We propose a complete superradiant and subradiant states that can be manipulated and prepared in a three-dimensional atomic array. These subradiant states can be realized by absorbing a single photon and imprinting the spatially-dependent phases on the atomic system. We find that the collective decay rates and associated cooperative Lamb shifts are highly dependent on the phases we manage to imprint, and the subradiant state of long lifetime can be found for various lattice spacings and atom numbers. We also investigate both optically thin and thick atomic arrays, which can serve for systematic studies of super- and sub-radiance. Our proposal offers an alternative scheme for quantum memory of light in a three-dimensional array of two-level atoms, which is applicable and potentially advantageous in quantum information processing.
We propose a set of subradiant states which can be prepared and detected in a one-dimensional optical lattice. We find that the decay rates are highly dependent on the spatial phases imprinted on the atomic chain, which gives systematic investigations of the subradiance in the fluorescence experiments. The time evolution of these states can have long decay time where up to hundred milliseconds of lifetime is predicted for one hundred atoms. They can also show decayed Rabi-like oscillations with a beating frequency determined by the difference of cooperative Lamb shift in the subspace. Experime…
A scheme for coherent manipulation of collective atomic states is developed such that total subradiant states, in which spontaneous emission is suppressed into all directions due to destructive interference between neighbor atoms, can be created in an extended atomic ensemble. The optimal conditions for creation of such states and suitability of them for quantum storage are discussed. It is shown that in order to achieve the maximum signal-to-noise ratio the shape of a light pulse to be stored and reconstructed using a homogeneously broadened absorbtion line of an atomic system should be a tim…
We study the subradiant collective states of a periodic chain of two-level atoms with either transversal or longitudinal transition dipole moments with respect to the chain axis. We show that long-lived subradiant states can be obtained for the transversal polarization by properly choosing the chain period for a given number of atoms in the case of no open diffraction channels. These highly subradiant states have a linewidth that decreases with the number of atoms much faster than it was shown previously. In addition, our study shows that such states are present even if there are additional in…
We study collective `free-space' radiation properties of two distant single-layer arrays of quantum emitters as two-level atoms. We show that this system can support a long-lived Bell superposition state of atomic excitations exhibiting strong subradiance, which corresponds to a non-local excitation of the two arrays. We describe the preparation of these states and their application in quantum information as resource of non-local entanglement, including deterministic quantum state transfer with high fidelity between the arrays representing quantum memories. We discuss experimental realizations…
The exact dynamics of $N$ two-level atoms coupled to a common electromagnetic bath and closely located inside a lossy cavity is reported. Stationary radiation trapping effects are found and very transparently interpreted in the context of our approach. We prove that initially injecting one excitation only in the $N$ atoms-cavity system, loss mechanisms asymptotically drive the matter sample toward a long-lived collective subradiant Dicke state. The role played by the closeness of the $N$ atoms with respect to such a cooperative behavior is brought to light and carefully discussed.
The Hermitian part of the dipole-dipole interaction in infinite periodic arrays of two-level atoms yields an energy band of singly excited states. In this Letter, we show that a dispersion relation, $ω_k-ω_{k_\ex} \propto (k-k_{\ex})^s$, near the band edge of the infinite system leads to the existence of subradiant states of finite one-dimensional arrays of $N$ atoms with decay rates scaling as $N^{-(s+1)}$. This explains the recently discovered $N^{-3}$ scaling and it leads to the prediction of power law scaling with higher power for special values of the lattice period. For the quantum optic…
We theoretically investigate the light scattering of the super- and subradiant states which can be prepared by the excitation of a single photon which carries an orbital angular momentum (OAM).\ With this helical phase imprinted on the stacked ring of atomic arrays, the subradiant modes show directional side scattering in the far-field, allowing for light collimation and quantum storage of light with OAM.\ For the excitations with linear polarizations, we find a discrete $C_4$ rotational symmetry in scattering for the number of atoms $N$ $=$ $4n $ with integers $n$, while for circular polariza…
We experimentally investigate the formation of subradiant atomic momentum states in Bose-Einstein condensates inside a recoil resolving optical ring resonator according to the theoretical proposal of Cola, Bigerni, and Piovella. The atoms are pumped from the side with laser light that contains two frequency components. They resonantly drive cavity assisted Raman transitions between three discreet atomic momentum states. Within a few hundred microseconds, the system evolves into a stationary subradiant state. In this state, the condensate develops two density gratings suitable to diffract the t…
The propagation of a step pulse through a thick resonant absorber with homogeneously broadened absorption line is considered. It is shown that a specific subradiant state is naturally developed in the absorber due to the formation of the spatial domains of the atomic coherence with opposite phases. It is proposed to divide the absorber into slices in accord with these domains and place the phase shifters in front of the first slice and between the other slices. If the phase shifters are switched on simultaneously at a particular moment of time, elapsed from the beginning of the step pulse, a s…
