Publications

62.(2021) Physical Review X. 11, 1, 011008. Abstract
We introduce and demonstrate a scheme for eliminating the inhomogeneous dephasing of a collective quantum state. The scheme employs offresonant fields that continuously dress the collective state with an auxiliary sensor state, which has an enhanced and opposite sensitivity to the same source of inhomogeneity. We derive the optimal conditions under which the dressed state is fully protected from dephasing when using either one or two dressing fields. The latter provides better protection, circumvents qubit phase rotation, and suppresses the sensitivity to drive noise. We further derive expressions for all residual, higherorder sensitivities. We experimentally study the scheme by protecting a collective excitation of an atomic ensemble, where inhomogeneous dephasing originates from thermal motion. Using photon storage and retrieval, we demonstrate complete suppression of inhomogeneous dephasing and, consequently, a prolonged memory time. Our scheme may be applied to eliminate motional dephasing in other systems, improving the performance of quantum gates and memorieswith neutral atoms. It is also generally applicable to various gas, solid, and engineered systems, where sensitivity to variations in time, space, or other domains limits possible scaleup of the system.

61.(2020) arXiv. AbstractBoosting photonic quantum computation with moderate nonlinearity
Photonic measurementbased quantum computation (MBQC) is a promising route towards faulttolerant universal quantum computing. A central challenge in this effort is the huge overhead in the resources required for the construction of large photonic graphs using probabilistic linearoptics gates. Although strong singlephoton nonlinearity ideally enables deterministic construction of such clusters, it is challenging to realise in a scalable way. Here we explore the prospects of using moderate nonlinearity (with conditional phase shift smaller than $\pi$) to boost photonic quantum computing and significantly reduce its resources overhead. The key element in our scheme is a nonlinear router that preferentially directs photonic wavepackets to different output ports depending on their intensity. As a relevant example, we analyze the nonlinearity provided by Rydberg blockade in atomic ensembles, in which the tradeoff between the nonlinearity and the accompanying loss is well understood. We present protocols for efficient Bell measurement and GHZstate preparation  both key elements in the construction of graph states, as well as for the CNOT gate and quantum factorization. Given the large number of operations involved in the construction of graph states for faulttolerant MBQC, the increase in success probability provided by our protocols already at moderate nonlinearity can result in a dramatic reduction in the required resources.

60.(2020) Science Advances. 6, 45, eabd0650. Abstract
The periodicity inherent to any interferometric signal entails a fundamental tradeoff between sensitivity and dynamic range of interferometrybased sensors. Here, we develop a methodology for substantially extending the dynamic range of such sensors without compromising their sensitivity, stability, and bandwidth. The scheme is based on simultaneous operation of two nearly identical interferometers, providing a moirélike period much larger than 2π and benefiting from closetomaximal sensitivity and from suppression of commonmode noise. The methodology is highly suited to atom interferometers, which offer record sensitivities in measuring gravitoinertial forces but suffer from limited dynamic range. We experimentally demonstrate an atom interferometer with a dynamicrange enhancement of more than an order of magnitude in a single shot and more than three orders of magnitude within a few shots for both static and dynamic signals. This approach can considerably improve the operation of interferometric sensors in challenging, uncertain, or rapidly varying conditions.

59.(2020) Optics Express. 28, 22, p. 3370833717 Abstract
Bessel beams are renowned members of a wide family of nondiffracting (propagationinvariant) fields. We report on experiments showing that nondiffracting fields are also immune to diffusion. We map the phase and magnitude of structured laser fields onto the spatial coherence between two internal states of warm atoms undergoing diffusion. We measure the field after a controllable, effective, diffusion time by continuously generating light from the spatial coherence. The coherent diffusion of BesselGaussian fields and more intricate, nondiffracting fields is quantitatively analyzed and directly compared to that of diffracting fields. To elucidate the origin of diffusion invariance, we show results for nondiffracting fields whose phase pattern we flatten.

58.(2020) arXiv. arXiv:2010. AbstractSuperextended nanofiberguided field for coherent interaction with hot atoms[All authors]
We fabricate an extremely thin optical fiber that supports a superextended mode with a diameter as large as 13 times the optical wavelength, residing almost entirely outside the fiber and guided over thousands of wavelengths (5 mm), in order to couple guided light to warm atomic vapor. This unique configuration balances between strong confinement, as evident by saturation powers as low as tens of nW, and long interaction times with the thermal atoms, thereby enabling fast and coherent interactions. We demonstrate narrow coherent resonances (tens of MHz) of electromagnetically induced transparency for signals at the singlephoton level and long relaxation times (10 ns) of atoms excited by the guided mode. The dimensions of the guided mode's evanescent field are compatible with the Rydberg blockade mechanism, making this platform particularly suitable for observing quantum nonlinear optics phenomena.

57.(2020) Optics Express. 28, 22, p. 3273832749 Abstract
We describe a fiber Raman amplifier for nanosecond and subnanosecond pulses centered around 1260 nm. The amplification takes place inside a 4.5mlong polarizationmaintaining phosphorusdoped fiber, pumped at 1080 nm by 3nslong pulses with a repetition rate of 200 kHz and up to 1.75 kWpeak power. The input seed pulses are of submW peakpower and minimal duration of 0.25 ns, carved out of a continuouswave laser with subMHz linewidth. We obtain linearly polarized output pulses with peak powers of up to 1.4 kW, corresponding to peakpower conversion efficiency of over 80%. An ultrahigh small signal gain of 90 dB is achieved, and the signaltonoise ratio 3 dB below the saturation power is above 20 dB. No significant temporal and spectral broadening is observed for output pulses up to 400 W peak power, and broadening at higher powers can be reduced by phase modulation of the seed pulse. Thus, nearlytransformlimited pulses with peak power up to 1 kW are obtained. Finally, we demonstrate the generation of pulses with controllable frequency chirp, pulses with variable width, and double pulses. This amplifier is thus suitable for coherent control of narrow atomic resonances, especially for the fast and coherent excitation of rubidium atoms to Rydberg states. These abilities open the way towards several important applications in quantum nonlinear optics.

