Single Photons Emitted by Nanocrystals Optically Trapped in a Deep Parabolic Mirror

Vsevolod Salakhutdinov, Markus Sondermann, Luigi Carbone, Elisabeth Giacobino, Alberto Bramati, Gerd Leuchs

We investigate the emission of single photons from CdSe/CdS dots-in-rod which are optically trapped in the focus of a deep parabolic mirror. Thanks to this mirror, we are able to image almost the full 4π emission pattern of nanometer-sized elementary dipoles and verify the alignment of the rods within the optical trap. From the motional dynamics of the emitters in the trap, we infer that the single-photon emission occurs from clusters comprising several emitters. We demonstrate the optical trapping of rod-shaped quantum emitters in a configuration suitable for efficiently coupling an ensemble of linear dipoles with the electromagnetic field in free space.

Measuring the temperature and heating rate of a single ion by imaging

Bharath Srivathsan, Martin Fischer, Lucas Alber, Markus Weber, Markus Sondermann, Gerd Leuchs

We present a technique based on high resolution imaging to measure the absolute temperature and the heating rate of a single ion trapped at the focus of a deep parabolic mirror. We collect the fluorescence light scattered by the ion during laser cooling and image it onto a camera. Accounting for the size of the point-spread function and the magnification of the imaging system, we determine the spatial extent of the ion, from which we infer the mean phonon occupation number in the trap. Repeating such measurements and varying the power or the detuning of the cooling laser, we determine the heating rate induced by any kind of effect other than photon scattering. In contrast to other established schemes for measuring the heating rate, the ion is always maintained in a state of thermal equilibrium at temperatures close to the Doppler limit.

Nonlinear optics with full three-dimensional illumination

Rojiar Penjweini, Markus Weber, Markus Sondermann, Robert W. Boyd, Gerd Leuchs

Nonlinear optical interactions play a crucial role in modern technology and lead to important applications such as optical switching, optical harmonic generation, and the characterization of ultrafast material processes. Nonlinear interactions are enhanced by using a tightly focused laser beam, but nonetheless they are typically excited by a loosely focused (that is, paraxial) laser beam. Here we investigate a specific process, third-harmonic generation, excited by a highly nonparaxial beam that illuminates an interaction region from a nearly full solid angle. We elucidate the influence of the focal volume and the pump intensity on the number of frequency-tripled photons by varying the solid angle from which the pump light is focused, and we find good agreement between the experiments and numerical calculations. As the pump light is focused to a spot size much smaller than the laser wavelength, the Gouy phase does not limit the yield of frequency-converted photons, in stark contrast to the paraxial regime. We believe that our findings are generic and apply to many other nonlinear optical processes when the pump light is focused from a full solid angle.

A Holography-Based Modal Wavefront Sensor for the Precise Positioning of a Light Emitter Using a High-Resolution Computer-Generated Hologram

Florian Loosen, Johannes Stehr, Lucas Alber, Irina Harder, Norbert Lindlein

In certain applications, modal wavefront sensors (MWFSs) can outperform zonal wavefront sensors, which are widely used due to their high flexibility. In this paper, a holography-based MWFS as described is developed for the fast position control of a light emitter in a deep parabolic mirror. The light source is located in the vicinity of the focal point. Instead of Zernike polynomials, more complex phase functions, which are related to certain dislocations of the light source are used as detector modes. The performance of the sensor is verified with a test setup, where the test wavefront is generated by a spatial light modulator instead of a real parabolic mirror. The design and fabrication of the required high-resolution holographic element is described and an easy way of multiplexing several single mode sensors is demonstrated.

Off-resonant emission of photon pairs in nonlinear optical cavities

Valentin Averchenko, Gerhard Schunk, Michael Förtsch, Martin Fischer, Dmitry Strekalov, Gerd Leuchs, Christoph Marquardt

