Bound states of massive particles, such as nuclei, atoms or molecules, are ubiquitous in nature and constitute the bulk of the visible world around us. In contrast, photons typically only weakly influence each other due to their very weak interactions and vanishing mass. We report the observation of traveling three-photon bound states in a quantum nonlinear medium where the interactions between photons are mediated by atomic Rydberg states. In particular, photon correlation and conditional phase measurements reveal the distinct features associated with three-photon and two-photon bound states. Such photonic trimers and dimers can be viewed as quantum solitons with shape-preserving wavefunctions that depend on the constituent photon number. The observed bunching and strongly nonlinear optical phase are quantitatively described by an effective field theory (EFT) of Rydberg-induced photon-photon interactions, which demonstrates the presence of a substantial effective three-body force between the photons. These observations pave the way towards the realization, studies, and control of strongly interacting quantum many-body states of light.

%B Science %V 359 %P 783-786 %8 2018/02/16 %G eng %U http://science.sciencemag.org/content/359/6377/783 %N 6377 %R 10.1126/science.aao7293 %0 Journal Article %J Physical Review Letters %D 2014 %T Many-body dynamics of dipolar molecules in an optical lattice %A Kaden R. A. Hazzard %A Bryce Gadway %A Michael Foss-Feig %A Bo Yan %A Steven A. Moses %A Jacob P. Covey %A Norman Y. Yao %A Mikhail D. Lukin %A Jun Ye %A Deborah S. Jin %A Ana Maria Rey %X Understanding the many-body dynamics of isolated quantum systems is one of the central challenges in modern physics. To this end, the direct experimental realization of strongly correlated quantum systems allows one to gain insights into the emergence of complex phenomena. Such insights enable the development of theoretical tools that broaden our understanding. Here, we theoretically model and experimentally probe with Ramsey spectroscopy the quantum dynamics of disordered, dipolar-interacting, ultracold molecules in a partially filled optical lattice. We report the capability to control the dipolar interaction strength, and we demonstrate that the many-body dynamics extends well beyond a nearest-neighbor or mean-field picture, and cannot be quantitatively described using previously available theoretical tools. We develop a novel cluster expansion technique and demonstrate that our theoretical method accurately captures the measured dependence of the spin dynamics on molecule number and on the dipolar interaction strength. In the spirit of quantum simulation, this agreement simultaneously benchmarks the new theoretical method and verifies our microscopic understanding of the experiment. Our findings pave the way for numerous applications in quantum information science, metrology, and condensed matter physics. %B Physical Review Letters %V 113 %8 2014/11/7 %G eng %U http://arxiv.org/abs/1402.2354v1 %N 19 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.113.195302 %0 Journal Article %J Science %D 2013 %T All-Optical Switch and Transistor Gated by One Stored Photon %A Wenlan Chen %A Kristin M. Beck %A Robert Bücker %A Michael Gullans %A Mikhail D. Lukin %A Haruka Tanji-Suzuki %A Vladan Vuletic %X The realization of an all-optical transistor where one 'gate' photon controls a 'source' light beam, is a long-standing goal in optics. By stopping a light pulse in an atomic ensemble contained inside an optical resonator, we realize a device in which one stored gate photon controls the resonator transmission of subsequently applied source photons. A weak gate pulse induces bimodal transmission distribution, corresponding to zero and one gate photons. One stored gate photon produces fivefold source attenuation, and can be retrieved from the atomic ensemble after switching more than one source photon. Without retrieval, one stored gate photon can switch several hundred source photons. With improved storage and retrieval efficiency, our work may enable various new applications, including photonic quantum gates, and deterministic multiphoton entanglement. %B Science %V 341 %P 768 - 770 %8 2013/07/04 %G eng %U http://arxiv.org/abs/1401.3194v1 %N 6147 %! Science %R 10.1126/science.1238169 %0 Journal Article %J Nature (London) %D 2013 %T Attractive Photons in a Quantum Nonlinear Medium %A Ofer Firstenberg %A Thibault Peyronel %A Qi-Yu Liang %A Alexey V. Gorshkov %A Mikhail D. Lukin %A Vladan Vuletic %B Nature (London) %V 502 %P 71 %G eng %U http://dx.doi.org/10.1038/nature12512 %0 Journal Article %J Physical Review A %D 2013 %T Quantum Logic between Remote