56.(2020) arXiv. AbstractOptical quantum memory with optically inaccessible noblegas spins
Optical quantum memories, which store and preserve the quantum state of photons, rely on a coherent mapping of the photonic state onto matter states that are optically accessible. Here we outline a new physical mechanism to map the state of photons onto the longlived but optically inaccessible collective state of noblegas spins. The mapping employs the coherent spinexchange interaction arising from random collisions with alkali vapor. We analyze optimal strategies for highefficiency storage and retrieval of nonclassical light at various parameter regimes. Based on these strategies, we identify feasible experimental conditions for realizing efficient quantum memories with noblegas spins having hourslong coherence times at room temperature and above

55.(2020) arXiv. AbstractOptimal control of an optical quantum memory based on noblegas spins
In Ref. [Katz et al., arXiv:2007.08770 (2020)], we present a mechanism and optimal procedures for mapping the quantum state of photons onto an optically inaccessible macroscopic state of noblegas spins, which functions as a quantum memory. Here we introduce and analyze a detailed model of the memory operation. We derive the equations of motion for storage and retrieval of nonclassical light and design optimal control strategies. The detailed model accounts for quantum noise and for thermal atomic motion, including the effects of optical mode structure and imperfect antirelaxation wall coating. We conclude with proposals of practical experimental configurations of the memory, with lifetimes ranging from seconds to hours.

54.(2020) Optics Letters. 45, 13, p. 34313434 Abstract
The FresnelFizeau effect of transverse drag, in which the trajectory of a light beam changes due to transverse motion of the optical medium, is usually extremely small and hard to detect. We observe transverse drag in a moving hotvapor cell, utilizing slow light due to electromagnetically induced transparency (EIT). The drag effect is enhanced by a factor 400,000, corresponding to the ratio between the light speed in vacuum and the group velocity under the EIT conditions. We study the contribution of the thermal atomic motion, which is much faster than the mean medium velocity, and identify the regime where its effect on the transverse drag is negligible.

53.(2020) Physical Review A. 102, 1, 012822. Abstract
Ensembles of alkalimetal or noblegas atoms at room temperature and above are widely applied in quantum optics and metrology owing to their longlived spins. Their collective spin states maintain nonclassical nonlocal correlations, despite the atomic thermal motion in the bulk and at the boundaries. Here we present a stochastic, fully quantum description of the effect of atomic diffusion in these systems. We employ the BlochHeisenbergLangevin formalism to account for the quantum noise originating from diffusion and from various boundary conditions corresponding to typical wall coatings, thus modeling the dynamics of nonclassical spin states with spatial interatomic correlations. As examples, we apply the model to calculate spin noise spectroscopy, temporal relaxation of squeezed spin states, and the coherent coupling between two spin species in a hybrid system.

52.(2020) Physical Review A. 102, 1, 013326. Abstract
Pointsource atom interferometry is a promising approach for implementing robust, highsensitivity, rotation sensors using cold atoms. However, its scale factor, i.e., the ratio between the interferometer signal and the actual rotation rate, depends on the initial conditions of the atomic cloud, which may drift in time and result in bias instability, particularly in compact devices with short interrogation times. We present two methods to stabilize the scale factor. One relies on a modelbased correction which exploits correlations between multiple features of the interferometer output and works on a singleshot basis. The other is a selfcalibrating method where a known bias rotation is applied to every other measurement, requiring no prior knowledge of the underlying model but reducing the sensor bandwidth by a factor of two. We demonstrate both schemes experimentally with complete suppression of scalefactor drifts, maintaining the original rotation sensitivity and allowing for biasfree operation over several hours.

51.(2020) Physical Review Applied. 13, 5, 054053. Abstract
Atom interferometers offer excellent sensitivity to gravitational and inertial signals but have limited dynamic range. We introduce a scheme that improves this tradeoff by a factor of 50 using composite fringes, obtained from sets of measurements with slightly varying interrogation times, as in a moire effect. We analyze analytically the performance gain in this approach and the tradeoffs it entails between sensitivity, dynamic range, and bandwidth, and we experimentally validate the analysis over a wide range of parameters. Combining compositefringe measurements with a particlefilter estimation protocol, we demonstrate continuous tracking of a rapidly varying signal over a span 2 orders of magnitude larger than the dynamic range of a traditional atom interferometer.

50.(2020) arXiv. 2004.02295. AbstractOptical protection of a collective state from inhomogeneous dephasing
We introduce and demonstrate a scheme for eliminating the inhomogeneous dephasing of a collective quantum state. The scheme employs offresonant optical fields that dress the collective state with an auxiliary sensor state, which has an enhanced and opposite sensitivity to the same source of inhomogeneity. We derive the optimal conditions under which the dressed state is fully protected from dephasing, when using either one or two dressing fields. The latter provides better protection, prevents global phase rotation, and suppresses the sensitivity to drive noise. We further provide expressions for all residual, higherorder, sensitivities. We experimentally study the scheme by protecting a collective excitation of an atomic ensemble, where inhomogeneous dephasing originates from thermal motion. Using photon storage and retrieval, we demonstrate complete suppression of inhomogeneous dephasing and consequently a prolonged memory time. Our scheme may be applied to eliminate motional dephasing in other systems, improving the performance of quantum gates and memories with neutral atoms. It is also generally applicable to various gas, solid, and engineered systems, where sensitivity to variations in time, space, or other domains limits possible scaleup of the system.

