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Physical Review Research

Quantum phase transitions in driven Fock-state lattices with synthetic gauge fields

Jingbin Yuan, Jinfeng Deng, Xiao Qi Wei, Dawei Wang

Published Nov 20, 2025• 1 citation
Publisher

Abstract

Quantum phase transitions (QPTs) typically emerge in the thermodynamic limit, yet a single-atom QPT can arise when it is coupled to a coherently driven cavity, which provides a simple and unique platform to engineer quantum states with quantum criticality. In this driven Jaynes-Cummings (JC) model, the cavity field becomes squeezed near the critical point. However, vanishing energy gaps at the critical points lead to nonadiabaticity, hindering the practical realization of squeezing. In this work, we introduce a spin-dependent cavity drive, which induces a synthetic gauge field in the Fock-state lattice and enriches the phase diagram of the driven JC model. Remarkably, the energy spectrum can remain discrete for all driving strengths, allowing an adiabatic preparation of squeezed states with robust energy gaps. Moreover, we identify a topological phase transition characterized by projected winding numbers in the presence of broken chiral symmetry. Our results unveil topology and QPTs in a quantized light-matter system and offer a robust strategy for realizing squeezed states.

DOI
10.1103/4fq1-nb4r

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Quantum phase transitions (QPTs) typically emerge in the thermodynamic limit, yet a single-atom QPT can arise when it is coupled to a coherently driven cavity, which provides a simple and unique platform to engineer quantum states with quantum criticality. In this driven Jaynes-Cummings (JC) model, the cavity field becomes squeezed near the critical point. However, vanishing energy gaps at the critical points lead to nonadiabaticity, hindering the practical realization of squeezing. In this work, we introduce a spin-dependent cavity drive, which induces a synthetic gauge field in the Fock-state lattice and enriches the phase diagram of the driven JC model. Remarkably, the energy spectrum can remain discrete for all driving strengths, allowing an adiabatic preparation of squeezed states with robust energy gaps. Moreover, we identify a topological phase transition characterized by projected winding numbers in the presence of broken chiral symmetry. Our results unveil topology and QPTs in a quantized light-matter system and offer a robust strategy for realizing squeezed states.
Phase transitions are commonly held to occur only in the thermodynamical limit of a large number of system components. Here, we exemplify at the hand of the exactly solvable Jaynes-Cummings (JC) model and its generalization to finite JC lattices that finite component systems of coupled spins and bosons may exhibit quantum phase transitions (QPTs). For the JC model we find a continuous symmetry-breaking QPT, a photonic condensate with a macroscopic occupation as the ground state, and a Goldstone mode as a low-energy excitation. For the two site JC lattice we show analytically that it undergoes a Mott-insulator to superfluid QPT. We identify as the underlying principle of the emergence of finite system QPTs the combination of increasing atomic energy and increasing interaction strength between the atom and the bosonic mode, which allows for the exploration of an increasingly large portion of the infinite dimensional Hilbert space of the bosonic mode. This suggests that finite system phase transitions will be present in a broad range of physical systems.
The interplay between topology and nonlinearity represents a central challenge in modern physics. Here, we investigate this interplay by considering a synthetic Su-Schrieffer-Heeger lattice with all-to-all nonlocal interactions. We find that the distinctive nonlinearity maintains an effective chiral symmetry and leads to a quantized nonlinear winding and Berry phase, as corroborated by the developed Bogoliubov nonlinear adiabatic theory. Increasing nonlinearity drives a sequence of topological transitions signaled by the appearance of characteristic swallowtail band structures at intermediate interaction strengths and band swapping in the strong nonlinear regime. The band swapping results in quantized fractional windings and double-period Bloch oscillations that are closely related to discrete time crystals. Remarkably, even starting from a topologically trivial linear system, nonlocal nonlinearity can induce an emergent topological phase with fractional windings. Experimentally, our model can be realized using photons in a degenerate optical cavity with Rydberg-mediated interactions. Our results establish a rigorous framework and pave the way for exploring nonlinear topological phenomena and their applications in synthetic quantum platforms.
Systems of strongly interacting atoms and photons, which can be realized wiring up individual cavity QED systems into lattices, are perceived as a new platform for quantum simulation. While sharing important properties with other systems of interacting quantum particles, here we argue that the nature of light-matter interaction gives rise to unique features with no analogs in condensed matter or atomic physics setups. By discussing the physics of a lattice model of delocalized photons coupled locally with two-level systems through the elementary light-matter interaction described by the Rabi model, we argue that the inclusion of counterrotating terms, so far neglected, is crucial to stabilize finite-density quantum phases of correlated photons out of the vacuum, with no need for an artificially engineered chemical potential. We show that the competition between photon delocalization and Rabi nonlinearity drives the system across a novel Z(2) parity symmetry-breaking quantum criticality between two gapped phases that share similarities with the Dicke transition of quantum optics and the Ising critical point of quantum magnetism. We discuss the phase diagram as well as the low-energy excitation spectrum and present analytic estimates for critical quantities.
Periodic driving is a ubiquitous tool for controlling experimental quantum systems. When the drive fields are of comparable, incommensurate frequencies, new theoretical tools are required to treat the resulting quasiperiodic time dependence. Similarly, new and surprising phenomena of topological origin may emerge in this regime, including the quantized pumping of energy from one drive field to another. This dissertation will describe how to exploit this energy pumping to coherently translate––or boost––quantum states of a cavity in the Fock basis. This protocol enables the preparation of highly excited Fock states for use in quantum metrology––one need only boost low occupation Fock states. Energy pumping, and hence boosting, may be achieved nonadiabatically as a robust edge effect associated to an anomalous localized topological phase (ALTP) of fermions on a wire, called the quasiperiodic Floquet-Thouless energy pump (QP pump). We present a simple coupled-layer model for the QP pump, and describe the broader topological classification which characterizes its robust properties. Finally, we argue that energy pumping by the edge modes is robust to the introduction of weak interactions between fermions, making the QP pump a stable, interacting, non-equilibrium phase of matter.
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.
Quantum sensing improves the accuracy of measurements of relevant parameters by exploiting the unique properties of quantum systems. The divergent susceptibility of physical systems near a critical point for quantum phase transition enables criticality-enhanced quantum sensing. The quantum Rabi model (QRM), composed of a single qubit coupled to a single bosonic field, represents a good candidate for realizing such critical enhancement for its simplicity, but it is experimentally challenging to achieve the ultrastrong qubit-field coupling required to realize the critical phenomena. In this work, we explore an alternative to construct the analog of the QRM for the sensing, exploiting the criticality appearing in the Jaynes-Cummings (JC) model whose bosonic field is parametrically driven, not necessitating the ultrastrong coupling condition, thus to some extent relaxing the requirement for practical implementation.