Quantum Registers %A Norman Y. Yao %A Zhe-Xuan Gong %A Chris R. Laumann %A Steven D. Bennett %A L. -M. Duan %A Mikhail D. Lukin %A Liang Jiang %A Alexey V. Gorshkov %X We analyze two approaches to quantum state transfer in solid-state spin systems. First, we consider unpolarized spin-chains and extend previous analysis to various experimentally relevant imperfections, including quenched disorder, dynamical decoherence, and uncompensated long range coupling. In finite-length chains, the interplay between disorder-induced localization and decoherence yields a natural optimal channel fidelity, which we calculate. Long-range dipolar couplings induce a finite intrinsic lifetime for the mediating eigenmode; extensive numerical simulations of dipolar chains of lengths up to L=12 show remarkably high fidelity despite these decay processes. We further consider the extension of the protocol to bosonic systems of coupled oscillators. Second, we introduce a quantum mirror based architecture for universal quantum computing which exploits all of the spins in the system as potential qubits. While this dramatically increases the number of qubits available, the composite operations required to manipulate "dark" spin qubits significantly raise the error threshold for robust operation. Finally, as an example, we demonstrate that eigenmode-mediated state transfer can enable robust long-range logic between spatially separated Nitrogen-Vacancy registers in diamond; numerical simulations confirm that high fidelity gates are achievable even in the presence of moderate disorder. %B Physical Review A %V 87 %8 2013/2/6 %G eng %U http://arxiv.org/abs/1206.0014v1 %N 2 %! Phys. Rev. A %R 10.1103/PhysRevA.87.022306 %0 Journal Article %J Physical Review Letters %D 2013 %T Realizing Fractional Chern Insulators with Dipolar Spins %A Norman Y. Yao %A Alexey V. Gorshkov %A Chris R. Laumann %A Andreas M. Läuchli %A Jun Ye %A Mikhail D. Lukin %X Strongly correlated quantum systems can exhibit exotic behavior controlled by topology. We predict that the \nu=1/2 fractional Chern insulator arises naturally in a two-dimensional array of driven, dipolar-interacting spins. As a specific implementation, we analyze how to prepare and detect synthetic gauge potentials for the rotational excitations of ultra-cold polar molecules trapped in a deep optical lattice. While the orbital motion of the molecules is pinned, at finite densities, the rotational excitations form a fractional Chern insulator. We present a detailed experimental blueprint for KRb, and demonstrate that the energetics are consistent with near-term capabilities. Prospects for the realization of such phases in solid-state dipolar systems are discussed as are their possible applications. %B Physical Review Letters %V 110 %8 2013/4/29 %G eng %U http://arxiv.org/abs/1212.4839v1 %N 18 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.110.185302 %0 Journal Article %J Nature Communications %D 2013 %T Topologically Protected Quantum State Transfer in a Chiral Spin Liquid %A Norman Y. Yao %A Chris R. Laumann %A Alexey V. Gorshkov %A Hendrik Weimer %A Liang Jiang %A J. Ignacio Cirac %A Peter Zoller %A Mikhail D. Lukin %X Topology plays a central role in ensuring the robustness of a wide variety of physical phenomena. Notable examples range from the robust current carrying edge states associated with the quantum Hall and the quantum spin Hall effects to proposals involving topologically protected quantum memory and quantum logic operations. Here, we propose and analyze a topologically protected channel for the transfer of quantum states between remote quantum nodes. In our approach, state transfer is mediated by the edge mode of a chiral spin liquid. We demonstrate that the proposed method is intrinsically robust to realistic imperfections associated with disorder and decoherence. Possible experimental implementations and applications to the detection and characterization of spin liquid phases are discussed. %B Nature Communications %V 4 %P 1585 %8 2013/3/12 %G eng %U http://arxiv.org/abs/1110.3788v1 %! Nat Comms %R 10.1038/ncomms2531 %0 Journal Article %J Nature Communications %D 2012 %T Scalable Architecture for a Room Temperature Solid-State Quantum Information Processor %A Norman Y. Yao %A Liang Jiang %A Alexey V. Gorshkov %A Peter C. Maurer %A Geza Giedke %A J. Ignacio Cirac %A Mikhail D. Lukin %X The realization of a scalable quantum information processor has emerged over the past decade as one of the central challenges at the interface of fundamental science and engineering. Much progress has been made towards this goal. Indeed, quantum operations have been demonstrated on several trapped ion qubits, and