We study non-perturbative effects in N-body scattering of Rydberg polaritons using effective field theory (EFT). We develop an EFT in one dimension and show how a suitably long medium can be used to prepare shallow N-body bound states. We then derive the effective N-body interaction potential for Rydberg polaritons and the associated N-body contact force that arises in the EFT. We use the contact force to find the leading order corrections to the binding energy of the N-body bound states and determine the photon number at which the EFT description breaks down. We find good agreement throughout between the predictions of EFT and numerical simulations of the exact two and three photon wavefunction transmission.

1 aGullans, Michael1 aThompson, J., D.1 aWang, Y.1 aLiang, Q., -Y.1 aVuletic, V.1 aLukin, M., D.1 aGorshkov, Alexey, V. uhttp://arxiv.org/abs/1605.0565101507nas a2200229 4500008004100000245005700041210005700098260001500155300001100170490000800181520087400189100002701063700002101090700001601111700001301127700001501140700002001155700001801175700002101193700002501214856003801239 2015 eng d00aCoulomb bound states of strongly interacting photons0 aCoulomb bound states of strongly interacting photons c2015/09/16 a1236010 v1153 a We show that two photons coupled to Rydberg states via electromagnetically induced transparency can interact via an effective Coulomb potential. This interaction gives rise to a continuum of two-body bound states. Within the continuum, metastable bound states are distinguished in analogy with quasi-bound states tunneling through a potential barrier. We find multiple branches of metastable bound states whose energy spectrum is governed by the Coulomb potential, thus obtaining a photonic analogue of the hydrogen atom. Under certain conditions, the wavefunction resembles that of a diatomic molecule in which the two polaritons are separated by a finite "bond length." These states propagate with a negative group velocity in the medium, allowing for a simple preparation and detection scheme, before they slowly decay to pairs of bound Rydberg atoms. 1 aMaghrebi, Mohammad, F.1 aGullans, Michael1 aBienias, P.1 aChoi, S.1 aMartin, I.1 aFirstenberg, O.1 aLukin, M., D.1 aBüchler, H., P.1 aGorshkov, Alexey, V. uhttp://arxiv.org/abs/1505.03859v101278nas a2200205 4500008004100000245009000041210006900131260001400200490000700214520065300221100001600874700001300890700002000903700002700923700002100950700001800971700002500989700002101014856003701035 2014 eng d00aScattering resonances and bound states for strongly interacting Rydberg polaritons 0 aScattering resonances and bound states for strongly interacting c2014/11/30 v903 a We provide a theoretical framework describing slow-light polaritons interacting via atomic Rydberg states. We use a diagrammatic method to analytically derive the scattering properties of two polaritons. We identify parameter regimes where polariton-polariton interactions are repulsive. Furthermore, in the regime of attractive interactions, we identify multiple two-polariton bound states, calculate their dispersion, and study the resulting scattering resonances. Finally, the two-particle scattering properties allow us to derive the effective low-energy many-body Hamiltonian. This theoretical platform is applicable to ongoing experiments. 1 aBienias, P.1 aChoi, S.1 aFirstenberg, O.1 aMaghrebi, Mohammad, F.1 aGullans, Michael1 aLukin, M., D.1 aGorshkov, Alexey, V.1 aBüchler, H., P. uhttp://arxiv.org/abs/1402.7333v101759nas a2200169 4500008004100000245008100041210006900122260001400191490000700205520124300212100002101455700001801476700001901494700002101513700001801534856003701552 2013 eng d00aPreparation of Non-equilibrium Nuclear Spin States in Double Quantum Dots 0 aPreparation of Nonequilibrium Nuclear Spin States in Double Quan c2013/7/150 v883 a We theoretically study the dynamic polarization of lattice nuclear spins in GaAs double quantum dots containing two electrons. In our prior work [Phys. Rev. Lett. 104, 226807 (2010)] we identified three regimes of long-term dynamics, including the build up of a large difference in the Overhauser fields across the dots, the saturation of the nuclear polarization process associated with formation of so-called "dark states," and the elimination of the difference field. In particular, when the dots are different sizes