We propose a technique to obtain subwavelength resolution in quantum imaging with potentially 100% contrast using incoherent light. Our method requires neither path-entangled number states nor multiphoton absorption. The scheme makes use of N photons spontaneously emitted by N atoms and registered by N detectors. It is shown that for coincident detection at particular detector positions a resolution of =N can be achieved. DOI: 10.1103/PhysRevLett.99.133603 PACS numbers: 42.50.St, 03.65.Ud, 42.30.ÿd, 42.50.Dv In Young's double slit experiment (or in a MachZehnder interferometer) the probability G 1 r to detect a photon at position r results from the interference of the two possible paths a single photon can take to reach the detector. This is expressed by the state Quantum entanglement is able to bypass the Rayleigh limit [2 -11]. Consider, for example, the path-entangledBecause the N-photon state jNi has N times the energy of the single-photon state j1i in a given mode it accumulates phase N times as fast when propagating through the setup. This gives rise to an N-photon absorption rate of the form G N r; . . . ; r / 1 cosN r exhibiting a fringe spacing N times narrower than that of G 1 r [4]. This gain in resolution can be fruitfully applied to a wide range of applications, e.g., to lithography [4,5], microscopy [8], spectroscopy [9], and even magnetometry [10]. In order to implement this N-fold increase in resolution commonly an entangled state of the form j N i in combination with a nonlinear medium sensitive to N-photon absorption is needed [11].In this Letter we propose a different scheme to achieve a resolution of =N involving neither of the above requirements. In what follows we will apply this scheme in the context of microscopy. The method employs N photons spontaneously emitted from N atoms subsequently detected by N detectors where by means of post-selection it is ensured that precisely one photon is recorded at each of the N detectors. We demonstrate that in this case, for certain detector positions r 2 ; . . . ; r N , the Nth order correlation function as a function of r 1 takes the form 1 cosN r 1 , resulting in a phase modulation with a theoretical contrast of 100% and a fringe spacing determined by =N. As with path-entangled number states, this corresponds to an N-fold reduced fringe spacing compared to G 1 r while keeping a contrast of potentially 100%. Hereby, only tools of linear optics are employed as a single photon is registered at each detector.To understand this outcome let us consider N identical two-level atoms excited by a single laser pulse. After the spontaneous emission the N photons are registered by N detectors at positions r 1 ; . . . ; r N . For the sake of simplicity let us consider coincident detection [12]. In that case the Nth order correlation function [13] can be written (up to an insignificant prefactor) as [14] G N r 1 ; . . . ; r N hD y r 1 . . .whereHere n r i r i =r i stands for the unit vector in the direction of detector i; the sum is over all atom positions R ,...

We calculate the radiative characteristics of emission from a system of entangled atoms which can have a relative distance larger than the emission wavelength. We develop a quantum multipath interference approach which explains both super-and subradiance though the entangled states have zero dipole moment. We derive a formula for the radiated intensity in terms of different interfering pathways. We further show how the interferences lead to directional emission from atoms prepared in symmetric W-states. As a byproduct of our work we show how Dicke's classic result can be understood in terms of interfering pathways. In contrast to the previous works on ensembles of atoms, we focus on finite numbers of atoms prepared in well characterized states.

We propose to use multiphoton interferences from statistically independent light sources in combination with linear optical detection techniques to enhance the resolution in imaging. Experimental results with up to five independent thermal light sources confirm this approach to improve the spatial resolution. Since no involved quantum state preparation or detection is required, the experiment can be considered an extension of the Hanbury Brown-Twiss experiment for spatial intensity correlations of order N>2.