other solid-state systems are approaching similar levels of control. Extending these techniques to achieve fault-tolerant operations in larger systems with more qubits remains an extremely challenging goal, in part, due to the substantial technical complexity of current implementations. Here, we propose and analyze an architecture for a scalable, solid-state quantum information processor capable of operating at or near room temperature. The architecture is applicable to realistic conditions, which include disorder and relevant decoherence mechanisms, and includes a hierarchy of control at successive length scales. Our approach is based upon recent experimental advances involving Nitrogen-Vacancy color centers in diamond and will provide fundamental insights into the physics of non-equilibrium many-body quantum systems. Additionally, the proposed architecture may greatly alleviate the stringent constraints, currently limiting the realization of scalable quantum processors. %B Nature Communications %V 3 %P 800 %8 2012/4/24 %G eng %U http://arxiv.org/abs/1012.2864v1 %! Nat Comms %R 10.1038/ncomms1788 %0 Journal Article %J Physical Review Letters %D 2012 %T Topological Flat Bands from Dipolar Spin Systems %A Norman Y. Yao %A Chris R. Laumann %A Alexey V. Gorshkov %A Steven D. Bennett %A Eugene Demler %A Peter Zoller %A Mikhail D. Lukin %X We propose and analyze a physical system that naturally admits two-dimensional topological nearly flat bands. Our approach utilizes an array of three-level dipoles (effective S = 1 spins) driven by inhomogeneous electromagnetic fields. The dipolar interactions produce arbitrary uniform background gauge fields for an effective collection of conserved hardcore bosons, namely, the dressed spin-flips. These gauge fields result in topological band structures, whose bandgap can be larger than the corresponding bandwidth. Exact diagonalization of the full interacting Hamiltonian at half-filling reveals the existence of superfluid, crystalline, and supersolid phases. An experimental realization using either ultra-cold polar molecules or spins in the solid state is considered. %B Physical Review Letters %V 109 %8 2012/12/26 %G eng %U http://arxiv.org/abs/1207.4479v3 %N 26 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.109.266804 %0 Journal Article %J Physical Review Letters %D 2011 %T Photon-Photon Interactions via Rydberg Blockade %A Alexey V. Gorshkov %A Johannes Otterbach %A Michael Fleischhauer %A Thomas Pohl %A Mikhail D. Lukin %X We develop the theory of light propagation under the conditions of electromagnetically induced transparency (EIT) in systems involving strongly interacting Rydberg states. Taking into account the quantum nature and the spatial propagation of light, we analyze interactions involving few-photon pulses. We demonstrate that this system can be used for the generation of nonclassical states of light including trains of single photons with an avoided volume between them, for implementing photon-photon quantum gates, as well as for studying many-body phenomena with strongly correlated photons. %B Physical Review Letters %V 107 %8 2011/9/22 %G eng %U http://arxiv.org/abs/1103.3700v1 %N 13 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.107.133602 %0 Journal Article %J Physical Review A %D 2011 %T Quantum Magnetism with Polar Alkali Dimers %A Alexey V. Gorshkov %A Salvatore R. Manmana %A Gang Chen %A Eugene Demler %A Mikhail D. Lukin %A Ana Maria Rey %X We show that dipolar interactions between ultracold polar alkali dimers in optical lattices can be used to realize a highly tunable generalization of the t-J model, which we refer to as the t-J-V-W model. The model features long-range spin-spin interactions J_z and J_perp of XXZ type, long-range density-density interaction V, and long-range density-spin interaction W, all of which can be controlled in both magnitude and sign independently of each other and of the tunneling t. The "spin" is encoded in the rotational degree of freedom of the molecules, while the interactions are controlled by applied static electric and continuous-wave microwave fields. Furthermore, we show that nuclear spins of the molecules can be used to implement an additional (orbital) degree of freedom that is coupled to the original rotational degree of freedom in a tunable way. The presented system is expected to exhibit exotic physics and to provide insights into strongly correlated phenomena in condensed matter systems. Realistic experimental imperfections are discussed. %B Physical Review A %V 84 %8 2011/9/15 %G eng %U http://arxiv.org/abs/1106.1655v1 %N 3 %! Phys. Rev. A %R 10.1103/PhysRevA.84.033619 %0 Journal Article %J Physical