49.(2020) Physical Review Letters. 124, 4, 043602. Abstract
Nuclear spins of noblegas atoms are exceptionally isolated from the environment and can maintain their quantum properties for hours at room temperature. Here we develop a mechanism for entangling two such distant macroscopic ensembles by using coherent light input. The interaction between the light and the noblegas spins in each ensemble is mediated by spinexchange collisions with alkalimetal spins, which are only virtually excited. The relevant conditions for experimental realizations with He3 or Xe129 are outlined.

48.(2019) New Journal of Physics. 21, 10, 103024. Abstract
Doppler broadening in thermal ensembles degrades the absorption crosssection and the coherence time of collective excitations. In two photon transitions, it is common to assume that this problem becomes worse with larger wavelength mismatch. Here we identify an opposite mechanism, where such wavelength mismatch leads to cancellation of Doppler broadening via the counteracting effects of velocitydependent lightshifts and Doppler shifts. We show that this effect is general, common to both absorption and transparency resonances, and favorably scales with wavelength mismatch. We experimentally confirm the enhancement of transitions for different lowlying orbitals in rubidium atoms and use calculations to extrapolate to highlying Rydberg orbitals. These calculations predict a dramatic enhancement of up to 20fold increase in absorption, even in the presence of large homogeneous broadening. More general configurations, where an auxiliary dressing field is used to counteract Doppler broadening, are also discussed and experimentally demonstrated. The mechanism we study can be applied as well for rephasing of spin waves and increasing the coherence time of quantum memories.

47.(2019) Optica. 6, 11, p. 14061411 Abstract
Partially coherent fields are abundant in many physical systems. While the propagation of partially coherent light undergoing diffraction is well understood, its evolution in the presence of coherent diffusion (i.e., diffusion of complex fields) remains largely unknown. Here we develop an analytic model describing the diffusion of partially coherent beams and study it experimentally. Our model is based on a diffusion analog of the famous Van Cittert–Zernike theorem. Experimentally, we use a fourwave mixing scheme with electromagnetically induced transparency to couple optical speckle patterns to diffusing atoms in a warm vapor. The spatial coherence properties of the speckle fields are monitored under diffusion and are compared to our model and to the familiar evolution of spatial coherence of light speckles under diffraction. We identify several important differences between the evolution dynamics of the spatial coherence under diffraction and diffusion. Our findings shed light on the propagation of partially coherent fields in media where multiple scattering or thermal motion lead to coherent diffusion.

46.(2019) Physical Review Letters. 123, 17, 173203. Abstract
The resonant absorption of light by an ensemble of absorbers decreases when the resonance is in homogeneously broadened. Recovering the lost absorption cross section is of great importance for various applications of lightmatter interactions, particularly in quantum optics, but no recovery mechanism has yet been identified and successfully demonstrated. Here, we formulate the limit set by the inhomogeneity on the absorption, and present a mechanism able to circumvent this limit and fully recover the homogeneous absorption of the ensemble. We experimentally study this mechanism using two different level schemes in atomic vapors and demonstrate up to fivefold enhancement of the absorption above the inhomogeneous limit. Our scheme relies on light shifts induced by auxiliary fields and is thus applicable to various physical systems and inhomogeneity mechanisms.

45.(2019) Physical Review A. 100, 2, 023617. Abstract
We present techniques for inertialsensing atom interferometers which produce multiple phase measurements per experimental cycle. With these techniques, we realize two types of multiport measurements, namely, quadrature phase detection and realtime systematic phase cancellation, which address challenges in operating highsensitivity coldatom sensors in mobile and field applications. We confirm experimentally the increase in sensitivity due to quadrature phase detection in the presence of large phase uncertainty, and demonstrate suppression of systematic phases on a singleshot basis.

44.(2019) Communications Physics. 2, 58. Abstract
Optical pumping is an efficient method for initializing and maintaining atomic spin ensembles in a welldefined quantum spin state. Standard optical pumping methods orient the spins by transferring photonic angular momentum to spin polarization. Generally the spins are oriented along the propagation direction of the light due to selection rules of the dipole interaction. Here we present and experimentally demonstrate that by modulating the light polarization, angular momentum perpendicular to the optical axis can be transferred efficiently to cesium vapor. The transverse pumping scheme employs transversely oriented dark states, allowing for control of the trajectory of the spins on the Bloch sphere. This new mechanism is suitable and potentially beneficial for diverse applications, particularly in quantum metrology.

43.(2019) arXiv. 1905.12532. AbstractQuantum interface for noblegas spins
An ensemble of noblegas nuclear spins is a unique quantum system that could maintain coherence for many hours at room temperature and above, owing to exceptional isolation from the environment. This isolation, however, is a mixed blessing, limiting the ability of these ensembles to coherently interface with other quantum systems. Here we show that spinexchange collisions with alkalimetal atoms render a quantum interface for noblegas spins without impeding their long coherence times. We formulate the manybody theory of the hybrid system and reveal a collective mechanism that strongly couples the macroscopic quantum states of the two spin ensembles. Despite their stochastic and random nature, weak collisions enable entanglement and reversible exchange of nonclassical excitations in an efficient, controllable, and deterministic process. We outline feasible parameters for reaching the strongcoupling regime, paving the way towards an experimental realization of hourlong quantum memories and entanglement at roomtemperature.

