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Programm und Abstracts der Sitzung Q 9

Ein Einweg-Quantenrechner

•Robert Raussendorf und Hans J. Briegel
Theresienstrasse 37, 80333 München

Wir zeigen, dass eine spezielle Klasse hochverschränkter quantenmechanischer Zustände, die Clusterzustände [1], als Quantenkomputer dienen kann [2]. Es wird dargelegt, wie ein universeller Satz von Quantengattern - CNOT-Gatter und beliebige Ein-Qubit-Rotationen - allein durch Ein-Qubit- Messungen realisiert werden kann. Diese Gatter können zu Netzwerken kombiniert werden. Clusterzustände bilden ein Substrat für quantenlogische Netzwerke. Das Netzwerk wird dem Clusterzustand durch die Einteilchenmessungen aufgeprägt. Andererseits wird der Clusterzustand durch die Rechnung aufgebraucht, da die Messungen die Verschränkung in ihm zerstören. Somit stellen Clusterzustände eine Resource für Quantencomputing dar. Clusterzustände können als Einweg-Quantenrechner angesehen werden. Die Menge der vorgenommenen Einteilchen-Messungen bildet dabei das Programm.

[1] Hans J. Briegel and R. Raussendorf, Persistent entanglement in arrays of interacting particles. quant-ph/0004051 (2000). [2] R. Raussendorf and H.J. Briegel, Quantum computing via measurements only. quant-ph/0010033 (2000).

Information Flow in Qubit Lattices

•Daniel E Browne, Robert Raussendorf und Hans J Briegel
Theoretische Physik, Ludwig-Maximilians-Universität, Theresienstr. 37, D-80333 München.

Cluster states are highly entangled multi-particle states which occur naturally in a qubit lattice with an Ising-type interaction. Measurements of particles in the cluster exhibit certain quantum mechanical and classical correlations. These allow the processing of quantum information on the cluster through measurement alone, making a ``one-way'' quantum computer [1]. More generally, due to these correlations the process of measuring is accompanied by a flow of information. We construct a ``classical'' counterpart to the cluster state exhibiting the classical part of the correlations. In doing so we gain insight in the character of entanglement as a resource for performing quantum algorithms.

[1] R. Raussendorf and H. J. Briegel, quant-ph/0010033 (2000).

The Schmidt measure as a tool for quantifying multi-particle entanglement

•Jens Eisert^1,2 und Hans-J. Briegel^3
1Institut für Physik, Universität Potsdam, 14469 Potsdam, Germany
²Optics Section, Blackett Laboratory, Imperial College, London SW7 2BZ, United Kingdom
³Sektion Physik, Ludwig-Maximilians-Universität München, 80333 München, Germany

We present a measure of quantum entanglement which is capable of quantifying the degree of entanglement of a general multi-partite quantum system. Based on a generalization of the Schmidt rank of a pure state, this measure is defined on the full state space and is shown to be an entanglement monotone. That is, it cannot increase on average under local quantum operations with classical communication and under mixing. Partly due to the fact that it is a non-continuous and coarse grained measure, it can be calculated exactly for a large class of mixed states. In particular, it provides a detailed classification of mixed states in the multi-party domain.

Single-atom multi-photon entanglement mediated by a high-finesse Cavity

•Thomas Legero, Markus Hennrich, Stefan Nussmann, Axel Kuhn und Gerhard Rempe
Max-Planck-Institut für Quantenoptik, D-85748 Garching

Starting from a proposal of Gheri and Ritsch [1] we investigate the experimental feasibility of an entanglement between the internal states of a single atom and a large number of optical photons.

A single atom strongly coupled to a high-finesse optical cavity allows to control the path of the photons impinging the cavity. This can be achieved with two long-lived atomic states. One of these states leads to reflection of the photons, the other to transmission. If the atom is prepared in a quantum superposition of the two states, an entanglement of atomic state and photon path will be generated.