Review Letters %D 2011 %T Robust Quantum State Transfer in Random Unpolarized Spin Chains %A Norman Y. Yao %A Liang Jiang %A Alexey V. Gorshkov %A Zhe-Xuan Gong %A Alex Zhai %A L. -M. Duan %A Mikhail D. Lukin %X We propose and analyze a new approach for quantum state transfer between remote spin qubits. Specifically, we demonstrate that coherent quantum coupling between remote qubits can be achieved via certain classes of random, unpolarized (infinite temperature) spin chains. Our method is robust to coupling strength disorder and does not require manipulation or control over individual spins. In principle, it can be used to attain perfect state transfer over arbitrarily long range via purely Hamiltonian evolution and may be particularly applicable in a solid-state quantum information processor. As an example, we demonstrate that it can be used to attain strong coherent coupling between Nitrogen-Vacancy centers separated by micrometer distances at room temperature. Realistic imperfections and decoherence effects are analyzed. %B Physical Review Letters %V 106 %8 2011/1/27 %G eng %U http://arxiv.org/abs/1011.2762v2 %N 4 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.106.040505 %0 Journal Article %J Physical Review Letters %D 2011 %T Tunable Superfluidity and Quantum Magnetism with Ultracold Polar Molecules %A Alexey V. Gorshkov %A Salvatore R. Manmana %A Gang Chen %A Jun Ye %A Eugene Demler %A Mikhail D. Lukin %A Ana Maria Rey %X By selecting two dressed rotational states of ultracold polar molecules in an optical lattice, we obtain a highly tunable generalization of the t-J model, which we refer to as the t-J-V-W model. In addition to XXZ spin exchange, the model features density-density interactions and novel density-spin interactions; all interactions are dipolar. We show that full control of all interaction parameters in both magnitude and sign can be achieved independently of each other and of the tunneling. As a first step towards demonstrating the potential of the system, we apply the density matrix renormalization group method (DMRG) to obtain the 1D phase diagram of the simplest experimentally realizable case. Specifically, we show that the tunability and the long-range nature of the interactions in the t-J-V-W model enable enhanced superfluidity. Finally, we show that Bloch oscillations in a tilted lattice can be used to probe the phase diagram experimentally. %B Physical Review Letters %V 107 %8 2011/9/8 %G eng %U http://arxiv.org/abs/1106.1644v1 %N 11 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.107.115301 %0 Journal Article %J Physical Review A %D 2010 %T Adiabatic preparation of many-body states in optical lattices %A Anders S. Sorensen %A Ehud Altman %A Michael Gullans %A J. V. Porto %A Mikhail D. Lukin %A Eugene Demler %X We analyze a technique for the preparation of low entropy many body states of atoms in optical lattices based on adiabatic passage. In particular, we show that this method allows preparation of strongly correlated states as stable highest energy states of Hamiltonians that have trivial ground states. As an example, we analyze the generation of antiferromagnetically ordered states by adiabatic change of a staggered field acting on the spins of bosonic atoms with ferromagnetic interactions. %B Physical Review A %V 81 %8 2010/6/22 %G eng %U http://arxiv.org/abs/0906.2567v3 %N 6 %! Phys. Rev. A %R 10.1103/PhysRevA.81.061603 %0 Journal Article %J Physical Review A %D 2010 %T Fast Entanglement Distribution with Atomic Ensembles and Fluorescent Detection %A Jonatan B. Brask %A Liang Jiang %A Alexey V. Gorshkov %A Vladan Vuletic %A Anders S. Sorensen %A Mikhail D. Lukin %X Quantum repeaters based on atomic ensemble quantum memories are promising candidates for achieving scalable distribution of entanglement over long distances. Recently, important experimental progress has been made towards their implementation. However, the entanglement rates and scalability of current approaches are limited by relatively low retrieval and single-photon detector efficiencies. We propose a scheme, which makes use of fluorescent detection of stored excitations to significantly increase the efficiency of connection and hence the rate. Practical performance and possible experimental realizations of the new protocol are discussed. %B Physical Review A %V 81 %8 2010/2/12 %G eng %U http://arxiv.org/abs/0907.3839v2 %N 2 %! Phys. Rev. A %R 10.1103/PhysRevA.81.020303 %0 Journal Article %J Physical Review Letters %D 2010 %T Photonic Phase Gate via an Exchange of Fermionic Spin Waves in a Spin Chain %A Alexey V. Gorshkov %A Johannes Otterbach %A Eugene Demler %A Michael Fleischhauer %A Mikhail D. Lukin %X