we found that the Overhauser field becomes larger in the smaller dot. Here we present a detailed theoretical analysis of these problems including a model of the polarization dynamics and the development of a new numerical method to efficiently simulate semiclassical central-spin problems. When nuclear spin noise is included, the results agree with our prior work indicating that large difference fields and dark states are stable configurations, while the elimination of the difference field is unstable; however, in the absence of noise we find all three steady states are achieved depending on parameters. These results are in good agreement with dynamic nuclear polarization experiments in double quantum dots. 1 aGullans, Michael1 aKrich, J., J.1 aTaylor, J., M.1 aHalperin, B., I.1 aLukin, M., D. uhttp://arxiv.org/abs/1212.6953v301034nas a2200169 4500008004100000245005800041210005700099260001500156490000800171520053900179100002100718700001800739700002300757700002900780700001800809856003700827 2013 eng d00aSingle-photon nonlinear optics with graphene plasmons0 aSinglephoton nonlinear optics with graphene plasmons c2013/12/110 v1113 a We show that it is possible to realize significant nonlinear optical interactions at the few photon level in graphene nanostructures. Our approach takes advantage of the electric field enhancement associated with the strong confinement of graphene plasmons and the large intrinsic nonlinearity of graphene. Such a system could provide a powerful platform for quantum nonlinear optical control of light. As an example, we consider an integrated optical device that exploits this large nonlinearity to realize a single photon switch. 1 aGullans, Michael1 aChang, D., E.1 aKoppens, F., H. L.1 ade Abajo, F., J. García1 aLukin, M., D. uhttp://arxiv.org/abs/1309.2651v301154nas a2200205 4500008004100000245004700041210004700088260001400135490000800149520061400157100002100771700001500792700001800807700001400825700002100839700001800860700001500878700001800893856003700911 2012 eng d00aNanoplasmonic Lattices for Ultracold atoms0 aNanoplasmonic Lattices for Ultracold atoms c2012/12/60 v1093 a We propose to use sub-wavelength confinement of light associated with the near field of plasmonic systems to create nanoscale optical lattices for ultracold atoms. Our approach combines the unique coherence properties of isolated atoms with the sub-wavelength manipulation and strong light-matter interaction associated with nano-plasmonic systems. It allows one to considerably increase the energy scales in the realization of Hubbard models and to engineer effective long-range interactions in coherent and dissipative many-body dynamics. Realistic imperfections and potential applications are discussed. 1 aGullans, Michael1 aTiecke, T.1 aChang, D., E.1 aFeist, J.1 aThompson, J., D.1 aCirac, J., I.1 aZoller, P.1 aLukin, M., D. uhttp://arxiv.org/abs/1208.6293v301401nas a2200217 4500008004100000245005600041210005600097260001300153490000800166520081300174100002100987700001801008700001901026700001401045700002101059700001901080700001401099700001501113700001801128856003701146 2010 eng d00aDynamic Nuclear Polarization in Double Quantum Dots0 aDynamic Nuclear Polarization in Double Quantum Dots c2010/6/40 v1043 aWe theoretically investigate the controlled dynamic polarization of lattice nuclear spins in GaAs double quantum dots containing two electrons. Three regimes of long-term dynamics are identified, including the build up of a large difference in the Overhauser fields across the dots, the saturation of the nuclear polarization process associated with formation of so-called "dark states," and the elimination of the difference field. We show that in the case of unequal dots, build up of difference fields generally accompanies the nuclear polarization process, whereas for nearly identical dots, build up of difference fields competes with polarization saturation in dark states. The elimination of the difference field does not, in general, correspond to a stable steady state of the polarization process. 