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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Quantum interference in light scattering and propagation

Jörg Evers, Mohammad Mahmoudi, Mihai Macovei

Published Jun 7, 2007• 0 citations
Publisher

Abstract

Light scattered by a regular structure of atoms exhibits spatial interference signatures, similar to Young's classical double-slit experiment. The first-order interferences, however, are known to vanish for strong light intensities, where the incoherently fluctuating part of the emitted light dominates. Here, we show how to overcome these limitations to quantum interference in stronger laser fields, and how to recover the first-order interference in strong fields by a tailored electromagnetic vacuum with a suitable frequency dependence. We also discuss higher-order correlation functions of the scattered light, with applications, e.g., to lithography. In the second part, we study light propagation of a probe field pulse in closed-loop atomic systems. The closed interaction loop induces a sensitivity to the relative driving field phase, but in general prohibits a stationary steady state. In particular, the finite frequency width of the short probe pulse requires a time-dependent analysis beyond the so-called multiphoton resonance assumption. Using a Floquet decomposition, we identify the different contributions to the medium response, and demonstrate sub- and superluminal light propagation with small absorption or even gain, where a coupling field Rabi frequency allows to switch between sub- and superluminal light propagation.

DOI
10.1117/12.724343

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In this thesis we discuss an extension of the historical Hanbury Brown and Twiss experiment and investigate spatial intensity correlations of higher-orders in the radiation field of statistically independent light sources. The light sources can be non-classical like single-photon emitters or classical, obeying thermal or coherent statistics. Although the light sources are assumed to emit the photons in an incoherent manner, we find spatial photon correlations in the far field which can be explained by the quantum mechanical concept of multi-photon interferences. We demonstrate that spatial correlation measurements between indistinguishable photons based on linear optical detection techniques can be used to overcome the resolution limit of classical optics (Abbe/Rayleigh limit) and also to manipulate the spatial radiation characteristic of the light sources. Both remarkable properties of higher-order intensity correlations have been experimentally verified using statistically independent pseudothermal light sources. Due to the fact that the reported correlation measurements require neither special quantum tailoring of light nor N-photon absorbing media, they are of particular interest for the field of quantum imaging and quantum information processing. The thesis is divided into three main parts: In the first part (Chapter 2 and 3) we introduce a quantum path formalism which allows to describe multi-photon interferences arising in both classical and nonclassical light fields. This quantum path approach explains the origin of the underlying interference mechanism of the higher-order spatial intensity correlation functions in a transparent and simple manner. Moreover, it enables us to compare the multi-photon interferences obtained by nonclassical single-photon emitters with those generated by classical light sources. In the course of this discussion it appears that Dirac's famous statement “Each photon interferes only with itself. Interference between two different photons never occurs.” should better read “A multi-photon state of independent photons only interferes with itself. Interference between different multi-photon states never occurs.” This general statement summarizes the physics behind all multi-photon interference phenomena investigated in this thesis. In the second part of the thesis (Chapter 4) we investigate particular multi-photon interference measurements of independent light sources in the context of quantum imaging. We demonstrate that the Nth-order spatial intensity correlation functions display at specific ‘magic’ detector positions the ability to filter sub-wavelength information out of the light fields arising from N incoherently radiating light sources. These multi-photon interference patterns achieve a higher resolution for N>2 than the classical Abbe/Rayleigh limit for imaging the light source. In case of N single-photon emitters we theoretically show that the super-resolving interference patterns obtained for the ‘magic’ detector positions are identical to the ones generated by NOON states with N-1 photons. Quite unexpected, the same is true for N thermal light sources, except for a reduced visibility. Experimental results with up to eight independent thermal light sources confirm this approach to improve the spatial resolution in imaging. In the last part of this thesis (Chapter 5) we finally demonstrate that multi-photon detections can lead to a strong angular focussing of incoherent photons emitted again by either uncorrelated single-photon sources or statistically independent classical light sources. For this effect the sources can be far away from each other and do not interact. The mth-order intensity correlation measurement causes source correlations which produce a heralded peaked emission pattern for the initially uncorrelated light sources. In particular, we show that if m-1 photons have been detected in a particular direction, the conditional probability to detect the mth photon in the same direction can be as high as 100 %. Owing to the great flexibility of detector positions for the correlation measurement, a wide variety of additional detection schemes exists which produces similar directional photon emission patterns. This theoretically predicted measurement-induced focussing was experimentally confirmed with up to eight pseudothermal light sources for three particular detection schemes.

