Abstract

We study the Dicke-Ising model: an Ising chain in which all spins couple to a common boson mode. Due to competing spin-spin (Ising) and spin-boson (Dicke) interaction channels, different sectors of the phase diagram exhibit both second- and first-order superradiant quantum phase transitions (QPTs). At the QPT, the system evolves from a trivial ferromagnetic configuration with an empty boson mode to a highly entangled superradiant state with a boson condensate. In the first part of the talk, we discuss the free-energy landscape near the QPT, obtained after integrating out the spin variables. In the second part, we propose a digital-analog quantum simulator for this model based on an ensemble of interacting qubits coupled to a single-mode photonic resonator. We present a quantum circuit in which the many-body propagator is decomposed via Trotterization into layers with single- and two-qubit rotations alternating with Jaynes-Cummings (JC) gates that emulate spin-boson coupling. The JC gate has already been implemented with a tunable transmon coupled to a resonator [Langford et al., Nat. Comms. 8, 1715 (2017)]. This gate is analog because it exploits rotations in the resonator’s native Hilbert space. We show that the superradiant phase can be approximated by the circuit with a relatively short depth. Applying a selective measurement of global qubit parity, one obtains a Schrödinger cat state in the photonic subspace—a hallmark of the superradiant ground state in finite-size systems. The cat state can be probed via Wigner tomography of the resonator field. For further details, see [Shapiro et al., PRA 112, 042412 (2025)]