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arXiv:1809.01147

Single-photon bound states in atomic ensembles

Yidan Wang, Michael J. Gullans, Antoine Browaeys, J. V. Porto, Darrick E. Chang, Alexey Vyacheslavovich Gorshkov

Published Sep 4, 2018• 1 citation
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Abstract

We illustrate the existence of single-excitation bound states for propagating photons interacting with $N$ two-level atoms. These bound states can be calculated from an effective spin model, and their existence relies on dissipation in the system. The appearance of these bound states is in a one-to-one correspondence with zeros in the single-photon transmission and with divergent bunching in the second-order photon-photon correlation function. We also formulate a dissipative version of Levinson's theorem for this system by looking at the relation between the number of bound states and the winding number of the transmission phases. This theorem allows a direct experimental measurement of the number of bound states using the measured transmission phases.

DOI
10.48550/arxiv.1809.01147

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We illustrate the existence of single-excitation bound states for propagating photons interacting with NNN two-level atoms. These bound states can be calculated from an effective spin model, and their existence relies on dissipation in the system. The appearance of these bound states is in a one-to-one correspondence with zeros in the single-photon transmission and with divergent bunching in the second-order photon-photon correlation function. We also formulate a dissipative version of Levinson's theorem for this system by looking at the relation between the number of bound states and the winding number of the transmission phases. This theorem allows a direct experimental measurement of the number of bound states using the measured transmission phases.
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The interaction between photons and a single two-level atom constitutes a fundamental paradigm in quantum physics. The nonlinearity provided by the atom leads to a strong dependence of the light-matter interface on the number of photons interacting with the two-level system within its emission lifetime. This nonlinearity unveils strongly correlated quasiparticles known as photon bound states, giving rise to key physical processes such as stimulated emission and soliton propagation. Although signatures consistent with the existence of photon bound states have been measured in strongly interacting Rydberg gases, their hallmark excitation-number-dependent dispersion and propagation velocity have not yet been observed. Here we report the direct observation of a photon-number-dependent time delay in the scattering off a single artificial atom-a semiconductor quantum dot coupled to an optical cavity. By scattering a weak coherent pulse off the cavity-quantum electrodynamics system and measuring the time-dependent output power and correlation functions, we show that single photons and two- and three-photon bound states incur different time delays, becoming shorter for higher photon numbers. This reduced time delay is a fingerprint of stimulated emission, where the arrival of two photons within the lifetime of an emitter causes one photon to stimulate the emission of another.
We study two-photon scattering of a tightly focused weak light beam from a small atomic ensemble of two-level atoms (2LAs). This is similar to the scattering of photons from an atomic ensemble in a one-dimensional waveguide. The scaling of two-photon nonlinearity at single-photon resonance shows a nonmonotonic behavior with an increasing number of few identical 2LAs. The two-photon nonlinearity decays monotonically with an increasing number of atoms for incident photons detuned from single-photon resonance. Single-photon transport in two 2LAs is similar to that in a single VVV-type three-level atom (3LA). However, two-photon transport in these two systems shows very different line shapes. When single-photon transmission is zero in these systems, two transmitted photons are bunched together in a VVV-type 3LA, while their correlation is zero in two 2LAs. The difference in the two-photon line shape persists for few 2LAs and 3LAs. Therefore, the two-photon scattering of a tightly focused weak light beam can be used as a probe to detect atomic level structures of different atoms with similar transition energies.
We study the properties of atom-photon bound states and single-photon cooperative dynamics in a waveguide system which consists of a finite-bandwidth channel with model dispersion and an ensemble of two-level atoms whose size is ignorable when compared with the lattice constant. The bound states are formed by all atoms and a localized photonic excitation. We find that the effect of atomic collection is equivalent to the case of one atom by rescaling the coupling strength with the square root of the atom number, as far as the eigenenergy equation is concerned. Besides, it is found there is a quantum phase transition when more than one type of atom are present. The characteristic lengths and wave functions are analyzed near the phase transition point. The exact analytical results for the cooperative dynamics at the single excitation level are obtained and we point out the dark state in this system leads to a universal population trapping in the time evolution process. This type of trapping obeys a simple law that is only associated with the atom number. A direct conclusion that results from the trapping law is that the single-photon cooperative emission is suppressed when the number of atoms is large enough.
Bound states of massive particles, such as nuclei, atoms, or molecules, constitute the bulk of the visible world around us. By contrast, photons typically only interact weakly. We report the observation of traveling three-photon bound states in a quantum nonlinear medium where the interactions between photons are mediated by atomic Rydberg states. Photon correlation and conditional phase measurements reveal the distinct bunching and phase features associated with three-photon and two-photon bound states. Such photonic trimers and dimers possess shape-preserving wave functions that depend on the constituent photon number. The observed bunching and strongly nonlinear optical phase are described by an effective field theory of Rydberg-induced photon-photon interactions. These observations demonstrate the ability to realize and control strongly interacting quantum many-body states of light.