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arXiv:1803.04156 · Physical Review A

Adiabatic flux insertion and growing of Laughlin states of cavity Rydberg polaritons

Peter A. Ivanov, Fabian Letscher, Jonathan Simon, Michael Fleischhauer

Published Jul 27, 2018• 12 citations
arXivHTMLPDF

Abstract

Recently, the creation of a strong magnetic field in a photonic cavity system has been demonstrated [N. Schine et al., Nature (London) 534, 671 (2016).]. Using this setup, we propose a scheme to adiabatically transfer flux quanta simultaneously to all cavity photons. The flux transfer is achieved using external light fields with orbital angular momentum and a near-resonant dense atomic medium as a mediator. Furthermore, by coupling the cavity fields to a Rydberg state, strong photon-photon interactions can be realized and fractional quantum Hall states can be prepared. To this end, a growing protocol is discussed consisting of a sequence of flux insertion and subsequent single-photon insertion. Specifically, we discuss the growing of the $\ensuremath{\nu}=1/2$ bosonic Laughlin state. First we adiabatically insert two photonic flux quanta, creating a two-quasihole excitation, and second we refill the hole with a single photon using the strong photon-photon interactions.

DOI
10.1103/physreva.98.013847

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•Mar 4, 2021•0 citations
Recently, the creation of a strong magnetic field in a photonic cavity system has been demonstrated [N. Schine et al., Nature (London) 534, 671 (2016).]. Using this setup, we propose a scheme to adiabatically transfer flux quanta simultaneously to all cavity photons. The flux transfer is achieved using external light fields with orbital angular momentum and a near-resonant dense atomic medium as a mediator. Furthermore, by coupling the cavity fields to a Rydberg state, strong photon-photon interactions can be realized and fractional quantum Hall states can be prepared. To this end, a growing protocol is discussed consisting of a sequence of flux insertion and subsequent single-photon insertion. Specifically, we discuss the growing of the \ensuremathν=1/2\ensuremath{\nu}=1/2\ensuremathν=1/2 bosonic Laughlin state. First we adiabatically insert two photonic flux quanta, creating a two-quasihole excitation, and second we refill the hole with a single photon using the strong photon-photon interactions.
We propose a scheme for realizing fractional quantum Hall states of light. In our scheme, photons of two polarizations are coupled to different atomic Rydberg states to form two flavors of Rydberg polaritons that behave as an effective spin. An array of optical cavity modes overlapping with the atomic cloud enables the realization of an effective spin-1/21/21/2 lattice. We show that the dipolar interaction between such polaritons, inherited from the Rydberg states, can be exploited to create a flat, topological band for a single spin-flip excitation. At half filling, this gives rise to a photonic (or polaritonic) fractional Chern insulator---a lattice-based, fractional quantum Hall state of light.
Synthetic quantum materials offer an exciting opportunity to explore quantum many-body physics and novel states of matter under controlled conditions. In particular, they provide an avenue to exchange the short length scales and large energy scales of the solid state for an engineered system with better control over the system Hamiltonian, more accurate state preparation, and higher fidelity state readout. Here we propose a unique platform to study quantum phases of strongly interacting photons. We introduce ideas for controlling the dynamics of individual photons by manipulating the geometry of a multimode optical cavity, and combine them with recently established techniques to mediate strong interactions between photons using Rydberg atoms. We demonstrate that this approach gives rise to crystalline- and fractional quantum Hall- states of light, opening the door to studies of strongly correlated quantum many-body physics in a photonic material.
Particle loss is the ultimate challenge for preparation of strongly correlated many-body states of photons. An established way to overcome the loss is to employ a stabilization setup that autonomously injects new photons in place of the lost ones. However, as we show, the effectiveness of such a stabilization setup is compromised for fractional quantum Hall states. There, a hole formed by a lost photon can separate into several remote quasiholes none of which can be refilled by injecting a photon locally. By deriving an exact expression for the steady-state density matrix, we demonstrate that isolated quasiholes proliferate in the steady state which damages the quality of the state preparation. The motion of quasiholes leading to their separation is allowed by a repeated process in which a photon is first lost and then quickly refilled in the vicinity of the quasihole. We develop the theory of this dissipative quasihole dynamics and show that it has diffusive character. Our results demonstrate that fractionalization might present an obstacle for both creation and stabilization of strongly-correlated states with photons.
