With the objective of simulating the physical behavior of electrons in a dynamic background, we investigate a cold atomic Bose-Fermi mixture confined in an optical lattice potential solely affecting the bosons. The bosons, residing in the deep superfluid regime, inherit the periodicity of the optical lattice, subsequently serving as a dynamic potential for the polarized fermions. Owing to the atom-phonon interaction between the fermions and the condensate, the coupled system exhibits a Berezinskii-Kosterlitz-Thouless transition from a Luttinger liquid to a Peierls phase. However, under sufficiently strong Bose-Fermi interaction, the Peierls phase loses stability, leading to either a collapsed or a separated phase. We find that the primary function of the optical lattice is to stabilize the Peierls phase. Furthermore, the presence of a confining harmonic trap induces a diverse physical behavior, surpassing what is observed for either bosons or fermions individually trapped. Notably, under attractive Bose-Fermi interaction, the insulating phase may adopt a fermionic wedding-cake-like configuration, reflecting the dynamic nature of the underlying lattice potential. Conversely, for repulsive interaction, the trap destabilizes the Peierls phase, causing the two species to separate.

We explore the statistical behavior of the light emanating from a coherently driven Jaynes–Cummings (JC) oscillator operating in the regime of multiphoton blockade with two monitored output channels causing the loss of coherence at equal rates. We do so by adopting an operational approach that draws the particle and wave aspects of the forward-scattered radiation together, building upon the relationship between quantum optical correlation functions and conditional measurements. We first derive an analytical expression of the intensity cross-correlation function at the peak of the two-photon JC resonance to demonstrate the breakdown of detailed balance. The application of the quantum trajectory theory in parallel with the quantum regression formula subsequently uncovers various aspects of temporal asymmetry in the quantum fluctuations characterizing the cascaded process through which a multiphoton resonance is established and read out. We find that monitoring different quadratures of the cavity field in conditional homodyne detection affects the times waited between successive photon counter “clicks,” which in turn trigger the sampling of the homodyne current. Despite the fact that the steady-state cavity occupation is of the order of a photon, monitoring of the developing bimodality also impacts the ratio between the emissions directed along the two decoherence channels.

2023 marked the 60th anniversary of the Jaynes–Cummings model, a foundational model in quantum optics. Over the years, its importance has expanded beyond traditional light–matter interaction systems, such as cavity QED. This special issue presents a collection of articles that showcase the evolution of the model’s applications, blending traditional topics with contemporary developments.

The Jaynes-Cummings Model (JCM) has been at the forefront of modern physics as one of the simplest, yet intricately nonlinear, models of light-matter interaction. Focusing on the omnipresence of the JCM across a range of disciplines, this significantly updated and comprehensive review conveys to the reader the fundamental generality of its formalism, looking at a wide range of applications in specific physical systems and across disciplines including atomic physics, quantum optics, solid-state physics and quantum information sciences. An ideal reference for researchers in quantum physics and quantum optics, the book also comprises an accessible introduction for students engaged with non-equilibrium quantum phase transitions, quantum computing and simulation, quantum many-body physics, cavity, circuit and waveguide quantum electrodynamics. Part of IOP Series in Quantum Technology. Full abstract Key features • Collects JCM physics and applications scattered across literature and different applications. • The exposition guides the reader through a rich and appealing landscape interlacing quantum optics and condensed-matter physics. • All chapters discuss theory and experiment, linked historically to the development of the various directions stemming from JC physics. This is accompanied by a thorough list of references to the key publications. • The presentation is kept concise, while continuous text is interspersed with various illustrations and an economical use of mathematical expressions.

