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arXiv:1505.05356 · Physical Review B

Detecting photon-photon interactions in a superconducting circuit

Li-Jing Jin, Manuel Houzet, Julia S. Meyer, Harold U. Baranger, F. W. J. Hekking

Published Oct 6, 2015• 7 citations
arXivHTMLPDF

Abstract

A local interaction between photons can be engineered by coupling a nonlinear system to a transmission line. The required transmission line can be conveniently formed from a chain of Josephson junctions. The nonlinearity is generated by side-coupling this chain to a Cooper pair box. We propose to probe the resulting photon-photon interactions via their effect on the current-voltage characteristic of a voltage-biased Josephson junction connected to the transmission line. Considering the Cooper pair box to be in the weakly anharmonic regime, we find that the dc current through the probe junction yields features around the voltages $2eV=n\ensuremath{\hbar}{\ensuremath{\omega}}_{s}$, where ${\ensuremath{\omega}}_{s}$ is the plasma frequency of the superconducting circuit. The features at $n\ensuremath{\ge}2$ are a direct signature of the photon-photon interaction in the system.

DOI
10.1103/physrevb.92.134503

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A local interaction between photons can be engineered by coupling a nonlinear system to a transmission line. The required transmission line can be conveniently formed from a chain of Josephson junctions. The nonlinearity is generated by side-coupling this chain to a Cooper pair box. We propose to probe the resulting photon-photon interactions via their effect on the current-voltage characteristic of a voltage-biased Josephson junction connected to the transmission line. Considering the Cooper pair box to be in the weakly anharmonic regime, we find that the dc current through the probe junction yields features around the voltages 2eV=n\ensuremathℏ\ensuremathωs2eV=n\ensuremath{\hbar}{\ensuremath{\omega}}_{s}2eV=n\ensuremathℏ\ensuremathωs​, where \ensuremathωs{\ensuremath{\omega}}_{s}\ensuremathωs​ is the plasma frequency of the superconducting circuit. The features at n\ensuremath≥2n\ensuremath{\ge}2n\ensuremath≥2 are a direct signature of the photon-photon interaction in the system.
We investigate electromagnetic radiation emitted by a small voltage-biased Josephson junction connected to a superconducting transmission line. At frequencies below the well-known emission peak at the Josephson frequency (2eV/h), extra radiation is triggered by quantum fluctuations in the transmission line. For weak tunneling couplings and typical Ohmic transmission lines, the corresponding photon-flux spectrum is symmetric around half the Josephson frequency, indicating that the photons are predominately created in pairs. By establishing an input-output formalism for the microwave field in the transmission line, we give further evidence for this nonclassical photon pair production, demonstrating that it violates the classical Cauchy-Schwarz inequality for two-mode flux cross correlations. In connection to recent experiments, we also consider a stepped transmission line, where resonances increase the signal-to-noise ratio.
Motivated by recent experiments on superconducting circuits consisting of a dc-voltage-biased Josephson junction in series with a resonator, quantum properties of these devices far from equilibrium are studied. This includes a crossover from a domain of incoherent to a domain of coherent Cooper pair tunneling, where the circuit realizes a driven nonlinear oscillator. Equivalently, weak photon-charge coupling turns into strong correlations captured by a single degree of freedom. Radiated photons offer a new tool to monitor charge flow and current noise gives access to nonlinear dynamics, which allows us to analyze quantum-classical boundaries.
In this talk, I will start by briefly introducing the Josephson-junction, which is the non-linear circuit element used to engineer the artificial atoms. Then I will discuss two qualitatively different methods using this non-linear element for generating entangled photon pairs in superconducting circuits. One approach builds on parametric down-conversion of a coherent ac drive (see fig. 1)[2] while the other relies on the ac Josephson effect, requiring only a dc voltage bias (see fig. 2) [3]. Finally, I will discuss a few recent experimental implementations [4-8].
The strong interaction of superconducting integrated circuits with microwave photons forms the basis of circuit quantum electrodynamics (cQED), an attractive paradigm for scalable quantum computing and a test bed for quantum optics in the strong coupling regime [1–6]. While singlephoton detectors are an important component of the standard quantum optics toolbox [7], they have not played a role in cQED, as there are no microwave photon counters currently available. In the search for a microwave component that will emulate the nonlinearity of traditional optical photon counters, it is natural to consider the Josephson junction—a nonlinear, nondissipative superconducting circuit element with tunable microwave-frequency transitions. There has been recent interest in the development of on-chip detectors to probe the microwave radiation emitted by mesoscopic quantum circuits [8–14], including proposals to utilize Josephson circuits as photon counters in the context of cQED [8,9]. This study represents the first experimental measurement of the coincidence counting statistics of microwave photons. We exploit microwaveinduced transitions between discrete energy levels in a Josephson junction to realize an efficient, versatile microwave detector. Moreover, we use a parallelized detector circuit to probe the counting statistics of both coherent and thermal microwave sources. Acircuitdiagramofthesingle-channeldetectorisshown in Fig. 1(a). The Josephson junction is current biased near thecriticalcurrent I0.Thejunctionpotentialenergyisgiven by Uð� Þ¼� I
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.
Abstract We propose to generate photon-pair blockade in a Josephson-photonics circuit that consists of a dc voltage-biased Josephson junction in series with a superconducting charge qubit and two nondegenerate microwave resonators. The two-level charge qubit is utilized to create anticorrelations of the charge transport; that is, the simultaneous Cooper pair tunneling events are inhibited. When the Josephson frequency matches the sum of resonance frequencies of the charge qubit and the two resonators, we demonstrate that the two resonators can release their energies in the form of antibunched pairs of two strongly correlated photons. The present work provides a practical way for producing a bright microwave source of antibunched photon pairs, with potential applications ranging from spectroscopy and metrology to quantum information processing.