Cavity-assisted spontaneous parametric down-conversion (SPDC) and spontaneous four-wave mixing (SFWM) in nonlinear optical materials are practical and versatile methods to generate narrowband time-energy entangled photon pairs. Time- energy entangled photons with tailored spectro-temporal properties are particularly useful for efficient quantum optical interfaces. In this work we study the generation of photon pairs in cavity-assisted SPDC and SFWM for the general case of off-resonant conversion, namely, when the frequencies of the generated photons do not match the cavity resonances. Such a frequency mismatch in particular depends on temperature and requires an additional control in the experiment. First, we propose a generic model, for description of cavity-assisted SPDC and SFWM. We show that in both processes the mismatch reduces the generation rate of photons, distorts the spectrum and the auto-correlation function of the generated fields, as well as affects the photon generation dynamics. Second, we verify the results experimentally using parametric generation of photon pairs in a nonlinear whispering gallery mode resonator (WGMR) as an experimental platform with controlled frequency mismatch. Our work reveals the role of the frequency mismatch in the photon generation process and shows a way to control it. Obtained results constitute one more step in the direction of full control over the spectro-temporal properties of entangled photon pairs and the heralded generation of single-photon pulses with a tailored temporal mode.

Focusing characteristics of a 4 pi parabolic mirror light-matter interface

Lucas Alber, Martin Fischer, Marianne Bader, Klaus Mantel, Markus Sondermann, Gerd Leuchs

Background: Focusing with a 4 pi parabolic mirror allows for concentrating light from nearly the complete solid angle, whereas focusing with a single microscope objective limits the angle cone used for focusing to half solid angle at maximum. Increasing the solid angle by using deep parabolic mirrors comes at the cost of adding more complexity to the mirror's fabrication process and might introduce errors that reduce the focusing quality. Methods: To determine these errors, we experimentally examine the focusing properties of a 4p parabolic mirror that was produced by single-point diamond turning. The properties are characterized with a single Yb-174(+) ion as a mobile point scatterer. The ion is trapped in a vacuum environment with a movable high optical access Paul trap. Results: We demonstrate an effective focal spot size of 209 nm in lateral and 551 nm in axial direction. Such tight focusing allows us to build an efficient light-matter interface. Conclusion: Our findings agree with numerical simulations incorporating a finite ion temperature and interferometrically measured wavefront aberrations induced by the parabolic mirror. We point at further technological improvements and discuss the general scope of applications of a 4p parabolic mirror.

Preparation of single photon states with rising exponential shape

Bharath Srivathsan, Curpreet Kaur Gulati, Victor Leong, Mathias Seidler, Matthias Steiner, Alessandro Cere, Christian Kurtsiefer

We prepare single photons with a temporal envelope with rising exponential shape, resembling the time-reversed version of photons from the spontaneous decay process using a parametric conversion process in a cold atomic vapor. The mechanism is based on correlated photon pair preparation and heralding of one photon by the other one after engineering the temporal envelope of the herald.(1) Such a temporal single photon profile is ideal for absorption by a two level system.(2, 3) We demonstrate this in an experiment showcasing the absorption by a single Rubidium atom.(4)

Shifting the phase of a coherent beam with a Yb-174(+) ion: influence of the scattering cross section

Martin Fischer, Bharath Srivathsan, Lucas Alber, Markus Weber, Markus Sondermann, Gerd Leuchs

We discuss and measure the phase shift imposed onto a radially polarized light beam when focusing it onto an Yb-174(+) ion. In the derivation of the expected phase shifts, we include the properties of the involved atomic levels. Furthermore, we emphasize the importance of the scattering cross section and its relation to the efficiency for coupling the focused light to an atom. The phase shifts found in the experiment are compatible with the expected ones when accounting for known deficiencies of the focusing optics and the motion of the trapped ion at the Doppler limit of laser cooling (Hensch and Schawlow in Opt Commun 13:68-69,1975).

Resonant photo-ionization of Yb+ to Yb2+

Simon Heugel, Martin Fischer, Vladimir Elman, Robert Maiwald, Markus Sondermann, Gerd Leuchs

We demonstrate the controlled creation of a Yb-174(2+) ion by photo-ionizing Yb-174(+) with weak continuous-wave lasers at ultraviolet wavelengths. The photo-ionization is performed by resonantly exciting transitions of the Yb-174(+) ion in three steps. Starting from an ion crystal of two laser-cooled Yb-174(+) ions localized in a radio-frequency trap, the verification of the ionization process is performed by characterizing the properties of the resulting mixed-species ion-crystal. The obtained results facilitate fundamental studies of physics involving Yb2+ ions.

