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Formation of dark-state polaritons and two-polariton bound states in arrays of atoms and optical cavities

Angelo Maggitti

Published Apr 7, 2016• 0 citations
OpenAlex

Abstract

This thesis covers a theoretical analysis of non-interacting and interacting quasi\nparticles, called polaritons. Polaritons are composites, based on photonic and atomic\nexcitations in a tunable and controlled manner. Dark-state polaritons, as a subclass\nof polaritons, are very curious objects, as they can act as a quantum memory of\nphotons within an ensemble of alkali-metal atoms in -type conguration which\nadmit electromagnetically induced transparency (EIT). This thesis focus on the\nformation of dark-state polaritons in degenerate two-level systems, where two light\nelds, a quantum probe and a classical driving eld, couple the same transition\nbetween the ground state and excited state manifold. An algorithm is going to\nbe derived in order to determine the dispersion relation and inherent composition\nof the dark-state polaritons in the degenerate two-level system. The algorithm is\nbased on a microscopic equation of motion technique and provides an extension of\nthe non-degenerate case. Depending on the polarization of the light elds, it will be\nshown that either one or two dark-state polaritons can exist. Further, the calculated\ndark-state polaritons can be used in order to perform a frequency conversion and\neven a conversion of linear light polarization.\nIn the second part of the thesis, interacting polaritons in arrays of coupled QED\ncavities will be discussed. In rst place, the standard Jaynes-Cummings model is\ndiscussed in order to provide a better insight to polaritons in QED cavities. Then,\na modied Jaynes-Cummings model is introduced and derived in order to study\ndark-polaritons and their interaction. It will be shown that dark-polaritons directly\ndepend on the common single photon detuning of the two coupling elds, quantum\nprobe and classical driving eld. The interaction between dark-polaritons will be\ndiscussed where the emergence of dark-polariton bound pairs will be shown. By\ntuning the Stark-shift due to the classical control eld, the number and the composition\nof dark-polariton bound pairs can be controlled. It will be demonstrated\nthat there exists a dark-polariton bound pair which diers from the aforementioned\nones, because it represents a ground state of the system. Using that kind of a darkpolariton\nbound pair, storage and retrieval of a single photon can be performed,\neven though that the photons are in a two-photon bound state.\nIn the last part of the thesis, disorder between QED cavities will be introduced\nin a controlled manner through staggered inter-cavity photon hopping strengths J1\nand J2. Further, the appearance of a dark-polariton bound pair of a completely\ndierent type will be presented.

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We investigate the formation of dark-state polaritons in an ensemble of degenerate two-level atoms admitting electromagnetically induced transparency. Using a generalization of microscopic equation-of-motion technique, multiple collective polariton modes are identified depending on the polarizations of two coupling fields. For each mode, the polariton dispersion relation and composition are obtained in a closed form out of a matrix eigenvalue problem for arbitrary control field strengths. We illustrate the algorithm by considering the F g = 2 → F e = 1 transition of the D 1 line in 87 Rb atomic vapor. In addition, an application of dark-state polaritons to the frequency and/or polarization conversion, using D 1 and D 2 transitions in cold Rb atoms, is given.

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Towards many-body physics with Rydberg-dressed cavity polaritons

