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Photonic quantum simulators: Mimicking condensed matter physics using photons

Dimitris G. Angelakis

Published Aug 1, 2011• 0 citations
Publisher

Abstract

The author starts by describing the basic motivation for using strongly interacting systems of photons to simulate condensed matter phenomena. A brief review of the results on the simulations of Mott to superfluid phase transitions in coupled cavities doped with two level systems from the previous work by Angelakis et. al (2007) were presented. The main ideas behind the photonic simulation of quantum spin models, the fractional Hall effect, and many-body entanglement in dissipative cavity arrays were also referenced. The main part of the paper is devoted in analyzing recent results in the simulation of quantum Luttinger liquids and spin-charge separation using photons in a hollow fiber filled with atoms. The work towards the realization of the sine-Gordon model and the “pinning transition” in the same system in the work of Angelakis et. al (2011) was also presented .

DOI
10.1109/iqec-cleo.2011.6194144

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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jun 1, 2007•1 citation
The author starts by describing the basic motivation for using strongly interacting systems of photons to simulate condensed matter phenomena. A brief review of the results on the simulations of Mott to superfluid phase transitions in coupled cavities doped with two level systems from the previous work by Angelakis et. al (2007) were presented. The main ideas behind the photonic simulation of quantum spin models, the fractional Hall effect, and many-body entanglement in dissipative cavity arrays were also referenced. The main part of the paper is devoted in analyzing recent results in the simulation of quantum Luttinger liquids and spin-charge separation using photons in a hollow fiber filled with atoms. The work towards the realization of the sine-Gordon model and the “pinning transition” in the same system in the work of Angelakis et. al (2011) was also presented .
I will start by describing the basic motivation for using strongly interacting systems of photons to simulate condensed matter phenomena. I will proceed by briefly reviewing our founding results on the simulations of Mott to superfluid phase transitions in coupled cavities [1,2] doped with two level systems. I will also epigrammatically mention the main ideas behind the photonic simulation of quantum spin models [3], the Fractional Hall effect [4], and many-body entanglement in dissipative cavity arrays [5].
I will start by reviewing our early works for observing photon-blockade induced Mott transitions in coupled cavity QED systems [1]. After briefly touching on the idea of simulating spin-models and the Fractional Hall effect [2], I will analyze more recent developments in realizing continuous 1D models in nonlinear optical fibers exhibiting electromagnetically induced transparency nonlinearities. Here the concept of the “photonic Luttinger liquid” will be introduced, along with a proposal to observe spin-charge separation with polarized photons in a nonlinear slow light set up [3]. I will continue by presenting our recent efforts in simulating 1D lattice models in the non-relativistic regime, such as the sine-Gordon and Bose-Hubbard [4], and the efforts for simulations of out of equilibrium phenomena using driven systems [5,6]. I will conclude by presenting ongoing work on interacting relativistic models (Thirring)[7]. Possible experimental implementations in quantum optical systems such as photonic crystals, optical fibers coupled to cold atoms, and Circuit QED will be discussed.
Simulating quantum many-body systems on a classical computer generally requires a computational cost that grows exponential with the number of particles. This computational complexity has been the main obstacle to understanding various fundamental emergent phenomena in condensed matters such as high-Tc superconductivity and the fractional quantum-Hall effect. The difficulty arises because even the simplest models that are proposed to capture those phenomena cannot be simulated on a classical computer. Recognizing this problem in 1981, Richard Feynman envisioned a quantum simulator, an entirely new type of machine that exploits quantum superposition and operates by individually manipulating its constituting quantum particles and their interactions. Recent advances in various experimental platforms from cold atoms in optical lattices, trapped ions, to solid-state systems have brought the idea of Feynman to the realm of reality. Among those, interacting photons in superconducting circuits has been one of the promising platforms thanks to their local controllability and long coherence times. Early theoretical proposals have shown possibilities to realize quantum many-body phenomena of light using coupled cavity arrays such as Mott to superfluid transitions and fractional quantum Hall states. Start-of-the-art experiments include realization of interacting chiral edge states and stroboscopic signatures of localization of interacting photons in a three-site and a nine-site superconducting circuit, respectively. Interacting photons also serve as a natural platform to simulate driven-dissipative quantum many-body phenomena. A 72-site superconducting circuit has also recently been fabricated to study a dissipative phase transition of light.