We propose a new protocol for implementing the two-qubit photonic phase gate. In our approach, the pi phase is acquired by mapping two single photons into atomic excitations with fermionic character and exchanging their positions. The fermionic excitations are realized as spin waves in a spin chain, while photon storage techniques provide the interface between the photons and the spin waves. Possible imperfections and experimental systems suitable for implementing the gate are discussed. %B Physical Review Letters %V 105 %8 2010/8/5 %G eng %U http://arxiv.org/abs/1001.0968v3 %N 6 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.105.060502 %0 Journal Article %J Physical Review Letters %D 2009 %T Alkaline-Earth-Metal Atoms as Few-Qubit Quantum Registers %A Alexey V. Gorshkov %A Ana Maria Rey %A Andrew J. Daley %A Martin M. Boyd %A Jun Ye %A Peter Zoller %A Mikhail D. Lukin %X We propose and analyze a novel approach to quantum information processing, in which multiple qubits can be encoded and manipulated using electronic and nuclear degrees of freedom associated with individual alkaline-earth atoms trapped in an optical lattice. Specifically, we describe how the qubits within each register can be individually manipulated and measured with sub-wavelength optical resolution. We also show how such few-qubit registers can be coupled to each other in optical superlattices via conditional tunneling to form a scalable quantum network. Finally, potential applications to quantum computation and precision measurements are discussed. %B Physical Review Letters %V 102 %8 2009/3/18 %G eng %U http://arxiv.org/abs/0812.3660v2 %N 11 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.102.110503 %0 Journal Article %J Physical Review A %D 2009 %T Realization of Coherent Optically Dense Media via Buffer-Gas Cooling %A Tao Hong %A Alexey V. Gorshkov %A David Patterson %A Alexander S. Zibrov %A John M. Doyle %A Mikhail D. Lukin %A Mara G. Prentiss %X We demonstrate that buffer-gas cooling combined with laser ablation can be used to create coherent optical media with high optical depth and low Doppler broadening that offers metastable states with low collisional and motional decoherence. Demonstration of this generic technique opens pathways to coherent optics with a large variety of atoms and molecules. We use helium buffer gas to cool 87Rb atoms to below 7 K and slow atom diffusion to the walls. Electromagnetically induced transparency (EIT) in this medium allows for 50% transmission in a medium with initial OD >70 and for slow pulse propagation with large delay-bandwidth products. In the high-OD regime, we observe high-contrast spectrum oscillations due to efficient four-wave mixing. %B Physical Review A %V 79 %8 2009/1/6 %G eng %U http://arxiv.org/abs/0805.1416v2 %N 1 %! Phys. Rev. A %R 10.1103/PhysRevA.79.013806 %0 Journal Article %J Nature Physics %D 2008 %T Anyonic interferometry and protected memories in atomic spin lattices %A Liang Jiang %A Gavin K. Brennen %A Alexey V. Gorshkov %A Klemens Hammerer %A Mohammad Hafezi %A Eugene Demler %A Mikhail D. Lukin %A Peter Zoller %X Strongly correlated quantum systems can exhibit exotic behavior called topological order which is characterized by non-local correlations that depend on the system topology. Such systems can exhibit remarkable phenomena such as quasi-particles with anyonic statistics and have been proposed as candidates for naturally fault-tolerant quantum computation. Despite these remarkable properties, anyons have never been observed in nature directly. Here we describe how to unambiguously detect and characterize such states in recently proposed spin lattice realizations using ultra-cold atoms or molecules trapped in an optical lattice. We propose an experimentally feasible technique to access non-local degrees of freedom by performing global operations on trapped spins mediated by an optical cavity mode. We show how to reliably read and write topologically protected quantum memory using an atomic or photonic qubit. Furthermore, our technique can be used to probe statistics and dynamics of anyonic excitations. %B Nature Physics %V 4 %P 482 - 488 %8 2008/4/20 %G eng %U http://arxiv.org/abs/0711.1365v1 %N 6 %! Nat Phys %R 10.1038/nphys943 %0 Journal Article %J Physical Review Letters %D 2008 %T Coherence of an optically illuminated single nuclear spin qubit %A Liang Jiang %A M. V. Gurudev Dutt %A Emre Togan %A Lily Childress %A Paola Cappellaro %A J. M. Taylor %A Mikhail D. Lukin %X We investigate the coherence properties of individual nuclear spin quantum bits in diamond [Dutt et al., Science, 316, 1312 (2007)] when a proximal electronic spin associated with a nitrogen-vacancy (NV) center is being interrogated by optical radiation. The resulting nuclear spin dynamics are governed by time-dependent hyperfine interaction associated with rapid electronic transitions, which can be described by a spin-fluctuator model. We show that due to a process analogous to motional averaging in nuclear magnetic resonance, the nuclear spin coherence can be preserved after a large number of optical excitation cycles. Our theoretical analysis is in good agreement with experimental results. It indicates a novel approach that could potentially isolate the nuclear spin system completely from the electronic environment. %B Physical Review Letters %V 100 %8 2008/2/19 %G eng %U http://arxiv.org/abs/0707.1341v2 %N 7 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.100.073001 %0 Journal Article %J Physical Review Letters %D 2008 %T Coherent Quantum Optical Control with Subwavelength Resolution %A Alexey V. Gorshkov %A Liang Jiang %A Markus Greiner %A Peter Zoller %A Mikhail D. Lukin %X We suggest a new method for quantum optical control with nanoscale resolution. Our method allows for coherent far-field manipulation of individual quantum systems with spatial selectivity that is not limited by the wavelength of radiation and can, in principle, approach a few nanometers. The selectivity is enabled by the nonlinear atomic response, under the conditions of Electromagnetically Induced Transparency, to a control beam with intensity vanishing at a certain location. Practical performance of this technique and its potential applications to quantum information science with cold atoms, ions, and solid-state qubits are discussed. %B Physical Review Letters %V 100 %8 2008/3/7 %G eng %U http://arxiv.org/abs/0706.3879v2 %N 9 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.100.093005 %0 Journal Article %J Physical Review A %D 2008 %T Photon storage in Lambda-type optically dense atomic media. IV. Optimal control using gradient ascent %A Alexey V. Gorshkov %A Tommaso Calarco %A Mikhail D. Lukin %A Anders S. Sorensen %X We use the numerical gradient ascent method from optimal control theory to extend efficient photon storage in Lambda-type media to previously inaccessible regimes and to provide simple intuitive explanations for our optimization techniques. In particular, by using gradient ascent to shape classical control pulses used to mediate photon storage, we open up the possibility of high efficiency photon storage in the non-adiabatic limit, in which analytical solutions to the equations of motion do not exist. This control shaping technique enables an order-of-magnitude increase in the bandwidth of the memory. We also demonstrate that the often discussed connection between time reversal and optimality in photon storage follows naturally from gradient ascent. Finally, we discuss the optimization of controlled reversible inhomogeneous broadening. %B Physical Review A %V 77 %8 2008/4/4 %G eng %U http://arxiv.org/abs/0710.2698v2 %N 4 %! Phys. Rev. A %R 10.1103/PhysRevA.77.043806 %0 Journal Article %J Physical Review Letters %D 2007 %T Optimal control of light pulse storage and retrieval %A Irina Novikova %A Alexey V. Gorshkov %A David F. Phillips %A Anders S. Sorensen %A Mikhail D. Lukin %A Ronald L. Walsworth %X We demonstrate experimentally a procedure to obtain the maximum efficiency for the storage and retrieval of light pulses in atomic media. The procedure uses time reversal to obtain optimal input signal pulse-shapes. Experimental results in warm Rb vapor are in good agreement with theoretical predictions and demonstrate a substantial improvement of efficiency. This optimization procedure is applicable to a wide range of systems. %B Physical Review Letters %V 98 %8 2007/6/15 %G eng %U http://arxiv.org/abs/quant-ph/0702266v1 %N 24 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.98.243602 %0 Journal Article %J Physical Review A %D 2007 %T Photon storage in Lambda-type optically dense atomic media. I. Cavity model %A Alexey V. Gorshkov %A Axel Andre %A Mikhail D. Lukin %A Anders S. Sorensen %X In a recent paper [Gorshkov et al., Phys. Rev. Lett. 98, 123601 (2007)], we used a universal physical picture to optimize and demonstrate equivalence between a wide range of techniques for storage and retrieval of photon wave packets in Lambda-type atomic media in free space, including the adiabatic reduction of the photon group velocity, pulse-propagation control via off-resonant Raman techniques, and photon-echo-based techniques. In the present paper, we perform the same analysis for the cavity model. In particular, we show that the retrieval efficiency is equal to C/(1+C) independent of the retrieval technique, where