We consider a circuit-QED setup that allows the induction and control of non-Markovian dynamics of a qubit. Non-Markovianity is enforced over the qubit by means of its direct coupling to a bosonic mode which is controllably coupled to other qubit-mode system. We show that this configuration can be achieved in a circuit-QED setup consisting of two initially independent superconducting circuits, each formed by one charge qubit and one transmission-line resonator, which are put in interaction by coupling the resonators to a current-biased Josephson junction. We solve this problem exactly and then proceed with a thorough investigation of the emergent non-Markovianity in the dynamics of the qubits. Our study might serve the context for a first experimental assessment of non-Markovianity in a multi-element solid-state device.Comment: 8 pages, 7 figures, slightly changed titl

We present a study of the strong coupling between radiation and matter, considering a system of two quantum dots, which are in mutual interaction and interact with a single mode of light confined in a semiconductor nanocavity. We take into account dissipative mechanisms such as the escape of the cavity photons, decay of the quantum dot excitons by spontaneous emission, and independent exciton pumping. It is shown that the mutual interaction between the dots can be measured off-resonance only if the strong coupling condition is reached. Using the quantum regression theorem, a reasonable definition of the dynamical coupling regimes is introduced in terms of the complex Rabi frequency. Finally, the emission spectrum for relevant conditions is presented and compared with the above definition, demonstrating that the interaction between the excitons does not affect the strong coupling.

The interaction of qubits with quantized modes of electromagnetic fields has been largely addressed in the quantum optics literature under the rotating wave approximation (RWA), where rapid oscillating terms in the qubit-mode interaction picture Hamiltonian can be neglected. At the same time, it is generally accepted that provided the interaction is sufficiently strong or for long times, the RWA tends to describe physical phenomena incorrectly. In this work, we extend the investigation of the validity of the RWA to a more involved setup where two qubit-mode subsystems are brought to interaction through their harmonic coordinates. Our treatment is all analytic thanks to a sequence of carefully chosen unitary transformations which allows us to diagonlize the Hamiltonian within and without the RWA. By also considering qubit dephasing, we find that the purity of the two-qubit state presents non-Markovian features which become more pronounced as the coupling between the modes gets stronger and the RWA loses its validity. In the same regime, there occurs fast generation of entanglement between the qubits which is also not correctly described under the RWA. The setup and results presented here clearly show the limitations of the RWA in a scenario amenable to exact description and free from numerical uncertainties. Consequently, it may be of interest for the community working with cavity or circuit quantum electrodynamic systems in the strong coupling regime.

We study the strong coupling between light and two interacting excitons in Quantum-dots (QDs). We derive a reasonable definition of the dynamical regimes in the system by incorporating coherent and spontaneous emission and incoherent pumping.OCIS codes: 250.5230 Photoluminescence, 140.3945 Microcavities Cavity Quantum Electrodynamics (CQED) has provided an appropriate framework for understanding the interaction between light and matter in a full quantum level. One of the most important accomplishments of CQED is the reversible exchange of energy between light and matter, the strong coupling (SC) regime. This regime was achieved in high finesse cavities with Rydberg atoms several years ago [1]. It was also realized in semiconductor systems in which the discrete level structure of QDs resembles the atomic CQED physics [2]. Recently it was pointed out that the paradigm of atomic physics is not fully equivalent to its counterpart in solid state nano structures [3]. This is because at variance to what happens in atomic CQED what is observed in photoluminescence experiments in nano cavities is the light that escapes from the system when it has reached its steady state (SS). This SS corresponds to an statistical mixture of states with different number of photons and matter excitations and its brought to existence by the different nature of the excitation mechanisms used in solid state systems. In this work we extend the model presented in [3] to include one more exciton in a spatially separated QD, allowing the two excitons to interact via a Förster interaction that permits the hopping of the excitations between the two QDs[4]. The Hamiltonian dynamics is given byĤwhere the first term corresponds to the free field Hamiltonian with creationâ † and annihilationâ operators of photons with energy ω 0 = ω X − ∆. The first term in the sum is the exciton energy. The operatorsσ † i = |X i G i | andσ i = |G i X i | are the creation and annihilation operators of the ith exciton. The exciton is modeled as a two level system, where the ground state |G (exciton state |X ) corresponds to the absence (presence) of excitations. The transition energy between these states is ω X . The second term in the sum describes the dipolar interaction between the QDs and the light mode in the rotating wave approximation. The strength of such interaction is given by g. Finally, the last term accounts for the Förster exciton-exciton interaction, with coupling constant g 12 . We use a quantum master equation to include dissipative effects such as coherent and spontaneous emission (with rates κ and γ) and incoherent pumping of the QDs (with rate P). The master equation that we use to model the system iswhere LÔ{ρ} = 2ÔρÔ † −Ô †Ôρ −ρÔ †Ô . We derive the emission spectrum of the system by taking the Fourier transform of the first order correlation function in the stationary limit G(τ) = lim t→∞ G (1) (t, τ) = lim t→∞ â † (t + τ)â(t) . In the limit of small yet not negligible pumping (because in this case the SS is the light-matter vacuum) of the dots...

In this comment we show that there is a direct connection between coherent exchange of energy among light and matter and the emission spectrum of a microcavity quantum dot system as modeled in Phys. Rev. B 79, 235325 (2009) by F. P. Laussy, E. del Valle, and C. Tejedor. To do so, we show that in their model the necessary and sufficient conditions for having eigenvalues with non-zero imaginary parts in the propagator of the bare mode populations, are the same as for having strong coupling in the emission spectrum. This amounts to saying that, whenever there is strong coupling there will be oscillating frequencies in the dynamics of the populations. These conditions are valid both for the case where matter is treated as bosonic or fermionic, in the spontaneous emission case.