1 aGullans, Michael1 aKrich, J., J.1 aTaylor, J., M.1 aBluhm, H.1 aHalperin, B., I.1 aMarcus, C., M.1 aStopa, M.1 aYacoby, A.1 aLukin, M., D. uhttp://arxiv.org/abs/1003.4508v201250nas a2200229 4500008004100000245006800041210006700109260001400176300001400190490000600204520061800210100001900828700001900847700001800866700001400884700001500898700001900913700001500932700001800947700001800965856003700983 2008 eng d00aHigh-sensitivity diamond magnetometer with nanoscale resolution0 aHighsensitivity diamond magnetometer with nanoscale resolution c2008/9/14 a810 - 8160 v43 aWe present a novel approach to the detection of weak magnetic fields that takes advantage of recently developed techniques for the coherent control of solid-state electron spin quantum bits. Specifically, we investigate a magnetic sensor based on Nitrogen-Vacancy centers in room-temperature diamond. We discuss two important applications of this technique: a nanoscale magnetometer that could potentially detect precession of single nuclear spins and an optical magnetic field imager combining spatial resolution ranging from micrometers to millimeters with a sensitivity approaching few femtotesla/Hz$^{1/2}$. 1 aTaylor, J., M.1 aCappellaro, P.1 aChildress, L.1 aJiang, L.1 aBudker, D.1 aHemmer, P., R.1 aYacoby, A.1 aWalsworth, R.1 aLukin, M., D. uhttp://arxiv.org/abs/0805.1367v101388nas a2200145 4500008004100000245009200041210006900133260001300202490000700215520092500222100001401147700001901161700001801180856004401198 2007 eng d00aA fast and robust approach to long-distance quantum communication with atomic ensembles0 afast and robust approach to longdistance quantum communication w c2007/7/20 v763 aQuantum repeaters create long-distance entanglement between quantum systems while overcoming difficulties such as the attenuation of single photons in a fiber. Recently, an implementation of a repeater protocol based on single qubits in atomic ensembles and linear optics has been proposed [Nature 414, 413 (2001)]. Motivated by rapid experimental progress towards implementing that protocol, here we develop a more efficient scheme compatible with active purification of arbitrary errors. Using similar resources as the earlier protocol, our approach intrinsically purifies leakage out of the logical subspace and all errors within the logical subspace, leading to greatly improved performance in the presence of experimental inefficiencies. Our analysis indicates that our scheme could generate approximately one pair per 3 minutes over 1280 km distance with fidelity (F>78%) sufficient to violate Bell's inequality. 1 aJiang, L.1 aTaylor, J., M.1 aLukin, M., D. uhttp://arxiv.org/abs/quant-ph/0609236v301375nas a2200181 4500008004100000245008800041210006900129260001400198490000700212520082100219100001901040700001801059700002001077700001501097700001901112700001801131856004401149 2007 eng d00aRelaxation, dephasing, and quantum control of electron spins in double quantum dots0 aRelaxation dephasing and quantum control of electron spins in do c2007/7/130 v763 aRecent experiments have demonstrated quantum manipulation of two-electron spin states in double quantum dots using electrically controlled exchange interactions. Here, we present a detailed theory for electron spin dynamics in two-electron double dot systems that was used to guide these experiments and analyze experimental results. The theory treats both charge and spin degrees of freedom on an equal basis. Specifically, we analyze the relaxation and dephasing mechanisms that are relevant to experiments and discuss practical approaches for quantum control of two-electron system. We show that both charge and spin dephasing play important roles in the dynamics of the two-spin system, but neither represents a fundamental limit for electrical control of spin degrees of freedom in semiconductor quantum bits. 1 aTaylor, J., M.1 aPetta, J., R.1 aJohnson, A., C.1 aYacoby, A.1 aMarcus, C., M.1 aLukin, M., D. uhttp://arxiv.org/abs/cond-mat/0602470v200966nas a2200121 4500008004100000245008500041210006900126260001500195520055300210100001900763700001800782856004400800 2006 eng d00aCavity quantum electrodynamics with semiconductor double-dot molecules on a chip0 aCavity quantum electrodynamics with semiconductor doubledot mole c2006/05/053 aWe describe a coherent control technique for coupling electron spin states associated with semiconductor double-dot molecule to a microwave stripline resonator on a chip. We identify a novel regime of operation in which strong interaction between a molecule and a resonator can be achieved with minimal decoherence, reaching the so-called strong coupling regime of cavity QED. We describe potential applications of such a system, including low-noise coherent electrical control, fast QND measurements of spin states, and long-range spin coupling. 