Spectral signature of high-order photon processes enhanced by Cooper-pair pairing
W. C. Smith, A. Borgognoni, Marius Villiers, E. Roverc’h, José M. Palomo, Matthieu R. Delbecq, Takis Kontos, Philippe Campagne-Ibarcq, Benoît Douçot, Zaki Leghtas
Inducing interactions between individual photons is key for photonic quantum information and studying many-body photon states. Superconducting circuits are well suited to combine strong interactions with low losses. Typically, microwave photons are stored in an LC oscillator shunted by a Josephson junction, where the zero-point phase fluctuations across the junction determine the strength and order of photon interactions. Most superconducting nonlinear oscillators operate with small phase fluctuations, where two-photon Kerr interactions dominate. In our experiment, we shunt a high-impedance LC oscillator with a dipole element favoring the tunneling of paired Cooper pairs. This leads to large phase fluctuations of 3.4, accessing a regime where transition frequencies shift non-monotonically with excitation number. From spectroscopy, we extract two-, three-, and four-photon interaction energies, all of similar strength and exceeding the photon loss rate. Our results open a new regime of high-order photon interactions in microwave quantum optics. In superconducting circuits, the nonlinearity of Josephson junctions mediates photon interactions, but they are typically dominated by two-photon processes. Here the authors observe multi-photon interactions in a superconducting circuit with Cooper-pair pairing, revealing a new regime of microwave quantum optics.
Inducing interactions between individual photons is key for photonic quantum information and studying many-body photon states. Superconducting circuits are well suited to combine strong interactions with low losses. Typically, microwave photons are stored in an LC oscillator shunted by a Josephson junction, where the zero-point phase fluctuations across the junction determine the strength and order of photon interactions. Most superconducting nonlinear oscillators operate with small phase fluctuations, where two-photon Kerr interactions dominate. In our experiment, we shunt a high-impedance LC oscillator with a dipole element favoring the tunneling of paired Cooper pairs. This leads to large phase fluctuations of 3.4, accessing a regime where transition frequencies shift non-monotonically with excitation number. From spectroscopy, we extract two-, three-, and four-photon interaction energies, all of similar strength and exceeding the photon loss rate. Our results open a new regime of high-order photon interactions in microwave quantum optics. In superconducting circuits, the nonlinearity of Josephson junctions mediates photon interactions, but they are typically dominated by two-photon processes. Here the authors observe multi-photon interactions in a superconducting circuit with Cooper-pair pairing, revealing a new regime of microwave quantum optics.
We analyze the quantum dynamics of two electromagnetic oscillators coupled in series to a voltage-biased Josephson junction. When the applied voltage leads to a Josephson frequency across the junction which matches the sum of the two mode frequencies, tunneling Cooper pairs excite photons in both modes simultaneously leading to far-from-equilibrium states. These states display highly nonclassical features including strong antibunching, violation of Cauchy-Schwartz inequalities, and number squeezing. We obtain approximate analytic results for both the regimes of low and high photon occupancies which are supported by a full numerical treatment. The impact of asymmetries between the two modes is explored, revealing a pronounced enhancement of number squeezing when the modes are damped at different rates.
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.
The flexible engineering of superconducting circuits, together with the nonlinearity available from Josephson junctions, have made microwave quantum optics a blooming research field in the past decade. Key experiments originally performed in the optical domain have become very accessible on this microwave-frequency, such that strong atom-field interactions and optical parametric interactions in microwave. From the latter, one example is the implementation of spontaneous parametric downconversion (SPDC). This process is particularly interesting as it can act as a nonclassical radiation source which give a number of potential applications in quantum information processing. We will focus on studying SPDC in microwave throughout this thesis. \n \nIn the first half of this thesis, from designs to measurements, we will explore the well-known two-photon parametric processes, SPDC and coherent coupling, which are generated by quadratic Hamiltonians. Using three resonant modes of a SQUID-terminated parametric cavity, we proceeded to combine different two-photon processes in an effort to demonstrate a multipartite nonclassical radiation source. With detailed system gain and noise calibration of our cryogenic microwave network, we confirmed our implementation by experimentally verifying that the generated states contain genuine tripartite entanglement. This multimode entangled radiation source can be an important resource for future experiments on quantum networking. \n \nWhile two-photon parametric processes have found numerous important applications, they have also been the limit of experiments for over three decades, with higher-order parametric processes seemingly out of reach. In the second half of this thesis, we explore the potential of parametric resonators for achieving such higher-order processes. To do this, we first studied the necessary conditions for accessing cubic Hamiltonians through our SQUID-based interactions. We then fabricated a device dedicated to performing three-photon processes through these cubic Hamiltonians. For the first time, we observed a direct generation of photon triplets by a single SPDC process in microwave . The generation rate can exceed a photon flux density of 60 photon per second per Hertz at the device output, far surpassing any record to date for photon triplets. We studied various pump configurations corresponding to different three-photon SPDC processes starting from a cold vacuum state. Pumping at triple the frequency of a single mode, we observed a phase-space distribution with a non-Gaussian profile which shows strong skewness (third moment) in the quadrature amplitude distribution. We reconstruct the Wigner function of the propagating states from the directly measured moment matrix, demonstrating Wigner negativity. Pumping at the sum frequency of three modes, we observed non-zero coskewness between the quadrature amplitudes of the modes. By analysing the output signals and comparing their characteristics to the predicted theoretical signatures, we confirm our implementation of three-photon SPDC processes generated by specific cubic Hamiltonians. These types of non-Gaussian states have been suggested as a resource enabling universal quantum computation with continuous variables. Our results thus open up the realm of three-photon quantum optics, enabling a wealth of novel experimental and theoretical studies.