To show this entanglement, the atom-cavity system should be used as the first beamsplitter of a Mach-Zehnder interferometer. With the path of the photons stored in the internal atomic state, no fringes will be visible at the output ports. However, a suitable measurement performed on the atom allows to erase this ``which-way'' information, and in correlation with this measurement, the photons detected at the output ports should show interference fringes, which depend on the phase difference of the two paths. Furthermore, we show that the fringe spacing will depend on the number of photons interacting with the atom-cavity system.

[1] K.M. Gheri and H.Ritsch, Phys.Rev.A 56 , 3187 (1997)

Quantum optical weak measurements can visualize photon dynamics in real time

•Thomas Konrad, Jürgen Audretsch und Artur Scherer
Fakultät für Physik der Universität Konstanz, Germany

An experiment is proposed to visualize stroboscopically in real time the dynamics of a photon oscillating between two cavities. The visualization is implemented by a sequence of weak measurements (POVM), which are carried out by probing one of the cavities with a Rydberg atom and detecting a resulting phase shift by Ramsey interferometry. This way to measure the number of photons in a cavity was experimentally realized by Brune et al. . We suggest a feedback mechanism which minimizes the disturbance due to the measurement and enables a detection of the original evolution of the radiation field.

[1

Multiparticle entanglement purification

•Aldo Delgado¹, Gernot Alber¹ und Igor Jex^2
1Abteilung fuer Quantenphysik, Universitaet Ulm
²Department of Physics, FNSPE Czech Technical University Prague

Entanglement plays an important role in quantum information processing. It allows processes such as quantum teleportation, quantum cryptography and quantum state and key sharing. Unfortunately, entanglement is a very fragile resource. Any coupling with the environment leads to dissipative effects which turn entangled pure states into mixed states. However, the environment does not always destroy the entanglement completely. In this case it is possible to use entanglement purification protocols which produce maximally entangled pure states from mixed states. In this contribution we present an entanglement purification protocol based on a non-linear quantum operation and the Fourier transformation. This protocol is able to purify Werner states up to the separability limit in arbitrary finite dimensional Hilbert spaces and achieves a higher efficiency than previously known protocols [1]. Motivated by recent applications of multiparticle entanglement to quantum state and key sharing we extend the protocol to the direct purification of Aharonov states and GHZ states. In the latter case the protocol has a better range of convergence than the protocol proposed in Ref. [2].

[1] M. Horodecki and P. Horodecki, Phys. Rev. A 59, 4206 (1999)

[2] M. Murao, M. B. Plenio, S. Popescu, V. Vedral and P. L. Knight Phys. Rev. A 57, R4075 (1998)

Conditional teleportation with entangled single-photon states

•Jens Clausen, Ludwig Knöll und Dirk-Gunnar Welsch
Friedrich-Schiller-Universität Jena, Theoretisch-Physikalisches Institut, Max-Wien-Platz 1, D-07743 Jena, Germany

We study the conditional teleportation of single-mode quantum states whose Fock-expansion breaks off at a given number N. Instead of a two-mode squeezed vacuum state the two parties share a sequence of N pulses each containing a single photon which has been spatially split using a beam splitter. Alice and Bob perform zero and single photon number measurements. If the appropriate measurement outcome is yielded, the teleportation is completed without need to further manipulate the quantum state obtained at Bob's receiving station. The information transmitted via the classical channel is therefore reduced to Alice's confirmation that the correct measurement result has been obtained. Since the success probability decreases exponentially with increasing N, attention is limited to states containing only few photons.

Dissipation-assisted adiabatic passage into an entangled state

•Almut Beige und Gerhard Rempe
Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching

We propose a new scheme to entangle two spatially separated atoms in a dissipative environment in a controlled way. To do so, the atoms are moved slowly in and out of an optical cavity. In addition, only a single laser is required which does not need to address each atom separately.

The scheme is based on the existence of dark states in which the atoms do not interact with the cavity mode and which can correspond to highly entangled atomic states. Initially in a dark state, the atoms remain always decoupled from the cavity mode. The system follows the dark state adiabatically which changes in the same way as the system parameters do.