42.(2018) 2018 Asia Communications and Photonics Conference, ACP 2018. Abstract
Future quantum photonic networks require coherent optical memories for synchronizing quantum sources and gates of probabilistic nature. Room temperature operation is also desirable for ease of scaling up. Until now, however, roomtemperature atomic memories have suffered from an intrinsic readout noise due to spontaneous fourwavemixing. Here we demonstrate a new scheme for storing photons at room temperature, the fast ladder memory (FLAME). In this scheme, stimulated twophoton absorption is used instead of the previously used stimulated Raman scattering. As here the competing spontaneous processes would require spontaneous absorption of an optical photon, rather than emission, the noise is greatly suppressed. Furthermore, high external efficiency can be achieved as the control is well separated in frequency from the signal, and could be filtered out using highly efficient interference filters. We run the protocol in rubidium vapour, both on and off singlephoton resonance, demonstrating a ratio of 50 between storage time and signal pulse width, an external total efficiency of over 25%, and only 2.3 × 10 4 noise photons per extracted signal photon. This paves the way towards the efficient synchronization of probabilistic gates and sources at room temperature, and the controlled production of large quantum states of light.

41.(2018) Physical Review A. 98, 1, 012712. Abstract
The spins of gaseous alkalimetal atoms are commonly assumed to oscillate at a constant hyperfine frequency, which for many years has been used to define a standard unit of time, the second. Indeed, under standard experimental conditions, the spins oscillate independently, only weakly perturbed and slowly decaying due to random spinspin collisions. Here we consider a different, unexplored regime of very dense gas, where collisions, more frequent than the hyperfine frequency, dominate the dynamics. We find that the hyperfine oscillations become significantly longer lived, and their frequency becomes dependent on the state of the ensemble, manifesting strong nonlinear dynamics. We reveal that the nonlinearity originates from a manybody interaction which synchronizes the electronic spins, driving them into a single collective mode. The conditions for experimental realizations of this regime are outlined.

40.(2018) Nature Communications. 9, 2074. Abstract
Light storage, the controlled and reversible mapping of photons onto longlived states of matter, enables memory capability in optical quantum networks. Prominent storage media are warm alkali vapors due to their strong optical coupling and longlived spin states. In a dense gas, the random atomic collisions dominate the lifetime of the spin coherence, limiting the storage time to a few milliseconds. Here we present and experimentally demonstrate a storage scheme that is insensitive to spinexchange collisions, thus enabling long storage times at high atomic densities. This unique property is achieved by mapping the light field onto spin orientation within a decoherencefree subspace of spin states. We report on a record storage time of 1 s in roomtemperature cesium vapor, a 100fold improvement over existing storage schemes. Furthermore, our scheme lays the foundations for hourlong quantum memories using raregas nuclear spins.

39.(2018) Science advances. 4, 1, eaap8598. Abstract
Future quantum photonic networks require coherent opticalmemories for synchronizing quantum sources and gates of probabilistic nature. We demonstrate a fast ladder memory (FLAME) mapping the optical field onto the superposition between electronic orbitals of rubidium vapor. Using a ladderlevel system of orbital transitions with nearly degenerate frequencies simultaneously enables high bandwidth, low noise, and long memory lifetime. We store and retrieve 1.7nslong pulses, containing 0.5 photons on average, and observe shorttime external efficiency of 25%, memory lifetime (1/e) of 86 ns, and below 10(4) added noise photons. Consequently, coupling this memory to a probabilistic source would enhance the ondemand photon generation probability by a factor of 12, the highest number yet reported for a noisefree, room temperature memory. This paves the way toward the controlled production of large quantum states of light from probabilistic photon sources.

38.(2017) Journal of Physics B: Atomic, Molecular and Optical Physics. 50, 21, 215003. Abstract
We use a fourwave mixing process to readout light from atomic coherence which is continuously written. The light is continuously generated after an effective delay, allowing the atomic coherence to evolve during the process. Contrary to slowlight delay, which depends on the medium optical depth, here the generation delay is determined solely by the intensive properties of the system, approaching the atomic coherence lifetime at the weak driving limit. The atomic evolution during the generation delay is further manifested in the spatial profile of the generated light due to atomic diffusion. Continuous generation of light with a long intrinsic delay can replace discrete writeread procedures when the atomic evolution is the subject of interest.

37.(2017) Physical Review Letters. 119, 11, 113601. Abstract
Effective cavities can be optically induced in atomic media and employed to strengthen optical nonlinearities. Here we study the integration of induced cavities with a photonic quantum gate based on Rydberg blockade. Accounting for loss in the atomic medium, we calculate the corresponding finesse and gate infidelity. Our analysis shows that the conventional limits imposed by the blockade optical depth are mitigated by the induced cavity in long media, thus establishing the total optical depth of the medium as a complementary resource.

36.(2017) Journal of Physics B: Atomic, Molecular and Optical Physics. 50, 13, 133001. Abstract
The strong interaction between individual Rydberg atoms provides a powerful tool exploited in an evergrowing range of applications in quantum information science, quantum simulation and ultracold chemistry. One hallmark of the Rydberg interaction is that both its strength and angular dependence can be finetuned with great flexibility by choosing appropriate Rydberg states and applying external electric and magnetic fields. More and more experiments are probing this interaction at short atomic distances or with such high precision that perturbative calculations as well as restrictions to the leading dipoledipole interaction term are no longer sufficient. In this tutorial, we review all relevant aspects of the full calculation of Rydberg interaction potentials. We discuss the derivation of the interaction Hamiltonian from the electrostatic multipole expansion, numerical and analytical methods for calculating the required electric multipole moments and the inclusion of electromagnetic fields with arbitrary direction. We focus specifically on symmetry arguments and selection rules, which greatly reduce the size of the Hamiltonian matrix, enabling the direct diagonalization of the Hamiltonian up to higher multipole orders on a desktop computer. Finally, we present example calculations showing the relevance of the full interaction calculation to current experiments. Our software for calculating Rydberg potentials including all features discussed in this tutorial is available as open source.