Collective decays of multiply-excited atoms become subradiant and bound in space when they are strongly coupled to the guided modes in an atom-waveguide interface. In this interface, we analyze their average density-density and modified third-order correlations via Kubo cumulant expansions, which can arise and sustain for long time. The shape-preserving dimers and trimers of atomic excitations emerge in the most subradiant coupling regime of light-induced dipole-dipole interactions. This leads to a potential application of quantum information processing and quantum storage in the encoded nonre…
We propose to generate the multiphoton subradiant states and investigate their fluorescences in an array of two-level atoms. These multiphoton states are created initially from the timed-Dicke states. Then we can use either a Zeeman or Stark field gradient pulse to imprint linearly increasing phases on the atoms, and this phase-imprinting process unitarily evolves the system to the multiphoton subradiant states. The fluorescence engages a long-range dipole-dipole interaction which originates from a system-reservoir coupling in the dissipation. We locate some of the subradiant multiphoton state…
We experimentally study subradiance in a dilute cloud of ultracold rubidium (Rb) atoms where $n λ_a^3 \approx 10^{-2}$ ($n$: atomic density, $λ_a$ excitation wavelength) and the on-resonance optical depth of the cloud is of order unity. We show that in the strong excitation regime, the subradiant time-scales depend on the excitation fraction of the cloud; i.e., to the intensity of the excitation pulse. In this regime, the decay dynamics are highly complicated and there is not a single decay time-constant. Instead, the decay time constant varies during the dynamics. Specifically, we were able t…
Single-photon super- and subradiance are important for the quantum memory and quantum information. We investigate one-dimensional atomic arrays under the spatially periodic magnetic field with a tunable phase, which provides a distinctive physics aspect of revealing exotic two-dimensional topological phenomena with a synthetic dimension. A butterfly-like nontrivial bandstructure associated with the non-Hermitian physics involving strong long-range interactions has been discovered. It leads to pairs of topologically-protected edge states, which exhibit the robust super- or subradiance behavior,…
We show that the onset of steady-state superradiance in a bad cavity laser is preceded by a dissipative phase transition between two distinct phases of steady-state subradiance. The transition is marked by a non-analytic behavior of the cavity output power and the mean atomic inversion, as well as a discontinuity in the variance of the collective atomic inversion. In particular, for repump rates below a critical value, the cavity output power is strongly suppressed and does not increase with the atom number, while it scales linearly with atom number above this value. Remarkably, we find that t…
The cause of decoherence in a quantum system can be traced back to the interaction with the environment. As it has been pointed out first by Dicke, in a system of N two-level atoms where each of the atoms is individually dipole coupled to the environment, there are collective, subradiant states, that have no dipole coupling to photon modes, and therefore they are expected to decay slower. This property also implies that these type of states, which form an N-1 dimensional subspace of the atomic subsytem, also decohere slower. We propose a scheme which will create such states. First the two-leve…
We report the observation of subradiance in dense ensembles of cold $^{87}$Rb atoms operating near Dicke's regime of a large number of atoms in a volume with dimensions smaller than the transition wavelength. We validate that the atom number is the only cooperativity parameter governing subradiance. We probe the dynamics in the many-body regime and support the picture that multiply-excited subradiant states are built as a superposition of singly-excited states that decay independently. Moreover, we implement an experimental procedure to release the excitation stored in the long-lived modes in …
Coherent control of collective spontaneous emission in an extended atomic ensemble resonantly interacting with single-photon wave packets is analyzed. A scheme for coherent manipulation of collective atomic states is developed such that superradiant states of the atomic system can be converted into subradiant ones and vice versa. Possible applications of such a scheme for optical quantum state storage and single-photon wave packet shaping are discussed. It is shown that also in the absence of inhomogeneous broadening of the resonant line, single-photon wave packets with arbitrary pulse shape m…
Optical non-linearities at the single photon level are key features to build efficient photon-photon gates and to implement quantum networks. Such optical non-linearities can be obtained using an ideal two-level system such as a single atom coupled to an optical cavity. While efficient, such atom-photon interface however presents a fixed bandwidth, determined by the spontaneous emission time and thus the spectral width of the cavity-enhanced two-level transition, preventing an efficient transmission to bandwidth-mismatched atomic systems in a single quantum network. In the present work, we pro…
Heralded Free-Electron Writing of the Most Subradiant State in an Atomic Array
School of Physics and Technology, Wuhan University（武汉大学物理科学与技术学院）；Department of Physics, Friedrich-Alexander University (FAU) Erlangen-Nürnberg（埃尔朗根-纽伦堡弗里德里希·亚历山大大学物理系）；Wuhan Institute of Quantum Technology（武汉量子技术研究院）