H. R. Kong

An exciting frontier in quantum information science is the creation and manipulation of \nbottom-up quantum systems that are built and controlled one by one. For the past 30 \nyears, we have witnessed signi cant progresses in harnessing strong atom- eld interactions \nfor critical applications in quantum computation, communication, simulation, and metrology. \nBy extension, we can envisage a quantum network consisting of material nodes coupled \ntogether with in nite-dimensional bosonic quantum channels. In this context, there \nhas been active research worldwide to achieve quantum optical circuits, for which single \natoms are wired by freely-propagating single photons through the circuit elements. For all \nthese systems, the system-size expansion with atoms and photons results in a fundamental \npathologic scaling that linearizes the very atom- eld interaction, and signi cantly limits \nthe degree of non-classicality and entanglement in analog atom- eld quantum systems for \natom number N 1. \nThe long-term motivation of this MSc thesis is (i) to discover new physical mechanisms \nthat extend the inherent scaling behavior of atom- eld interactions and (ii) to \ndevelop quantum optics toolkits that design dynamical gauge structures for the realization \nof lattice-gauge-theoretic quantum network and the synthesis of novel quantum optically \ngauged materials. The basic premise is to achieve the strong coupling regime for a quantum \nmany-body material system interacting with the quantized elds of an optical cavity. Our \nlaboratory e ort can be described as the march towards \\many-body QED," where optical \n elds acquire some properties of the material interactions that constrain their dynamical \nprocesses, as with quantum eld theories. While such an e ort currently do not exist elsewhere, \nwe are convicted that our work will become an essential endeavor to enable cavity \nquantum electrodynamics (QED) in the bona- de regime of quantum many-body physics \nin this entanglement frontier. \nIn this context, I describe an example in Chapter 2 that utilizes strong RydbergRydberg \ninteractions to design dynamical gauge structures for the quantum square ice \nmodels. Quantum \nuctuations driven by cavity-mediated in nite-range interaction stabilize \nthe quantum-gauged system into a long-range entangled quantum spin liquid that may \nbe detected through the time-ordered photoelectric statistics for photons leaking out of the \ncavity. Fractionalized \\spinon" and \\vison" excitations can be manipulated for topological \nquantum computation, and the emergent photons of arti cial QED in our lattice gauge \ntheoretic system can be directly measured and studied. \nThe laboratory challenge towards strongly coupled cavity Rydberg polaritons encompasses \nthree daunting research milestones that push the technological boundaries beyond of the state-of-the-arts. In Chapter 3, I discuss our extreme-high-vacuum chamber (XHV) \ncluster system that allows the world's lowest operating vacuum environment P ' 10 \nTorr for an ultracold AMO experiment with long background-limited trap lifetimes. In \nChapter 4, I discuss our ultrastable laser systems stabilized to the ultra-low-expansion \noptical cavities. Coupled with a scalable eld-programmable-gate-array (FPGA) digitalanalog \ncontrol system, we can manipulate arbitrarily the phase-amplitude relationship of \nseveral dozens of laser elds across 300 nm to 1550 nm at mHz precision. In Chapter 5, \nwe discuss the quantum trajectory simulations for manipulating the external degrees of \nfreedom of ultracold atoms with external laser elds. Electrically tunable liquid crystal \nlens creates a dynamically tunable optical trap to move the ultracold atomic gases over \nlong distance within the ultra-high-vacuum (UHV) chamber system. \nIn Chapter 6, I discuss our collaborative development of two science cavity platforms \n{ the \\Rydberg" quantum dot and the many-body QED platforms. An important development \nwas the research into new high-index IBS materials, where we have utilized our \nlow-loss optical mirrors for extending the world's highest cavity nesse F 500k! We discuss \nthe unique challenges of implementing optical cavity QED for Rydberg atoms, which \nrequired tremendous degrees of electromagnetic shielding and eld control. Single-crystal \nSapphire structure, along with Angstrom-level diamond-turned Ti blade electrodes, is utilized \nfor the eld compensation and extinction by > 60 dB. Single-crystal PZTs on silica \nV-grooves are utilized for the stabilization of the optical cavity with length uncertainty less \nthan 1=100 of a single nucleon, along with extreme level of vibration isolation in a XHV \nenvironment. The capability to perform in-situ RF plasma cleaning allows the regeneration \nof optical mirrors when coated with a few Cs atoms. Lastly but not the least, we combine \nsingle-atom resolution quantum gas microscopy technique with superpixel holographic algorithm \nto project arbitrary real-time recon gurable di raction-limited optical potential \nlandscapes for the preparation of low-entropy atom arrays.