35.(2017) Reviews of Modern Physics. 89, 2, 21001. Abstract
Photonphoton scattering in vacuum is extremely weak. However, strong effective interactions between single photons can be realized by employing strong lightmatter coupling. These interactions are a fundamental building block for quantum optics, bringing manybody physics to the photonic world and providing important resources for quantum photonic devices and for optical metrology. This Colloquium reviews the physics of strongly interacting photons in onedimensional systems with no optical confinement along the propagation direction. It focuses on two recently demonstrated experimental realizations: superconducting qubits coupled to open transmission lines and interacting Rydberg atoms in a cold gas. Advancements in the theoretical understanding of these systems are presented in complementary formalisms and compared to experimental results. The experimental achievements are summarized alongside a description of the quantum optical effects and quantum devices emerging from them.

34.(2016) Journal of Physics B: Atomic, Molecular and Optical Physics. 49, 15, 152003. Abstract
By mapping the strong interaction between Rydberg excitations in ultracold atomic ensembles onto single photons via electromagnetically induced transparency, it is now possible to realize a medium which exhibits a strong optical nonlinearity at the level of individual photons. We review the theoretical concepts and the experimental stateoftheart of this exciting new field, and discuss first applications in the field of alloptical quantum information processing.

33.(2015) Physical Review Letters. 115, 12, 123601. Abstract
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 twobody bound states. Within the continuum, metastable bound states are distinguished in analogy with quasibound 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 wave function 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.

32.(2015) Physical Review Letters. 115, 11, 113003. Abstract
Random spinexchange collisions in warm alkali vapor cause rapid decoherence and act to equilibrate the spin state of the atoms in the vapor. In contrast, here we demonstrate experimentally and theoretically a coherent coupling of one alkali species to another species, mediated by these random collisions. We show that the minor species (potassium) inherits the magnetic properties of the dominant species (rubidium), including its lifetime (T1),coherence time (T2), gyromagnetic ratio, and spinexchange relaxationfree magneticfield threshold. We further show that this coupling can be completely controlled by varying the strength of the magnetic field. Finally, we explain these phenomena analytically by mode mixing of the two species via spinexchange collisions.

31.(2015) Optics Express. 23, 5, p. 63796391 Abstract
We suggest a scheme to manipulate paraxial diffraction by utilizing the dependency of a fourwave mixing process on the relative angle between the light fields. A microscopic model for fourwave mixing in a.type level structure is introduced and compared to recent experimental data. We show that images with feature size as low as 10 mu m can propagate with very little or even negative diffraction. The mechanism is completely different from that conserving the shape of spatial solitons in nonlinear media, as here diffraction is suppressed for arbitrary spatial profiles. At the same time, the gain inherent to the nonlinear process prevents loss and allows for operating at high optical depths. Our scheme does not rely on atomic motion and is thus applicable to both gaseous and solid media.

30.(2015) Physical Review A. 91, 3, 33838. Abstract
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 spin1/2 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 spinflip excitation. At half filling, this gives rise to a photonic (or polaritonic) fractional Chern insulatora latticebased, fractional quantum Hall state of light.

29.(2014) Physical Review A. 90, 5, 053804. Abstract
We provide a theoretical framework describing slowlight polaritons interacting via atomic Rydberg states. The method allows us to analytically derive the scattering properties of two polaritons. We identify parameter regimes where polaritonpolariton interactions are repulsive. Furthermore, in the regime of attractive interactions, we identify multiple twopolariton bound states, calculate their dispersion, and study the resulting scattering resonances. Finally, the twoparticle scattering properties allow us to derive the effective lowenergy manybody Hamiltonian. This theoretical platform is applicable to ongoing experiments.

28.(2013) Optics and Photonics News. 24, 12, p. 4848 Abstract
Quantumoptics researchers have been trying to achieve strong interactions between individual photons for decades.1 These interactions constitute a fundamental tool toward the ultimate control of light fields "quantum by quantum."

27.(2013) Nature. 502, 7469, p. 71+ Abstract
The fundamental properties of light derive from its constituent particlesmassless quanta (photons) that do not interact with one another(1). However, it has long been known that the realization of coherent interactions between individual photons, akin to those associated with conventional massive particles, could enable a wide variety of novel scientific and engineering applications(2,3). Here we demonstrate a quantum nonlinear medium inside which individual photons travel as massive particles with strong mutual attraction, such that the propagation of photon pairs is dominated by a twophoton bound state(47). We achieve this through dispersive coupling of light to strongly interacting atoms in highly excited Rydberg states. We measure the dynamical evolution of the twophoton wavefunction using timeresolved quantum state tomography, and demonstrate a conditional phase shift(8) exceeding one radian, resulting in polarizationentangled photon pairs. Particular applications of this technique include alloptical switching, deterministic photonic quantum logic and the generation of strongly correlated states of light(9).

26.(2013) Reviews of Modern Physics. 85, 3, p. 941960 Abstract
Coherent diffusion pertains to the motion of atomic dipoles experiencing frequent collisions in vapor while maintaining their coherence. Recent theoretical and experimental studies on the effect of coherent diffusion on key Raman processes, namely, Raman spectroscopy, slow polariton propagation, and stored light, are reviewed in this Colloquium.

