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arXiv:2605.14096

Transitions as the Native Objects of Dispersive Light-Matter Dynamics

Mohamed Meguebel, Maxime Federico, Louis Garbe, Nadia Belabas, Nicolas Fabre

quant-phSubmitted May 13, 2026• Announced May 15, 2026• 0 citations• Revised Jul 10, 2026 (v2)
v1 · May 13, 2026v2 · Jul 10, 2026v3 · Jul 13, 2026
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Abstract

We introduce a framework where light-matter transitions, rather than states, are the primary dynamical objects. Successive compositions of elementary transitions yield multiphoton processes with compact diagrammatic bookkeeping of resonant and off-resonant pathways. This approach enables transparent derivations of effective high-order Hamiltonians in the dispersive regime, foundational to quantum-information applications. Applied to the paradigmatic Jaynes-Cummings model, our framework reveals a photon-number-independent intrinsic Rabi frequency and persistent polaritonic hybridization in the dispersive regime, unifying resonant and dispersive limits.

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We introduce a framework where light-matter transitions, rather than states, are the primary dynamical objects. Successive compositions of elementary transitions yield multiphoton processes with compact diagrammatic bookkeeping of resonant and off-resonant pathways. This approach enables transparent derivations of effective high-order Hamiltonians in the dispersive regime, foundational to quantum-information applications. Applied to the paradigmatic Jaynes-Cummings model, our framework reveals a photon-number-independent intrinsic Rabi frequency and persistent polaritonic hybridization in the dispersive regime, unifying resonant and dispersive limits.
This work presents a pedagogical and self-contained derivation of the first-order effective Hamiltonian for the two-mode Jaynes-Cummings model in the dispersive regime. A perturbative unitary transformation removes nonresonant atom-field terms, revealing dispersive frequency shifts leading to an atom-induced effective beam-splitter interaction between the field modes. The resulting Hamiltonian is diagonalized through a simple geometric rotation in the two-mode bosonic space, providing a transparent interpretation of the underlying dynamics. The exposition emphasized clarity and physical insight, making effective Hamiltonian methods accessible for teaching and learning in multimode light-matter interactions.
We propose an adiabatic-elimination formalism in the dispersive regime based on a transition-centric perturbation theory. The perturbative expansion is recast into a diagrammatic framework, while adiabatic elimination is implemented through controlled projections onto transition subspaces. Our approach applies systematically at arbitrary perturbation order, and is suited to multilevel systems and multiple qubits in both cavity and waveguide quantum electrodynamics. It ultimately enables the explicit construction of effective higher-order Hamiltonians while bypassing important limitations of existing techniques, thereby providing a practical toolbox for multiphoton processes in the dispersive regime.
We follow the passage from complex amplitude bistability to phase bistability in the driven dissipative Jaynes-Cummings oscillator. Quasi -distribution functions in the steady state are employed, for varying qubit-cavity detuning and drive parameters, in order to track a first-order dissipative quantum phase transition up to the critical point marking a second-order transition and spontaneous symmetry breaking. We demonstrate the photon blockade breakdown in the dispersive regime, and find that the coexistence of cavity states in the regime of quantum bistability is accompanied by pronounced qubit-cavity entanglement. Focusing on the effect of quantum-activated switching for both coupled degrees of freedom, we move from a region of minimal entanglement in the dispersive regime, where we derive analytical perturbative results, to the threshold behaviour of spontaneous dressed-state polarization at resonance.
Photon-based strongly correlated lattice models like the Jaynes–Cummings and Rabi lattices differ from their more conventional relatives like the Bose–Hubbard model by the presence of an additional tunable parameter: the frequency detuning between the pseudo-spin degree of freedom and the harmonic mode frequency on each site. Whenever this detuning is large compared to relevant coupling strengths, the system is said to be in the dispersive regime. The physics of this regime is well-understood at the level of a single Jaynes–Cummings or Rabi site. Here, we extend the theoretical description of the dispersive regime to lattices with many sites, for both strong and ultra-strong coupling. We discuss the nature and spatial range of the resulting qubit–qubit and photon–photon coupling, demonstrate the emergence of photon-pairing and squeezing and illustrate our results by exact diagonalization of the Rabi dimer.
The dissipative quantum phase transitions experienced by a driven optical system are studied in order to understand the underlying light-matter coupling. The primary system under study is composed of a cavity mode coupled to a two-level system with dissipation being introduced through the interaction with a surrounding environment; an external coherent field is included to drive the system out of the ground state. The coupling is given by a generalized Rabi Hamiltonian, where rotating, gr, and counter-rotating, ngr, couplings are both present and can be adjusted independently. A comprehensive study of the different phases the system can exhibit as gr and n are varied is presented. From this, we construct a bridge between two limiting scenarios: (i) the Jaynes-Cummings limit (n = 0), where the system undergoes a phase transition by means of the breakdown of the photon blockade, and (ii) the driven Dicke limit ( = 1 ), where the normal to super-radiant phase transition is found. Novel behaviour encountered in an intermediate regime (1 > n > 0) is discussed. Attention is drawn towards the strong coupling regime, where changes at the one-photon level induce nonlinear effects and behaviour reminiscent of phase transitions is encountered with just a few photons present. A comparison between weak and strong coupling regimes, and, thus, an exploration of the effect of fluctuations over quantum phase transitions of light, is given through a survey of the phases an auxiliary optical system exhibits. This system is composed of two coupled nonlinear cavities that are driven coherently and damped through the interaction with the environment; it is seen to exhibit three phases. Two phases present high-correlation between the cavities and are differentiated by the photon statistics, transitioning from classical to quantum. The third phase is characterized by a highly localized field in one of the cavities. The departure from mean-field results is highlighted and a new way to characterize the possible phases of the system is proposed. Finally, the crucial role of quantum fluctuations is quantified and used to define the phases at hand.
We present a time-dependent variational approach with the multiple-Davydov-D2{\text{D}}_{2}D2​ trial state to simulate the dynamics of light-matter systems when the field is initially in a coherent state with an arbitrary finite mean photon number. The variational approach captures not only the system dynamics but also the field dynamics and is applicable to a variety of quantum models of light-matter interaction such as the Jaynes-Cummings model, Rabi model, and Dicke model and is capable of tackling multimode quantized fields. With a comparison of the variational and semiclassical dynamics of both the system and field, we illustrate that the variational dynamics from the quantum models agrees with those from the corresponding semiclassical models as long as the mean number of photons is sufficiently large. Moreover, we illustrate that in the crossover between the quantum and semiclassical limits, the quantum corrections lead to the collapse of the oscillations in dynamics, which is absent in the semiclassical models. The variational approach provides a unified treatment of light-matter interaction from the quantum to the semiclassical limit.