The fabric of the nonlinear quantum field behind optical solitons suggests the many-particle structure of the photon wave function in optical solitons. This wave function derives from the bound states of the original quantum field and is found as the ground-state eigenfunction of a many-body Hamiltonian with a delta-function interaction potential. Drawing on the properties of such a many-particle photon wave function, we show how classical solitons with their signature hyperbolic secant field intensity profiles emerge from quantum nonlinear fields in the limit of very large photon numbers.
The fabric of the nonlinear quantum field behind optical solitons suggests the many-particle structure of the photon wave function in optical solitons. This wave function derives from the bound states of the original quantum field and is found as the ground-state eigenfunction of a many-body Hamiltonian with a delta-function interaction potential. Drawing on the properties of such a many-particle photon wave function, we show how classical solitons with their signature hyperbolic secant field intensity profiles emerge from quantum nonlinear fields in the limit of very large photon numbers.
Summary form only given. Optical solitons in fibres are attractive macroscopical quantum objects, which are particle-like pulses propagating over large distances without distortion due to the balance between Kerr nonlinearity and group velocity dispersion effects. However, in the frame of the quantum theory, they exhibit a complicated internal quantum structure with nontrivial nonlinear dynamics. In the process of the propagation along a fiber, the nonlinear dynamics of secant hyperbolical shaped optical pulses lead to the formation of classically stable soliton pulses with a rich variety of nonclassical properties, such as quantum noise reduction, spectral quantum noise correlations, and quantum non-demolition interactions. We discuss the experimental characterisation of these quantum properties of femtosecond optical solitons at the telecommunication wavelength of 1.5 /spl mu/m experiencing nonlinear-interactions in silica fibres.
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.
We review recent developments in quantum and classical soliton theory, leading to the possibility of observing both classical and quantum parametric solitons in higher-dimensional environments. In particular, we consider the theory of three bosonic fields interacting via both parametric (cubic) and quartic couplings. In the case of photonic fields in a nonlinear optical medium this corresponds to the process of sum frequency generation (via (2) nonlinearity) modified by the (3) nonlinearity. Potential applications include an ultrafast photonic AND-gate. The simplest quantum solitons or energy eigenstates (bound-state solutions) of the interacting field Hamiltonian are obtained exactly in three space dimensions. They have a point-like structure - even though the corresponding classical theory is nonsingular. We show that the solutions can be regularized with the imposition of a momentum cut-off on the nonlinear couplings. The case of three-dimensional matter-wave solitons in coupled atomic/molecular Bose-Einstein condensates is discussed.
Solitons are known to occur in the context of atom-light interaction via the well-known semiclassical phenomenon of self-induced transparency (SIT). Separately, in the regime where both light and atoms are fully treated quantum mechanically, quantum few-photon bound states are known to be a ubiquitous phenomenon that arises in different systems such as atoms coupled to chiral or bidirectional waveguides, and in Rydberg atomic media. In the specific case of two-level atoms coupled to a chiral waveguide, a recent analysis based on Bethe ansatz has established that SIT emerges from the quantum realm as a superposition of quantum many-photon bound states. Beyond this case, however, the nature of any connection between the full quantum many-body regime and semiclassical behavior has not been established. Here, we employ a general spin-model formulation of quantum atom-light interfaces to numerically investigate this problem, taking advantage of the fact that this approach readily allows for powerful many-body simulations based on matrix product states (MPS). We first analytically derive the two-photon bound state dispersion relation for a variety of atom-light interfaces and then proceed to numerically investigate the multiexcitation bound states dynamics. Interestingly, for all the specific systems studied, we find that the large-photon number limit always coincides with the soliton phenomenon of self-induced transparency or immediate generalizations thereof.
We consider the quantum field theory of two bosonic fields interacting via both parametric (cubic) and quartic couplings. In the case of photonic fields in a nonlinear optical medium, this corresponds to the process of second-harmonic generation (via ${\ensuremath{\chi}}^{(2)}$ nonlinearity) modified by the ${\ensuremath{\chi}}^{(3)}$ nonlinearity. The quantum solitons or energy eigenstates (bound-state solutions) are obtained exactly in the simplest case of two-particle binding, in one, two, and three space dimensions. We also investigate three-particle binding in one space dimension. The results indicate that the exact quantum solitons of this field theory have a singular, pointlike structure in two and three dimensions---even though the corresponding classical theory is nonsingular. To estimate the physically accessible radii and binding energies of the bound states, we impose a momentum cutoff on the nonlinear couplings. In the case of nonlinear optical interactions, the resulting radii and binding energies of these photonic particlelike excitations in highly nonlinear parametric media appear to be close to physically observable values.