C is the cooperativity parameter. We also derive the optimal strategy for storage and, in particular, demonstrate that at any detuning one can store, with the optimal efficiency of C/(1+C), any smooth input mode satisfying T C gamma >> 1 and a certain class of resonant input modes satisfying T C gamma ~ 1, where T is the duration of the input mode and 2 gamma is the transition linewidth. In the two subsequent papers of the series, we present the full analysis of the free-space model and discuss the effects of inhomogeneous broadening on photon storage. %B Physical Review A %V 76 %8 2007/9/7 %G eng %U http://arxiv.org/abs/quant-ph/0612082v2 %N 3 %! Phys. Rev. A %R 10.1103/PhysRevA.76.033804 %0 Journal Article %J Physical Review A %D 2007 %T Photon storage in Lambda-type optically dense atomic media. II. Free-space model %A Alexey V. Gorshkov %A Axel Andre %A Mikhail D. Lukin %A Anders S. Sorensen %X In a recent paper [Gorshkov et al., Phys. Rev. Lett. 98, 123601 (2007)], we presented a universal physical picture for describing a wide range of techniques for storage and retrieval of photon wave packets in Lambda-type atomic media in free space, including the adiabatic reduction of the photon group velocity, pulse-propagation control via off-resonant Raman techniques, and photon-echo based techniques. This universal picture produced an optimal control strategy for photon storage and retrieval applicable to all approaches and yielded identical maximum efficiencies for all of them. In the present paper, we present the full details of this analysis as well some of its extensions, including the discussion of the effects of non-degeneracy of the two lower levels of the Lambda system. The analysis in the present paper is based on the intuition obtained from the study of photon storage in the cavity model in the preceding paper [Gorshkov et al., Phys. Rev. A 76, 033804 (2007)]. %B Physical Review A %V 76 %8 2007/9/7 %G eng %U http://arxiv.org/abs/quant-ph/0612083v2 %N 3 %! Phys. Rev. A %R 10.1103/PhysRevA.76.033805 %0 Journal Article %J Physical Review A %D 2007 %T Photon storage in Lambda-type optically dense atomic media. III. Effects of inhomogeneous broadening %A Alexey V. Gorshkov %A Axel Andre %A Mikhail D. Lukin %A Anders S. Sorensen %X In a recent paper [Gorshkov et al., Phys. Rev. Lett. 98, 123601 (2007)] and in the two preceding papers [Gorshkov et al., Phys. Rev. A 76, 033804 (2007); 76, 033805 (2007)], we used a universal physical picture to optimize and demonstrate equivalence between a wide range of techniques for storage and retrieval of photon wave packets in homogeneously broadened Lambda-type atomic media, including the adiabatic reduction of the photon group velocity, pulse-propagation control via off-resonant Raman techniques, and photon-echo-based techniques. In the present paper, we generalize this treatment to include inhomogeneous broadening. In particular, we consider the case of Doppler-broadened atoms and assume that there is a negligible difference between the Doppler shifts of the two optical transitions. In this situation, we show that, at high enough optical depth, all atoms contribute coherently to the storage process as if the medium were homogeneously broadened. We also discuss the effects of inhomogeneous broadening in solid state samples. In this context, we discuss the advantages and limitations of reversing the inhomogeneous broadening during the storage time, as well as suggest a way for achieving high efficiencies with a nonreversible inhomogeneous profile. %B Physical Review A %V 76 %8 2007/9/7 %G eng %U http://arxiv.org/abs/quant-ph/0612084v2 %N 3 %! Phys. Rev. A %R 10.1103/PhysRevA.76.033806 %0 Journal Article %J Physical Review Letters %D 2007 %T Universal Approach to Optimal Photon Storage in Atomic Media %A Alexey V. Gorshkov %A Axel Andre %A Michael Fleischhauer %A Anders S. Sorensen %A Mikhail D. Lukin %X We present a universal physical picture for describing storage and retrieval of photon wave packets in a Lambda-type atomic medium. This physical picture encompasses a variety of different approaches to pulse storage ranging from adiabatic reduction of the photon group velocity and pulse-propagation control via off-resonant Raman fields to photon-echo based techniques. Furthermore, we derive an optimal control strategy for storage and retrieval of a photon wave packet of any given shape. All these approaches, when optimized, yield identical maximum efficiencies, which only depend on the optical depth of the medium. %B Physical Review Letters %V 98 %8 2007/3/19 %G eng %U http://arxiv.org/abs/quant-ph/0604037v3 %N 12 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.98.123601