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We explore excitation transport within a one-dimensional chain of atoms where the atomic transition dipoles are coupled to the free radiation field. When the atoms are separated by distances smaller or comparable to the wavelength of the transition, the exchange of virtual photons leads to the transport of the excitation through the lattice. Even though this is a strongly dissipative system, we find that the transport is subradiant, that is, the excitation lifetime is orders of magnitude longer than the one of an individual atom. In particular, we show that a subspace of the spectrum is formed by subradiant states with a linear dispersion relation, which allows for the dispersionless transport of wave packets over long distances with virtually zero decay rate. Moreover, the group velocity and direction of the transport can be controlled via an external uniform magnetic field while preserving its subradiant character. The simplicity and versatility of this system, together with the robustness of subradiance against disorder, makes it relevant for a range of applications such as lossless energy transport and long-time light storage.
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A ring of sub-wavelength spaced dipole-coupled quantum emitters possesses only few radiant but many extraordinarily subradiant collective modes. These exhibit a 3D-confined spatial radiation field pattern forming a nano-scale high-Q optical resonator. We show that tailoring the geometry, orientation and distance between two such rings allows for increasing the ratio of coherent ring-to-ring coupling versus free-space emission by several orders of magnitude. In particular we find that subradiant excitations, when delocalized over several ring sites, are effectively transported between the rings with a high fidelity.
We investigate a one-dimensional quantum emitter chain where transport of excitations and correlations takes place via nearest neighbor, dipole-dipole interactions. In the presence of collective radiative emission, we show that a phase imprinting wavepacket initialization procedure can lead to subradiant transport and can preserve quantum correlations. In the context of cavity mediated transport, where emitters are coupled to a common delocalized optical mode, we analyze the effect of frequency disorder and nonidentical photon-emitter couplings on excitation transport.
Coherent transport of excitations along chains of coupled quantum systems represents an interesting problem with a number of applications ranging from quantum optics to solar cell technology. A convenient tool for studying such processes are quantum walks. They allow to determine in a quantitative way all the process features. We study the survival probability and the transport efficiency on a simple, highly symmetric graph represented by a ring. The propagation of excitation is modeled by a discrete-time (coined) quantum walk. For a two-state quantum walk, where the excitation (walker) has to leave its actual position to the neighboring sites, the survival probability decays exponentially and the transport efficiency is unity. The decay rate of the survival probability can be estimated using the leading eigenvalue of the evolution operator. However, if the excitation is allowed to stay at its present position, i.e. the propagation is modeled by a lazy quantum walk, then part of the wave-packet can be trapped in the vicinity of the origin and never reaches the sink. In such a case, the survival probability does not vanish and the excitation transport is not efficient. The dependency of the transport efficiency on the initial state is determined. Nevertheless, we show that for some lazy quantum walks dynamical percolations of the ring eliminate the trapping effect and efficient excitation transport can be achieved.
We study the collective decay rates of multi-dimensional quantum networks in which one-dimensional waveguides form an intersecting hyper-rectangular lattice, with qubits located at the lattice points. We introduce and motivate the emph{dimensional reduction of poles} (DRoP) conjecture, which identifies all collective decay rates of such networks via a connection to waveguides with a one-dimensional topology (e.g. a linear chain of qubits). Using DRoP, we consider many-body effects such as superradiance, subradiance, and bound-states in continuum in multi-dimensional quantum networks. We find that, unlike one-dimensional linear chains, multi-dimensional quantum networks have superradiance in distinct levels, which we call multi-dimensional superradiance. Furthermore, we generalize the $N^{-3}$ scaling of subradiance in a linear chain to $d$-dimensional networks.
Dickes original thought experiment with two spins coupled to a photon mode has recently been experimentally realized. We propose extending this experiment to N spins and show that it naturally gives rise to highly entangled states. In particular, it gives rise to dark states which have resonating valence bond (RVB) character. We first consider a system of N two level spins in a cavity with only one spin in the excited state. This initial state is a linear combination of a dark state and a bright state. We point out the dark state is a coherent superposition of singlets with resonating valence bond character. We show that the coupling to the photon mode takes the spin system into a mixed state with an entangled density matrix. We next consider an initial state with half of the spins in the excited state. We show that there is a non-zero probability for this to collapse into a dark state with RVB character. In the lossy cavity limit, if no photon is detected within several decay time periods, we may deduce that the spin system has collapsed onto the dark RVB state. We show that the probability for this scales as 2/N, making it possible to generate RVB states of 20 spins or more.
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