•Jan 1, 2012•0 citations
Light scattered by a regular structure of atoms exhibits spatial interference signatures, similar to Young's classical double-slit experiment. The first-order interferences, however, are known to vanish for strong light intensities, where the incoherently fluctuating part of the emitted light dominates. Here, we show how to overcome these limitations to quantum interference in stronger laser fields, and how to recover the first-order interference in strong fields by a tailored electromagnetic vacuum with a suitable frequency dependence. We also discuss higher-order correlation functions of the scattered light, with applications, e.g., to lithography. In the second part, we study light propagation of a probe field pulse in closed-loop atomic systems. The closed interaction loop induces a sensitivity to the relative driving field phase, but in general prohibits a stationary steady state. In particular, the finite frequency width of the short probe pulse requires a time-dependent analysis beyond the so-called multiphoton resonance assumption. Using a Floquet decomposition, we identify the different contributions to the medium response, and demonstrate sub- and superluminal light propagation with small absorption or even gain, where a coupling field Rabi frequency allows to switch between sub- and superluminal light propagation.
The light propagation of a probe field pulse in a four-level double-lambda type system driven by laser fields that form a closed interaction loop is studied. The finite frequency width of the probe pulse requires a time-dependent analysis beyond the multiphoton resonance assumption. We apply a Floquet decomposition to the equations of motion to solve this time-dependent problem and to identify the different scattering processes contributing to the medium response. We find that the response oscillating in phase with the probe field is phase-independent. The phase dependence arises from a scattering of the coupling fields into the probe field mode at a frequency which in general differs from the probe field frequency. In particular for short pulses with a large frequency width, inducing a closed loop interaction contour may lead to a distortion of the pulse shape via this phase-sensitive scattering. Finally, we demonstrate that both the closed loop and the nonclosed loop configuration allow for sub- and superluminal light propagation with small absorption or even gain, where one of the coupling field Rabi frequencies acts as a control parameter that enables one to switch between sub- and superluminal light propagation.
Light scattered by a regular structure of atoms can exhibit interference signatures, similar to the classical double-slit. These first-order interferences, however, vanish for strong light intensities, restricting potential applications. Here, we show how to overcome these limitations to quantum interference in strong fields. First, we recover the first-order interference in strong fields via a tailored electromagnetic bath with a suitable frequency dependence. At strong driving, the optical properties for different spectral bands are distinct, thus extending the set of observables. We further show that for a two-photon detector as, e.g., in lithography, increasing the field intensity leads to twice the spatial resolution of the second-order interference pattern compared to the weak-field case.
Photon correlations and cross-correlations of light scattered by a regular structure of strongly driven atoms are investigated. At strong driving, the scattered light separates into distinct spectral bands, such that each band can be treated as independent, thus extending the set of observables. We focus on second-order intensity-intensity correlation functions in two- and multi-atom systems. We demonstrate that for a single two-photon detector as, e.g., in lithography, increasing the driving field intensity leads to an increased spatial resolution of the second-order two-atom interference pattern. We show that the cross-correlations between photons emitted in the spectral sidebands violate Cauchy-Schwartz inequalities, and that their emission ordering cannot be predicted. Finally, the results are generalized for multi-particle structures, where we find results different from those in a Dicke-type sample.
The appearance of quantum interference in the microscopic world is one of the deepest mysteries at the very root of quantum mechanics. When light interacts with atoms, it can induce transitions by way of distinct but indistinguishable pathways and yield unexpected and often counter-intuitive results. Electromagnetically Induced Transparency (EIT), Coherent Population Trapping (CPT), and Lasing Without Inversion (LWI) are modern examples of phenomena where the traditional rules that govern absorption and dispersion undergo major revisions. Spectacular consequences of this new state of affairs include the ability of a light beam to propagate through a normally absorbing medium with little or no absorption, or to undergo amplification even if the active medium is not prepared in a state of population inversion. Light signals have been shown to travel with strongly subluminal group velocities of only a handful of meters per second and, even, to propagate at speed greater than the ordinary speed of light, but without violation of causality or of the established rules that control the transfer of optical information through space. Three-level atoms can interact with two coherent electromagnetic fields according to three different systems, known as Cascade, Lambda and Vee systems. The propagation of a weak probe field can be deeply affected by the presence of a second stronger beam, the so-called coupling field. Transparency windows, splitting of emission and absorption lines and enormously enhanced dispersion have been documented in numerous experiments. In this thesis we explore the physical origin of the transparency induced in these systems by the simultaneous interplay of the coupling and probe fields. We focus our attention on the Cascade system and study its two configurations, Cascade-EIT and Cascade-AT. We develop a variety of complementary approaches for the description of these two configurations, some semiclassical and others fully quantum mechanical. We prove the existence of quantum interference in Electromagnetically Induced Transparency and also the surprising absence of interference in a closely related phenomenon, known as the Autler-Townes effect. Finally we complement the traditional machinery of theoretical quantum optics with techniques borrowed from quantum scattering theory, and offer what we believe is the most convincing physical evidence for the appearance, or for the absence, of quantum interference effects.