Optical trapping of nanoparticles by full solid-angle focusing

Vsevolod Salakhutdinov, Markus Sondermann, Luigi Carbone, Elisabeth Giacobino, Alberto Bramati, Gerd Leuchs

Photon-Atom Coupling with Parabolic Mirrors

Markus Sondermann, Gerd Leuchs

Efficient coupling of light to single atomic systems has gained considerable attention over the past decades. This development is driven by the continuous growth of quantum technologies. The efficient coupling of light and matter is an enabling technology for quantum information processing and quantum communication. And indeed, in recent years much progress has been made in this direction. But applications aside, the interaction of photons and atoms is a fundamental physics problem. There are various possibilities for making this interaction more efficient, among them the apparently 'natural' attempt of mode-matching the light field to the free-space emission pattern of the atomic system of interest. Here we will describe the necessary steps of implementing this mode-matching with the ultimate aim of reaching unit coupling efficiency. We describe the use of deep parabolic mirrors as the central optical element of a free-space coupling scheme, covering the preparation of suitable modes of the field incident onto these mirrors as well as the location of an atom at themirror's focus. Furthermore, we establish a robust method for determining the efficiency of the photon-atom coupling.

Efficient saturation of an ion in free space

Martin Fischer, Marianne Bader, Robert Maiwald, Andrea Golla, Markus Sondermann, Gerd Leuchs

We report on the demonstration of a lightmatter interface coupling light to a single Yb-174(+) ion in free space. The interface is realized through a parabolic mirror partially surrounding the ion. It transforms a La-guerre- Gaussian beam into a linear dipole wave converging at the mirror's focus. By measuring the non-linear response of the atomic transition, we deduce the power required for reaching an upper-level population of 1/4 to be 692 +/- 20pW at half linewidth detuning from the atomic resonance. Performing this measurement while scanning the ion through the focus provides a map of the focal intensity distribution. From the measured power, we infer a coupling efficiency of 7.2 +/- 0.2% on the linear dipole transition when illuminating from half solid angle, being among the best coupling efficiencies reported for a single atom in free space.

Generation of entangled matter qubits in two opposing parabolic mirrors

N. Trautmann, J. Z. Bernad, M. Sondermann, G. Alber, L. L. Sanchez-Soto, G. Leuchs

We propose a scheme for the remote preparation of entangled matter qubits in free space. For this purpose, a setup of two opposing parabolic mirrors is considered, each one with a single ion trapped at its focus. To get the required entanglement in this extreme multimode scenario, we take advantage of the spontaneous decay, which is usually considered as an apparent nuisance. Using semiclassical methods, we derive an efficient photon-path representation to deal with this problem. We also present a thorough examination of the experimental feasibility of the scheme. The vulnerabilities arising in realistic implementations reduce the success probability, but leave the fidelity of the generated state unaltered. Our proposal thus allows for the generation of high- fidelity entangled matter qubits with high rate.

SCATTERING OF AN EXPONENTIAL PULSE BY A SINGLE ATOM

Markus Sondermann, Gerd Leuchs

We discuss the scattering of a light pulse by a single atom in free space using a purely semi-classical framework. The atom is treated as a linear elastic scatterer allowing to treat each spectral component of the incident pulse separately. For an increasing exponential pulse with a dipole radiation pattern incident from full solid angle the spectrum resulting from interference of incident and scattered components is a decreasing exponential pulse.*

Full Solid Angle Ion-Light Interface

Martin Fischer, Robert Maiwald, Andrea Golla, Marianne Bader, Markus Sondermann, Gerd Leuchs

We present an optical system covering 81 % of the solid angle into which an ion emits light. With this configuration we focus light close to the diffraction limit, while also approaching optimal light matter coupling. (C) 2013 Optical Society of America

The phase shift induced by a single atom in free space

M. Sondermann, G. Leuchs

In this article we theoretically study the phase shift a single atom imprints onto a coherent state light beam in free space. The calculations are performed in a semiclassical framework. The key parameters governing the interaction and thus the measurable phase shift are the solid angle from which the light is focused onto the atom and the overlap of the incident radiation with the atomic dipole radiation pattern. The analysis includes saturation effects and discusses the associated Kerr-type non-linearity of a single atom.