We present a physical setup with which it is possible to produce arbitrary symmetric long-lived multiqubit entangled states in the internal ground levels of photon emitters, including the paradigmatic GHZ and W states. In the case of three emitters, where each tripartite entangled state belongs to one of two well-defined entanglement classes, we prove a one-to-one correspondence between welldefined sets of experimental parameters, i.e., locally tunable polarizer orientations, and multiqubit entanglement classes inside the symmetric subspace.PACS numbers: 42.50. Ex, 03.65.Ud, 03.67.Bg, 42.50.Dv Entanglement is a distinctive property of quantum physics associated with the nonseparable character of multipartite quantum systems. For the case of two-qubit systems, entanglement is well understood and can be precisely quantified [1]. Apart from the trivial disentangled case, three qubits possess two genuine tripartite inequivalent entanglement classes [2,3]. Efforts have been done recently towards higher number of qubits [4,5,6], including an inductive method [7], though so far no comprehensive and scalable classification has been developed. In this letter, we introduce a physical setup consisting of N emitters, incoherently radiating single photons that may be absorbed remotely by detectors equipped with polarizers and producing long-lived multiqubit entangled states among the emitters. We show that it is possible to associate well-defined sets of locally tuned polarizer orientations with multiqubit entanglement classes, allowing their monitoring in an operational manner. Hereby, multipath quantum interferences, associated with qubit permutation symmetry, play a key role in explaining the underlying physics.We consider a chain of N equally separated single photon emitters, say trapped neutral atoms, trapped ions, quantum dots, or any other equivalent physical system with access to similar behaviour. Each emitter defines a three-level Λ system, where |e denotes the excited state and the two long-lived sublevels, |+ and |− , define a qubit. We assume that the transitions between the excited state and the two lower sublevels have an equal wavenumber and dipole moment, and that they are circularly polarized, σ + and σ − , respectively. Figure 1 exemplifies the N -emitter case discussed throughout this paper. All emitters are initially excited and we will study the cases in which all spontaneously emitted photons are detected by N detectors located in the far-field re- gion, each of them being equipped with a polarization filter in front. The far-field detection ensures the erasure of which-way information of the arriving photons, and the polarizers allow the generation of quantum superpositions of the lower atomic states when considering arbitrary polarizations. As a consequence each photodetection event projects the emitters onto linear combinations of the long-lived states |+ and |− [8]. This results at the end in a coherent superposition between the qubit states |±, . . . , ± . The indeterminacy of which detector

Superradiance is one of the outstanding problems in quantum optics since Dicke introduced the concept of enhanced directional spontaneous emission by an ensemble of identical two-level atoms. The effect is based on correlated collective Dicke states which turn out to be highly entangled. Here we show that enhanced directional emission of spontaneous radiation can be produced also with statistically independent incoherent sources via the measurement of higher order correlation functions of the emitted radiation. Our analysis is applicable to a wide variety of quantum systems like trapped atoms, ions, quantum dots or NV-centers, and is also valid for statistically independent incoherent classical emitters. This is experimentally confirmed with up to eight independent thermal light sources.PACS numbers: 42.50. Gy, 42.50.Nn, 42.50.Dv, 03.67.Bg Dicke superradiance [1][2][3][4][5] remains an important problem in quantum optics primarily due to ones inability to generate entangled states of a modest number of atoms. Using single photon excitation one can produce Dicke states where only one atom out of the ensemble is excited. For this case several ground breaking experiments have been recently reported, including observation of collective Lamb shifts in regular arrays of nuclei [6,7] or directed forward scattering from atomic ensembles in collective first excited [8][9][10][11] or Rydberg states [12][13][14]. Beyond single-photon excited Dicke states the production of Dicke states with higher number of excitations remains a challenge. One option is the repeated measurements of photons at particular positions starting from the fully excited system. This amounts to measuring the m-th order photon correlation function for N > m emitters. In this case, if the detection is unable to identify the individual photon source, the collective system cascades down the ladder of symmetric Dicke states each time a photon is recorded via projective measurements. This is another example of measurement induced entanglement among parties which do not directly interact with each other [15][16][17][18][19][20][21][22].The inability to distinguish the emitters is fulfilled in case of atoms confined to a region smaller than the wavelength λ of the emitted radiation. However, if the dipole-dipole interaction between the atoms is taken into account the collective system quickly leaves the symmetric subspace populating different super-and subradiant states so that the superradiant phenomena are obscured [3,5].The condition of indistinguishability can also be met in case of widely separated emitters as long as the detection occurs in the far field [1][2][3][4][5]23]. This is fulfilled for example for atomic clouds involving many particles, relevant for most experiments in the optical domain. However, in this regime the superradiant characteristics depend critically on the geometry of the sample due to diffraction and propagation effects [3,5] so that the superradiant behavior is concealed by geometrical considerations.To observe the effects o...