25.(2013) Optics Letters. 38, 8, p. 12031205 Abstract
The close relation between the processes of paraxial diffraction and coherent diffusion is reflected in the similarity between their shapepreserving solutions, notably the Gaussian modes. Differences between these solutions enter only for highorder modes. Here we experimentally study the behavior of shapepreserving highorder modes of coherent diffusion, known as "elegant" modes, and contrast them with the nonshapepreserving evolution of the corresponding "standard" modes of optical diffraction. Diffusion of the light field is obtained by mapping it onto the atomic coherence field of a diffusing vapor in a storageoflight setup. The growth of the elegant mode fits well the theoretical expectations. (C) 2013 Optical Society of America

24.(2013) Nature (London). 502, p. 7175 Abstract
The fundamental properties of light derive from its constituent particles—massless quanta (photons) that do not interact with one another. However, it has long been known that the realization of coherent interactions between individual photons, akin to those associated with conventional massive particles, could enable a wide variety of novel scientific and engineering applications. Here we demonstrate a quantum nonlinear medium inside which individual photons travel as massive particles with strong mutual attraction, such that the propagation of photon pairs is dominated by a twophoton bound state. We achieve this through dispersive coupling of light to strongly interacting atoms in highly excited Rydberg states. We measure the dynamical evolution of the twophoton wavefunction using timeresolved quantum state tomography, and demonstrate a conditional phase shift exceeding one radian, resulting in polarizationentangled photon pairs. Particular applications of this technique include alloptical switching, deterministic photonic quantum logic and the generation of strongly correlated states of light.

23.(2012) Nature. 488, 7409, p. 5760 Abstract
The realization of strong nonlinear interactions between individual light quanta (photons) is a longstanding goal in optical science and engineering, being of both fundamental and technological significance. In conventional optical materials, the nonlinearity at light powers corresponding to single photons is negligibly weak. Here we demonstrate a medium that is nonlinear at the level of individual quanta, exhibiting strong absorption of photon pairs while remaining transparent to single photons. The quantum nonlinearity is obtained by coherently coupling slowly propagating photons to strongly interacting atomic Rydberg states in a cold, dense atomic gas. Our approach paves the way for quantumbyquantum control of light fields, including singlephoton switching, alloptical deterministic quantum logic and the realization of strongly correlated manybody states of light.

22.(2012) Nature (London). 488, p. 5760 Abstract
The realization of strong nonlinear interactions between individual light quanta (photons) is a longstanding goal in optical science and engineering, being of both fundamental and technological significance. In conventional optical materials, the nonlinearity at light powers corresponding to single photons is negligibly weak. Here we demonstrate a medium that is nonlinear at the level of individual quanta, exhibiting strong absorption of photon pairs while remaining transparent to single photons. The quantum nonlinearity is obtained by coherently coupling slowly propagating photons to strongly interacting atomic Rydberg states in a cold, dense atomic gas. Our approach paves the way for quantumbyquantum control of light fields, including singlephoton switching, alloptical deterministic quantum logic and the realization of strongly correlated manybody states of light.

21.(2011) Physical Review A  Atomic, Molecular, and Optical Physics. 83, 5, 053812. Abstract
We describe the effect of thermal motion and buffergas collisions on a fourlevel closed N system interacting with strong pump(s) and a weak probe. This is the simplest system that experiences electromagnetically induced absorption (EIA) due to transfer of coherence via spontaneous emission from the excited state to the ground state. We investigate the influence of Doppler broadening, velocitychanging collisions (VCC), and phasechanging collisions (PCC) with a buffer gas on the EIA spectrum of optically active atoms. In addition to exact expressions, we present an approximate solution for the probe absorption spectrum, which provides physical insight into the behavior of the EIA peak due to VCC, PCC, and the wavevector difference between the pump and probe beams. VCC are shown to produce a wide pedestal at the base of the EIA peak, which is scarcely affected by the pumpprobe angular deviation, whereas the sharp central EIA peak becomes weaker and broader due to the residual DopplerDicke effect. Using diffusionlike equations for the atomic coherences and populations, we construct a spatialfrequency filter for a spatially structured probe beam and show that Ramsey narrowing of the EIA peak is obtained for beams of finite width.

20.(2011) Physical Review A. 83, p. 053812 Abstract
We describe the effect of thermal motion and buffergas collisions on a fourlevel closed N system interacting with strong pump(s) and a weak probe. This is the simplest system that experiences electromagnetically induced absorption (EIA) due to transfer of coherence via spontaneous emission from the excited state to the ground state. We investigate the influence of Doppler broadening, velocitychanging collisions (VCC), and phasechanging collisions (PCC) with a buffer gas on the EIA spectrum of optically active atoms. In addition to exact expressions, we present an approximate solution for the probe absorption spectrum, which provides physical insight into the behavior of the EIA peak due to VCC, PCC, and the wavevector difference between the pump and probe beams. VCC are shown to produce a wide pedestal at the base of the EIA peak, which is scarcely affected by the pumpprobe angular deviation, whereas the sharp central EIA peak becomes weaker and broader due to the residual DopplerDicke effect. Using diffusionlike equations for the atomic coherences and populations, we construct a spatialfrequency filter for a spatially structured probe beam and show that Ramsey narrowing of the EIA peak is obtained for beams of finite width.

19.(2011) in "The angular momentum of light".
Edited by D. Andrews and M. Babiker (Cambridge University Press).

