We present and analyze a reservoir-engineering approach to stabilizing Fock states in a superconducting microwave cavity which does not require any microwave-frequency control drives. Instead, our system makes use of a Josephson junction biased by a dc voltage which is coupled to both a principal storage cavity and a second auxiliary cavity. Our analysis shows that Fock states can be stabilized with an extremely high fidelity. We also show how the same system can be used to prepare on-demand propagating Fock states, again without the use of microwave pulses.
We present and analyze a reservoir-engineering approach to stabilizing Fock states in a superconducting microwave cavity which does not require any microwave-frequency control drives. Instead, our system makes use of a Josephson junction biased by a dc voltage which is coupled to both a principal storage cavity and a second auxiliary cavity. Our analysis shows that Fock states can be stabilized with an extremely high fidelity. We also show how the same system can be used to prepare on-demand propagating Fock states, again without the use of microwave pulses.
Quantum states can be stabilized in the presence of intrinsic and environmental losses by either applying an active feedback condition on an ancillary system or through reservoir engineering. Reservoir engineering maintains a desired quantum state through a combination of drives and designed entropy evacuation. We propose and implement a quantum-reservoir engineering protocol that stabilizes Fock states in a microwave cavity. This protocol is realized with a circuit quantum electrodynamics platform where a Josephson junction provides direct, nonlinear coupling between two superconducting waveguide cavities. The nonlinear coupling results in a single-photon-resolved cross-Kerr effect between the two cavities enabling a photon-number-dependent coupling to a lossy environment. The quantum state of the microwave cavity is discussed in terms of a net polarization and is analyzed by a measurement of its steady state Wigner function.
Bright sources of quantum microwave light are an important building block for various quantum technological applications. Josephson junctions coupled to microwave cavities are a particularly versatile and simple source for microwaves with quantum characteristics, such as different types of squeezing. Due to the inherent nonlinearity of the system, a pure dc-voltage bias can lead to the emission of correlated pairs of photons into a stripline resonator. However, a drawback of this method is that it suffers from bias voltage noise, which disturbs the phase of the junction and consequently destroys the coherence of the photons, severely limiting its applications. Here we describe how adding a small ac reference signal either to the dc bias or directly into the cavity can stabilize the system and counteract the sensitivity to noise. We first consider the injection locking of a single-mode device before turning to the more technologically relevant locking of two-mode squeezed states, where phase locking preserves the entanglement between photons. Finally, we describe locking by directly injecting a microwave into the cavity, which breaks the symmetry of the squeezing ellipse. In all cases, locking can mitigate the effects of voltage noise and enable the use of squeezed states in quantum technological applications.
DC-voltage-biased Josephson junctions have been recently employed in superconducting circuits for Hamiltonian engineering, demonstrating microwave amplification, single photon sources and entangled photon generation. Compared to more conventional approaches based on parametric pumps, this solution typically enables larger interaction strengths. In the context of quantum information, a two-to-one photon interaction can stabilize cat qubits, where bit-flip errors are exponentially suppressed, promising significant resource savings for quantum error correction. This work investigates how the DC bias approach to Hamiltonian engineering can benefit cat qubits. We find a simple circuit design that is predicted to showcase a two-to-one photon exchange rate larger than that of the parametric pump-based implementation while dynamically averaging typically resonant parasitic terms such as Kerr and cross Kerr. In addition to addressing qubit stabilization, we propose to use injection locking with a cat-qubit adapted frequency filter to prevent long-term drifts of the cat qubit angle associated to DC voltage noise. The whole scheme is simulated without rotating-wave approximations, highlighting for the first time the amplitude of related oscillatory effects in cat-qubit stabilization schemes. This study lays the groundwork for the experimental realization of such a circuit.
