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arXiv:1409.1353 · Journal of Nanophotonics

Multiphoton interaction of a qutrit with single-mode quantized field in the ultrastrong and deep strong coupling regimes

Hamlet K. Avetissian, Ara K. Avetissian, Garnik F. Mkrtchian, Oleg V. Kibis

Published Jul 23, 2015• 1 citation
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Abstract

We consider the multiphoton dynamics of a quantum system composed of a three-state atom (a qutrit) and a single-mode photonic field in the ultrastrong and deep strong coupling regimes, when the coupling strength is comparable to or larger than the oscillator energy scale. We assume a qutrit to be in a L configuration, where an upper level is coupled to a twofold degenerate lower level. Direct multiphoton resonant transitions revealing generalized Rabi oscillations, collapse, and revivals in atomic excitation probabilities for the ultrastrong couplings are studied. In the deep strong coupling regime, particular emphasis is placed on the ground state of the considered system which strictly exhibits nonclassical properties.

DOI
10.1117/1.jnp.9.093064

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We consider the multiphoton dynamics of a quantum system composed of a three-state atom (a qutrit) and a single-mode photonic field in the ultrastrong and deep strong coupling regimes, when the coupling strength is comparable to or larger than the oscillator energy scale. We assume a qutrit to be in a L configuration, where an upper level is coupled to a twofold degenerate lower level. Direct multiphoton resonant transitions revealing generalized Rabi oscillations, collapse, and revivals in atomic excitation probabilities for the ultrastrong couplings are studied. In the deep strong coupling regime, particular emphasis is placed on the ground state of the considered system which strictly exhibits nonclassical properties.
Multiphoton resonant excitation of a three-state quantum system (a qutrit) with a single-mode photonic field is considered in the ultrastrong coupling regime, when the qutrit–photonic field coupling rate is comparable to appreciable fractions of the photon frequency. For ultrastrong couplings, the obtained solutions of the Schrödinger equation that reveal multiphoton Rabi oscillations in qutrits with the interference effects leading to the collapse and revival of atomic excitation probabilities at the direct multiphoton resonant transitions.
The prototypical system constituted by a two-level atom interacting with a quantized single-mode electromagnetic field is described by the quantum Rabi model (QRM). The QRM is potentially valid at any light-matter interaction regime, ranging from the weak (where the decay rates exceeds the coupling rate) to the deep strong coupling (where the interaction rate exceeds the bare transition frequencies of the subsystems). However, when reaching the ultrastrong coupling regime, several theoretical issues may prevent the correct description of the observable dynamics of such a system: (i) the standard quantum optics master equation fails to correctly describe the interaction of this system with the reservoirs; (ii) the correct output photon rate is no longer proportional to the intracavity photon number; and (iii) they appear to violate gauge invariance. Here, we study the photon flux emission rate of this system under the incoherent excitation of the two-level atom for any light-matter interaction strength and consider different effective temperatures. The dependence of the emission spectra on the coupling strength is the result of the interplay between energy levels, matrix elements of the observables, and the density of states of the reservoirs. Within this approach, we also study the occurrence of light-matter decoupling in the deep strong-coupling regime and show how all of the obtained results are gauge invariant.
When an atom is strongly coupled to a cavity, the two systems can exchange a single photon through a coherent Rabi oscillation. This process enables precise quantum-state engineering and manipulation of atoms and photons in a cavity, which play a central role in quantum information and measurement. Recently, a new regime of cavity QED was reached experimentally where the strength of the interaction between light and artificial atoms (qubits) becomes comparable to the atomic transition frequency or the resonance frequency of the cavity mode. Here we show that this regime can strongly modify the concept of vacuum Rabi oscillations, enabling multiphoton exchanges between the qubit and the resonator. We find that experimental state-of-the-art circuit-QED systems can undergo two- and three-photon vacuum Rabi oscillations. These anomalous Rabi oscillations can be exploited for the realization of efficient Fock-state sources of light and complex entangled states of qubits.
We study the system involving mutual interaction between three qubits and an oscillator within the ultrastrong coupling regime. We apply the adiabatic approximation approach to explore two extreme regimes: (i) the oscillator's frequency is far larger than each qubit's frequency and (ii) the qubit's frequency is far larger than the oscillator's frequency, and analyze the energy-level spectrum and the ground-state property of the qubit-oscillator system under the conditions of various system parameters. For the energy-level spectrum, we concentrate on studying the degeneracy in low-energy levels. For the ground state, we focus on its nonclassical properties that are necessary for preparing the nonclassical states. We show that the minimum qubit-oscillator coupling strength needed for generating the nonclassical states of the Schr\"odinger-cat type in the oscillator is just one half of that in the Rabi model. We find that the qubit-qubit entanglement in the ground state vanishes if the qubit-oscillator coupling strength is strong enough, for which the entropy of three qubits remains larger than 1. We also observe the phase-transition-like behavior in the regime where the qubit's frequency is far larger than the oscillator's frequency.
We compare the semiclassical and quantum predictions for the unitary dynamics of a two-level atom interacting with a single-mode electromagnetic field under parametric modulation of the atomic parameters in the regime of multiphoton atom–field resonances. We derive approximate analytic solutions for the semiclassical Rabi model when the atomic transition frequency and the atom–field coupling strength undergo harmonic external modulations. These solutions are compared to the predictions of the quantum Rabi model, which we solve numerically for an initial coherent state with a large average photon number (on the order of 104), in the regime of three-photon resonance. We show that, for short enough times and sufficiently intense coherent states, the semiclassical dynamics agrees quite well with the quantum dynamics, although it inevitably fails at longer times due to the absence of collapse–revival behavior. Furthermore, we describe how the field state evolves throughout the interaction, presenting numerical results for the average photon number, entropies (related to atom–field entanglement), and other quantities characterizing the photon number statistics of the electromagnetic field.
We theoretically investigate quantum Rabi oscillations in a system consisting of a two-level atom (qubit) strongly coupled to a one-dimensional open waveguide. In contrast to conventional cavity quantum electrodynamics, the qubit interacts with a continuum of propagating modes, which gives rise to fundamentally different dynamical behavior. Within the rotating-wave approximation, we express the multimode Jaynes-Cummings Hamiltonian in terms of collective bosonic operators and show that the system possesses two integrals of motion, enabling an exact diagonalization of the Hamiltonian in the single-excitation subspace. We show that for a strongly interacting qubit-photon system, the dynamics are captured by a reduced two-level model. In this framework, each level is defined as the product of the atomic excited state and a specific field mode, which takes the form of a multiphoton Fock-like state. In this picture, the Rabi oscillations represent a collective phenomenon corresponding to oscillations between multiphoton states differing by a single photon. We then extend our analysis to multiphoton processes in which the initial field is a coherent state with a continuous spectrum. In this case, the Rabi frequency is shown to be sensitive to the spectral profile of the function that generates the coherent state.