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Physical Review A

Two-photon bound states: The diphoton bullet in dispersive self-focusing media

Ivan Deutsch, R. Y. Chiao, J. C. Garrison

Published Apr 1, 1993• 21 citations
Publisher

Abstract

We consider two-photon bound states which may be excited in a planar waveguide filled with a self-focusing Kerr material. These bound states are the quantum analogs of the classical light bullets which form under the combined effects of self-focusing, diffraction, self-phase-modulation, and anomalous group-velocity dispersion. A variational approach is used to establish a threshold condition on the strength of the nonlinearity for the existence of the bound state, and a gedanken experiment is proposed to outline the principles for creation and detection of this quasiparticle.

DOI
10.1103/physreva.47.3330

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Propagation of light beams in a Fabry-Perot resonator filled with a self-focusing Kerr material is described by the nonlinear Schrodinger equation. If the degrees of freedom are restricted to one transverse dimension through the use of a line focus at the input face, the system possesses classical soliton solutions analogous to those for travelling-wave self-trapped beams. When the classical field theory is quantized, one obtains an effective nonrelativistic many-body field theory in which pairs of photons interact through attractive delta function potentials. The existence of bound states between photons is the microscopic phenomenon that prevents beams from spreading by diffraction. The fundamental bound state consists of two photons, which we call the "diphoton." We consider production of these quasi-particles in a single longitudinal mode Fabry-Perot resonator filled with an alkali vapor. The injected light is strongly attenuated to excite few photons in the cavity and is detuned slightly above the atomic resonance, giving rise to the self-focusing nonlinearity. Detection of the diphoton can be achieved by rejecting the unbound component by using a spatial filter and detecting the remaining signal in coincidence counting. The diphoton signature is a characteristic Lorentzian-squared two-point correlation profile.1

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arXiv:1808.00752•Physical Review Letters•Sep 27, 2018•24 citations
We consider two-photon bound states which may be excited in a planar waveguide filled with a self-focusing Kerr material. These bound states are the quantum analogs of the classical light bullets which form under the combined effects of self-focusing, diffraction, self-phase-modulation, and anomalous group-velocity dispersion. A variational approach is used to establish a threshold condition on the strength of the nonlinearity for the existence of the bound state, and a gedanken experiment is proposed to outline the principles for creation and detection of this quasiparticle.
Propagation of light beams in a Fabry-Perot resonator filled with a self-focusing Kerr material is described by the nonlinear Schrodinger equation. If the degrees of freedom are restricted to one transverse dimension through the use of a line focus at the input face, the system possesses classical soliton solutions analogous to those for travelling-wave self-trapped beams. When the classical field theory is quantized, one obtains an effective nonrelativistic many-body field theory in which pairs of photons interact through attractive delta function potentials. The existence of bound states between photons is the microscopic phenomenon that prevents beams from spreading by diffraction. The fundamental bound state consists of two photons, which we call the "diphoton." We consider production of these quasi-particles in a single longitudinal mode Fabry-Perot resonator filled with an alkali vapor. The injected light is strongly attenuated to excite few photons in the cavity and is detuned slightly above the atomic resonance, giving rise to the self-focusing nonlinearity. Detection of the diphoton can be achieved by rejecting the unbound component by using a spatial filter and detecting the remaining signal in coincidence counting. The diphoton signature is a characteristic Lorentzian-squared two-point correlation profile.1
The emergence of multi-photon bound states in quantum nonlinear media is an intriguing phenomenon that has attracted significant theoretical and experimental interest. Such bound states can emerge in quite different settings, such as arrays of quantum emitters coupled to photonic waveguides and Rydberg nonlinear media. The theoretical tools to characterize the bound states are equally diverse, ranging from Bethe ansatz to effective field theories. Here, we propose and utilize a spin-model formulation of quantum atom-light interactions as a general, unified framework to study bound states, and apply this formalism to several distinct systems. We show how to obtain the bound-state dispersion relation within the two-excitation subspace, and also numerically investigate how the properties of higher multi-photon bound states manifest themselves in the propagation of large photon number pulses and spatio-temporal correlations at the output. Interestingly, for all the specific systems studied (chiral and bi-directional waveguides, and Rydberg media), we find that the large-photon number limit always coincides with the well-known semi-classical soliton phenomenon of self-induced transparency or immediate generalizations thereof.
Alkali vapors excited by light near resonance are known to possess very large nonlinear optical coefficients n 2 , which can have either sign depending on the sign of the detuning. Spatial solitons in a Fabry-Perot resonator filled with such vapors can result from these nonlinearities. The nonlinear Schrodinger equation (NLS) obeyed by these solitons is formally equivalent to a nonrelativistic many-body field theory, in which photons behave like nonrelativistic bosons with pairwise interactions. When n 2 is positive, these interactions are attractive; when is negative, they are repulsive. With n 2 positive, it is predicted that a self-trapped, 1D spatial soliton (the hyperbolic secant solution to the ID NLS) should be observable, and we plan to perform soliton-soliton collision experiments with such solitons. At the quantum level, the light inside such a soliton should be self-squeezed, and we plan to observe this using the Shirasaki-Haus method. The possibility of observing the two-photon bound state, the diphoton, will be explored. With n 2 negative, a ID spatial dark soliton with antibunching of photons should result. Moreover, with n 2 negative, a 2D vortex soliton should form, and we plan to examine the dynamics of these photonic vortices at both classical and quantum levels. The possibility that these vortices obey anyonic statistics will be explored. These optical systems thus constitute an experimentally accessible arena in which many-body phenomena analogous to those in condensed matter physics, especially topological ones, such as the Kosterlitz-Thouless phase transition, superfluidity, and anyonic statistics, may be observed.
Photonic crystals doped with resonant atoms allow for uniquely advantageous nonlinear modes of optical propagation. The first type of mode is self-induced transparency (SIT) solitons and multidimensional localized “bullets” propagating at photonic-bandgap frequencies. Such modes can exist even at ultraweak intensities (few photons) and therefore differ substantially either from solitons in Kerr-nonlinear photonic crystals or from SIT solitons in uniform media. The second type of mode is cross coupling between pulses exhibiting electromagnetically induced transparency and SIT gap solitons. We show that extremely strong correlations (giant cross-phase modulation) can be formed between the two pulses. These features may find applications in high-fidelity classical and quantum optical communications.
We present experimental evidence of photon droplets in an attractive (focusing) nonlocal nonlinear medium. Photon droplets are self-bound, finite-sized states of light that are robust to size and shape perturbations due to a balance of competing attractive and repulsive forces. It has recently been shown theoretically, via a multipole expansion of the nonlocal nonlinearity, that the self-bound state arises due to competition between the s-wave and d-wave nonlinear terms, together with diffraction. The theoretical photon droplet framework encompasses both a solitonlike stationary ground state and the nonsolitonlike dynamics that ensue when the system is displaced from equilibrium, i.e., driven into an excited state. We present numerics and experiments supporting the existence of these photon droplet states and measurements of the dynamical evolution of the photon droplet orbital angular momentum.