Quantum Imaging with Incoherent Photons

Abstract

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 ,...

Sub-Rayleigh quantum imaging using single-photon sources

“…quantum paths may differ from each other by an optical phase, leading to destructive or constructive interferences between the N -photon amplitudes. This can be fruitfully exploited, e.g., to obtain information about the spatial distribution of the source even if of dimensions smaller than the optical wavelength λ [9,10]. In the following, we will extend this concept by introducing a distinct physical object between source and detectors which we aim to image with sub-Rayleigh resolution in an ordinary far-field imaging setup.…”

“…Though all proposals commonly aim to overcome the classical boundaries of image formation, only few improve the spatial resolution itself, i.e. the ability to image a physical object while overcoming the Rayleigh [12] or Abbe limit [13] of classical optics.So far, in quantum imaging sub-classical resolution has been achieved by using sources of entangled photons [5,8], but it was also shown recently that initially uncorrelated light can be used for that purpose [10,14]. All those methods exploit second (or N th) order correlations between two (or N ) photons, i.e.…”

“…So far, in quantum imaging sub-classical resolution has been achieved by using sources of entangled photons [5,8], but it was also shown recently that initially uncorrelated light can be used for that purpose [10,14]. All those methods exploit second (or N th) order correlations between two (or N ) photons, i.e.…”

“…In earlier articles [9,10], it was demonstrated how a source of single-photon emitters with a separation d < λ can be imaged and resolved using ordinary photon detectors and joint detection techniques. In contrast, the scheme developed in this paper enables to resolve details of a distinct physical object, e.g.…”

“…For example, if we detect N (N > 1) photons by N different detectors placed in the far-field region of a source consisting of N single photon emitters, there are generally N ! possibilities how the N photons may propagate from the N atoms to the N detectors [10]. Hereby, the N !…”