A high decay rate of photons inside the cavity mode can improve the fidelity of the prepared state. Deviations from the dark state are then damped away during the no-photon time evolution of the system. Another advantage of our scheme is that spontaneous emission by the atoms is highly reduced and that it is stable against fluctuations of most system parameters.

Bright EPR-entangled beams

•Christine Silberhorn¹, Michael Langer¹, Ping Koy Lam^2,1, Natalia Korolkova¹ und Gerd Leuchs^1
2Department of Physics, Faculty of Science, ANU, ACT 0200, Australia
¹Zentrum für Moderne Optik, Universität Erlangen, Staudtstr. 7 / B2, 91058 Erlangen, Germany

We report on a new source for multi-photon EPR-entanglement [1]. For the generation of bright entangled beams the Kerr nonlinearity in an optical fibre is employed to produce two independently amplitude squeezed beams. To transform the squeezing of the beams into EPR-entanglement the light fields are superimposed at a 50:50 beam splitter. The quality of the EPR-entanglement generated in this interference depends on the initial squeezing of the two input beams. In the experiment the 130 fs pulses are injected into an asymmetric fibre Sagnac interferometer. This is operated simultaneously at two orthogonal polarizations to obtain the two squeezed beams for the interference. The pulses at the output ports of the beam splitter show an anti-correlation of 4.0 ±0.2 dB below the quantum limit for the amplitude and a correlation of 4.0 ±0.4 dB for the phase quadrature. For the demonstration of EPR-entanglement the product of the inferred uncertainties for one beam is calculated to be 0.64 ±0.08 well below the EPR limit of unity. The state is proven to fulfill the Peres-Horodecki criterion for nonseparability of continuous variable systems by the sum of the inferred variances 0.40 ±0.02 < 1 [2].

[1] Ch. Silberhorn et al, PRL, submitted (2000).

[2] M. D. Reid et al, PRL 60,2731 (1988); L. Duan, et al, PRL 84, 2722, (2000); Simon, PRL 84, 2726, (2000).

Decomposition of Mixed Quantum States

•Alexander Otte und Günter Mahler
Universität Stuttgart, Institut für Theoretische Physik I, Pfaffenwaldring 57/IV, 70550 Stuttgart

The decomposition of non-pure quantum states into a mixture of product states has for long been a problem in quantum mechanics and is of special importance in the context of quantum information theory.

We propose a simple constructive method to decompose a separable mixed density matrix into pure product states. It is an iterative method with an intuitive geometrical interpretation. The result can be transformed to give a decomposition into no more than n² pure product states, if n is the dimension of the overall Hilbert-space. We further want to discuss the interesting point of generality for our proposed method as a separability criterion.

Estimating quantum channels

•Dietmar G. Fischer, Holger Mack, Markus A. Cirone und Matthias Freyberger
Abteilung für Quantenphysik, Universität Ulm

Quantum channels are a widely discussed topic in quantum information. However, mainly the properties of previously known quantum channels have been investigated yet. We look at the inverse problem: How can we determine a priori unknown quantum channels from finite resources? We present efficient schemes to estimate the parameters characterizing a quantum channel and discuss the role of the cost function and entanglement. It will turn out that entanglement can serve as an essential resource that leads to an improved estimation quality.

We acknowledge financial support by the Deutsche Forschungsgemeinschaft.

Quantum correlations in fermionic and bosonic systems

•Kai Eckert¹, Maciej Lewenstein¹ und John Schliemann^2
1Institut fuer Theoretische Physik, Universität Hannover, Appelstr. 2, D-30167 Hannover, Germany
²Department of Physics, The University of Texas, Austin, TX 78712

The characterization of quantum correlations at distances where the indistinguishable character of the particles involved has to be taken into account is important for proposals of quantum information processing based on quantum dots technology.

Quantum correlations in two-fermion systems have recently been classified[1]. We generalize these results to special systems consisting of more than two fermions, especially analyzing criteria for possible slater decompositions. We also extend the results to bosonic systems.

