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Chinese Physics B

Observation of quantum phase transitions toward the thermodynamic limit in a driven-dissipative hybrid quantum system

Zhen Chen, Guo-Qiang Zhang, Haifeng Yu, J. Q. You

Published Mar 10, 2026• 0 citations
Publisher

Abstract

Abstract Quantum phase transition (QPT) in the Dicke model has long attracted considerable interest due to its fundamental importance in quantum optics and many-body physics. Recent studies indicate that QPT-like behavior may also arise in the driven Tavis-Cummings (TC) model—a simplified variant of the Dicke model that neglects counter-rotating-wave coupling terms. Hybrid quantum systems, capitalizing on the advantages of different components, offer a promising platform to realize such many-body systems. Here, we experimentally observe a dissipative phase transition in the thermodynamic limit using a driven TC model, implemented by coupling an electron spin ensemble to a superconducting microwave resonator. This QPT behavior is detected via the measurements of Rabi splitting, which exhibits a unique dependence on the collective spin excitations of the system. Our findings provide a route to experimentally investigate critical phenomena in realistic many-body systems under decoherence, and promise potential applications in quantum simulation and other emerging quantum technologies.

DOI
10.1088/1674-1056/ae4f6f

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Abstract Quantum phase transition (QPT) in the Dicke model has long attracted considerable interest due to its fundamental importance in quantum optics and many-body physics. Recent studies indicate that QPT-like behavior may also arise in the driven Tavis-Cummings (TC) model—a simplified variant of the Dicke model that neglects counter-rotating-wave coupling terms. Hybrid quantum systems, capitalizing on the advantages of different components, offer a promising platform to realize such many-body systems. Here, we experimentally observe a dissipative phase transition in the thermodynamic limit using a driven TC model, implemented by coupling an electron spin ensemble to a superconducting microwave resonator. This QPT behavior is detected via the measurements of Rabi splitting, which exhibits a unique dependence on the collective spin excitations of the system. Our findings provide a route to experimentally investigate critical phenomena in realistic many-body systems under decoherence, and promise potential applications in quantum simulation and other emerging quantum technologies.
Quantum phase transitions (QPTs) describe when a many-body quantum system displays non-analytic behavior associated with a discontinuous change in a property of the ground state as a parameter is varied. The QPT in prototypical Dicke model is difficult to reach experimentally as the spin–field coupling strength must be quite large. In this work we describe a new model—the off-resonant Tavis–Cummings model where we drive the common mode, and discover a new type of QPT at quite low coupling strengths which are comparable with the geometric mean of the atomic and field detunings . Through analytic methods we demonstrate this QPT for both finite and infinite numbers of spins and show that |〈 J x ( J z )〉|/( N /2) ∼ | λ / λ c − 1| γ x ( γ z ) and 〈 a † a 〉/ N ∼ | λ / λ c − 1| γ a for λ ⩾ λ c , with critical exponents γ x ≈ 1/2, γ z ≈ 1 and γ a ≈ 1. We show that this QPT can be immediately observed by laboratory cavity-QED setups such as Bose–Einstein condensate in optical cavity and superconducting circuit-QED as well as a line of trapped ultracold ions.
Abstract We investigate the steady-state quantum phases and associated collective phenomena of an open Tavis–Cummings (TC) model driven by a two-photon source. The standard (non-dissipative) TC model describes the quantum phases of an ensemble of N q two-level quantum emitters interacting with a single-mode electromagnetic field. The interplay among coherent driving, dissipation, and dipole interactions of the open TC model results in emergent collective phenomena, leading to a dissipative or non-equilibrium phase transition from the normal to the superradiant phase. We solve the Liouvillian equation analytically using the semi-classical mean-field approximation. We carry out stability analysis of the steady-state phases and determine the phase boundary. The use of Holstein–Primakoff transformation in the thermodynamic limit N q → ∞ reduces the system to an effective coupled-oscillator model, the solution of which yields collective modes.
Abstract Quantum phase transitions (QPTs) are usually associated with many-body systems in the thermodynamic limit when their ground states show abrupt changes at zero temperature with variation of a parameter in the Hamiltonian. Recently it has been realized that a QPT can also occur in a system composed of only a two-level atom and a single-mode bosonic field, described by the quantum Rabi model (QRM). Here we report an experimental demonstration of a QPT in the QRM using a 171 Yb + ion in a Paul trap. We measure the spin-up state population and the average phonon number of the ion as two order parameters and observe clear evidence of the phase transition via adiabatic tuning of the coupling between the ion and its spatial motion. An experimental probe of the phase transition in a fundamental quantum optics model without imposing the thermodynamic limit opens up a window for controlled study of QPTs and quantum critical phenomena.
Quantum phase transitions play an important role in many-body systems and have been a research focus in conventional condensed-matter physics over the past few decades. Artificial atoms, such as superconducting qubits that can be individually manipulated, provide a new paradigm of realising and exploring quantum phase transitions by engineering an on-chip quantum simulator. Here we demonstrate experimentally the quantum critical behaviour in a highly controllable superconducting circuit, consisting of four qubits coupled to a common resonator mode. By off-resonantly driving the system to renormalize the critical spin-field coupling strength, we have observed a four-qubit nonequilibrium quantum phase transition in a dynamical manner; that is, we sweep the critical coupling strength over time and monitor the four-qubit scaled moments for a signature of a structural change of the system's eigenstates. Our observation of the nonequilibrium quantum phase transition, which is in good agreement with the driven Tavis-Cummings theory under decoherence, offers new experimental approaches towards exploring quantum phase transition-related science, such as scaling behaviours, parity breaking and long-range quantum correlations.
Abstract Quantum phase transitions (QPTs) are usually associated with many-body systems in the thermodynamic limit when their ground states show abrupt changes at zero temperature with variation of a parameter in the Hamiltonian. Recently it has been realized that a QPT can also occur in a system composed of only a two-level atom and a single-mode bosonic field, described by the quantum Rabi model (QRM). Here we report an experimental demonstration of a QPT in the QRM using a 171Yb+ ion in a Paul trap. We measure the spin-up state population and the average phonon number of the ion as two order parameters and observe clear evidence of the phase transition via adiabatic tuning of the coupling between the ion and its spatial motion. An experimental probe of the phase transition in a fundamental quantum optics model without imposing the thermodynamic limit opens up a window for controlled study of QPTs and quantum critical phenomena.
Phase transitions are fundamental phenomena in physics, characterized by abrupt changes in the properties of a system. While classical phase transitions occur due to thermal fluctuations, quantum phase transitions (QPTs) are driven by quantum fluctuations at zero temperature. In this work, we explore the presence of QPTs in cavity quantum electrodynamics systems using the Time-Dependent Variational Principle (TDVP), a semi-classical approach for analyzing complex quantum systems. Beginning with the Rabi model, where a single qubit interacts with a single-mode cavity field, we examine the influence of counter-rotating terms on the system's ground state properties. Subsequently, we extend our analysis to the Jaynes-Cummings model, where rotating-wave approximation applies, and finally, to the Dicke model, which considers the collective interaction of multiple qubits with a bosonic mode. For each model, we derive analytical expressions for the ground state properties and identify critical coupling strengths indicative of phase transitions. Our findings reveal second-order quantum phase transitions, including superradiant phases with distinct ground state behaviors, emphasizing the utility of TDVP in understanding QPTs across a variety of systems.