1 aTaylor, J., M.1 aLukin, M., D. uhttp://arxiv.org/abs/cond-mat/0605144v101138nas a2200157 4500008004100000245007600041210006900117260001400186490000700200520065300207100001800860700001900878700002100897700001800918856004400936 2006 eng d00aFault-tolerant Quantum Communication with Minimal Physical Requirements0 aFaulttolerant Quantum Communication with Minimal Physical Requir c2006/2/230 v963 aWe describe a novel protocol for a quantum repeater which enables long distance quantum communication through realistic, lossy photonic channels. Contrary to previous proposals, our protocol incorporates active purification of arbitrary errors at each step of the protocol using only two qubits at each repeater station. Because of these minimal physical requirements, the present protocol can be realized in simple physical systems such as solid-state single photon emitters. As an example, we show how nitrogen vacancy color centers in diamond can be used to implement the protocol, using the nuclear and electronic spin to form the two qubits. 1 aChildress, L.1 aTaylor, J., M.1 aSorensen, A., S.1 aLukin, M., D. uhttp://arxiv.org/abs/quant-ph/0410123v301484nas a2200121 4500008004100000245007100041210006900112260001500181520108500196100001901281700001801300856004401318 2005 eng d00aDephasing of quantum bits by a quasi-static mesoscopic environment0 aDephasing of quantum bits by a quasistatic mesoscopic environmen c2005/12/073 aWe examine coherent processes in a two-state quantum system that is strongly coupled to a mesoscopic spin bath and weakly coupled to other environmental degrees of freedom. Our analysis is specifically aimed at understanding the quantum dynamics of solid-state quantum bits such as electron spins in semiconductor structures and superconducting islands. The role of mesoscopic degrees of freedom with long correlation times (local degrees of freedom such as nuclear spins and charge traps) in qubit-related dephasing is discussed in terms of a quasi-static bath. A mathemat- ical framework simultaneously describing coupling to the slow mesoscopic bath and a Markovian environment is developed and the dephasing and decoherence properties of the total system are investigated. The model is applied to several specific examples with direct relevance to current ex- periments. Comparisons to experiments suggests that such quasi-static degrees of freedom play an important role in current qubit implementations. Several methods of mitigating the bath-induced error are considered. 1 aTaylor, J., M.1 aLukin, M., D. uhttp://arxiv.org/abs/quant-ph/0512059v201771nas a2200157 4500008004100000245012200041210006900163260001500232490000700247520123500254100002201489700001901511700002101530700001801551856004401569 2005 eng d00aFault-tolerant quantum repeaters with minimal physical resources, and implementations based on single photon emitters0 aFaulttolerant quantum repeaters with minimal physical resources c2005/11/280 v723 aWe analyze a novel method that uses fixed, minimal physical resources to achieve generation and nested purification of quantum entanglement for quantum communication over arbitrarily long distances, and discuss its implementation using realistic photon emitters and photonic channels. In this method, we use single photon emitters with two internal degrees of freedom formed by an electron spin and a nuclear spin to build intermediate nodes in a quantum channel. State-selective fluorescence is used for probabilistic entanglement generation between electron spins in adjacent nodes. We analyze in detail several approaches which are applicable to realistic, homogeneously broadened single photon emitters. Furthermore, the coupled electron and nuclear spins can be used to efficiently implement entanglement swapping and purification. We show that these techniques can be combined to generate high-fidelity entanglement over arbitrarily long distances. We present a specific protocol that functions in polynomial time and tolerates percent-level errors in entanglement fidelity and local operations. The scheme has the lowest requirements on physical resources of any current scheme for fully fault-tolerant quantum repeaters. 