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arXiv:1602.00926 · Physical Review A

Non-Markovian dynamics in chiral quantum networks with spins and photons

Tomás Ramos, Benoît Vermersch, Philipp Hauke, Hannes Pichler, P. Zoller

Published Jun 2, 2016• 130 citations
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Abstract

We study the dynamics of chiral quantum networks consisting of nodes coupled by unidirectional or asymmetric bidirectional quantum channels. In contrast to familiar photonic networks where driven two-level atoms exchange photons via 1D photonic nanostructures, we propose and study a setup where interactions between the atoms are mediated by spin excitations (magnons) in 1D $XX$ spin chains representing spin waveguides. While Markovian quantum network theory eliminates quantum channels as structureless reservoirs in a Born-Markov approximation to obtain a master equation for the nodes, we are interested in non-Markovian dynamics. This arises from the nonlinear character of the dispersion with band-edge effects, and from finite spin propagation velocities leading to time delays in interactions. To account for the non-Markovian dynamics we treat the quantum degrees of freedom of the nodes and connecting channel as a composite spin system with the surrounding of the quantum network as a Markovian bath, allowing for an efficient solution with time-dependent density matrix renormalization-group techniques. We illustrate our approach showing non-Markovian effects in the driven-dissipative formation of quantum dimers, and we present examples for quantum information protocols involving quantum state transfer with engineered elements as basic building blocks of quantum spintronic circuits.

DOI
10.1103/physreva.93.062104

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We study the dynamics of chiral quantum networks consisting of nodes coupled by unidirectional or asymmetric bidirectional quantum channels. In contrast to familiar photonic networks where driven two-level atoms exchange photons via 1D photonic nanostructures, we propose and study a setup where interactions between the atoms are mediated by spin excitations (magnons) in 1D XXXXXX spin chains representing spin waveguides. While Markovian quantum network theory eliminates quantum channels as structureless reservoirs in a Born-Markov approximation to obtain a master equation for the nodes, we are interested in non-Markovian dynamics. This arises from the nonlinear character of the dispersion with band-edge effects, and from finite spin propagation velocities leading to time delays in interactions. To account for the non-Markovian dynamics we treat the quantum degrees of freedom of the nodes and connecting channel as a composite spin system with the surrounding of the quantum network as a Markovian bath, allowing for an efficient solution with time-dependent density matrix renormalization-group techniques. We illustrate our approach showing non-Markovian effects in the driven-dissipative formation of quantum dimers, and we present examples for quantum information protocols involving quantum state transfer with engineered elements as basic building blocks of quantum spintronic circuits.
We study the dynamics of photonic quantum circuits consisting of nodes coupled by quantum channels. We are interested in the regime where the time delay in communication between the nodes is significant. This includes the problem of quantum feedback, where a quantum signal is fed back on a system with a time delay. We develop a matrix product state approach to solve the quantum stochastic Schrödinger equation with time delays, which accounts in an efficient way for the entanglement of nodes with the stream of emitted photons in the waveguide, and thus the non-Markovian character of the dynamics. We illustrate this approach with two paradigmatic quantum optical examples: two coherently driven distant atoms coupled to a photonic waveguide with a time delay, and a driven atom coupled to its own output field with a time delay as an instance of a quantum feedback problem.
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.
In this paper, we present a scheme to construct a quantum network based on optomagnonic systems where the photon-magnon coupling systems are connected by a waveguide. We derive the effective master equation of magnon modes by eliminating the waveguide modes and optical modes. By diagonalizing the dissipative part of the master equation, we identify dark modes so as to eliminate the effect of the dissipation induced by the waveguide. Employing dark modes, we investigate the quantum state transfer and entangled state generation in the two-node cascaded or chiral quantum network. We extend the method to an NNN-node quantum network and show the generation of a W state. We also consider the influence of experimental imperfections. Our scheme is meaningful for building a quantum network based on a magnonic system.
In this paper, we develop a quantum transport theory to describe photonic transport in photonic networks. The photonic networks concerned in the paper consist of all-optical circuits incorporating photonic bandgap waveguides and driven resonators. The photonic transport flowing through waveguides are entirely determined from the exact master equation of the driven resonators. The master equation of the driven resonators is obtained by explicitly eliminating all the waveguide degrees of freedom while the back-reactions between resonators and waveguides are fully taken into account. The relations between the driven photonic dynamics and photocurrents are obtained. The non-Markovian memory structure and quantum coherence and decoherence effects in photonic transport are also fully included. This quantum transport theory unifies two fundamental nonequilibrium approaches, the Keldysh's nonequilibrium Green function technique and the Feynman-Vernon influence functional approach, together to make the investigation of the transient quantum photonic transport become more powerful. As an illustration, the theory is applied to the transport phenomena of a driven nanocavity coupled to two waveguides in photonic crystals. The controllability of photonic transport through the driven resonator is demonstrated.
Harnessing power-law interactions ( 1/r^\alpha 1 / r α ) in a large variety of physical systems are increasing. We study the dynamics of chiral spin chains as a possible multi-directional quantum channel. This arises from the nonlinear character of the dispersion with complex quantum interference effects. Using complementary numerical and analytical techniques, we propose a model to guide quantum states to a desired direction. We illustrate our approach using the long-range XXZ model modulated by Dzyaloshinskii-Moriya (DM) interaction. By exploring non-equilibrium dynamics after a local quantum quench, we identify the interplay of interaction range \alpha α and Dzyaloshinskii-Moriya coupling giving rise to an appreciable asymmetric spin excitations transport. This could be interesting for quantum information protocols to transfer quantum states, and it may be testable with current trapped-ion experiments. We further explore the growth of block entanglement entropy in these systems, and an order of magnitude reduction is distinguished.
The implementation of quantum routers is an important and desired task in quantum information science, since quantum routers are important components of quantum networks. Here, we propose a scheme for implementing single-photon routers in a waveguide-QED system, which consists of two coupled two-level atoms coupled to two waveguides to form a four-port quantum device. We obtain the exact analytical expressions of the single-photon scattering amplitudes using the real-space method. By taking the propagating time of photons between two coupling points into account or not, we consider the system working in the Markovian and non-Markovian regimes, respectively. In addition, we introduce the chiral coupling, which breaks the symmetry of the waveguide model, to manipulate the transmission of single photons. We find that when the system works in the non-Markovian regime, the single photon can be transmitted on demand by adjusting the asymmetry coefficient. More interestingly, the complete single-photon routing in this device does not require an ideal chiral coupling, loosening the photon transport conditions. This work will motivate the studies concerning the nonreciprocal and chiral quantum devices in the waveguide-QED platform.