Abstract Photonic materials are an emerging platform to explore quantum matter (Carusotto and Ciuti 2013 Rev. Mod. Phys. 85 299; Sommer et al 2015 arXiv: 1506.00341 ) and quantum dynamics (Peyronel et al 2012 Nature 488 57). The development of Rydberg electromagnetically induced transparency (Weatherill et al 2008 J. Phys. B: At. Mol. Opt. Phys. 41 201002; Petrosyan et al 2011 Phys. Rev. Lett. 107 213601) provided a clear route to strong interactions between individual optical photons. In conjunction with carefully designed optical resonators, it is now possible to achieve extraordinary control of the properties of individual photons, introducing tunable gauge fields (Schine et al 2016 Nature 534 671) whilst imbuing the photons with mass and embedding them on curved spatial manifolds (Sommer et al 2016 New J. Phys. 18 035008). Building on work formalizing Rydberg mediated interactions between propagating photons (Gorshkov et al 2011 Phys. Rev. Lett. 107 133602; Gullans et al 2016 Phys. Rev. Lett. 117 113601), we develop a theory of interacting Rydberg polaritons in multimode optical resonators, where the strong interactions are married with tunable single particle properties to build and probe exotic matter. In the presence of strong coupling between the resonator field and a Rydberg-dressed atomic ensemble, a quasiparticle called the ‘cavity Rydberg polariton’ emerges. We investigate its properties, finding that it inherits both the fast dynamics of its photonic constituents and the strong interactions of its atomic constituents. We develop tools to properly renormalize the interactions when polaritons approach each other, and investigate the impact of atomic motion on the coherence of multi-mode polaritons, showing that most channels for atom-polariton cross-thermalization are strongly suppressed. Finally, we propose to harness the repeated diffraction and refocusing of the optical resonator to realize interactions which are local in momentum-space. This work points the way to efficient modeling of polaritonic quantum materials in properly renormalized strongly interacting effective theories, thereby enabling experimental studies of photonic fractional quantum Hall fluids and crystals (Sommer et al 2015 arXiv: 1506.00341 ; Umucalılar et al 2014 Phys. Rev. A 89 023803; Grusdt and Fleischhauer 2013 Phys. Rev. A 87 043628), plus photonic quantum information processors and repeaters (Jaksch et al 2000 Phys. Rev. Lett. 85 2208; Saffman et al 2010 Rev. Mod. Phys. 82 2313; Han et al 2010 Phys. Rev. A 81 , 052311).
Mapping the strong interaction between Rydberg excitations in ultra-cold atomic ensembles onto single photons enables the realization of optical nonlinearities which can modify light on the level of individual photons.This novel approach forms the basis of a growing Rydberg quantum optics toolbox, which already contains photonic logic building-blocks such as single-photon sources, switches, transistors, and conditional π-phase shifts.This thesis reports on two experiments investigating strong photon-photon interactions mediated by Rydberg interactions.First, applying a ladder-type EIT scheme to Rydberg atoms in D-states with high principal quantum number results in the Rydberg interaction mediated nonlinearity accompanied by a time-dependent decay of transmission of probe light through the medium.In a joint experimental and theoretical analysis, this effect is attributed to the dephasing of propagating polaritons into stationary Rydberg excitations caused by the state mixing interaction occurring with Rydberg D-state atoms.Second, via a two-photon Raman excitation scheme Rydberg atoms are efficiently excited in a small atomic cloud.As the size of the Rydberg blockade exceeds the dimension of the medium, only a single Rydberg excitation can be present at a time.By fast engineered dephasing this Rydberg excitation is decoupled from the light field.Measurement of the transmitted light and the amount of excited Rydberg atoms gives evidence for the realization of a deterministic single-photon absorber.
A long-standing goal of quantum optics is to reach a regime where interactions between single photons can take place. This would lead to new perspectives in the domain of quantum communication and quantum simulation. This work presents the assembly and characterization of a hybrid experimental platform for the study and creation of deterministic interactions between single photons, an important milestone in quantum technologies. The experimental setup combines different technologies from cavity quantum electrodynamics and cold atoms techniques. A cold atom cloud is transported in a specially designed optical resonator, allowing the temporary conversion of intracavity photons into atomic Rydberg polaritons, creating a medium which enables strong interactions. This setup should allow us to deterministically entangle optical photons in order to generate non-classical light, to develop photonic quantum logic gates, and to emulate low-dimensional highly correlated condensed-matter systems. In a first part the setup is presented, including the manner in which the different subsystems work together. In a second part, the first EIT measurements are shown and analyzed, before describing the latest advancement made.