Lightmatter interaction in free space

Gerd Leuchs, Markus Sondermann

We review recent experimental advances in the field of efficient coupling of single atoms and light in free space. Furthermore, a comparison of efficient free space coupling and strong coupling in cavity quantum electrodynamics (QED) is given. Free space coupling does not allow for observing oscillatory exchange between the light field and the atom which is the characteristic feature of strong coupling in cavity QED. Like cavity QED, free space QED does, however, offer full switching of the light field, a 180 degrees phase shift conditional on the presence of a single atom as well as 100% absorption probability of a single photon by a single atom. Furthermore, free space cavity QED comprises the interaction with a continuum of modes.

Simulating single-photon-single-atom absorption experiments with an optical resonator

Marianne Bader, Simon Heugel, Alexander Chekhov, Markus Sondermann, Gerd Leuchs

Efficient coupling to an optical resonator by exploiting time-reversal symmetry

M. Bader, S. Heugel, A. L. Chekhov, M. Sondermann, G. Leuchs

The interaction of a cavity with an external field is symmetric under time reversal. Thus, coupling to a resonator is most efficient when the incident light is the time reversed version of a free cavity decay, i.e. when it has a rising exponential shape matching the cavity lifetime. For light entering the cavity from only one side, the maximally achievable coupling efficiency is limited by the choice of the cavity mirrors' reflectivities. Such an empty-cavity experiment serves also as a model system for single-photon single-atom absorption dynamics. We present experiments coupling exponentially rising pulses to a cavity system which allows for high coupling efficiencies. The influence of the time constant of the rising exponential is investigated as well as the effect of a finite pulse duration. We demonstrate coupling 94% of the incident TEM00 mode into the resonator.

Time-reversal symmetry in optics

G. Leuchs, M. Sondermann

The utilization of time-reversal symmetry in designing and implementing (quantum) optical experiments has become more and more frequent over the last few years. We review the basic idea underlying time-reversal methods, illustrate it with several examples and discuss a number of implications.

Generation of a wave packet tailored to efficient free space excitation of a single atom

A. Golla, B. Chalopin, M. Bader, I. Harder, K. Mantel, R. Maiwald, N. Lindlein, M. Sondermann, G. Leuchs

We demonstrate the generation of an optical dipole wave suitable for the process of efficiently coupling single quanta of light and matter in free space. We employ a parabolic mirror for the conversion of a transverse beam mode to a focused dipole wave and show the required spatial and temporal shaping of the mode incident onto the mirror. The results include a proof of principle correction of the parabolic mirror's aberrations. For the application of exciting an atom with a single photon pulse, we demonstrate the creation of a suitable temporal pulse envelope. We infer coupling strengths of 89% and success probabilities of up to 87% for the application of exciting a single atom for the current experimental parameters.

Generation and Characterization of Multimode Quantum Frequency Combs

Olivier Pinel, Pu Jian, Renne Medeiros de Araujo, Jinxia Feng, Benoit Chalopin, Claude Fabre, Nicolas Treps

Multimode nonclassical states of light are an essential resource in quantum computation with continuous variables, for example, in cluster state computation. We report in this Letter the first experimental evidence of a multimode nonclassical frequency comb in a femtosecond synchronously pumped optical parametric oscillator. In addition to a global reduction of its quantum intensity fluctuations, the system features quantum correlations between different parts of its frequency spectrum. This allows us to show that the frequency comb is composed of several uncorrelated eigenmodes having specific spectral shapes, two of them at least being squeezed, and to characterize their spectral shapes.

Dipole pulse theory: Maximizing the field amplitude from 4 pi focused laser pulses

Ivan Gonoskov, Andrea Aiello, Simon Heugel, Gerd Leuchs

We present a class of exact nonstationary solutions of Maxwell equations in vacuum from dipole pulse theory: electric and magnetic dipole pulses. These solutions can provide for a very efficient focusing of electromagnetic field and can be generated by 4 pi focusing systems, such as parabolic mirrors, by using radially polarized laser pulses with a suitable amplitude profile. The particular cases of a monochromatic dipole wave and a short dipole pulse with either quasi-Gaussian or Gaussian envelopes in the far-field region are analyzed and compared in detail. As a result, we propose how to increase the maximum field amplitude in the focus by properly shaping the temporal profile of the input laser pulses with given main wavelength and peak power.