•May 23, 2018•2 citations

Dark-state polaritons in single- and double- Λ media

Y. D. Chong, Marin Soljacic A

We derive the properties of polaritons in single-$\ensuremath{\Lambda}$ and double-$\ensuremath{\Lambda}$ media using a microscopic equation-of-motion technique. In each case, the polaritonic dispersion relation and composition arise from a matrix eigenvalue problem for arbitrary control field strengths. We show that the double-$\ensuremath{\Lambda}$ medium can be used to up- or down-convert single photons while preserving quantum coherence. The existence of a dark-state polariton protects this single-photon four-wave mixing effect against incoherent decay of the excited atomic states. The efficiency of this conversion is limited mainly by the sample size and the lifetime of the metastable state.

arXiv:0708.1750•Physical Review A•Jan 23, 2008•21 citations
This thesis covers a theoretical analysis of non-interacting and interacting quasi\nparticles, called polaritons. Polaritons are composites, based on photonic and atomic\nexcitations in a tunable and controlled manner. Dark-state polaritons, as a subclass\nof polaritons, are very curious objects, as they can act as a quantum memory of\nphotons within an ensemble of alkali-metal atoms in -type conguration which\nadmit electromagnetically induced transparency (EIT). This thesis focus on the\nformation of dark-state polaritons in degenerate two-level systems, where two light\nelds, a quantum probe and a classical driving eld, couple the same transition\nbetween the ground state and excited state manifold. An algorithm is going to\nbe derived in order to determine the dispersion relation and inherent composition\nof the dark-state polaritons in the degenerate two-level system. The algorithm is\nbased on a microscopic equation of motion technique and provides an extension of\nthe non-degenerate case. Depending on the polarization of the light elds, it will be\nshown that either one or two dark-state polaritons can exist. Further, the calculated\ndark-state polaritons can be used in order to perform a frequency conversion and\neven a conversion of linear light polarization.\nIn the second part of the thesis, interacting polaritons in arrays of coupled QED\ncavities will be discussed. In rst place, the standard Jaynes-Cummings model is\ndiscussed in order to provide a better insight to polaritons in QED cavities. Then,\na modied Jaynes-Cummings model is introduced and derived in order to study\ndark-polaritons and their interaction. It will be shown that dark-polaritons directly\ndepend on the common single photon detuning of the two coupling elds, quantum\nprobe and classical driving eld. The interaction between dark-polaritons will be\ndiscussed where the emergence of dark-polariton bound pairs will be shown. By\ntuning the Stark-shift due to the classical control eld, the number and the composition\nof dark-polariton bound pairs can be controlled. It will be demonstrated\nthat there exists a dark-polariton bound pair which diers from the aforementioned\nones, because it represents a ground state of the system. Using that kind of a darkpolariton\nbound pair, storage and retrieval of a single photon can be performed,\neven though that the photons are in a two-photon bound state.\nIn the last part of the thesis, disorder between QED cavities will be introduced\nin a controlled manner through staggered inter-cavity photon hopping strengths J1\nand J2. Further, the appearance of a dark-polariton bound pair of a completely\ndierent type will be presented.
We investigate the formation of dark-state polaritons in an ensemble of degenerate two-level atoms admitting electromagnetically induced transparency. Using a generalization of microscopic equation-of-motion technique, multiple collective polariton modes are identified depending on the polarizations of two coupling fields. For each mode, the polariton dispersion relation and composition are obtained in a closed form out of a matrix eigenvalue problem for arbitrary control field strengths. We illustrate the algorithm by considering the F g = 2 → F e = 1 transition of the D 1 line in 87 Rb atomic vapor. In addition, an application of dark-state polaritons to the frequency and/or polarization conversion, using D 1 and D 2 transitions in cold Rb atoms, is given.