We discuss the conditional measurement of field amplitudes by a nonclassical photon sequence in the Jaynes-Cummings (JC) model under multiphoton operation. We do so by employing a correlator of immediate experimental relevance to reveal a distinct nonclassical evolution in the spirit of Foster et al. [Phys. Rev. Lett. 85, 3149 (2000)]. The correlator relies on the complementary nature of the pictures obtained from different unravelings of a JC source master equation. We demonstrate that direct photodetection entails a conditioned separation of timescales, a quantum beat, and a semiclassical oscillation, produced by the coherent light-matter interaction in its strong-coupling limit. We single out the quantum beat in the analytical expression for the waiting-time distribution, pertaining to the particle nature of the scattered light, and find a negative spectrum of quadrature amplitude squeezing, characteristic of its wave nature for certain operation settings. Finally, we jointly detect the dual aspects through the wave-particle correlator, showing an asymmetric regression of fluctuations to the steady state which depends on the quadrature amplitude being measured.

We find that the phase-space representation of the electromagnetic field inside a driven cavity strongly coupled to a two-level atom can be employed to distinguish photon emissions along a ladder of dressed states sustaining a two-photon resonance. The emissions are told apart by means of the different quantum beats generated by the conditional states they prepare. Sample quantum trajectories explicitly reveal the difference in the transient due to the initial condition, in a background set by the Jaynes–Cummings spectrum and revealed by the strong-coupling limit. Their ensemble-averaged evolution is tracked for a time period similar to that waited for the loss of a next photon as the maximum non-exclusive probability, indicated by the peak of the intensity correlation function.

We show that the saturation of a multiphoton transition is accompanied by a gradual collapse of quantum multimodality in the strong-coupling limit of the weakly driven Jaynes-Cummings (JC) model. By means of a perturbative method, we illustrate the prominent role of quantum fluctuations by focusing on the two- and three-photon resonance operation in a regime where the steady-state average photon number is below or marginally above unity. We also reveal two coexistent quantum beats in the intensity correlation function of the forwards scattered photons. These beats, originating from the states mediating the cascaded decay, arise as a direct consequence of the distinct JC spectrum. Their interference coordinates with the alternation of positive and negative values of the Wigner function around the phase-space origin in the transient conditioned on a photodetection.

We calculate the cavity-field distribution in the Wigner representation for the two-photon resonance of the weakly driven Jaynes-Cummings (JC) oscillator in its strong-coupling limit. Using an effective four-level system, we analytically demonstrate the presence of steady-state and transient bimodality which breaks azimuthal symmetry in phase space. The two steady-state peaks are located at opposite positions and do not correspond to the two-photon amplitude of the driven transition. The developing bimodality is portrayed in parallel with the evolution of the intensity correlation function for the forward-scattered photons, before being finally contrasted to the few-photon steady-state and transient phase-space profiles for the cavity mode in the JC model driven on resonance.

We explore the role of quantum fluctuations in the strong-coupling limit of the dissipative Jaynes-Cummings oscillator driven on resonance. For weak excitation, we derive analytical expressions for the spectrum and the intensity correlation function for the photons scattered by the two-state atom coupled to the coherently driven cavity mode. We do so by writing down a birth-death process adding the higher orders in the excitation strength needed to go beyond the pure-state factorization, following the method introduced in Carmichael (2008). Our results for the first and second-order correlation functions are complemented by the numerical investigation of the waiting-time distribution for the photon emissions directed sideways, and the comparison with ordinary resonance fluorescence. To close out our discussion, we increase the driving field amplitude and approach the critical point organizing a second-order dissipative quantum phase transition by depicting the excitation pathways in the intracavity field distribution for a finite system size.

Critical slowing down of the time it takes a system to reach equilibrium is a key signature of bistability in dissipative first-order phase transitions. Understanding and characterizing this process can shed light on the underlying many-body dynamics that occur close to such a transition. Here, we explore the rich quantum activation dynamics and the appearance of critical slowing down in an engineered superconducting quantum circuit. Specifically, we investigate the intermediate bistable regime of the generalized Jaynes-Cummings Hamiltonian (GJC), realized by a circuit quantum electrodynamics (cQED) system consisting of a transmon qubit coupled to a microwave cavity. We find a previously unidentified regime of quantum activation in which the critical slowing down reaches saturation and, by comparing our experimental results with a range of models, we shed light on the fundamental role played by the qubit in this regime.