[1] J. Schliemann, J.I. Cirac, M. Ku\'s, M. Lewenstein, D. Loss, quant-ph/0012094

Towards practical Quantum Cryptography

•Matthäus Halder¹, David Weikersdorfer¹, Patrick Zarda², Christian Kurtsiefer¹ und Harald Weinfurter^1,2
1Sektion Physik der LMU München, Schellingstr. 4/III, 80799 München
²Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching

Quantum Cryptography bases provable security on fundamental laws of quantum mechanics. It will become the first practical application of quantum communication as soon as compact and stable systems have been developed.

We present first tests of new modules where all optical components necessary for the BB84 protocol are assembled within 5×5 cm². In the sender module (Alice), four pulsed laser diodes (853nm) produce the four necessary polarization states (H,V,+45^°,-45^°) and are coupled into a single mode optical fiber. On the other side, the receiver (Bob) analyzes the incoming polarized photons randomly in the (H,V) or (+45^°,-45^°) basis without the need for active optical components. Synchronisation between Alice and Bob and polarization control is realized via the quantum channel.

Both modules (including optics and electronics) will find place in compact quantum cryptography modems, or possibly even on pc-cards and will enable fast (keyrate some kHz) quantum key generation.

Quantum messages of variable length

•Kim Bostroem
Kim Bostroem, Universitaet Potsdam, Institut fuer Physik, Am Neuen Palais 10, 14469 Potsdam, Germany

In information theory, codewords of variable length provide an important approach to information measures and compression algorithms. Though while in classical information theory it is not a problem to consider messages of variable length, conceptual difficulties arise in the quantum case. The standard restriction to block messages of fixed length in finite-dimensional Hilbert spaces prevent a straightforward treatment. These difficulties can be overcome by an appropriate theoretical framework allowing for quantum messages with components of arbitrary length. This way, quantum coding obtains some useful features, e.g. lossless compression and instantaneous coding.

Processing of quantum information with optical solitons

•Viktor V. Kozlov, Matthias Freyberger und Wolfgang P. Schleich
Abteilung für Quantenphysik, Universität Ulm

Optical solitons preserve their shape while propagating through a nonlinear dispersive fiber. This feature makes them attractive for the use in classical communication. A quantum soliton propagates in the same, undistorted fashion and can be used as an efficient carrier of quantum information through fiber networks. Several nonclassical properties such as the entanglement of quantum optical solitons are investigated from the point of view of a controlled engineering. Corresponding applications in quantum information science are discussed.

Highly stable wavelength reference for a near-infrared tunable monochromatic laser

•Ph. Leick, A. Keil, K. Abich, W. Neuhauser, Ch. Wunderlich und P. E. Toschek
Institut für Laser-Physik, Universität Hamburg, Jungiusstr. 9, 20355 Hamburg

Electronic and motional states of trapped Ba⁺ ions can be used to store and manipulate quantum information [1]. The E2 resonance, 6S_1/2 - 5D_5/2, (effective lifetime of the metastable state » 40 s) of a single laser cooled ¹³⁸Ba⁺-ion in a Paul trap is driven using a color centre laser ( l = 1762 nm) or, alternatively, an optical parametric oscillator. Implementation of quantum logic gates requires long-term frequency stability of these laser sources. This is achieved by locking the laser to a transmission mode of a cavity made of glass ceramics, suspended on springs in an ultra-high vacuum environment. Frictional damping of the cavity vibration permits to keep the setup compact. Measurements of absorption and emission spectra on the E2-transition characterize the residual instability of the cavity.

[1] B. Appasamy, Y. Stalgies, P. E. Toschek, Phys. Rev. Lett. 80, 2805 (1998).

