The present work Materwave Optics with Dark-state Polaritons: Applications to Interferometry and Quantum Information deals in a broad sense with the subject of dark-states and in particular with the so-called dark-state polaritons introduced by M. Fleischhauer and M. D. Lukin. The dark-state polaritons can be regarded as a combined excitation of electromagnetic fields and spin/matter-waves. Within the framework of this thesis the special optical properties of the combined excitation are studied. On one hand a new procedure to spatially manipulate and to increase the excitation density of stored photons is described and on the other hand the properties are used to construct a new type of Sagnac Hybrid interferometer. The thesis is devided into four parts. In the introduction all notions necessary to understand the work are described, e.g.: electromagnetically induced transparency (EIT), dark-state polaritons and the Sagnac effect. The second chapter considers the method developed by A. Andre and M. D. Lukin to create stationary light pulses in specially dressed EIT-media. In a first step a set of field equations is derived and simplified by introducing a new set of normal modes. The absorption of one of the normal modes leads to the phenomenon of pulse-matching for the other mode and thereby to a diffusive spreading of its field envelope. All these considerations are based on a homogeneous field setup of the EIT preparation laser. If this restriction is dismissed one finds that a drift motion is superimposed to the diffusive spreading. By choosing a special laser configuration the drift motion can be tailored such that an effective force is created that counteracts the spreading. Moreover, the force can not only be strong enough to compensate the diffusive spreading but also to exceed this dynamics and hence to compress the field envelope of the excitation. The compression can be discribed using a Fokker-Planck equation of the Ornstein-Uhlenbeck type. The investigations show that the compression leads to an excitation of higher-order modes which decay very fast. In the last section of the chapter this exciation will be discussed in more detail and conditions will be given how the excitation of higher-order modes can be avoided or even suppressed. All results given in the chapter are supported by numerical simulatons. In the third chapter the matterwave optical properties of the dark-state polaritons will be studied. They will be used to construct a light-matterwave hybrid Sagnac interferometer. First the principle setup of such an interferometer will be sketched and the relevant equations of motion of light-matter interaction in a rotating frame will be derived. These form the basis of the following considerations of the dark-state polariton dynamics with and without the influence of external trapping potentials on the matterwave part of the polariton. It will be shown that a sensitivity enhancement compared to a passive laser gyroscope can be anticipated if the gaseous medium is initially in a superfluid quantum state in a ring-trap configuration. To achieve this enhancement a simultaneous coherence and momentum transfer is furthermore necessary. In the last part of the chapter the quantum sensitivity limit of the hybrid interferometer is derived using the one-particle density matrix equations incorporating the motion of the particles. To this end the Maxwell-Bloch equations are considered perturbatively in the rotation rate of the noninertial frame of reference and the susceptibility of the considered 3-level \(\Lambda\)-type system is derived in arbitrary order of the probe-field. This is done to determine the optimum operation point. With its help the anticipated quantum sensitivity of the light-matterwave hybrid Sagnac interferometer is calculated at the shot-noise limit and the results are compared to state-of-the-art laser and matterwave Sagnac interferometers. The last chapter of the thesis originates from a joint theoretical and experimental project with the AG Bergmann. This chapter does no longer consider the dark-state polaritons of the last two chapters but deals with the more general concept of dark states and in particular with the transient velocity selective dark states as introduced by E. Arimondo et al. In the experiment we could for the first time measure these states. The chapter starts with an introduction into the concept of velocity selective dark states as they occur in a \(\Lambda\)-configuration. Then we introduce the transient velocity selective dark-states as they occur in an particular extension of the \(\Lambda\)-system. For later use in the simulations the relevant equations of motion are derived in detail. The simulations are based on the solution of the generalized optical Bloch equations. Finally the experimental setup and procedure are explained and the theoretical and experimental results are compared.