Collecting more than half the fluorescence photons from a single ion

Robert Maiwald, Andrea Golla, Martin Fischer, Marianne Bader, Simon Heugel, Benoit Chalopin, Markus Sondermann, Gerd Leuchs

We demonstrate the trapping of a single ion in the focus of a deep parabolic mirror that covers 81% of the solid angle surrounding the ion. Accounting for the reflectivity of the mirror we infer a photon collection efficiency of 54.8% for our setup. The underlying experimentally detected maximum fluorescence rate is 1.91 x 10(6) s(-1) from a single Yb-174(+) ion, mainly limited by the quantum efficiency of our photon detector. Besides the high collection efficiency, the integration of an ion trap into a parabolic mirror is a key ingredient for efficient coupling of light to a single ion in free space.

Direct generation of a multi-transverse mode non-classical state of light

Benoit Chalopin, Francesco Scazza, Claude Fabre, Nicolas Treps

Quantum computation and communication protocols require quantum resources which are in the continuous variable regime squeezed and/or quadrature entangled optical modes. To perform more and more complex and robust protocols, one needs sources that can produce in a controlled way highly multimode quantum states of light. One possibility is to mix different single mode quantum resources. Another is to directly use a multimode device, either in the spatial or in the frequency domain. We present here the first experimental demonstration of a device capable of producing simultanuously several squeezed transverse modes of the same frequency and which is potentially scalable. We show that this device, which is an Optical Parametric Oscillator using a self-imaging cavity, produces a multimode quantum resource made of three squeezed transverse modes. (C) 2011 Optical Society of America

Robustness of bipartite Gaussian entanglement subject to channel losses

A. S. Villar, F. A. S. Barbosa, A. S. Coelho, A. J. de Faria, K. N. Cassemiro, P. Nussenzveig, M. Martinelli

Entanglement as a collective property of quantum systems follows its own dynamics as environmental disturbances enter the quantum channel. It can either withstand undesired external influences or completely vanish even for very small disturbances. Only the first kind of quantum states are suitable for real applications in quantum networks. We show the conditions under which a bipartite Gaussian state remains entangled under partial energy loss of one party.

Generation of Kerr non-Gaussian motional states of trapped ions

M. Stobinska, A. S. Villar, G. Leuchs

Non-Gaussian states represent a powerful resource for quantum information protocols in the continuous variables regime. Cat states, in particular, have been produced in the motional degree of freedom of trapped ions by controlled displacements dependent on the ionic internal state. An alternative method harnesses the Kerr nonlinearity naturally present in this kind of system. We perform detailed calculations confirming its feasibility for typical experimental conditions. Additionally, this method permits generation of all other complex non-Gaussian states with negative Wigner functions resulting from Kerr nonlinear interaction. Especially, superpositions of several coherent states are achieved at a fraction of the time necessary to produce the cat state. Copyright (C) EPLA, 2011

Disentanglement in bipartite continuous-variable systems

F. A. S. Barbosa, A. J. de Faria, A. S. Coelho, K. N. Cassemiro, A. S. Villar, P. Nussenzveig, M. Martinelli

Entanglement in bipartite continuous-variable systems is investigated in the presence of partial losses such as those introduced by a realistic quantum communication channel, e. g., by propagation in an optical fiber. We find that entanglement can vanish completely for partial losses, in a situation reminiscent of so-called entanglement sudden death. Even states with extreme squeezing may become separable after propagation in lossy channels. Having in mind the potential applications of such entangled light beams to optical communications, we investigate the conditions under which entanglement can survive for all partial losses. Different loss scenarios are examined, and we derive criteria to test the robustness of entangled states. These criteria are necessary and sufficient for Gaussian states. Our study provides a framework to investigate the robustness of continuous-variable entanglement in more complex multipartite systems.

On the Analogy between a Single Atom and an Optical Resonator

S. Heugel, A. S. Villar, M. Sondermann, U. Peschel, G. Leuchs

A single atom in free space can have a strong influence on a light beam and a single photon can have a strong effect on a single atom in free space. Regarding this interaction, two conceptually different questions can be asked: can a single atom fully absorb a single photon and can a single atom fully reflect a light beam. The conditions for achieving the full effect in either case are different. Here we discuss related questions in the context of an optical resonator. When shaping a laser pulse properly it will be fully absorbed by an optical resonator, i.e., no light will be reflected and all the pulse energy will accumulate inside the resonator before it starts leaking out. We show in detail that in this case the temporal pulse shape has to match the time-reversed pulse obtained by the cavity's free decay. On the other hand a resonator, made of highly reflecting mirrors which normally reflect a large portion of any incident light, may fully transmit the light, as long as the light is narrow band and resonant with the cavity. The analogy is the single atom-normally letting most of the light pass-which under special conditions may fully reflect the incident light beam. Using this analogy we are able to study the effects of practical experimental limitations in the atom-photon coupling, such as finite pulses, bandwidths, and solid angle coverage, and to use the optical resonator as a test bed for the implementation of the quantum experiment.