Simulating quantum many-body systems on a classical computer generally requires a computational cost that grows exponential with the number of particles. This computational complexity has been the main obstacle to understanding various fundamental emergent phenomena in condensed matters such as high-Tc superconductivity and the fractional quantum-Hall effect. The difficulty arises because even the simplest models that are proposed to capture those phenomena cannot be simulated on a classical computer. Recognizing this problem in 1981, Richard Feynman envisioned a quantum simulator, an entirely new type of machine that exploits quantum superposition and operates by individually manipulating its constituting quantum particles and their interactions. Recent advances in various experimental platforms from cold atoms in optical lattices, trapped ions, to solid-state systems have brought the idea of Feynman to the realm of reality. Among those, interacting photons in superconducting circuits has been one of the promising platforms thanks to their local controllability and long coherence times. Early theoretical proposals have shown possibilities to realize quantum many-body phenomena of light using coupled cavity arrays such as Mott to superfluid transitions and fractional quantum Hall states. Start-of-the-art experiments include realization of interacting chiral edge states and stroboscopic signatures of localization of interacting photons in a three-site and a nine-site superconducting circuit, respectively. Interacting photons also serve as a natural platform to simulate driven-dissipative quantum many-body phenomena. A 72-site superconducting circuit has also recently been fabricated to study a dissipative phase transition of light.
In this review we discuss the works in the area of quantum simulation and many-body physics with light, from the early proposals on equilibrium models to the more recent works in driven dissipative platforms. We start by describing the founding works on Jaynes-Cummings-Hubbard model and the corresponding photon-blockade induced Mott transitions and continue by discussing the proposals to simulate effective spin models and fractional quantum Hall states in coupled resonator arrays (CRAs). We also analyse the recent efforts to study out-of-equilibrium many-body effects using driven CRAs, including the predictions for photon fermionisation and crystallisation in driven rings of CRAs as well as other dynamical and transient phenomena. We try to summarise some of the relatively recent results predicting exotic phases such as super-solidity and Majorana like modes and then shift our attention to developments involving 1D nonlinear slow light setups. There the simulation of strongly correlated phases characterising Tonks-Girardeau gases, Luttinger liquids, and interacting relativistic fermionic models is described. We review the major theory results and also briefly outline recent developments in ongoing experimental efforts involving different platforms in circuit QED, photonic crystals and nanophotonic fibres interfaced with cold atoms.
Summary form only given. The studies of insulator to superfluid transitions in many body systems and their realization in optical lattices have opened great possibilities for simulating many body systems. It is thus interesting to explore which other systems permit such phases and simulations, especially if the problem of accessibility of the individual sites is not present. Particularly arresting will be to find such phases in a system of photons which, by being non-interacting, are unlikely candidates for the studies of many-body phenomena. Here we show that a Mott phase can arise in an array of coupled high Q electromagnetic cavities between which photons can hop, when each cavity is coupled to a single two level system (atom/quantum dot/Cooper pair). In this phase each atom-cavity system has the same integral number of polaritonic (atomic plus photonic) excitations. It occurs for resonant photonic and atomic frequencies when photon blockade provides an effective repulsion between the excitations in each atom-cavity system. Detuning the atomic and photonic frequencies suppresses this repulsion and induces a transition from the Mott phase to a photonic superfluid. We also show that for zero detuning, the system can simulate the dynamics of a spin chain with arbitrary number of excitations and can be used to implement quantum information processing tasks.