Deterministic Generation of Single Photons
In recent years there has been increasing interest in systems capable to create photon fields with a preset number of photons. This has chiefly arisen from applications for which single photons are a necessary requirement, such as secure quantum communication and quantum cryptography. Here we present two systems in the field of cavity QED which are able to produce single photon fields on demand. In the first system, the micromaser, we investigate the strong coupling of single Rydberg atoms to a high Q microwave cavity. The cavity has a Q value of 4 · 10^4 corresponding to a photon lifetime of 0.3 s. Especially interesting are the so called trapping states where single photon states can be stored as a steady state of the cavity. So the physical properties of the single photon states can be investigated and different state reconstruction protocols can be implemented. In the second system a single Calcium ion, stored in a linear radiofrequency trap is coupled to an optical cavity. Single photons in the visible spectral region could be produced on demand. The practically infinite storage time of the ions leads to a continuous operation of the single photon source. The setup is useful for quantum information processing, furthermore photon coupling between neighboring ions gets possible allowing to realize quantum gates without cooling the ions to the quantum ground state of motion.
Single photons on demand: New light for quantum information processing
Single photon sources have been realized in many different systems [1]. In this talk we concentrate on single photon sources based on semiconductor quantum dots [2]. We introduce two applications in quantum information processing. One is the demonstration of multiplexed quantum cryptography [3], the other one is an all-optical implementation of a quantum computing algorithm. Wide attention has been drawn recently to these approaches using solely linear optics since only standard optical components like beam splitters and phase shifters are used. It allows the optical simulation of smaller Hilbert spaces containing a limited number of qubits and can easily be cascaded for non-trivial small-scale computations. Previous experimental demonstrations along this line focused on coherent photon states from attenuated laser pulses [4] or spontaneous parametric down-conversion [5] in order to simulate simple quantum algorithms or to demonstrate concepts of noise resistant quantum computation [6]. We demonstrate the on-demand operation of the two-qubit Deutsch-Jozsa algorithm using a triggered single-photon source. A variation of our experimental setup enables us to implement ideas of the concept of decoherence-free subspaces [7] in a triggered quantum algorithm on the single-photon level.
[1] Focus issue of New Journal of Physics 6 (2004)
[2] V. Zwiller et al., Appl. Phys. Lett. 82, 1509 (2003)
[3] T. Aichele, G. Reinaudi, O. Benson, Phys. Rev. B 70, 235329 (2004)
[4] S. Takeuchi, Phys. Rev. A 62, 032301 (2000)
[5] M. Bourennane et al., Phys. Rev. Lett. 92, 107901 (2004)
[6] M. Mohseni et al., Phys. Rev. Lett. 91, 187903 (2003)
[7] P. Zanardi and M. Rasetti, Phys. Rev. Lett. 79, 3306 (1997)
Fault-tolerance thresholds for linear optical quantum computing
Put simply, a device is said to be fault tolerant if its overall functioning is not affected by occassional malfunctions of its components. Whatever physical components are used to construct a quantum computing device, we can safely assume that they will malfunction, and perhaps not so occassionally. The theory of fault-tolerant quantum computing concerns the design and evaluation of fault-tolerant protocols with which we can combat the effects of noise processes in quantum computers. The central result in this theory is the threshold theorem which asserts that, provided the noise is not too strong and not too correlated, arbitrarily long quantum computations can be implemented. The key quantities of interest in a fault-tolerant quantum protocol are firstly its threshold, which quantifies what is meant by "too strong", and secondly the amount of overhead it introduces into a computation. The threshold serves as a useful measure of how good a protocol is and also as a target for experimenters, and naturally we would like it to be as high as possible without incurring excessive overheads. This talk describes some very recent results in the study of fault-tolerance in optical quantum computers, meaning those whose qubits are encoded in the polarization (or spatial) modes of a single photon, and whose primitive operations are constructed using linear optical elements and high-efficiency photon detectors. We introduce a complete fault-tolerant protocol for an optical quantum computer, and present some numerical results that establish its thresholds for photon loss and depolarization. Attention will be paid to the basic experimental desiderata and the incurred resource overheads.
Entangled photons from semiconductor and violation of Bell's inequality
We demonstrate the generation of entangled photon pairs via biexciton-resonant hyper parametric scattering in CuCl crystal. Quantum state tomography show that the generated photon pairs have a high degree of polarization entanglement. We also show that the photon pairs violate Clauser-Horne-Shimony-Holt type Bell's inequality.