Weakly bound molecules have physical properties without atomic analogues, even as the bond length approaches dissociation. In particular, the internal symmetries of homonuclear diatomic molecules result in formation of two-body superradiant and subradiant excited states. While superradiance has been demonstrated in a variety of systems, subradiance is more elusive due to the inherently weak interaction with the environment. Here we characterize the properties of deeply subradiant molecular states with intrinsic quality factors exceeding $10^{13}$ via precise optical spectroscopy with the longe…
Subradiance is the cooperative inhibition of the radiation by several emitters coupled to the same electromagnetic modes. It was predicted by Dicke in 1954 and only recently observed in cold atomic vapors. Here we address the question to what extent this cooperative effect survives outside the limit of frozen two-level systems by studying the subradiant decay in an ensemble of cold atoms as a function of the temperature. Experimentally, we observe only a slight decrease of the subradiant decay time when increasing the temperature up to several millikelvins, and in particular we measure subradi…
We show how strong light-mediated resonant dipole-dipole interactions between atoms can be utilized in a control and storage of light. The method is based on a high-fidelity preparation of a collective atomic excitation in a single correlated subradiant eigenmode in a lattice. We demonstrate how a simple phenomenological model captures the qualitative features of the dynamics and sharp transmission resonances that may find applications in sensing.
Efficient and versatile interfaces for the interaction of light with matter are an essential cornerstone for quantum science. A fundamentally new avenue of controlling light-matter interactions has been recently proposed based on the rich interplay of photon-mediated dipole-dipole interactions in structured subwavelength arrays of quantum emitters. Here we report on the direct observation of the cooperative subradiant response of a two-dimensional (2d) square array of atoms in an optical lattice. We observe a spectral narrowing of the collective atomic response well below the quantum-limited d…
We study strong light-mediated resonant dipole-dipole interactions in two-dimensional planar lattices of cold atoms. We provide a detailed analysis for the description of the dipolar point emitter lattice plane as a "super-atom", whose response is similar to electromagnetically-induced transparency, but which exhibits an ultra-narrow collective size-dependent subradiant resonance linewidth. The super-atom model provides intuitively simple descriptions for the spectral response of the array, including the complete reflection, full transmission, narrow Fano resonances, and asymptotic expressions…
We theoretically investigate the far-field scattering properties of multiphoton super- and subradiant states which can be prepared by multiphoton excitations with orbital angular momentum (OAM).\ Due to multiphoton interference, the far-field patterns of the subradiant modes show directional scattering along the excitation direction or transverse scattering with number of peaks equal to the number of atoms.\ When more atoms are involved, we consider structures of stacked and concentric rings, which respectively show enhanced directional scattering and smoothed emission patterns.\ Our scheme gi…
We investigate superradiance and subradiance of indistinguishable atoms with quantized motional states, starting with an initial total state that factorizes over the internal and external degrees of freedom of the atoms. Due to the permutational symmetry of the motional state, the cooperative spontaneous emission, governed by a recently derived master equation [F. Damanet et al., Phys. Rev. A 93, 022124 (2016)], depends only on two decay rates $γ$ and $γ_0$ and a single parameter $Δ_{\mathrm{dd}}$ describing the dipole-dipole shifts. We solve the dynamics exactly for $N=2$ atoms, numerically f…
We study the collective optical response of an atomic ensemble confined within a single-mode optical cavity by stochastic electrodynamics simulations that include the effects of atomic position correlations, internal level structure, and spatial variations in cavity coupling strength and atom density. In the limit of low light intensity the simulations exactly reproduce the full quantum field-theoretical description for cold stationary atoms and at higher light intensities we introduce semiclassical approximations to atomic saturation that we compare with the exact solution in the case of two …
We explore excitation transport within a one-dimensional chain of atoms where the atomic transition dipoles are coupled to the free radiation field. When the atoms are separated by distances smaller or comparable to the wavelength of the transition, the exchange of virtual photons leads to the transport of the excitation through the lattice. Even though this is a strongly dissipative system, we find that the transport is subradiant, that is, the excitation lifetime is orders of magnitude longer than the one of an individual atom. In particular, we show that a subspace of the spectrum is formed…
We show how an initial localized radiative excitation in a two-dimensional array of cold atoms can be converted into highly-directional coherent emission of light by protecting the spreading of the excitation across the array in a subradiant collective eigenmode with a lifetime orders of magnitude longer than that of an isolated atom. We demonstrate how to reach two such strongly subradiant modes, a uniform one where all the dipoles are oscillating in phase normal to the plane and an antiferromagnetic mode where each dipole is $π$ out of phase with its nearest neighbor. The excitation, which c…
The cooperative resonance for a spin one half system interacting with dc and ac magnetic field is considered. This interaction in the system collective regime can result in parametic resonance and rapid excitation of the excited spin state of the dense atomic gas. The phenomenon is studied using the density matrix approach. We discuss the implementation of this effect and possible applications of the quantum amplification by superradiant emission of radiation.
