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arXiv:1606.07466 · Physical Review A

Chiral quantum optics with V-level atoms and coherent quantum feedback

Pierre-Olivier Guimond, Hannes Pichler, Arno Rauschenbeutel, P. Zoller

Published Sep 16, 2016• 57 citations
arXivHTMLPDF

Abstract

We study the dissipative dynamics of an atom in a V-level configuration driven by lasers and coupled to a semi-infinite waveguide. The coupling to the waveguide is chiral, in that each transition interacts only with the modes propagating in a given direction, and this direction is opposite for the two transitions. The waveguide is terminated by a mirror which coherently feeds the photon stream emitted by one transition back to the atom. First, we are interested in the dynamics of the atom in the Markovian limit where the time delay in the feedback is negligible. Specifically, we study the conditions under which the atom evolves towards a pure ``dark'' stationary state, where the photons emitted by both transitions interfere destructively thanks to the coherent feedback, and the overall emission vanishes. This is a single-atom analog of the quantum dimer, where a pair of laser-driven two-level atoms is coupled to a unidirectional waveguide and dissipates towards a pure entangled dark state. Our setup should be feasible with current state-of-the-art experiments. Second, we extend our study to non-Markovian regimes and investigate the effect of the feedback retardation on the steady state.

DOI
10.1103/physreva.94.033829

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We study the dissipative dynamics of an atom in a V-level configuration driven by lasers and coupled to a semi-infinite waveguide. The coupling to the waveguide is chiral, in that each transition interacts only with the modes propagating in a given direction, and this direction is opposite for the two transitions. The waveguide is terminated by a mirror which coherently feeds the photon stream emitted by one transition back to the atom. First, we are interested in the dynamics of the atom in the Markovian limit where the time delay in the feedback is negligible. Specifically, we study the conditions under which the atom evolves towards a pure ``dark'' stationary state, where the photons emitted by both transitions interfere destructively thanks to the coherent feedback, and the overall emission vanishes. This is a single-atom analog of the quantum dimer, where a pair of laser-driven two-level atoms is coupled to a unidirectional waveguide and dissipates towards a pure entangled dark state. Our setup should be feasible with current state-of-the-art experiments. Second, we extend our study to non-Markovian regimes and investigate the effect of the feedback retardation on the steady state.
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In this work, we investigate the non-Markovian (NM) dynamical evolution of a three-level atom coupled to a semi-infinite one-dimensional photonic waveguide and driven by a classical driving field. The single-end of waveguide behaves as a perfect mirror while light can pass through the opposite end with no backreflection. We derive the exact analytical expressions for the wave function of the driven three-level atom by solving a set of delay differential equations and give the conditions of atom-photon bound state formation that can inhibit the dissipation, which appears in the atom-mirror interspace in order to trap a considerable amount of initial atomic excitation. We show that when the evolution time of the system is shorter than the time delay taken by a photon to perform a round trip between the atom and mirror, the atomic dynamics exhibits Markovian properties, which depend on the driving strength and rescaled parameters. If the evolution time of the system exceeds the time delay, the photon can be reabsorbed by the atom with the photon emitted by the atom having completed the round trip, which exhibits NM memory effects, where the population eventually convergences to the finite-steady values. We also study the influence of the loss and dephasing on the formation of a bound state. Finally, the above results are extended to a more general quantum system involving single-end photonic waveguide coupled to an arbitrary number of noninteracting three-level atoms driven by the driving fields. The presented formalism might open a way to better understand exactly the NM dynamics of driven multilevel atoms coupled to a semi-infinite waveguide.
Abstract. In this paper, we demonstrate the application of quantum feedback control in creating desired states for atomic and photonic systems utilizing a semi-infinite waveguide coupled with multiple two-level atoms. In this approach, an initially excited atom can emit one photon into the waveguide, and the photon can be reflected by either the terminal mirror of the waveguide or other atoms, establishing various feedback loops through the coherent interactions between the atom and photon. When there are no more than two excitations in the waveguide quantum electrodynamics (QED) system, the evolution of quantum states can be effectively elucidated through the lens of random graph theory. However, this process is influenced by the environment. We propose that the environment-induced dynamics in the coherent feedback loop can be eliminated by measurement-based feedback control or coherent drives. Consequently, in the atom-waveguide interactions in open quantum systems, measurement-based feedback has the potential to modulate the quantum steady states. Additionally, the homodyne detection noise during the measurement process can induce errors upon quantum states, which can be influenced by the coherent feedback parameter designs.
Non-Markovian dynamics with ΛΛΛ-type atomic systems in a single end photonic waveguide
In this work, we investigate the non-Markovian dynamical evolution of a ΛΛΛ-type atom interacting with a semi-infinite one-dimensional photonic waveguide via two atomic transitions. The waveguide terminates at a perfect mirror, which reflects the light and introduces boundary effects. We derive exact analytical expressions and show that, under suitable conditions, the instantaneous and retarded decay rates reach equilibrium, leading to the formation of an atom-photon bound state that suppresses dissipation. Consequently, the atom retains a long-lived population in the asymptotic time limit. Furthermore, we analyze the output field intensity and demonstrate that blocking one of the coupling channels forces the atomic system to emit photons of a single frequency. Finally, we extend the model to a two-atom system and examine the disentanglement dynamics of the two spatially separated atoms. These findings elucidate the dynamic process of spontaneous emission involving multi-frequency photons from multi-level atoms and provide insights into the complex interference between different decay pathways.
We consider the nonequilibrium dynamics of a driven dissipative spin chain with chiral coupling to a one-dimensional (1D) bosonic bath, and its atomic implementation with a two-species mixture of cold quantum gases. The reservoir is represented by a spin-orbit coupled 1D quasicondensate of atoms in a magnetized phase, while the spins are identified with motional states of a separate species of atoms in an optical lattice. The chirality of reservoir excitations allows the spins to couple differently to left- and right-moving modes, which in our atomic setup can be tuned from bidirectional to purely unidirectional. Remarkably, this leads to a pure steady state in which pairs of neighboring spins form dimers that decouple from the remainder of the chain. Our results also apply to current experiments with two-level emitters coupled to photonic waveguides.
We investigated the spontaneous emission of a giant atom coupled with a semi-infinite waveguide. Our model considers the giant atom a two-level system coupled to the semi-infinite waveguide at two points. Based on the Hamiltonian in real space, the first-order delay-differential equation for the atomic excitation amplitude is obtained using the Schrödinger equation. Furthermore, the dynamics of spontaneous emission controlled by quantum coherent feedback due to the semi-infinite waveguide in the non-Markov regime are discussed in two cases, with the coupling strengths between the giant atom and the semi-infinite waveguide at the two coupling points being identical in one case and having a phase difference in the other case. The spontaneous emission exhibits partial decay due to multiple excitations from the quantum feedback and two-point coupling. When the coupling strengths are identical, the decay of the atomic excitation can be either increased or inhibited substantially, even forming a steady state, due to the self-interference due to the two-point coupling. The quantum coherent feedback can either further increase the decay of the excited state or maintain the steady state formed by self-interference. Moreover, a new steady state can be built due to quantum coherent feedback, which cannot exist in the self-interference system. The decay rates can also be increased or decreased by manipulating the phase difference between the coupling strengths at the two coupling points. It can destroy the steady state formed by self-interference or build a steady state based on the chosen phase difference. One can leverage quantum coherent feedback to manipulate the steady state value of the population of the excited states by adjusting the phase difference. The dissipation can increase the decay rates of the excited states. Furthermore, it also destroys steady states. Our results may find applications in developing quantum devices such as quantum memory based on giant atom-waveguide systems.