We present a theoretical scheme to study optical cavity quantum electrodynamics using dark-state polaritons. Exploiting the highly tunable lifetimes of the photons in the form of cavity dark-state polaritons, we push the strong coupling of single optical photons to an effective two-level emitter in a Rydberg-blockade atomic ensemble to an unprecedented regime. The resulting Jaynes--Cummings model with extremely strong coupling is of fundamental interest. We discuss applications in controlled quantum Rabi oscillation, nonlinear spectroscopy of the Jaynes-Cummings ladder, as well as the generation of nonclassical states, all based on light-matter interactions in the optical domain.
We investigate a one-dimensional modified Jaynes-Cummings-Hubbard chain of NNN identical QED cavities with nearest-neighbor photon tunneling and periodic boundary conditions. Each cavity contains an embedded three-level atom which is coupled to a cavity mode and an external classical control field. In the case of two excitations and common large detuning of two Raman-resonant fields, we show the emergence of two different species of dark-polariton bound pairs (DPBPs) that are mutually localized in their relative spatial coordinates. Due to the high degree of controllability, we show the appearance of either one or two DPBPs, having the energies within the energy gaps between three bands of mutually delocalized eigenstates. Interestingly, in a different parameter regime with negatively detuned Raman fields, we find that the ground state of the system is a DPBP which can be utilized for the photon storage, retrieval, and controllable state preparation. Moreover, we propose an experimental realization of our model system.
Most phenomena around us can be explained by classical optics since photons interact weakly with atoms. When the interaction is strong enough where one photon affects the properties of other photons, we go to the regime of quantum photon-photon nonlinear optics. The work in this thesis explores this regime of physics. This paves the path to exploring strongly interacting many-body physics with photons which is still a largely unexplored domain. The ability to control strongly interacting photons is also of central importance in quantum science and engineering. We use the approach of Electromagnetically Induced Transparency (EIT) in atomic ensembles to create strong interactions and demonstrate coherent control between single photons. Using EIT, we coherently map single photons onto the atoms which travel as coupled excitations of light and matter called dark-state polaritons. When the medium is optically dense, the polariton propagates as a massive particle with a velocity that is much smaller than the speed of light. These polaritons interact with each other via their atomic component. In this thesis, we show robust symmetry-protected collisions between photons that imprint a large phase of π/2 with little loss and extend the nature of photon-photon interactions to the repulsive regime, which are essential for quantum communication and metrology. We use the technique of photon blockade to make a fast optical detector of Rydberg states, directly demonstrating the use of quantum nonlinear optics for quantum computation. We also study the extensions of the attractive and repulsive photons for three particles shedding light into the formation of bound states and crystals of photons and paving the way to studying many-body physics of photons.
An exciting frontier in quantum information science is the creation and manipulation of \nbottom-up quantum systems that are built and controlled one by one. For the past 30 \nyears, we have witnessed signi cant progresses in harnessing strong atom- eld interactions \nfor critical applications in quantum computation, communication, simulation, and metrology. \nBy extension, we can envisage a quantum network consisting of material nodes coupled \ntogether with in nite-dimensional bosonic quantum channels. In this context, there \nhas been active research worldwide to achieve quantum optical circuits, for which single \natoms are wired by freely-propagating single photons through the circuit elements. For all \nthese systems, the system-size expansion with atoms and photons results in a fundamental \npathologic scaling that linearizes the very atom- eld interaction, and signi cantly limits \nthe degree of non-classicality and entanglement in analog atom- eld quantum systems for \natom number N 1. \nThe long-term motivation of this MSc thesis is (i) to discover new physical mechanisms \nthat extend the inherent scaling behavior of atom- eld interactions and (ii) to \ndevelop quantum optics toolkits that design dynamical gauge structures for the realization \nof lattice-gauge-theoretic