Many-body physics is traditionally concerned with systems of interacting massive particles. Recent studies of effective interactions between photons, induced in the circuit QED architecture by coupling the microwave field to superconducting qubits, have paved the way for photon-based many-body physics. We derive the magnitude and intrinsic signs of photon hopping amplitudes in such circuit QED arrays. For a finite, ring-shaped Jaynes-Cummings lattice exposed to a synthetic gauge field we show that degeneracies in the single-excitation spectrum emerge, which can give rise to strong correlations for the interacting system with multiple excitations. We calculate the homodyne transmission for such a device, explain the generalization of vacuum Rabi splittings known for the single-site Jaynes-Cummings model, and identify fingerprints of interactions beyond the linear response regime.
Jaynes-Cummings-Hubbard arrays provide unique opportunities for quantum emulation as they exhibit convenient state preparation and measurement, and in-situ tuning of parameters. We show how to realise strongly correlated states of light in Jaynes-Cummings-Hubbard arrays under the introduction of an effective magnetic field. The effective field is realised by dynamic tuning of the cavity resonances. We demonstrate the existence of Fractional Quantum Hall states by com- puting topological invariants, phase transitions between topologically distinct states, and Laughlin wavefunction overlap.
We present a new method to observe direct experimental evidence of Jaynes--Cummings nonlinearities in a strongly dissipative cavity quantum electrodynamics system, where large losses compete with the strong light-matter interaction. This is a highly topical problem, particularly for quantum dots in microcavities where transitions from higher rungs of the Jaynes--Cummings ladder remain to be evidenced explicitly. We compare coherent and incoherent excitations of the system and find that resonant excitation of the detuned emitter make it possible to unambiguously evidence few photon quantum nonl…
We show that a set of N identical qubits coupled to a single cavity resonator can be decomposed into a set of independent subsystems, which can be thought of as higher pseudospin generalisations of the Jaynes-Cummings model. We derive and analyse the solutions to the equations of motion and demonstrate unusual beating behaviour resulting from a new form of square-root-n-type non-linearity appearing within a pseudospin ladder. Furthermore, we propose a relative phase shift transformation which allows one to switch/initiate the multi-qubit state in a desired pseudospin configuration, and show ho…
We study the nonlinear response of a driven cavity QED system in the extreme strong coupling regime where the saturation photon number is below one by many orders of magnitude. In this regime, multi-photon resonances within the Jaynes--Cummings spectrum up to high order can be resolved. We identify an intensity and frequency range of the external coherent drive for which the system exhibits bistability instead of resonant multi-photon transitions. The cavity field evolves into a mixture of the vacuum and another quasi-classical state well separated in phase space. The corresponding time evolut…
We highlight the importance of quantum fluctuations in organizing a dissipative quantum phase transition for the driven Jaynes-Cummings interaction with variable qubit-cavity detuning. The system response presents a substantial difference from the predictions of the semiclassical theory, the extent of which is revealed in the properties of quantum bistability, and visualized with the help of quasi-distribution functions for the cavity field, subject to an appropriate scale parameter. States anticipated by the neoclassical theory of radiation coexist in the quantum picture, following the occurr…
The connectivity and tunability of superconducting quantum devices provide a rich platform to build quantum simulators and study novel many-body physics. Here we study quantum phase transition in a detuned multi-connected Jaynes-Cummings lattice, which can be constructed with superconducting circuits. This model is composed of alternatively connected qubits and cavity modes. Using a numerical method, we show that by varying the detuning between the qubits and the cavities, a phase transition from the superfluid phase to the Mott insulator phase occurs at commensurate fillings in a one-dimensio…
We demonstrate a qubit readout scheme that exploits the Jaynes-Cummings nonlinearity of a superconducting cavity coupled to transmon qubits. We find that in the strongly-driven dispersive regime of this system, there is the unexpected onset of a high-transmission "bright" state at a critical power which depends sensitively on the initial qubit state. A simple and robust measurement protocol exploiting this effect achieves a single-shot fidelity of 87% using a conventional sample design and experimental setup, and at least 61% fidelity to joint correlations of three qubits.