The present work Materwave Optics with Dark-state Polaritons: Applications to Interferometry and Quantum Information deals in a broad sense with the subject of dark-states and in particular with the so-called dark-state polaritons introduced by M. Fleischhauer and M. D. Lukin. The dark-state polaritons can be regarded as a combined excitation of electromagnetic fields and spin/matter-waves. Within the framework of this thesis the special optical properties of the combined excitation are studied. On one hand a new procedure to spatially manipulate and to increase the excitation density of stored photons is described and on the other hand the properties are used to construct a new type of Sagnac Hybrid interferometer. The thesis is devided into four parts. In the introduction all notions necessary to understand the work are described, e.g.: electromagnetically induced transparency (EIT), dark-state polaritons and the Sagnac effect. The second chapter considers the method developed by A. Andre and M. D. Lukin to create stationary light pulses in specially dressed EIT-media. In a first step a set of field equations is derived and simplified by introducing a new set of normal modes. The absorption of one of the normal modes leads to the phenomenon of pulse-matching for the other mode and thereby to a diffusive spreading of its field envelope. All these considerations are based on a homogeneous field setup of the EIT preparation laser. If this restriction is dismissed one finds that a drift motion is superimposed to the diffusive spreading. By choosing a special laser configuration the drift motion can be tailored such that an effective force is created that counteracts the spreading. Moreover, the force can not only be strong enough to compensate the diffusive spreading but also to exceed this dynamics and hence to compress the field envelope of the excitation. The compression can be discribed using a Fokker-Planck equation of the Ornstein-Uhlenbeck type. The investigations show that the compression leads to an excitation of higher-order modes which decay very fast. In the last section of the chapter this exciation will be discussed in more detail and conditions will be given how the excitation of higher-order modes can be avoided or even suppressed. All results given in the chapter are supported by numerical simulatons. In the third chapter the matterwave optical properties of the dark-state polaritons will be studied. They will be used to construct a light-matterwave hybrid Sagnac interferometer. First the principle setup of such an interferometer will be sketched and the relevant equations of motion of light-matter interaction in a rotating frame will be derived. These form the basis of the following considerations of the dark-state polariton dynamics with and without the influence of external trapping potentials on the matterwave part of the polariton. It will be shown that a sensitivity enhancement compared to a passive laser gyroscope can be anticipated if the gaseous medium is initially in a superfluid quantum state in a ring-trap configuration. To achieve this enhancement a simultaneous coherence and momentum transfer is furthermore necessary. In the last part of the chapter the quantum sensitivity limit of the hybrid interferometer is derived using the one-particle density matrix equations incorporating the motion of the particles. To this end the Maxwell-Bloch equations are considered perturbatively in the rotation rate of the noninertial frame of reference and the susceptibility of the considered 3-level (\Lambda)-type system is derived in arbitrary order of the probe-field. This is done to determine the optimum operation point. With its help the anticipated quantum sensitivity of the light-matterwave hybrid Sagnac interferometer is calculated at the shot-noise limit and the results are compared to state-of-the-art laser and matterwave Sagnac interferometers. The last chapter of the thesis originates from a joint theoretical and experimental project with the AG Bergmann. This chapter does no longer consider the dark-state polaritons of the last two chapters but deals with the more general concept of dark states and in particular with the transient velocity selective dark states as introduced by E. Arimondo et al. In the experiment we could for the first time measure these states. The chapter starts with an introduction into the concept of velocity selective dark states as they occur in a (\Lambda)-configuration. Then we introduce the transient velocity selective dark-states as they occur in an particular extension of the (\Lambda)-system. For later use in the simulations the relevant equations of motion are derived in detail. The simulations are based on the solution of the generalized optical Bloch equations. Finally the experimental setup and procedure are explained and the theoretical and experimental results are compared.
In this work quantum coherence effects in dense rubidium atomic vapour are investigated. Prepared in a laser driven atomic system, coherent effects, like the well-known electromagnetically induced transparency, have a remarkable ability to significantly alter optical properties of the used medium. Electromagnetically induced transparency and related phenomena like slow and stored light can be explained in terms of dark state polaritons, representing quasiparticles consisting of light and matter components. In this thesis, experiments aiming to the concept of quasiparticles are described. Furthermore, in this thesis the concept of resonance retrieval of a stored coherence is investigated, a concept that might prove useful in metrology. In this thesis, the focus is set on the experimental study of the particle-like nature of dark state polaritons. Therefore, a radiofrequency spectroscopy is performed on stationary and moving polaritons with an internal level structure. To this end, an experimental setup is described that allows for the existence of two state dark polaritons in a tripod level scheme. The internal level structure of these polaritons is then probed by a radiofrequency field and a transfer of population between two dark states is observed. The measured population transfer, though with a limited contrast, strongly indicates that dark state polaritons can be considered as quasiparticles with an internal level structure. Since the dark state polaritons exhibit features of an effective magnetic dipole moment, the existence of the Aharonov-Casher phase effect for these quasiparticles is investigated experimentally. It is predicted by a known Aharonov-Casher effect that taking two particles with a finite magnetic dipole moment around a line of charge causes an accumulated phase difference between them. In this work, a detection system with a phase sensitivity of 10-5 rad is described, which sets the upper boundary on the experimentally detectable Aharonov-Casher phase for the hot rubidium gas system. In the last part of this thesis experiments on storage and resonant retrieval of an atomic coherence are described. To this end, an RF field creates an atomic coherence which is stored and subsequently read out with an optical field. The retrieved field is shown to be frequency locked to the optical field. The difference frequency is, within the limits of experimental sensitivity, at the atomic resonance frequency independently on the amplitude and frequency variations of the radiofrequency excitation field.