18.(2010) Physical Review Letters. 105, 18, 183602. Abstract
Selfsimilar solutions of the coherent diffusion equation are derived and measured. The set of real similarity solutions is generalized by the introduction of a nonuniform phase, based on the elegant Gaussian modes of optical diffraction. In a lightstorage experiment, the complex solutions are imprinted on a gas of diffusing atoms, and the selfsimilar evolution of both their amplitude and phase pattern is demonstrated. An algebraic decay depending on the mode order is measured. Notably, as opposed to the regular diffusion spreading, a subset of the solutions exhibits a selfsimilar contraction.

17.(2010) Optics Express. 18, 18, p. 1883218838 Abstract
We experimentally demonstrate an optical pumping technique to pump a dilute rubidium vapor into the mF = 0 ground states. The technique utilizes selection rules that forbid the excitation of the mF = 0 states by linearlypolarized light. A substantial increase in the transparency contrast of the coherentpopulationtrapping resonance used for frequency standards is demonstrated.

16.(2010) Physical Review A. 81, 4, 043835. Abstract
The population distribution within the ground state of an atomic ensemble is of great significance in a variety of quantumoptics processes. We present a method to reconstruct the detailed population distribution from a set of absorption measurements with various frequencies and polarizations, by utilizing the differences between the dipole matrix elements of the probed transitions. The technique is experimentally implemented on a thermal rubidium vapor, demonstrating a populationbased analysis in two opticalpumping examples. The results are used to verify and calibrate an elaborated numerical model, and the limitations of the reconstruction scheme, which result from the symmetry properties of the dipole matrix elements, are discussed.

15.(2010) Optics Express. 18, p. 1883218838 Abstract
We experimentally demonstrate an optical pumping technique to pump a dilute rubidium vapor into the mF = 0 ground states. The technique utilizes selection rules that forbid the excitation of the mF = 0 states by linearlypolarized light. A substantial increase in the transparency contrast of the coherentpopulationtrapping resonance used for frequency standards is demonstrated.

14.(2009) Optics and Photonics News. 20, 12, p. 3232 Abstract
Images imprinted on a laser pulse can be dramatically slowed when traversing an alkali vapor medium via electromagnetically induced transparency.

13.(2009) Optics Express. 17, 19, p. 1677616782 Abstract
A new magnetometry method based on electromagnetic induced transparency (EIT) with maximally polarized states is demonstrated. An EIT hyperfine resonance, comprising the mF = F state (endstate), is observed at a nonzero angle between the laser beam and the magnetic field. The method takes advantage of the process of endstate pumping, a wellknown rival of simpler EIT magnetometry schemes, and therefore benefits at a high laser power. An experimental demonstration and a numerical analysis of the magnetometry method are presented. The analysis points on a clear sensitivity advantage of the endstate EIT magnetometer.

12.(2009) p. 16491655 Abstract
In the standard derivation of the stressstrain curve from a Split Hopkinson Pressure Bar (SHPB) test, the initial region of the stressstrain curve, at low strains, does not reflect the real strength of the material. The measurement in this initial region is affected by reverberations in the specimen, and the standard assumption of stress equilibrium does not hold. For typical specimen dimensions and striker velocities, our SS304L specimens reach strains of 20–50%, but the equilibrium required for the analysis is achieved only above strains of 5–10%. Therefore, in calibrating a constitutive model, e.g. the JohnsonCook (JC) model, the free parameter of the model that expresses the material's initial strength cannot be fixed correctly from the experimental data. While conducting 2D simulations of SHPB tests with hatshaped specimens, we have found that the straingauge signals are sensitive to the behavior at low plastic strains. We have used this information as a complementary test for the calibration of a JC model at the low strain region. Using 2D simulations, we demonstrate the particular stress fields in the deforming hatspecimen as well. These simulations prove to be a powerful tool in the calibration procedure.

11.(2009) Nature Physics. 5, 9, p. 665668 Abstract
Any image, imprinted on a wave field and propagating in free space, undergoes a paraxial diffraction spreading. The reduction or manipulation of diffraction is desirable for many applications, such as imaging, waveguiding, microlithography and optical data processing. As was recently demonstrated, arbitrary images imprinted on light pulses are dramatically slowed(1,2) when traversing an atomic medium of electromagnetically induced transparency(3,4) and undergo diffusion due to the thermal atomic motion(5,6). Here we experimentally demonstrate a new technique to eliminate the paraxial diffraction and the diffusion of slow light, regardless of its position and shape(7). Unlike former suggestions for diffraction manipulation(812), our scheme is linear and operates in the wavevector space, eliminating the diffraction for arbitrary images throughout their propagation. By tuning the interaction, we further demonstrate acceleration of diffraction, biased diffraction and induced deflection, and reverse diffraction, implementing a negativediffraction lens(13). Alongside recent advances in slowlight amplification(14) and image entanglement(15), diffraction control opens various possibilities for classical and quantum image manipulation.

10.(2009) Physical Review Letters. 102, 15, Abstract
We report an experiment that directly measures the Laplace transform of the recurrence probability in one dimension using electromagnetically induced transparency (EIT) of coherent atoms diffusing in a vapor cell filled with buffer gas. We find a regime where the limiting form of the complex EIT spectrum is universal and only depends on the effective dimensionality in which the random recurrence takes place. In an effective onedimensional diffusion setting, the measured spectrum exhibits powerlaw dependence over two decades in the frequency domain with a critical exponent of 0.56 close to the expected value 0.5.

