Photonic quantum transport in a nonlinear optical fiber

We theoretically study the transmission of few-photon quantum fields through a strongly nonlinear optical medium. We develop a general approach to investigate nonequilibrium quantum transport of bosonic fields through a finite-size nonlinear medium and apply it to a recently demonstrated experimental system where cold atoms are loaded in a hollow-core optical fiber. We show that when the interaction between photons is effectively repulsive, the system acts as a single-photon switch. In the case of attractive interaction, the system can exhibit either antibunching or bunching, associated with the resonant excitation of bound states of photons by the input field. These effects can be observed by probing statistics of photons transmitted through the nonlinear fiber. Copyright c © EPLA, 2011 Quantum dynamics of strongly correlated systems far from equilibrium is a new frontier of many-body physics. Intriguing phenomena involving such dynamics have recently been observed in diverse physical systems ranging from ultra-cold atoms [1] to individual spins in semiconductors [2,3]. At the same time, recent experiments using ultra-cold atoms and optical photons [4–6] have opened the door for studies of a novel form of quantum transport involving strongly correlated photons. It has been predicted that these systems can allow for surprising behavior, such as the dynamical creation of a “crystal” of photons [7]. While many similarities exist between interacting photonic systems and condensedmatter systems involving massive particles [8–13], the photonic systems also present a unique set of challenges. In particular, they do not thermalize, and are inherently open, driven systems, which highlights the need to develop novel techniques for analysis. In this letter, we describe a general technique to study the quantum transport of a few field quanta through a finite-length, strongly nonlinear one-dimensional waveguide. This technique allows us to determine the full (a)Present address: Joint Quantum Institute, University of Maryland College Park, MD 20742, USA; E-mail: [email protected] spatial wave functions of the photons inside the waveguide as well as correlation functions of the outgoing reflected and transmitted light. We consider an optical waveguide in which the tight confinement of photons near the diffraction limit [4,6,14,15] and the large number of atoms with which they interact should enable large optical nonlinearities at the single-photon level, which is necessary for applications like single-photon switching and photonic quantum gates [16–18]. Such system is in contrast to standard nonlinear optical fibers where the nonlinearity is weak and large optical intensity is needed (see, e.g., refs. [19,20]). Moreover, unlike nonlinear optical effects in cavity quantum electrodynamics (QED) [21], where only a single spatial cavity mode is involved, these waveguide systems are more difficult to treat in that they contain a large number of spatial degrees of freedom, much like low-dimensional, strongly interacting condensed-matter systems [22–26] containing a few quanta. As a specific application, we use the calculated reflection and transmission amplitudes to demonstrate how such a system can be used to realize a single-photon switch. Our analysis reveals the tendency for photons to “organize” themselves due to an effective tunable repulsive or attractive interaction (as shown in fig. 1). In the latter case, we show that two-photon bound states can form inside the waveguide,