, retrieved 100μs later by spin-echo techniques, reaches 0.3% of the energy absorbed by the spins, and this storage efficiency is quantitatively accounted for by simulations. This figure of merit is sufficient to envision first implementations of a quantum memory for superconducting qubits.
Achieving individual qubit readout is a major challenge in the development of scalable superconducting quantum processors. We have implemented the multiplexed readout of a four transmonqubit circuit using non-linear resonators operated as Josephson bifurcation amplifiers. We demonstrate the simultaneous measurement of Rabi oscillations of the four transmons. We find that multiplexed Josephson bifurcation is an high-fidelity readout method, the scalability of which is not limited by the need of a large bandwidth nearly quantum-limited amplifier as is the case with linear readout resonators.
We have developed and measured a high-gain quantum-limited microwave parametric amplifier based on a superconducting lumped LC resonator with the inductor L including an array of 8superconducting quantum interference devices (SQUIDs). This amplifier is parametrically pumped by modulating the flux threading the SQUIDs at twice the resonator frequency. Around 5 GHz, a maximum gain of 31 dB, a product amplitude-gain x bandwidth above 60 MHz, and a 1 dB compression point of -123 dBm at 20 dB gain are obtained in the non-degenerate mode of operation. Phase sensitive amplification-deamplification is also measured in the degenerate mode and yields a maximum gain of 37 dB. The compression point obtained is 18 dB above what would be obtained with a single SQUID of the same inductance, due to the smaller nonlinearity of the SQUID array.