quantum network and the synthesis of novel quantum optically \ngauged materials. The basic premise is to achieve the strong coupling regime for a quantum \nmany-body material system interacting with the quantized elds of an optical cavity. Our \nlaboratory e ort can be described as the march towards \\many-body QED," where optical \n elds acquire some properties of the material interactions that constrain their dynamical \nprocesses, as with quantum eld theories. While such an e ort currently do not exist elsewhere, \nwe are convicted that our work will become an essential endeavor to enable cavity \nquantum electrodynamics (QED) in the bona- de regime of quantum many-body physics \nin this entanglement frontier. \nIn this context, I describe an example in Chapter 2 that utilizes strong RydbergRydberg \ninteractions to design dynamical gauge structures for the quantum square ice \nmodels. Quantum \nuctuations driven by cavity-mediated in nite-range interaction stabilize \nthe quantum-gauged system into a long-range entangled quantum spin liquid that may \nbe detected through the time-ordered photoelectric statistics for photons leaking out of the \ncavity. Fractionalized \\spinon" and \\vison" excitations can be manipulated for topological \nquantum computation, and the emergent photons of arti cial QED in our lattice gauge \ntheoretic system can be directly measured and studied. \nThe laboratory challenge towards strongly coupled cavity Rydberg polaritons encompasses \nthree daunting research milestones that push the technological boundaries beyond of the state-of-the-arts. In Chapter 3, I discuss our extreme-high-vacuum chamber (XHV) \ncluster system that allows the world's lowest operating vacuum environment P ' 10 \nTorr for an ultracold AMO experiment with long background-limited trap lifetimes. In \nChapter 4, I discuss our ultrastable laser systems stabilized to the ultra-low-expansion \noptical cavities. Coupled with a scalable eld-programmable-gate-array (FPGA) digitalanalog \ncontrol system, we can manipulate arbitrarily the phase-amplitude relationship of \nseveral dozens of laser elds across 300 nm to 1550 nm at mHz precision. In Chapter 5, \nwe discuss the quantum trajectory simulations for manipulating the external degrees of \nfreedom of ultracold atoms with external laser elds. Electrically tunable liquid crystal \nlens creates a dynamically tunable optical trap to move the ultracold atomic gases over \nlong distance within the ultra-high-vacuum (UHV) chamber system. \nIn Chapter 6, I discuss our collaborative development of two science cavity platforms \n{ the \\Rydberg" quantum dot and the many-body QED platforms. An important development \nwas the research into new high-index IBS materials, where we have utilized our \nlow-loss optical mirrors for extending the world's highest cavity nesse F 500k! We discuss \nthe unique challenges of implementing optical cavity QED for Rydberg atoms, which \nrequired tremendous degrees of electromagnetic shielding and eld control. Single-crystal \nSapphire structure, along with Angstrom-level diamond-turned Ti blade electrodes, is utilized \nfor the eld compensation and extinction by > 60 dB. Single-crystal PZTs on silica \nV-grooves are utilized for the stabilization of the optical cavity with length uncertainty less \nthan 1=100 of a single nucleon, along with extreme level of vibration isolation in a XHV \nenvironment. The capability to perform in-situ RF plasma cleaning allows the regeneration \nof optical mirrors when coated with a few Cs atoms. Lastly but not the least, we combine \nsingle-atom resolution quantum gas microscopy technique with superpixel holographic algorithm \nto project arbitrary real-time recon gurable di raction-limited optical potential \nlandscapes for the preparation of low-entropy atom arrays.
We derive the properties of polaritons in single-$\ensuremath{\Lambda}$ and double-$\ensuremath{\Lambda}$ media using a microscopic equation-of-motion technique. In each case, the polaritonic dispersion relation and composition arise from a matrix eigenvalue problem for arbitrary control field strengths. We show that the double-$\ensuremath{\Lambda}$ medium can be used to up- or down-convert single photons while preserving quantum coherence. The existence of a dark-state polariton protects this single-photon four-wave mixing effect against incoherent decay of the excited atomic states. The efficiency of this conversion is limited mainly by the sample size and the lifetime of the metastable state.