Dipole Blockade and Quantum Information Processing in Mesoscopic Atomic Ensembles

•M. Fleischhauer¹, M. Lukin², R. Cote³, L. Duang⁴, D. Jaksch⁴, I. Cirac⁴ und P. Zoller^4
1FB Physik, Univ. Kaiserslautern
²ITAMP, Harvard-Smithsonian
³Univ. Conneticut
⁴Univ. Innsbruck

We describe a technique for manipulating quantum information stored in collective states of mesoscopic ensembles [1]. Quantum processing is accomplished by optical excitation into states with strong dipole-dipole interactions. The resulting ``dipole blockade'' can be used to inhibit transitions into all but singly excited collective states. This can be employed for a controlled generation of collective atomic spin states as well as non-classical photonic states and for scalable quantum logic gates. An example involving a cold Rydberg gas is analyzed.

[1] M. Lukin, M. Fleischhauer, R. Cote, L. M. Duan, D. Jaksch, J. I. Cirac and P. Zoller, quant-ph/0011028

Lifetime measurement as a test of cooperative effects in ion strings

•M. Block, A. Drakoudis, H. Garcia-Prima, H. Leuthner, X. Luo und G. Werth
Institut für Physik der Johannes Gutenberg Universität, Staudingerweg 7, 55099 Mainz

We have measured the lifetime of the metastable 3D_5/2 level in ⁴⁰Ca⁺. The effective lifetime represents an upper limit for the coherence time in proposed quantum computation schemes using linear chains of ions [1]. We used the method of quantum jumps of a single trapped ion and obtained 1100(18)ms [2] as the lifetime. In a second stage we performed measurements on strings of ten ions which were observed individually by a CCD camera. In some of the runs we found a substantially reduced lifetime compared to the single ion value under nominally identical conditions. In these cases we observed more frequently coincident decays of two or more ions than one expects for statistically independent particles within the time window given by our detection system. Since the distance of the ions is large compared to the wavelength (about 10l) superradiance is excluded. Similar observations have been made in 1986 [3] for few ions but recently a similar experiment at Oxford did not show enhanced coincidences for two and three ions [4]. We are currently performing further experiments to confirm our

[observation and to search for an explanation. 1] Cirac,

[Zoller, PRL 74,4091 (1995) 2] Block et al., EPJD 7,461

[(1999) 3] Sauter et al. Opt. Commun. 60, 287 (1986)

[4] Donald et al. Europhys. Lett. 51, 388 (2000)

Light-induced decoherence in the driven evolution of an atom

•Ch. Balzer, Th. Hannemann, W. Neuhauser, P. E. Toschek und Ch. Wunderlich
Institut für Laser-Physik, Universität Hamburg, Jungiusstr. 9, 20355 Hamburg

The hyperfine Larmor precession of an individual ground-state ¹⁷¹Yb⁺ ion has been driven by resonant rf pulses, alternated with probe pulses of 369 nm laser light that excite resonance scattering [1]. Upon varying the length of the drive pulse and averaging over 50 measurements, this rf-optical double resonance reveals hyperfine flopping (rf nutation). Weak residual resonance light present during the driving light pulse generates optical pumping from the coherently nutating ion state into the upper F=1 eigenstate, that reduces the amplitude of nutation and saturates the evolving ion in an inverted mixed state. Adjustment of the level of residual light amounts to the design of artificial decoherence, useful when studying pertubations of quantum information processing on individual ions.

[1] R. Huesmann, Ch. Balzer, Ph. Courteille, W. Neuhauser, P. E. Toschek, Phys. Rev. Lett. 82, 1611 (1999).

Low Temperature Spectroscopy on Single Defect Centers

•Fedor Jelezko, Uwe Gerken, Carsten Tietz und Joerg Wrachtrup
3.Physikalisches Institut, Universität Stuttgart, 70550 Stuttgart

Due to their high photostability single nitrogen-vacancy (NV) defect centers in diamond are ideal atomic solid state light sources. Consequently, their use as single-photon emitters for quantum communication has be proposed recently. However, the low temperature properties of the defect have not been investigated in great detail up to now. We will present new results on low temperature high-resolution optical spectroscopy on single NV-defects in diamond. In thin highly strained diamond crystals the photophysical properties of NV-centers are such that despite rapid spectral diffusion or intersystem-crossing intense zero-phonon lines can be detected. The results will be discussed in the context of existing theories about the energetic structure of the center.

