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Journal of Experimental and Theoretical Physics Letters

Enhanced vibrational quantum dynamics beyond the rotating wave approximation

Sergiu Carlig, Mihai Macovei

Published Apr 1, 2017• 1 citation
Publisher

Abstract

We investigate the vibrational dynamics of a quantum mechanical resonator when an ensemble of laser pumped two-level emitters are fixed on it. Beyond the rotating wave approximation with respect to phonon’s variables, one can obtain an interesting phonon quantum dynamics if the quantum emitter’s variables are faster than those describing the mechanical resonator. Particularly, for certain parameters, one can obtain an enhanced phonon emission as well as larger phonon–phonon correlations in the steady state.

DOI
10.1134/s0021364017080033

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We investigate the vibrational dynamics of a quantum mechanical resonator when an ensemble of laser pumped two-level emitters are fixed on it. Beyond the rotating wave approximation with respect to phonon’s variables, one can obtain an interesting phonon quantum dynamics if the quantum emitter’s variables are faster than those describing the mechanical resonator. Particularly, for certain parameters, one can obtain an enhanced phonon emission as well as larger phonon–phonon correlations in the steady state.
The entanglement dynamics of a laser-pumped two-level quantum dot pair is investigated in the steady state. The closely spaced two-level emitters, embedded in a semiconductor substrate, interact with both the environmental vacuum modes of the electromagnetic field reservoir as well as with the lattice vibrational phonon thermostat. We have found that the entanglement among the pair’s components is substantially enhanced due to the presence of the phonon subsystem. The reason is phonon-induced decay among the symmetrical and antisymmetrical two-qubit collective states and, consequently, the population of the latter one. This also means that through thermal phonon bath engineering one can access the subradiant two-particle cooperative state.
We investigate the feasibility of correlating an optical cavity field and a vibrational phonon mode. A laser pumped quantum dot fixed on a nanomechanical resonator beam interacts as a whole with the optical resonator mode. When the quantum dot variables are faster than the optical and phonon ones, we obtain a final master equation describing the involved modes only. Increasing the temperature, which directly affects the vibrational degrees of freedom, one can as well influence the cavity photon intensity, i.e., the optical and phonon modes are correlated. Furthermore, the corresponding Cauchy-Schwarz inequality is violated demonstrating the quantum nature of those correlations.
"We investigate the collective quantum dynamics of an ensemble of two-level emitters, embedded in a crystal, and coherently pumped by a moderately intense, and externally applied coherent electromagnetic field. The ensemble is damped preponderantly via the surrounding phonon reservoir which mediates the inter-particle collective interactions. We have found that generally phonon transitions among the corresponding dressed states are taking place involving simultaneously many single emitters or pairs of two-level emitters, respectively. In both cases the phonon intensity can be proportional to the squared number of involved two-level emitters."
We generalize the dispersive theory of the Jaynes-Cummings model beyond the frequently employed rotating-wave approximation (RWA) in the coupling between the two-level system and the resonator. For a detuning sufficiently larger than the qubit-oscillator coupling, we diagonalize the non-RWA Hamiltonian and discuss the differences to the known RWA results. Our results extend the regime in which dispersive qubit readout is possible. If several qubits are coupled to one resonator, an effective qubit-qubit interaction of Ising type emerges, whereas RWA leads to isotropic XYXYXY interaction. This impacts on the entanglement characteristics of the qubits.
We study the dynamics of a quantum emitter coupled to a two-dimensional photonic crystal featuring a finite bandwidth with sharp edges and a Van-Hove singularity. We study the effect of strong system-bath coupling and non-Markovianity of the photonic environment using a nonperturbative approach based on the recently introduced NCA dynamical map for open quantum systems. We show that several characteristic features of the dynamics near a photonic band-edge such as the freezing of spontaneous emission and the maximum light-matter entanglement, get strongly modified in presence of counter-rotating terms in the system-bath coupling, beyond the rotating-wave approximation. Furthermore, by computing the spectral function of the quantum emitter we comment on the role played by atom-photon bound-state and show that this acquires a much larger lifetime once the rotating-wave approximation is relaxed.