This thesis covers a theoretical analysis of non-interacting and interacting quasi\nparticles, called polaritons. Polaritons are composites, based on photonic and atomic\nexcitations in a tunable and controlled manner. Dark-state polaritons, as a subclass\nof polaritons, are very curious objects, as they can act as a quantum memory of\nphotons within an ensemble of alkali-metal atoms in -type conguration which\nadmit electromagnetically induced transparency (EIT). This thesis focus on the\nformation of dark-state polaritons in degenerate two-level systems, where two light\nelds, a quantum probe and a classical driving eld, couple the same transition\nbetween the ground state and excited state manifold. An algorithm is going to\nbe derived in order to determine the dispersion relation and inherent composition\nof the dark-state polaritons in the degenerate two-level system. The algorithm is\nbased on a microscopic equation of motion technique and provides an extension of\nthe non-degenerate case. Depending on the polarization of the light elds, it will be\nshown that either one or two dark-state polaritons can exist. Further, the calculated\ndark-state polaritons can be used in order to perform a frequency conversion and\neven a conversion of linear light polarization.\nIn the second part of the thesis, interacting polaritons in arrays of coupled QED\ncavities will be discussed. In rst place, the standard Jaynes-Cummings model is\ndiscussed in order to provide a better insight to polaritons in QED cavities. Then,\na modied Jaynes-Cummings model is introduced and derived in order to study\ndark-polaritons and their interaction. It will be shown that dark-polaritons directly\ndepend on the common single photon detuning of the two coupling elds, quantum\nprobe and classical driving eld. The interaction between dark-polaritons will be\ndiscussed where the emergence of dark-polariton bound pairs will be shown. By\ntuning the Stark-shift due to the classical control eld, the number and the composition\nof dark-polariton bound pairs can be controlled. It will be demonstrated\nthat there exists a dark-polariton bound pair which diers from the aforementioned\nones, because it represents a ground state of the system. Using that kind of a darkpolariton\nbound pair, storage and retrieval of a single photon can be performed,\neven though that the photons are in a two-photon bound state.\nIn the last part of the thesis, disorder between QED cavities will be introduced\nin a controlled manner through staggered inter-cavity photon hopping strengths J1\nand J2. Further, the appearance of a dark-polariton bound pair of a completely\ndierent type will be presented.
We identify form-stable coupled excitations of light and matter ("dark-state polaritons") associated with the propagation of quantum fields in electromagnetically induced transparency. The properties of dark-state polaritons such as the group velocity are determined by the mixing angle between light and matter components and can be controlled by an external coherent field as the pulse propagates. In particular, light pulses can be decelerated and "trapped" in which case their shape and quantum state are mapped onto metastable collective states of matter. Possible applications of this reversible coherent-control technique are discussed.
This paper derives a wave equation in magnetized plasma under electromagnetically induced transparency (EIT) regime for probe electron cyclotron wave. The equation has a solution indicating a state analogous to “dark-state polaritons” [M. Fleischhauer and M. D. Lukin, Phys. Rev. Lett. 84, 5094 (2000)] in quantum atomic system. The state analogous to dark-state polaritons is a propagating coupled state of the probe-wave electric field and longitudinal plasma oscillation. The propagation of the coupled state can be stopped as its waveform is maintained if injection of pump wave is properly controlled in time domain. The “stop-light” is achieved by adiabatic transition from a state in which the probe-wave field is dominant to a state in which the longitudinal plasma oscillation is dominant. This study also recaptures a phenomenon analogous to “coherent population trap” in conventional EIT of quantum atomic system.
We propose and analyze a mechanism for Bose-Einstein condensation of stationary dark-state polaritons. Dark-state polaritons (DSPs) are formed in the interaction of light with laser-driven 3-level Lambda-type atoms and are the basis of phenomena such as electromagnetically induced transparency, ultraslow, and stored light. They have long intrinsic lifetimes and in a stationary setup, a 3D quadratic dispersion profile with variable effective mass. Since DSPs are bosons, they can undergo a Bose-Einstein condensation at a critical temperature which can be many orders of magnitude larger than that of atoms. We show that thermalization of polaritons can occur via elastic collisions mediated by a resonantly enhanced optical Kerr nonlinearity on a time scale short compared to the decay time. Finally, condensation can be observed by turning stationary into propagating polaritons and monitoring the emitted light.
An ideal and reversible transfer technique for the quantum state between light and metastable collective states of matter is presented and analyzed in detail. The method is based on the control of photon propagation in coherently driven three-level atomic media, in which the group velocity is adiabatically reduced to zero. Form-stable coupled excitations of light and matter (``dark-state polaritons'') associated with the propagation of quantum fields in electromagnetically induced transparency are identified, their basic properties discussed and their application for quantum memories for light analyzed.