In the last decade, the field of Quantum Optics has been enriched with a completely new platform: superconducting quantum circuits, also known as circuit-QED. This platform builds on the original designs of superconducting qubits, that is few-level systems made of superconducting islands and Josephson junctions, but adds to it a new ingredient, microwave photons. In this talk I will review circuit-QED with a focus on two complementary lines of research: ultrastrong light-matter coupling and strongly correlated propagating photons. The first topic deals with novel designs of superconducting qubits, engineering their coupling to the microwave radiation field to reach Rabi frequencies that approach the qubit and photon frequencies. In this regime, known as ”ultrastrong coupling”, the rotating wave approximation from Quantum Optics is no longer valid, the vacuum may spontaneously polarize, producing photons that get bound to the qubit, and novel physics is expected to emerge. I will review recent experiments on this topic, together with various theoretical proposals to tame this ultrastrong coupling. The second topic revolves around the notion of ”propagating” photons in these circuits. Most experiments in circuit-QED so far adopted the typical configuration of artificial atoms (qubits) interacting with artificial cavities (LC resonators). This proved useful in order to reach the strong coupling regime, demonstrating Rabi oscillations and developing a variety of protocols for quantum information, tomograhy, entanglement, etc. However, recent experiments have shown that it is possible to also work with propagating photons, replacing the LC resonators with open transmission lines, and studying the scattering properties of those artificial atoms. In this context we have worked on developing new technology to detect and control these photons, engineering single-photon detectors, quantum metamaterials and photonic crystals, or even new nonlinear media based on coupled cavities.
This manuscript summarizes my research activities devoted to the study of nonequilibrium phenomena in mesoscopic superconducting and semiconducting circuits. The work develops along two directions: the dynamics of metallic Josephson junctions driven out of equilibrium and the interaction between electrons and microwave photons in mesoscopic quantum circuits.The first part investigates diffusive superconductor–normal metal–superconductor Josephson junctions subjected to strong perturbations such as microwave irradiation or stochastic injection of high-energy quasiparticles. These experiments reveal how nonequilibrium excitations modify the Andreev spectrum and the phase dynamics of the junction. The second part addresses electron–photon coupling in mesoscopic circuits across different interaction regimes. Early work focused on semiconductor double quantum dots coupled to low-impedance microwave cavities in the weak coupling regime. Later work involved the fabrication and characterization of high-kineticinductance superconducting materials, allowing the realization of high-impedance resonators and stronger light-matter coupling. Finally, a superconducting tunnel junction coupled to a high-impedance granular aluminum cavity allowed bath engineering based on photo-assisted quasiparticle tunneling, efficient photon-toelectron conversion, and continuous single microwave photon detection.
Nonlinear effects play a central role in photonics as they form the foundation for most of the device functionalities such as amplification and quantum state preparation and detection. Typically the nonlinear effects are weak and emerge only at high photon numbers with strong drive. Here we present an experimental study of a Josephson junction -based high-impedance resonator. We show that by taking the resonator to the limit of consisting effectively only of one junction, results in strong nonlinear effects already for the second photon while maintaining a high impedance of the resonance mode. Our experiment yields thus resonators with strong interactions both between individual resonator photons and from the resonator photons to other electric quantum systems. We also present an energy diagram technique which enables to measure, identify and analyse different multi-photon optics processes along their energy conservation lines.