9.(2009) Physical Review Letters. 102, 4, Abstract
We present a scheme for eliminating the optical diffraction of slow light in a thermal atomic medium of electromagnetically induced transparency. Nondiffraction is achieved for an arbitrary paraxial image by manipulating the susceptibility in momentum space, in contrast to the common approach, which employs guidance of specific modes by manipulating the susceptibility in real space. For negative twophoton detuning, the moving atoms drag the transverse momentum components unequally, resulting in a Doppler trapping of light by atoms in two dimensions.

8.(2008) Physical Review A. 78, 6, Abstract
Twophoton processes that involve different sublevels of the ground state of an atom, are highly sensitive to depopulation and decoherence within the ground state. For example, the spectral width of electromagnetically induced transparency resonances in a Lambdatype system, are strongly affected by the groundstate depopulation and decoherence rates. We present a direct measurement of decay rates between hyperfine and Zeeman sublevels in the ground state of (87)Rb vapor. Similar to the relaxationinthedark technique, pumping lasers are used to prealign the atomic vapor in a welldefined quantum state. The free propagation of the atomic state is monitored using a Ramseylike method. Coherence times in the range 110 ms were measured for room temperature atomic vapor. In the range of the experimental parameters used in this study, the dominant process inducing Zeeman decoherence is the spinexchange collisions between rubidium atoms.

7.(2008) Physical Review Letters. 100, 22, Abstract
Reversible and coherent storage of light in an atomic medium is a promising method with possible applications in many fields. In this work, arbitrary twodimensional images are slowed and stored in warm atomic vapor for up to 30 mu s, utilizing electromagnetically induced transparency. Both the intensity and the phase patterns of the optical field are maintained. The main limitation on the storage resolution and duration is found to be the diffusion of atoms. A technique analogous to phaseshift lithography is employed to diminish the effect of diffusion on the visibility of the reconstructed image.

6.(2008) Physical Review A. 77, 4, Abstract
We present a theoretical model for electromagnetically induced transparency (EIT) in vapor that incorporates atomic motion and velocitychanging collisions into the dynamics of the densitymatrix distribution. Within a unified formalism, we demonstrate various motional effects, known for EIT in vapor: Doppler broadening of the absorption spectrum; Dicke narrowing and timeofflight broadening of the transmission window for a finitesized probe; diffusion of atomic coherence during storage of light and diffusion of the lightmatter excitation during slowlight propagation; and Ramsey narrowing of the spectrum for a probe and pump beams of finite size.

5.(2007) Physical Review A. 76, 2, Abstract
Dicke narrowing is a phenomenon that dramatically reduces the Doppler width of spectral lines, due to frequent velocitychanging collisions. A similar phenomenon occurs for electromagnetically induced transparency (EIT) resonances, and facilitates ultranarrow spectral features in roomtemperature vapor. We directly measure the Dickelike narrowing by studying EIT line shapes as a function of the angle between the pump and probe beams. The measurements are in good agreement with an analytic theory with no fit parameters. The results show that Dicke narrowing can increase substantially the tolerance of hotvapor EIT to angular deviations. We demonstrate the importance of this effect for applications such as imaging and spatial solitons using a singleshot imaging experiment, and discuss the implications for the feasibility of storing images in atomic vapor.

4.(2007) Physical Review A. 76, 1, Abstract
The Doppler effect is one of the dominant broadening mechanisms in thermal vapor spectroscopy. For twophoton transitions one would naively expect the Doppler effect to cause a residual broadening, proportional to the wavevector difference. In coherent population trapping (CPT), which is a twophoton narrowband phenomenon, such broadening was not observed experimentally. This has been commonly attributed to frequent velocitychanging collisions, known to narrow Dopplerbroadened onephoton absorption lines (Dicke narrowing). Here we show theoretically that such a narrowing mechanism indeed exists for CPT resonances. The narrowing factor is the ratio between the atom's mean free path and the wavelength associated with the wavevector difference of the two radiation fields. A possible experiment to verify the theory is suggested.

3.(2007) Physical Review Letters. 98, 20, Abstract
We report an experiment in which an optical vortex is stored in a vapor of Rb atoms. Because of its 2 pi phase twist, this mode, also known as the LaguerreGauss mode, is topologically stable and cannot unwind even under conditions of strong diffusion. For comparison, we stored a Gaussian beam with a dark center and a uniform phase. Contrary to the optical vortex, which stays stable for over 100 mu s, the dark center in the retrieved flatphased image was filled with light after a storage time as short as 10 mu s. The experiment proves that higher electromagnetic modes can be converted into atomic coherences and that modes with phase singularities are robust to decoherence effects such as diffusion. This opens the possibility to more elaborate schemes for classical and quantum information storage in atomic vapors.

2.(2006) Proceedings  8th International Conference on Mechanical and Physical Behaviour of Materials under Dyanmic Loading, EURODYMAT 2006. Vol. 134. p. 191196 Abstract
We propose a simple model to reproduce ductile failure by shear localization in simulations of perforations tests. The model incorporates a positive feedback process of shear strain localization which results in a catastrophic decrease of flow stress. We use the model for perforation tests with 304L stainless steel. It succeeds in reproducing perforation thresholds as well as qualitative features of the perforation process, including shear band formation in some of the projectiles.

1.(2003) Physical Review A  Atomic, Molecular, and Optical Physics. 67, 3, Abstract
A radiation source made up of two cavities and a beam splitter which may produce classicallike secondorder interference for a wide range of noncoherent initial conditions was shown. This coherent like behavior was apparent also in the fourthorder interference. Such results gives a strong indication that in many experiments coherent like behavior may be observed even for highly noncoherent initial states of the system, similar to Molmer's claim.