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arXiv:0712.0060 · Physical Review A

Dark-state polaritons for multicomponent and stationary light fields

Frank Zimmer, Johannes Otterbach, Razmik G. Unanyan, Bruce W. Shore, Michael Fleischhauer

Published Jun 16, 2008• 65 citations
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Abstract

We present a general scheme to determine the loss-free adiabatic eigensolutions (dark-state polaritons) of the interaction of multiple probe laser beams with a coherently driven atomic ensemble under conditions of electromagnetically induced transparency. To this end we generalize the Morris-Shore transformation to linearized Heisenberg-Langevin equations describing the coupled light-matter system in the weak excitation limit. For the simple lambda-type coupling scheme the generalized Morris-Shore transformation reproduces the dark-state polariton solutions of slow light. Here we treat a closed-loop dual-$V$ scheme wherein two counterpropagating control fields generate a quasistationary pattern of two counterpropagating probe fields---so-called stationary light. We show that contrary to previous predictions, there exists a single unique dark-state polariton; it obeys a simple propagation equation.

DOI
10.1103/physreva.77.063823

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We present a general scheme to determine the loss-free adiabatic eigensolutions (dark-state polaritons) of the interaction of multiple probe laser beams with a coherently driven atomic ensemble under conditions of electromagnetically induced transparency. To this end we generalize the Morris-Shore transformation to linearized Heisenberg-Langevin equations describing the coupled light-matter system in the weak excitation limit. For the simple lambda-type coupling scheme the generalized Morris-Shore transformation reproduces the dark-state polariton solutions of slow light. Here we treat a closed-loop dual-VVV scheme wherein two counterpropagating control fields generate a quasistationary pattern of two counterpropagating probe fields---so-called stationary light. We show that contrary to previous predictions, there exists a single unique dark-state polariton; it obeys a simple propagation equation.
A master equation approach for the description of dark-state polaritons in coherently driven atomic media is presented. This technique provides a description of light-matter interactions under conditions of electromagnetically induced transparency (EIT) that is well suited for the treatment of polariton losses. The master equation approach allows us to describe general polariton-polariton interactions that may be conservative, dissipative, or a mixture of both. In particular, it enables us to study dissipation-induced correlations as a means for the creation of strongly correlated polariton systems. Our technique reveals a loss mechanism for stationary-light polaritons that has not been discussed so far. We find that polariton losses in level configurations with nondegenerate ground states can be a multiple of those in level schemes with degenerate ground states.
Coupling light to Rydberg states of atoms under conditions of electromagnetically induced transparency (EIT) leads to the formation of interacting quasiparticles, termed Rydberg polaritons. We derive a one-dimensional model describing the time evolution of these polaritons under paraxial propagation conditions. Specifically, we obtain a master equation governing the dynamics of Rydberg polaritons and identify conditions when it can essentially be described by an effective Hamiltonian of a single-species polariton. We verify this Hamiltonian by numerical two-excitation simulations. Under typical stationary EIT conditions it is impossible to reach the strongly interacting regime where long-range density-density correlations emerge. In contrast, by employing the time dependence of the control field the regime of strong interactions can be reached where the polaritons attain quasicrystalline order. We provide a physical explanation for the differences between stationary and time-dependent schemes.
We identify form-stable coupled excitations of light and matter ("dark-state polaritons") associated with the propagation of quantum fields in electromagnetically induced transparency. The properties of dark-state polaritons such as the group velocity are determined by the mixing angle between light and matter components and can be controlled by an external coherent field as the pulse propagates. In particular, light pulses can be decelerated and "trapped" in which case their shape and quantum state are mapped onto metastable collective states of matter. Possible applications of this reversible coherent-control technique are discussed.
Abstract We consider propagation of a probe pulse in an atomic medium characterized by a combined tripod and Lambda (Λ) atom-light coupling scheme. The scheme involves three atomic ground states coupled to two excited states by five light fields. It is demonstrated that dark states can be formed for such an atom-light coupling. This is essential for formation of the electromagnetically induced transparency (EIT) and slow light. In the limiting cases the scheme reduces to conventional Λ- or N -type atom-light couplings providing the EIT or absorption, respectively. Thus, the atomic system can experience a transition from the EIT to the absorption by changing the amplitudes or phases of control lasers. Subsequently the scheme is employed to analyze the nonlinear pulse propagation using the coupled Maxwell–Bloch equations. It is shown that a generation of stable slow light optical solitons is possible in such a five-level combined tripod and Λ atomic system.
We analyze electromagnetically induced transparency and light storage in an ensemble of atoms with multiple excited levels (multi-$\ensuremath{\Lambda}$ configuration) which are coupled to one of the ground states by quantized signal fields and to the other one via classical control fields. We present a basis transformation of atomic and optical states which reduces the analysis of the system to that of electromagnetically induced transparency in a regular three-level configuration. We demonstrate the existence of dark state polaritons and propose a protocol to transfer quantum information from one optical mode to another by an adiabatic control of the control fields.
Dynamic control of a weak quantum probe light pulse for the generation and quantum manipulations of a stationary multi-color (MC-) light field in a resonant coherent atomic medium using electromagnetically induced transparency is proposed. The manipulations have been analyzed based on the analytical solution of the adiabatic limit in the evolution of MC-light fields resulting from interaction of the slow probe light with the new fields generated in the nondegenerate multi-wave mixing scheme. We have found a critical stopping condition for the MC-light fields where the group velocity of light should reduce down to zero. Semiclassical dynamics and behavior of specific quantum correlations of the MC-light fields have been studied in detail for particular initial quantum states of the probe pulse. The stationary MC-field dynamics are treated in terms of dark MC-polariton states constructed for the studied multi-wave mixing processes. We have found the conditions for optimal manipulation of the MC-light while preserving the delicate quantum correlations of the initial probe light pulse. The quantum manipulations leading to the frequency and direction switching of the initial probe light pulse as well as to the quantum swapping of probe light into the new multi-frequency light fields have been proposed. The possibilities of the interaction time lengthening and enhancement of the electric field amplitudes of the stationary MC-light are also discussed for enhancement of the interactions with weak quantum fields in the spatially limited media.