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arXiv:2406.12939 · Physical review. B./Physical review. B

Measurement of many-body quantum correlations in superconducting circuits

Kamal Sharma, Wade DeGottardi

Published Sep 17, 2025• 0 citations
arXivHTMLPDF

Abstract

Recent advances in superconducting circuit technology have made the fabrication of large, customizable circuits routine. This has led to applications beyond quantum information, including quantum simulation. A key challenge in this effort is the identification of the quantum states realized. Here, we propose a probe circuit capable of measuring many-body correlations in an analog quantum simulator superconducting circuit. This probe, which is specially designed for many-photon states, exploits the nonlinearity of the Josephson junction to measure two-point correlation functions of the superconducting phase operator. We demonstrate the capabilities of this design in the context of an LC-ladder with a quantum impurity. The proposed probe allows for the measurement of inherently quantum correlations, such as two-mode squeezing, and it has the potential to significantly expand the scope of analog quantum simulations using superconducting circuits.

DOI
10.1103/1wb4-df6c

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Recent advances in superconducting circuit technology have made the fabrication of large, customizable circuits routine. This has led to applications beyond quantum information, including quantum simulation. A key challenge in this effort is the identification of the quantum states realized. Here, we propose a probe circuit capable of measuring many-body correlations in an analog quantum simulator superconducting circuit. This probe, which is specially designed for many-photon states, exploits the nonlinearity of the Josephson junction to measure two-point correlation functions of the superconducting phase operator. We demonstrate the capabilities of this design in the context of an LC-ladder with a quantum impurity. The proposed probe allows for the measurement of inherently quantum correlations, such as two-mode squeezing, and it has the potential to significantly expand the scope of analog quantum simulations using superconducting circuits.
Superconducting quantum circuits are a promising approach for realizations of large scale quantum information processing and quantum simulations. The Josephson junction, which forms the basis of superconducting circuits, is the only known nonlinear non-dissipative circuit element, and its inherent nonlinearities have found many different applications. In this thesis I discuss specific implementations of these circuits. I show that strong two-photon nonlinearities can be induced by coupling photons in the microwave domain to Josephson nonlinearities. I then propose a method to simulate a parent Hamiltonian that can potentially be used to observe fractional quantum Hall states of light. I will also explore how superconducting circuits can be used to modify system-bath couplings to emulate a chemical potential for photons. Finally, I consider the limitations of devising a scheme to couple superconducting circuits to trapped ions, and consider the challenges for such hybrid approaches.
Analog quantum simulators can be used to study quantum correlation in novel many-body systems by emulating the Hamiltonian of these systems. One essential question in quantum simulation is to probe the properties of an emulated many-body system. Here we present a circuit QED scheme for probing such properties by measuring the spectrum of a superconducting resonator coupled to a quantum simulator. We first study a general framework of this approach and show that the spectrum of the resonator is directly related to the correlation function of the coupling operator between the resonator and the simulator. We then apply this scheme to a simulator of the transverse field Ising model implemented with superconducting qubits, where the resonance peaks in the resonator spectrum correspond to the frequencies of the elementary excitations. The effects of resonator damping, qubit decoherence, and resonator backaction are also discussed. This setup can be used to probe a broad range of many-body models.
Many-body systems with strong interactions often exhibit macroscopic behavior markedly absent in single-particle or noninteracting limits. Such emergent phenomena are well exemplified in lattice Hubbard models, where the interplay between interactions, geometric frustration, and magnetic flux gives rise to rich physics. Superconducting qubits naturally enable analog quantum simulation of Bose-Hubbard models, while offering tunable parameters, site-resolved control, and rapid experimental repetition rates. Here, we study a superconducting-qubit device that realizes the Bose-Hubbard model on a triangular-ladder lattice. By tuning the magnitude and sign of couplings, we engineer a synthetic magnetic flux to characterize the resulting half-filling ground state for various parameter regimes. We measure observables analogous to current-current correlators and bond kinetic energies, finding signatures consistent with chiral superfluids, Meissner superfluids, and bond-ordered insulators. Our results establish superconducting circuits as a platform for robustly probing quantum phases of matter in frustrated Bose-Hubbard systems, even in strongly correlated and gapless regimes.
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
Using modern micro and nano-fabrication techniques combined with superconducting materials we realize quantum electronic circuits in which we create, store, and manipulate individual microwave photons. The strong interaction of photons with superconducting quantum two-level systems allows us to probe fundamental quantum effects of microwave radiation and also to develop components for applications in quantum technology. Previously we have realized on-demand single photon sources which we have characterized using correlation function measurements [1] and full quantum state tomography [2]. For this purpose we have developed efficient methods to separate the quantum signals of interest from the noise added by the linear amplifiers used for quadrature amplitude detection [3]. We now regularly employ superconducting parametric amplifiers [4] to perform nearly quantum limited detection of propagating electromagnetic fields. These enable us to probe the entanglement which we generate on demand between stationary qubits and microwave photons freely propagating down a transmission line [5]. Using two independent microwave single photon sources, we have recently performed Hong-Ou-Mandel experiments at microwave frequencies [6] and have probed the coherence of two-mode multi-photon states at the out-put of a beam-splitter. The non-local nature of such states may prove to be useful for distributing entanglement in future small-scale quantum networks.
Superconducting circuits operated at low temperatures have led to rapid advances in quantum information processing as well as quantum optics in the microwave regime. Engineered quantum systems with a dense spectrum of modes coupled to artificial atoms, or qubits, formed from superconducting circuits offer an opportunity to explore large-scale entanglement or perform quantum simulations of many-body phenomena. Recent research efforts into artificial metamaterials have yielded microwave and optical systems with numerous counterintuitive properties, including left-handed transmission, where the group velocity and phase velocity for a wave point in opposite directions. Metamaterial resonators implemented with superconducting thin-film circuits provide a route to generating dense mode spectra in the microwave regime for coupling to qubits. In this thesis, we discuss the implementation of such superconducting metamaterial resonators. First, we derive the dispersion relation for one-dimensional metamaterial transmission lines and we describe the formation of resonators from such lines and their quality factors. Next, we describe the design and fabrication of transmission-line metamaterial resonators using superconducting thin films. We characterize the metamaterials through low-temperature microwave measurements as well as Laser Scanning Microscope (LSM) images of the microwave field distributions in the circuit. We compare these various measurements with numerical simulations of the microwave properties of the circuits, including simulated current density and charge density distributions for the excitation of different resonance modes. Following the successful realization of dense mode spectra in these circuits, we have initiated the first experiments with a superconducting transmon qubit coupled to a metamaterial resonator and we describe our progress in this direction.