Robustness of bipartite Gaussian entangled beams propagating in lossy channels

F. A. S. Barbosa, A. S. Coelho, A. J. de Faria, K. N. Cassemiro, A. S. Villar, P. Nussenzveig, M. Martinelli

Subtle quantum properties offer exciting new prospects in optical communications. For example, quantum entanglement enables the secure exchange of cryptographic keys(1) and the distribution of quantum information by teleportation(2,3). Entangled bright beams of light are increasingly appealing for such tasks, because they enable the use of well-established classical communications techniques(4). However, quantum resources are fragile and are subject to decoherence by interaction with the environment. The unavoidable losses in the communication channel can lead to a complete destruction of entanglement(5-8), limiting the application of these states to quantum-communication protocols. We investigate the conditions under which this phenomenon takes place for the simplest case of two light beams, and analyse characteristics of states which are robust against losses. Our study sheds new light on the intriguing properties of quantum entanglement and how they may be harnessed for future applications.

The quantum vacuum at the foundations of classical electrodynamics

G. Leuchs, A. S. Villar, L. L. Sanchez-Soto

In the classical theory of electromagnetism, the permittivity epsilon (0) and the permeability mu (0) of free space are constants whose magnitudes do not seem to possess any deeper physical meaning. By replacing the free space of classical physics with the quantum notion of the vacuum, we speculate that the values of the aforementioned constants could arise from the polarization and magnetization of virtual pairs in vacuum. A classical dispersion model with parameters determined by quantum and particle physics is employed to estimate their values. We find the correct orders of magnitude. Additionally, our simple assumptions yield an independent estimate for the number of charged elementary particles based on the known values of epsilon (0) and mu (0) and for the volume of a virtual pair. Such an interpretation would provide an intriguing connection between the celebrated theory of classical electromagnetism and the quantum theory in the weak-field limit.

Prospect for detecting squeezed states of light created by a single atom in free space

Magdalena Stobinska, Markus Sondermann, Gerd Leuchs

We discuss the possibilities of studying in detail the dynamics of spontaneous emission of a single photon by a single atom and measuring the transient degree of squeezing by means of full solid angle fluorescence detection. (C) 2009 Elsevier B.V. All rights reserved.

Optomechanical stochastic resonance in a macroscopic torsion oscillator

F. Mueller, S. Heugel, L. J. Wang

Linear mechanical oscillators have been applied to measure very small forces, mostly with the help of noise suppression. In contrast, adding noise to nonlinear oscillators can improve the measurement conditions. Here, this effect of stochastic resonance is demonstrated in a macroscopic torsion oscillator, for an optomechanical nonlinear potential. The signal output is enhanced for a subthreshold electronic signal. This nonlinear oscillator serves as a model system for the enhancement of signal-to-noise ratio in high precision optomechanical experiments.

Three-Color Entanglement

A. S. Coelho, F. A. S. Barbosa, K. N. Cassemiro, A. S. Villar, M. Martinelli, P. Nussenzveig

Entanglement is an essential quantum resource for the acceleration of information processing as well as for sophisticated quantum communication protocols. Quantum information networks are expected to convey information from one place to another by using entangled light beams. We demonstrated the generation of entanglement among three bright beams of light, all of different wavelengths (532.251, 1062.102, and 1066.915 nanometers). We also observed disentanglement for finite channel losses, the continuous variable counterpart to entanglement sudden death.

Extra phase noise from thermal fluctuations in nonlinear optical crystals

J. E. S. Cesar, A. S. Coelho, K. N. Cassemiro, A. S. Villar, M. Lassen, P. Nussenzveig, M. Martinelli

We show theoretically and experimentally that scattered light by thermal phonons inside a second-order nonlinear crystal is the source of additional phase noise observed in optical parametric oscillators. This additional phase noise reduces the quantum correlations and has hitherto hindered the direct production of multipartite entanglement in a single nonlinear optical system. We cooled the nonlinear crystal and observed a reduction in the extra noise. Our treatment of this noise can be successfully applied to different systems in the literature.

