Publications

38.(2018). Light storage for one second in roomtemperature alkali vapor. Nature Communications. 9:(1) 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.

37.(2018). Synchronization of strongly interacting alkalimetal spins. Physical Review A. 98:(1) 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.

36.(2018). Fast, noisefree memory for photon synchronization at room temperature. Science advances. 4:(1) 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.

35.(2017). Continuous generation of delayed light. Journal of Physics B: Atomic, Molecular and Optical Physics. 50:(21) 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.

34.(2017). Induced Cavities for Photonic Quantum Gates. Physical Review Letters. 119:(11) 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.

33.(2017). Calculation of Rydberg interaction potentials. JOURNAL OF PHYSICS BATOMIC MOLECULAR AND OPTICAL PHYSICS. 50:(13) 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.

32.(2017). Colloquium: Strongly interacting photons in onedimensional continuum. Reviews of Modern Physics. 89:(2) 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.

31.(2016). Nonlinear quantum optics mediated by Rydberg interactions. Journal of Physics B: Atomic, Molecular and Optical Physics. 49:(15) 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.

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29.(2015). Coherent Coupling of Alkali Atoms by Random Collisions. Physical Review Letters. 115:(11) 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.

28.(2015). Diffraction manipulation by fourwave mixing. Optics Express. 23:(5)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. (C) 2015 Optical Society of America

27.(2015). Fractional quantum Hall states of Rydberg polaritons. Physical Review A. 91:(3) 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.

26.(2014). Scattering resonances and bound states for strongly interacting Rydberg polaritons. Physical Review A. 90:(5) 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.

25.(2013). Attractive photons in a quantum nonlinear medium. Nature. 502:(7469)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).

24.(2013). Colloquium: Coherent diffusion of polaritons in atomic media. Reviews of Modern Physics. 85:(3)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.

23.(2013). Shapepreserving diffusion of a highorder mode. Optics Letters. 38:(8)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

22.(2013). Attractive photons in a quantum nonlinear medium. Nature (London). 502:7175. 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.

21.(2012). Quantum nonlinear optics with single photons enabled by strongly interacting atoms. Nature. 488:(7409)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.

20.(2012). Quantum nonlinear optics with single photons enabled by strongly interacting atoms. Nature (London). 488:5760. 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.

19.(2011). Effects of thermal motion on electromagnetically induced absorption. Physical Review A  Atomic, Molecular, and Optical Physics. 83:(5) 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.

18.(2011). Modes of complex diffusion. in "The angular momentum of light".
Edited by D. Andrews and M. Babiker (Cambridge University Press).

17.(2011). Effects of thermal motion on electromagneticallyinduced absorption. Physical Review A. 83:053812. 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.

16.(2010). SelfSimilar Modes of Coherent Diffusion. Physical Review Letters. 105:(18) 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.

15.(2010). Repumping groundstate population in a coherently driven atomic resonance. Optics Express. 18:(18)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.(2010). Alloptical reconstruction of atomic groundstate population. Physical Review A. 81:(4) 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.

13.(2010). Alloptical reconstruction of atomic groundstate population. Physical Review A. 81:043835. 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.

12.(2010). Repumping groundstate population in a coherently driven atomic resonance. Optics Express. 18:1883218838. 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.

11.(2009). Atomic magnetometry with maximally polarized states. Optics Express. 17:(19)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.

10.(2009). Elimination, reversal and directional bias of optical diffraction. Nature Physics. 5:(9)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.

9.(2009). Universal Spectra of Coherent Atoms in a Recurrent Random Walk. 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.

8.(2009). Elimination of the Diffraction of Arbitrary Images Imprinted on Slow Light. 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.

7.(2008). Ramseylike measurement of the decoherence rate between Zeeman sublevels. 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.

6.(2008). Storing images in warm atomic vapor. 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.

5.(2008). Theory of thermal motion in electromagnetically induced transparency: Effects of diffusion, Doppler broadening, and Dicke and Ramsey narrowing. 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.

4.(2007). Angular dependence of Dickenarrowed electromagnetically induced transparency resonances. 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.

3.(2007). Theory of Dicke narrowing in coherent population trapping. 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.

2.(2007). Topological stability of stored optical vortices. 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.

1.(2003). Optical interference with noncoherent states. 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.