This thesis deals with the study of propagation effects experienced by weak light pulses as they propagate in atomic media driven by strong pulses. We explore both the ultra-short and long pulse regime and investigate the phenomena that arise at these different time scales. In the short pulse regime, a strongly driven two level atomic system presents transient light shifts, and non-adiabatic transitions occur between these adiabatic levels. We have studied a method to probe these light shifts in real time by propagating a weak probe through the medium. The light shifts enrich the spectrum of the probe and the probe gets shaped as a result. In this way a strongly driven two-level system can act as an active pulse shaper, and can introduce oscillations in the temporal profile of an ultra-short pulse at a time scale shorter than the pulse duration. We also show that by driving the system with two time delayed non-resonant strong fields, the non-adiabatic effects can be rendered phase dependent. This gives very sensitive phase control of the excited state population and can be used to formulate new techniques in interferometry. In the long pulse regime we present a new method of slowing light that can be realized in a double two-level system interacting with two orthogonally polarized light pulses that propagate along different axis. Spatio-temporal dependence of the total polarization induces a grating in the ground Zeeman coherence. The stronger of the two fields (the control field) is diffracted from this grating into the direction of the weak probe field compensating for the absorption of this latter field. A transparency window is thus created in the absorption spectrum of the probe leading to the slowing down of light. The transparency window exhibits characteristics similar to the one obtained by EIT (electromagnetic induced transparency) method. However, the important difference between our method and the traditional EIT method, is that ours doesn't rely on realizing dark state in the system. This may open the possibility of slowing down light in more complex atomic media. Moreover, when the linear absorptive response of the medium is cancelled in this manner, the nonlinear response becomes more important. In the situation where fields propagate in the same direction and have same frequency, two regimes have been investigated. For small optical depths, the effective susceptibility behaves as chi_lin exp[2 i phi] (with phi the phase difference between two fields). This renders phase control of the medium response, and the medium can be changed from an absorber to an amplifier, with normal or anomalous dispersion, by adjusting the relative phase phi.  In the regime of large optical thickness, phase saturation takes place and the effective susceptibility turns into chi_lin*, changing an absorber into an amplifier without effecting the dispersive response (chi_lin is linear susceptibility).
In this thesis we discuss an extension of the historical Hanbury Brown and Twiss experiment and investigate spatial intensity correlations of higher-orders in the radiation field of statistically independent light sources. The light sources can be non-classical like single-photon emitters or classical, obeying thermal or coherent statistics. Although the light sources are assumed to emit the photons in an incoherent manner, we find spatial photon correlations in the far field which can be explained by the quantum mechanical concept of multi-photon interferences. We demonstrate that spatial correlation measurements between indistinguishable photons based on linear optical detection techniques can be used to overcome the resolution limit of classical optics (Abbe/Rayleigh limit) and also to manipulate the spatial radiation characteristic of the light sources. Both remarkable properties of higher-order intensity correlations have been experimentally verified using statistically independent pseudothermal light sources. Due to the fact that the reported correlation measurements require neither special quantum tailoring of light nor N-photon absorbing media, they are of particular interest for the field of quantum imaging and quantum information processing. The thesis is divided into three main parts: In the first part (Chapter 2 and 3) we introduce a quantum path formalism which allows to describe multi-photon interferences arising in both classical and nonclassical light fields. This quantum path approach explains the origin of the underlying interference mechanism of the higher-order spatial intensity correlation functions in a transparent and simple manner. Moreover, it enables us to compare the multi-photon interferences obtained by nonclassical single-photon emitters with those generated by classical light sources. In the course of this discussion it appears that Dirac's famous statement “Each photon interferes only with itself. Interference between two different photons never occurs.” should better read “A multi-photon state of independent photons only interferes with itself. Interference between different multi-photon states never occurs.” This general statement summarizes the physics behind all multi-photon interference phenomena investigated in this thesis. In the second part of the thesis (Chapter 4) we investigate particular multi-photon interference measurements of independent light sources in the context of quantum imaging. We demonstrate that the Nth-order spatial intensity correlation functions display at specific ‘magic’ detector positions the ability to filter sub-wavelength information out of the light fields arising from N incoherently radiating light sources. These multi-photon interference patterns achieve a higher resolution for N>2 than the classical Abbe/Rayleigh limit for imaging the light source. In case of N single-photon emitters we theoretically show that the super-resolving interference patterns obtained for the ‘magic’ detector positions are identical to the ones generated by NOON states with N-1 photons. Quite unexpected, the same is true for N thermal light sources, except for a reduced visibility. Experimental results with up to eight independent thermal light sources confirm this approach to improve the spatial resolution in imaging. In the last part of this thesis (Chapter 5) we finally demonstrate that multi-photon detections can lead to a strong angular focussing of incoherent photons emitted again by either uncorrelated single-photon sources or statistically independent classical light sources. For this effect the sources can be far away from each other and do not interact. The mth-order intensity correlation measurement causes source correlations which produce a heralded peaked emission pattern for the initially uncorrelated light sources. In particular, we show that if m-1 photons have been detected in a particular direction, the conditional probability to detect the mth photon in the same direction can be as high as 100 %. Owing to the great flexibility of detector positions for the correlation measurement, a wide variety of additional detection schemes exists which produces similar directional photon emission patterns. This theoretically predicted measurement-induced focussing was experimentally confirmed with up to eight pseudothermal light sources for three particular detection schemes.