Stylus ion trap for enhanced access and sensing

Robert Maiwald, Dietrich Leibfried, Joe Britton, James C. Bergquist, Gerd Leuchs, David J. Wineland

Small, controllable, highly accessible quantum systems can serve as probes at the single-quantum level to study a number of physical effects, for example in quantum optics or for electric- and magnetic-field sensing. The applicability of trapped atomic ions as probes is highly dependent on the measurement situation at hand and thus calls for specialized traps. Previous approaches for ion traps with enhanced optical access included traps consisting of a single ring electrode(1,2) or two opposing endcap electrodes(2,3). Other possibilities are planar trap geometries, which have been investigated for Penning traps(4,5) and radiofrequency trap arrays(6-8). By not having the electrodes lie in a common plane, the optical access can be substantially increased. Here, we report the fabrication and experimental characterization of a novel radiofrequency ion trap geometry. It has a relatively simple structure and provides largely unrestricted optical and physical access to the ion, of up to 96% of the total 4 pi solid angle in one of the three traps tested. The trap might find applications in quantum optics and field sensing. As a force sensor, we estimate sensitivity to forces smaller than 1 yN Hz(-1/2).

Interferometric null test of a parabolic reflector generating a Hertzian dipole field

G. Leuchs, K. Mantel, A. Berger, H. Konermann, M. Sondermann, U. Peschel, N. Lindlein, J. Schwider

Interferometric surface tests of stigmatic aspherics can be carried out in a null test configuration. Null tests require reference null elements either plane or spherical surfaces or both. A parabolic reflector transforms a plane into a spherical wave which converges to the focus of the paraboloid. Therefore, a spherical ball lens or a steel ball can be placed into the focus enabling a double-pass geometry for the null test. Here a Fizeau interferometer geometry has been selected in order to guarantee invariance against polarization distortions under the assumption that radially polarized laser light is used for the interferometer. Radial polarized light is necessary to mimic a Hertzian dipole field. Due to the extreme solid angle produced by the paraboloid the alignment of the setup is very critical and needs auxiliary systems for the control. Aberrations caused by misalignments are removed via fitting of suitable functionals provided through ray-trace simulations. It turned out that the usual vector approximations fail under these extreme circumstances. Test results arc given for a paraboloid with 2mm focal length transforming a plane wave into a near dipole wave comprising a solid angle of about 3,4 pi.

A new 4 pi geometry optimized for focusing on an atom with a dipole-like radiation pattern

N. Lindlein, R. Maiwald, H. Konermann, M. Sondermann, U. Peschel, G. Leuchs

Focusing electromagnetic radiation efficiently onto an atom requires an open geometry, which is as close to the full solid angle as possible. Additionally, the radiant intensity should be as close as possible to a dipole radiation in order to have a similar field distribution as in the emission process. Here, we propose to make use of a novel combination of a parabolic mirror and a diffractive optical element.

Analysis and optimization of coupling to external cavities in feedback experiments with vertical-cavity surface-emitting lasers

K. F. Jentsch, M. Sondermann, T. Ackemann

The feedback strength is a crucial parameter for feedback experiments using semiconductor lasers. In this article, the coupling efficiency of the field of vertical-cavity surface-emitting lasers (VCSELs) to external cavities containing one collimating lens has been analyzed in detail using ABCD-matrix methods. It is found that for a given set of parameters there are two distinct, experimentally realizable positions of the collimating lens which allow for optimal coupling, if the cavity length is sufficiently small. The predictions are verified in experiments using single-transverse-mode VCSELs. The obtained coupling efficiencies exceed 70%. (c) 2007 Elsevier B.V. All rights reserved.

Design of a mode converter for efficient light-atom coupling in free space

M. Sondermann, R. Maiwald, H. Konermann, N. Lindlein, U. Peschel, G. Leuchs

In this article, we describe how to develop a mode converter that transforms a plane electromagnetic wave into an inward-moving dipole wave. The latter one is intended to bring a single atom or ion from its ground state to an excited state by absorption of a single photon wave packet with near-100% efficiency.