The coherent dipole-dipole interactions of atoms in an atomic array are studied. It is found that the excitation probability of an atom in an array parallel to the direction of laser propagation ($\boldsymbol{\hat{k}}$) will either grow or decay logarithmically along $\boldsymbol{\hat{k}}$, depending on the detuning of the laser. The symmetry of the system for atomic separations of $δr = jλ/2$, where $j$ is an integer, causes the excitation distribution and scattered radiation to abruptly become symmetric about the center of the array. For atomic separations of $δr < λ/2$, the appearance of a …
We study numerically the slow (subradiant) decay of the fluorescence of motionless atoms after a weak pulsed excitation. We show that, in the linear-optics regime and for an excitation detuned by several natural linewidths, the slow decay rate can be dominated by close pairs of atoms (dimers) forming superradiant and subradiant states. However, for a large-enough resonant optical depth and at later time, the dynamics is dominated by collective many-body effects. In this regime, we study the polarization and the spectrum of the emitted light, as well as the spatial distribution of excitation in…
Two-dimensional regular arrays of atoms are a promising platform for quantum networks, with collective subradiant states providing long-lived storage and collimated emission allowing for natural coherent links between arrays in free space. However, a single-layer lattice can only efficiently absorb or emit light symmetrically in the forward and backward directions. Here we show how a bilayer lattice can absorb a single photon either incident from a single direction or an arbitrary superposition of forward and backward propagating components. The excitation can be stored in a subradiant state, …
We study the protection of subradiant states by the symmetry of the atomic distributions in the Dicke limit, in which collective Lamb shifts cannot be neglected. We find that anti-symmetric states are subradiant states for distributions with reflection symmetry. Continuous symmetry can also be used to achieve subradiance. This study is relevant to the problem of robust quantum memory with long storage time and fast readout.
Superradiance and subradiance are collective effects that emerge from coherent interactions between quantum emitters. Due to their many-body nature, theoretical studies of extended samples with length larger than the atomic transition wavelength are usually restricted to their early time behavior or to the few-excitation limit. We use herein a mean-field approach to reduce the complex many-body system to an effective two-atom master equation that includes all correlations up to second order and that can be numerically propagated in time. We find that three-dimensional and two-dimensional inver…
Subwavelength atomic arrays, recently labeled as quantum metamaterials, have emerged as an exciting platform for obtaining novel quantum optical phenomena. The strong interference effects in these systems generate subradiant excitations that propagate through the atomic array with very long lifetimes. Here, we demonstrate that one can harness these excitations to obtain tunable directional emission patterns and collective dissipative couplings when placing judiciously additional atoms nearby the atomic array. For doing that, we first characterize the optimal array geometry to obtain directiona…
Dipole-coupled subwavelength quantum emitter arrays respond cooperatively to external light fields as they may host collective delocalized excitations (a form of excitons) with super- or subradiant character. Deeply subwavelength separations typically occur in molecular ensembles, where in addition to photon-electron interactions, electron-vibron couplings and vibrational relaxation processes play an important role. We provide analytical and numerical results on the modification of super- and subradiance in molecular rings of dipoles including excitations of the vibrational degrees of freedom.…