Pulsed generation of photons by vacuum stimulated Raman scattering

•Markus Hennrich, Thomas Legero, Axel Kuhn und Gerhard Rempe
Max-Planck-Institut für Quantenoptik, D-85748 Garching

We have recently demonstrated that it is possible to generate single photons by stimulated emission in a single-mode optical cavity containing only the vacuum field. The photons are well collimated and well defined in frequency [1]. Here we report on the pulsed generation of such photons.

In our experiment, rubidium atoms are released from a magneto-optical trap and fall one by one through the mode of an optical cavity. A pump laser perpendicular to the cavity axis is switched on while an atom resides inside the cavity mode. Consequently a single photon is placed into the cavity mode by means of a highly efficient adiabatic Raman transfer where pump laser and the vacuum mode of the cavity drive the Raman transition. Since the photon leaves the cavity through the less reflecting mirror, the atom is not coupled to the cavity field any more. Therefore the pump laser can be switched off without adiabatic population return. Outside, the generated photons are detected by a single photon counting module. The correlation between the pump laser pulse and the detected photon shows clear evidence for a pulsed photon generation.

[1] M. Hennrich, T. Legero, A. Kuhn and G. Rempe, Phys. Rev. Lett. 85, 4872-4875 (2000).

Fock state preparation of the electromagnetic field using two-atom entanglement

•Thomas Wellens¹, Burkhard Kümmerer² und Andreas Buchleitner^1
1MPI für Physik komplexer Systeme, Nöthnitzer Str. 38, 01187 Dresden
²Mathematisches Institut A, Pfaffenwaldring 57, 70569 Stuttgart

If a single mode of the quantized electromagnetic field interacts with a sequence of N two-level atoms, the asymptotic completeness of the atoms-field interaction enables us to prepare any desired field state |cñ with arbitrarily high fidelity [1]. The initial atomic state required for this purpose in general exhibits entanglement between all N atoms. In order to prepare Fock states |nñ, however, we will show that a sequence of pairs of subsequent atoms with the appropriate two-particle entanglement is sufficient, which simplifies the experimental realization of our scheme. We discuss how the fidelity of the target state |nñ depends on the length N of the atomic sequence and the fidelity of the initial atomic state.

[1] T. Wellens, A. Buchleitner, B. Kümmerer, and H. Maassen, PRL 85, 3361 (2000).

Squeezed State Entanglement for Free Space Quantum Cryptography

•Stefan Lorenz, Christine Silberhorn, Michael Langer, Natalia Korolkova und Gerd Leuchs
Zentrum für moderne Optik, Physikalisches Institut, Staudtstr. 7 / B2, D-91058 Erlangen

Quantum key distribution is on the verge of commercial applications as means of establishing secure data transmissions. While most of the existing experiments use single photons, we intend to utilize EPR-entangled multi-photon pulse pairs. They can be generated at a higher repetition rate, leading to decreased key distribution times. The entanglement can be produced by interference of two quadrature squeezed pulses at a beamsplitter. To produce the quadrature squeezed pulses we will use an asymmetric fiber Sagnac interferometer [1].

In contrast to existing experiments, we use a microstructured fiber [2] instead of a standard single mode fiber in the interferometer. This fiber has a very small mode field diameter leading to enhanced nonlinearity. Therefore the fiber length can be reduced, minimizing other noise producing effects such as e.g. guided acoustic wave brillouin scattering. In addition, the zero dispersion wavelength of the fiber lies at about 800nm, giving us the possibility to produce bright entangled pulses at a wavelength which is suited for free space transmission. [1] S. Schmitt et al., Phys. Rev. Lett. 81, 2446 (1998) [2] J.K. Ranka et al., Optics Letters 25, No. 11, 796 (2000)

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