We study the dynamics of the photon entanglement, $E_{\mathrm{N}}(t)$, for the two-mode Jaynes-Cummings model in the few-photon case. The atomic transitions associated with the photons with different polarizations are assumed to be independent and, hence, the evolution of the "+"- and "-"-polarized photons is formally separable. However, due to the photons indistinguishability such interaction still leads to entanglement of initially disentangled states owing to the non-linear dependence of the characteristic frequencies on the photon population numbers. The time dependence of entanglement is …
A strong coupling expansion, based on the Kato-Bloch perturbation theory, which has recently been proposed by Eckardt et al. [Phys. Rev. B 79, 195131] and Teichmann et al. [Phys. Rev. B 79, 224515] is implemented in order to study various aspects of the Bose-Hubbard and the Jaynes-Cummings lattice model. The approach, which allows to generate numerically all diagrams up to a desired order in the interaction strength is generalized for disordered systems and for the Jaynes-Cummings lattice model. Results for the Bose-Hubbard and the Jaynes-Cummings lattice model will be presented and compared w…
We study analytically and numerically the properties of Jaynes-Cummings model under monochromatic driving. The analytical results allow to understand the regime of two branches of multi-photon excitation in the case of close resonance between resonator and driven frequencies. The rotating wave approximation allows to reduce the description of original driven model to an effective Jaynes-Cummings model with strong coupling between photons and qubit. The analytical results are in a good agreement with the numerical ones even if there are certain deviations between the theory and numerics in the …
An accurate modeling of a Josephson junction that is embedded in an arbitrary environment is of crucial importance for qubit design. We present a formalism to obtain a Lindblad master equation that describes the evolution of the system. As the qubit degrees of freedom oscillate with a well-defined frequency $ω_q$, the environment only has to be modeled close to this frequency. Different from alternative approaches, we show that this goal can be achieved by modeling the environment with only few degrees of freedom. We treat the example of a transmon qubit coupled to a stripline resonator. We de…
We analyze the Jaynes-Cummings model of quantum optics, in the strong-dispersive regime. In the bad cavity limit and on timescales short compared to the atomic coherence time, the dynamics are those of a nonlinear oscillator. A steady-state non-perturbative semiclassical analysis exhibits a finite region of bistability delimited by a pair of critical points, unlike the usual dispersive bistability from a Kerr nonlinearity. This analysis explains our quantum trajectory simulations that show qualitative agreement with recent experiments from the field of circuit quantum electrodynamics.
We explore how the Jaynes-Cummings ladder transpires in the emitted spectra of a two-level system in strong coupling with a single mode of light. We focus on the case of very strong coupling, that would be achieved with systems of exceedingly good quality (very long lifetimes for both the emitter and the cavity). We consider the incoherent regime of excitation, that is realized with semiconductors quantum dots in microcavities, and discuss how reasonable is the understanding of the systems in terms of transitions between dressed states of the Jaynes-Cummings Hamiltonian.
A generalisation of the Jaynes-Cummings-Hubbard model for coupled-cavity arrays is introduced, where the embedded two-level system in each cavity is replaced by a $Ξ$-type three-level system. We demonstrate that the resulting effective polariton-polariton interactions at each site are both two-body and three-body. By tuning the ratio of the two transition dipole matrix elements, we show that the strength and sign of the two-body interaction can be controlled whilst maintaining a three-body repulsion. We then proceed to demonstrate how different two-body and three-body interactions alter the me…
We study the quantum dynamics of a two-level system interacting with a quantized harmonic oscillator in the deep strong coupling regime (DSC) of the Jaynes-Cummings model, that is, when the coupling strength g is comparable or larger than the oscillator frequency w (g/w > 1). In this case, the rotating-wave approximation cannot be applied or treated perturbatively in general. We propose an intuitive and predictive physical frame to describe the DSC regime where photon number wavepackets bounce back and forth along parity chains of the Hilbert space, while producing collapse and revivals of the…
We study the effect of pure dephasing on the strong-coupling between a quantum dot and the single mode of a microcavity in the nonlinear regime. We show that the photoluminescence spectrum of the system has a robust tendency to display triplet structures, instead of the expected Jaynes-Cummings pairs of doublets at the incommensurate frequencies $\pm(\sqrt{n}\pm\sqrt{n-1})$ for integer $n$. We show that current experimental works may already manifest signatures of single photon nonlinearities.
We study experimentally and theoretically a coherently-driven strongly-coupled quantum dot-microcavity system. Our focus is on physics of the unexplored intermediate excitation regime where the resonant laser field dresses a strongly-coupled single exciton-photon (polariton) system resulting in a ladder of laser-dressed Jaynes-Cummings states. In that case both the coupling of the emitter to the confined light field of the microcavity and to the light field of the external laser are equally important, as proved by observation of injection pulling of the polariton branches by an external laser.…
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 …
We investigate the effects of considering two different incoherent pumpings over a microcavity-quantum dot system modelled using the Jaynes-Cummings Hamiltonian. When the system is incoherently pumped with polaritons it is able to sustain a large number of photons inside the cavity with Poisson-like statistics in the stationary limit, and also leads to a separable exciton-photon state. We also investigate the effects of both types of pumpings (Excitonic and Polaritonic) in the emission spectrum of the cavity. We show that the polaritonic pumping as considered here is unable to modify the dynam…