A resistively shunted Josephson junction with a DC-bias exhibits Josephson oscillations that link voltage and frequency through fundamental constants. These oscillations can synchronize their frequency to an external microwave signal achieving the metrological precision that underlies the modern Josephson voltage standard. Its electromagnetic dual, the phase-slip junction, exhibits Bloch oscillations that connect current to frequency in an analogous way. A current standard based on synchronized Bloch oscillations could close the quantum metrology triangle, providing a consistent test of the underlying fundamental relations between voltage, current, and resistance. The experimental realization, however, remains challenging, as external microwave lines introduce parasitic capacitances that can destroy the high-impedance environment required for Bloch oscillations. This work explores the use of on-chip synchronization to stabilize both Josephson and Bloch oscillations without the need for an external microwave drive. We review the theoretical framework of the synchronization between two coupled oscillators and the dynamics of superconducting circuits with a focus on quantum metrology. Building on this, we analyze a recent experiment on the mutual synchronization of Bloch oscillations in a pair of ultrasmall Josephson junctions. Our model in terms of correlated phase-slip junctions realized in the ground state of the device shows good agreement with the experimental results, confirming synchronized Bloch oscillations. At larger currents, nonadiabatic transitions wash out the coherence of the Bloch oscillations and therefore the synchronization features. Motivated by these findings, we propose an alternative circuit setup where the Bloch oscillations in a single phase-slip junction are stabilized by synchronization to on-chip Josephson oscillations. We study the back-action of the Bloch oscillations on the Josephson oscillations and identify a parameter regime in which it is minimized, rendering the latter an effectively rigid driving signal. Moreover, we find that the small remaining back-action further enhances the thermal stability of the synchronized Bloch oscillations compared to the externally driven case. Without a back-action mechanism, the coherence of Josephson oscillations is severely limited by thermal fluctuations. We relate this limitation to the thermodynamic uncertainty relation (TUR) in the field of stochastic thermodynamics. Recent findings show, that the TUR can be broken by a classical pendulum clock. We propose a circuit that mimics the dynamics of a pendulum clock as a flexible on-chip microwave source for high impedance environments. Due to an internal synchronization, the clock circuit emits coherent radiation beyond the limits of the TUR. Finally, we explore the use of symmetry breaking drives as a resource for nonreciprocal transport in superconducting circuits. We demonstrate that a biharmonic microwave signal applied to a conventional Josephson junction induces an ideal supercurrent diode effect with a tunable direction.
At its heart, a Josephson-photonics device combines macroscopic superconducting electronics and microscopic quantum optics. It consists of a dc-voltage biased Josephson junction that is connected in series to one or a few microwave cavities. Cooper pairs can tunnel incoherently across the junction by depositing their energy 2eVdc in the microwave cavities, creating photonic excitations in them. Many parameters, such as the eigenfrequencies ∝ (LC)^(−1/2) or zero-point fluctuations ∝ (L/C)^(1/4) of the microwave cavities, can be experimentally designed; other parameters, such as the strength of the Josephson nonlinearity and the dc voltage are easily modified in situ. In this way, Josephson-photonics devices constitute a versatile source of microwave photons with a wide variety of features extending from the classical to the deep quantum regime. To make them of use for quantum technological applications that rely on a well-defined phase of the microwave light, a crucial drawback must be overcome. The dc voltage does not provide a stable reference phase to Josephson-photonics devices, as it is subject to experimental noise, such that all phase information is lost. In this thesis, we develop the field of Josephson photonics in two directions: As first main result, we resolve the issue of phase instability in Josephson photonics. The phase can be stabilized either by injection locking to a small external signal with a stable and well-defined reference phase or by mutual synchronization to a second device. An alternative approach mitigates the issue for some use cases by optimizing an ansatz to reconstruct the undiffused stationary quantum state from experiments with phase diffusion. Secondly, we show how Josephson-photonics devices can be used for the challenging task of reliably detecting single itinerant microwave photons. The “Inelastic Cooper Pair Tunneling Photon Multiplier” exploits a resonance condition, where the energy provided by the dc voltage enables a multiplication process from one incoming to n outgoing photons. This process can be staged to reach a large number of outgoing photons. Here, we model itinerant Gaussian single-photon pulses of length T with Mølmer’s approach. Further, we define a detection scheme based on heterodyne quadrature measurement of the output signal. Most importantly, we show that realistic devices can achieve a detection efficiency of 84.5% with a small dark-count rate of 10^(−3)/T, promising to outperform competing schemes.
Superconducting electronic devices have reemerged as contenders for both classical and quantum computing due to their fast operation speeds, low dissipation, and long coherence times. An ultimate demonstration of coherence is lasing. We use one of the fundamental aspects of superconductivity, the ac Josephson effect, to demonstrate a laser made from a Josephson junction strongly coupled to a multimode superconducting cavity. A dc voltage bias applied across the junction provides a source of microwave photons, and the circuit's nonlinearity allows for efficient down-conversion of higher-order Josephson frequencies to the cavity's fundamental mode. The simple fabrication and operation allows for easy integration with a range of quantum devices, allowing for efficient on-chip generation of coherent microwave photons at low temperatures.