1 aChildress, L., I.1 aTaylor, J., M.1 aSorensen, A., S.1 aLukin, M., D. uhttp://arxiv.org/abs/quant-ph/0502112v101053nas a2200181 4500008004100000245007400041210006900115260001400184490000700198520052300205100001900728700001300747700001500760700001500775700001900790700001800809856004400827 2005 eng d00aSolid-state circuit for spin entanglement generation and purification0 aSolidstate circuit for spin entanglement generation and purifica c2005/6/150 v943 aWe show how realistic charge manipulation and measurement techniques, combined with the exchange interaction, allow for the robust generation and purification of four-particle spin entangled states in electrically controlled semiconductor quantum dots. The generated states are immunized to the dominant sources of noise via a dynamical decoherence-free subspace; all additional errors are corrected by a purification protocol. This approach may find application in quantum computation, communication, and metrology. 1 aTaylor, J., M.1 aDür, W.1 aZoller, P.1 aYacoby, A.1 aMarcus, C., M.1 aLukin, M., D. uhttp://arxiv.org/abs/cond-mat/0503255v201230nas a2200193 4500008004100000245007800041210006900119260001500188520065600203100001900859700001500878700001500893700001600908700001800924700001500942700001800957700001700975856004400992 2004 eng d00aQuantum information processing using localized ensembles of nuclear spins0 aQuantum information processing using localized ensembles of nucl c2004/07/233 aWe describe a technique for quantum information processing based on localized en sembles of nuclear spins. A qubit is identified as the presence or absence of a collective excitation of a mesoscopic ensemble of nuclear spins surrounding a single quantum dot. All single and two-qubit operations can be effected using hyperfine interactions and single-electron spin rotations, hence the proposed scheme avoids gate errors arising from entanglement between spin and orbital degrees of freedom. Ultra-long coherence times of nuclear spins suggest that this scheme could be particularly well suited for applications where long lived memory is essential. 1 aTaylor, J., M.1 aGiedke, G.1 aChrist, H.1 aParedes, B.1 aCirac, J., I.1 aZoller, P.1 aLukin, M., D.1 aImamoglu, A. uhttp://arxiv.org/abs/cond-mat/0407640v201129nas a2200145 4500008004100000245007400041210006900115260001500184490000700199520067900206100001900885700001700904700001800921856004400939 2003 eng d00aControlling a mesoscopic spin environment by quantum bit manipulation0 aControlling a mesoscopic spin environment by quantum bit manipul c2003/12/100 v913 aWe present a unified description of cooling and manipulation of a mesoscopic bath of nuclear spins via coupling to a single quantum system of electronic spin (quantum bit). We show that a bath cooled by the quantum bit rapidly saturates. Although the resulting saturated states of the spin bath (``dark states'') generally have low degrees of polarization and purity, their symmetry properties make them a valuable resource for the coherent manipulation of quantum bits. Specifically, we demonstrate that the dark states of nuclear ensembles can be used to coherently control the system-bath interaction and to provide a robust, long-lived quantum memory for qubit states. 1 aTaylor, J., M.1 aImamoglu, A.1 aLukin, M., D. uhttp://arxiv.org/abs/cond-mat/0308459v101085nas a2200145 4500008004100000245005000041210004900091260001400140490000700154520067800161100001900839700001900858700001800877856004400895 2003 eng d00aLong-lived memory for mesoscopic quantum bits0 aLonglived memory for mesoscopic quantum bits c2003/5/200 v903 aWe describe a technique to create long-lived quantum memory for quantum bits in mesoscopic systems. Specifically we show that electronic spin coherence can be reversibly mapped onto the collective state of the surrounding nuclei. The coherent transfer can be efficient and fast and it can be used, when combined with standard resonance techniques, to reversibly store coherent superpositions on the time scale of seconds. This method can also allow for ``engineering'' entangled states of nuclear ensembles and efficiently manipulating the stored states. We investigate the feasibility of this method through a detailed analysis of the coherence properties of the system. 1 aTaylor, J., M.1 aMarcus, C., M.1 aLukin, M., D. uhttp://arxiv.org/abs/cond-mat/0301323v1