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Physical Review Letters

Phase Matching in Lower Dimensions

Hikaru Tamura, Huy Minh Nguyen, P. R. Berman, A. Kuzmich

Published Oct 13, 2020• 11 citations
Publisher

Abstract

Phase matching refers to a process in which atom-field interactions lead to the creation of an output field that propagates coherently through the interaction volume. By studying light scattering from arrays of cold atoms, we show that conditions for phase matching change as the dimensionality of the system decreases. In particular, for a single atomic chain, there is phase-matched reflective scattering in a cone about the symmetry axis of the array that scales as the square of the number of atoms in the chain. For two chains of atoms, the phase-matched reflective scattering can be enhanced or diminished as a result of Bragg scattering. Such scattering can be used for mapping collective states within an array of neutral atoms onto propagating light fields and for establishing quantum links between separated arrays.

DOI
10.1103/physrevlett.125.163601

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Phase matching refers to a process in which atom-field interactions lead to the creation of an output field that propagates coherently through the interaction volume. By studying light scattering from arrays of cold atoms, we show that conditions for phase matching change as the dimensionality of the system decreases. In particular, for a single atomic chain, there is phase-matched reflective scattering in a cone about the symmetry axis of the array that scales as the square of the number of atoms in the chain. For two chains of atoms, the phase-matched reflective scattering can be enhanced or diminished as a result of Bragg scattering. Such scattering can be used for mapping collective states within an array of neutral atoms onto propagating light fields and for establishing quantum links between separated arrays.
We develop a general framework for the analysis of two-sided quantum interfaces, composed of collections of atoms interacting with paraxial light. Accounting for photon-mediated dipole-dipole interactions, our approach is based on the mapping of collective atom-photon interfaces onto a generic one-dimensional model of light scattering, characterized by a reflectivity parameter r 0 . This entails two key practical advantages: (i) the efficiency of the quantum interface in performing various quantum tasks, such as quantum memory or entanglement generation, is universally given by r 0 and is hence reduced to a measurement or classical calculation of a reflectivity; (ii) the efficiency can be greatly enhanced by a properly designed photon mode that spatially matches a collective-dipole eigenmode of the atoms. We demonstrate our approach for realistic cases of finite-size atomic arrays, partially filled arrays, and circular arrays. This provides a unified approach for treating collective light-matter coupling in various platforms, such as optical lattices and optical tweezers. Published by the American Physical Society 2024
We experimentally study resonant light scattering by a one-dimensional randomly filled chain of cold two-level atoms. By a local measurement of the light scattered along the chain, we observe constructive interferences in light-induced dipole-dipole interactions between the atoms. They lead to a shift of the collective resonance despite the average interatomic distance being larger than the wavelength of the light. This result demonstrates that strong collective effects can be enhanced by structuring the geometrical arrangement of the ensemble. We also explore the high intensity regime where atoms cannot be described classically. We compare our measurement to a mean-field, nonlinear coupled-dipole model accounting for the saturation of the response of a single atom.
We theoretically and computationally investigate the behavior of infinite atom arrays when illuminated by nearly resonant light. We use higher-order mean-field equations to investigate the coherent reflection and transmission and incoherent scattering of photons from a single array and from a pair of arrays as a function of detuning for different values of the Rabi frequency. For the single array case, we show how increasing the light intensity changes the probabilities for these different processes. For example, the incoherent scattering probability initially increases with light intensity before decreasing at higher values. For a pair of parallel arrays at near resonant separation, the effects from increasing light intensity can become apparent with incredibly low-intensity light. In addition, we derive the higher-order mean-field equations for these infinite arrays, giving a representation that can be evaluated with a finite number of equations.
A J=0J=0J=0 to J=1J=1J=1 to J=0J=0J=0 ladder scheme can be used as a prototype for probing optical coherence transfer in an atom array. Two incident ${\ensuremath{\sigma}}_{\ensuremath{-}}$ polarized fields drive transitions from the ground state to the intermediate state and the intermediate state to the uppermost state in the atoms. The uppermost state is taken to be a long-lived Rydberg level. In the absence of any atom-atom interactions, excitation to the Rydberg level is not allowed, owing to the selection rules. However, dipole-dipole interactions can provide a transfer of the state amplitude associated with the $m=\ensuremath{-}1$ sublevel in one atom to the m=+1m=+1m=+1 sublevel in another atom. The overall process of field excitation and optical coherence transfer can then lead to an excitation of the Rydberg level. One can then apply a readout pulse to obtain phase-matched emission from the array. For a linear array of atoms, the phase-matched signal can increase more rapidly than N2{N}^{2}N2, where NNN is the number of atoms in the array. For arrays that are invariant under a rotation $\ensuremath{\delta}\ensuremath{\phi}<\ensuremath{\pi}$ about the zzz axis, however, it turns out that the total field intensity vanishes identically in the phase-matched direction. For such arrays, the Rydberg state population can serve as a measure of the optical coherence transfer.
We theoretically investigate light scattering from an array of atoms into the guided modes of a waveguide. We observe that the scattering of a plane-wave laser field into the waveguide modes is dramatically enhanced for angles that deviate from the geometric Bragg angle. This modified Bragg condition arises from the dispersive interactions between the guided light and the atoms. We analytically identify various parameter regimes in which the scattering rate features a qualitatively different dependence on the atom number, such as linear, quadratic, oscillatory, or constant behavior. In combination with rigorous numerical calculations, we demonstrate that these scalings are independent of a possible asymmetry of the atom-light coupling. Finally, we show that our findings are robust against voids in the atomic array, facilitating their experimental observation and potential applications. Our work sheds light on collective light scattering and the interplay between geometry and interaction effects, with implications reaching beyond the optical domain.
We observe coherently enhanced reflection (Bragg scattering) of a near resonant laser beam from cesium atoms ordered by a periodic array of optical potential wells known as an optical lattice. The reflected light is enhanced by a factor of $\ensuremath{\sim}{10}^{5}$ over scattering from a disordered atomic sample. We measure the magnitude of the reflectivity and its detuning dependence as functions of the density and the degree of localization of the atoms. The change in lattice constant due to the frequency-dependent effective index of refraction seen by the lattice light field is observed.