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arXiv:0909.4219 · Physical Review Letters

Effective Magnetic Fields for Stationary Light

Johannes Otterbach, Julius Ruseckas, Razmik G. Unanyan, Gediminas Juzeliūnas, Michael Fleischhauer

Published Jan 21, 2010• 55 citations
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Abstract

We describe a method to create effective gauge potentials for stationary-light polaritons. When stationary light is created in the interaction with a rotating ensemble of coherently driven double-Lambda type atoms, the equation of motion is that of a massive Schrödinger particle in a magnetic field. Since the effective interaction area for the polaritons can be made large, degenerate Landau levels can be created with degeneracy well above 100. This opens up the possibility to study the bosonic analogue of the fractional quantum Hall effect for interacting stationary-light polaritons.

DOI
10.1103/physrevlett.104.033903

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We describe a method to create effective gauge potentials for stationary-light polaritons. When stationary light is created in the interaction with a rotating ensemble of coherently driven double-Lambda type atoms, the equation of motion is that of a massive Schrödinger particle in a magnetic field. Since the effective interaction area for the polaritons can be made large, degenerate Landau levels can be created with degeneracy well above 100. This opens up the possibility to study the bosonic analogue of the fractional quantum Hall effect for interacting stationary-light polaritons.
The quest of utilizing neutral particles to simulate the behaviour of charged particles in a magnetic field makes the generation of artificial magnetic field of great interest. The previous and the only proposal for the production of synthetic magnetic field for the dark state polaritons in electromagnetically induced transparency invokes the mechanical rotation of a sample. Here, we put forward an optical scheme to generate effective gauge potentials for stationary-light polaritons. 5To demonstrate the capabilities of our approach, we present recipes for having dark state polaritons in degenerate Landau levels and in driven quantum harmonic oscillator. Our scheme paves a novel way towards the investigation of the bosonic analogue of the fractional quantum Hall effect by electromagnetically induced transparency.
The adiabatic motion of ultra-cold, multi-level atoms in spatially varying laser fields creating a dark state can give rise to effective gauge potentials. We show that these potentials lead to effective magnetic fields if the light fields possess a relative orbital angular momentum. This allows to study quantum-Hall like effects in ultra-cold atomic gases in various geometries. If the atom-light interaction creates several degenerate adiabatic eigenstates, the associated gauge potentials are non-Abelian. A pair of such degenerate dark states emerges e.g. if laser fields couple three internal states of an atom to a fourth common one under pairwise two--photon-resonance conditions. For this so-called tripod scheme we derive general conditions for truly non-Abelian gauge potentials and discuss special examples. In particular we show that using orthogonal laser beams with orbital angular momentum an effective magnetic field can be generated that has a monopole component.
We propose a scheme to create an effective magnetic field for ultracold atoms in a planar geometry. The setup allows the experimental study of classical and quantum Hall effects in close analogy to solid-state systems including the possibility of finite currents. The present scheme is an extention of the proposal in Phys. Rev. Lett. 93, 033602 (2004), where the effective magnetic field is now induced for three-level $\ensuremath{\Lambda}$-type atoms by two counterpropagating laser beams with shifted spatial profiles. Under conditions of electromagnetically induced transparency the atom-light interaction has a space-dependent dark state, and the adiabatic center-of-mass motion of atoms in this state experiences effective vector and scalar potentials. The associated magnetic field is oriented perpendicular to the propagation direction of the laser beams. The field strength achievable is one flux quantum over an area given by the transverse beam separation and the laser wavelength. For a sufficiently dilute gas the field is strong enough to reach the lowest Landau level regime.
Landau levels (LLs) are the massively degenerate discrete energy spectra of charged particles in a transverse magnetic field, and they lie at the heart of many intriguing phenomena, such as the integer and fractional quantum Hall effects as well as quantized vortices. In this Letter, we consider coupling of LLs of a transversely driven, single charge-neutral particle in a synthetic gauge potential to a quantized field of an optical cavity-a setting reminiscent of superradiant self-ordering setups in quantum gases. We uncover that this complex system can be, surprisingly, described in terms of two highly nonlinearly coupled quantum harmonic oscillators, thus enabling a full quantum mechanical treatment. Light-matter coupling mixes the LLs and the superradiant photonic mode, leading to the formation of hybrid states referred to as "Landau polaritons." They partially inherit the degeneracy of the LLs and possess intriguing features such as nonzero light-matter entanglement and quadrature squeezing. Depending on the system parameters and the choice of initial state, the system exhibits diverse nonequilibrium quantum dynamics and multiple steady states with distinct physical properties. This Letter lays the foundation for further investigating the novel, driven-dissipative Landau-polariton physics in quantum-gas-cavity-QED settings.
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.
We propose and analyze a mechanism for Bose-Einstein condensation of stationary dark-state polaritons. Dark-state polaritons (DSPs) are formed in the interaction of light with laser-driven 3-level Lambda-type atoms and are the basis of phenomena such as electromagnetically induced transparency, ultraslow, and stored light. They have long intrinsic lifetimes and in a stationary setup, a 3D quadratic dispersion profile with variable effective mass. Since DSPs are bosons, they can undergo a Bose-Einstein condensation at a critical temperature which can be many orders of magnitude larger than that of atoms. We show that thermalization of polaritons can occur via elastic collisions mediated by a resonantly enhanced optical Kerr nonlinearity on a time scale short compared to the decay time. Finally, condensation can be observed by turning stationary into propagating polaritons and monitoring the emitted light.