Minimal resources for linear optical one-way computing
We systematically investigate how to optimally build up cluster states for quantum computing with linear optical means using fusion gates, entirely from the perspective of classical control. We develop a notion of classical strategies and consider the globally optimal one to prepare linear cluster states with probabilistic gates. We find that this optimal strategy - which is also the most robust with respect to decoherence processes - gives rise to an advantage of already more than an order of magnitude in the number of maximally entangled pairs when building chains with an expected length of L=40, compared to other legitimate strategies. For two-dimensional cluster states, we present a first scheme achieving the optimal quadratic asymptotic scaling in resource consumption. This analysis shows that the choice of appropriate classical control leads to a very significant reduction in resource consumption.
Beyond Linear Optics: Zeno Gates and Entangled Photon Holes
Several groups have made considerable progress in linear optics quantum computing, including demonstrations of CNOT gates, quantum error correction, and cluster states. Although cluster states are a promising approach, the probabilistic nature of the logic gates would require increased resources and highly efficient sources and detectors. All of the failure events in the APL CNOT gate are due to the emission of two photons into the same output port of a beam splitter. We are investigating the possibility of suppressing those failure events by using the quantum Zeno effect enforced by strong two-photon absorption. The generation of entangled photon holes, which are somewhat analogous to the holes of semiconductor theory, can have an effect on the operation of Zeno gates of that kind The entangled photon holes may also provide a robust method for quantum communication.
Error Analysis For Encoding A Qubit In An Oscillator
In the paper titled "Encoding A Qubit In An Oscillator" Gottesman, Kitaev, and Preskill [quant-ph/0008040] described a method to encode a qubit in the continuous Hilbert space of an oscillator's position and momentum variables. This encoding provides a natural error correction scheme that can correct errors due to small shifts of the position or momentum wave functions (i.e., use of the displacement operator). We will present bounds on the size of correctable shift errors when both qubit and ancilla states may contain errors. We will then use these bounds to constrain the quality of input qubit and ancilla states. Finally, we will describe some methods to prepare the encoded qubit states.
Schrödinger kittens and higher-order Fock states : a zoo of propagating light fields with negative Wigner functions.
We describe recent progress in the experimental realization of propagating light fields with observed negative Wigner functions, measured by pulsed homodyne quantum tomography. This includes in particular Schrödinger cat states with small amplitudes ("Schrödinger kittens"), and n=2 Fock states. Various applications of such states will be discussed in the context of linear optical quantum information processing.
Linear optical quantum computing, a review
Linear optics with photon counting is a prominent candidate for practical quantum computing. The protocol by Knill, Laflamme and Milburn [Nature 409, 46 (2001)] explicitly demonstrates that efficient scalable quantum computing with single photons, linear optical elements, and projective measurements is possible. Subsequently, several improvements on this protocol have started to bridge the gap between theoretical scalability and practical implementation. We review the original theory and its improvements, and we give a few examples of experimental two-qubit gates. We discuss the use of realistic components, the errors they induce in the computation, and how they can be corrected.
Optical resources for quantum information processing
In order to achieve the goal of practical quantum communication, and scalable quantum computing, there are a number of critical component developments. These include high efficiency detectors, single- and entangled-photon sources, and quantum storage systems. I will describe our present state-of-the-art in these areas.
Practical Quantum Repeater Using Intense Coherent Light
Long-distance (~1000 km) quantum communication will require a quantum repeater system. For most existing repeater proposals, reasonable qubit-communication rates require technologies which are currently impractical, such as stabilized interferometry over very long distances or large numbers of efficient single-photon sources and detectors. We present detailed theoretical calculations demonstrating the feasibility of a more practical quantum repeater employing intense coherent light interacting dispersively with single emitters (atoms, quantum dots, semiconductor impurities, etc.). For a sufficient interaction strength, each emitter must be located in a high-Q optical cavity, but the weak-coupling regime is sufficient. Distribution of the intense coherent light among the intermediate qubits of the quantum channel followed by homodyne detection of the optical phase generates noisy, post-selected entangled pairs with high success probability. Local operations used for entanglement purification and entanglement swapping may be done using the same coherent-light resources and weak interactions as for the initial entanglement distribution. Assuming small local optical loss and high-fidelity single-qubit rotations, these local operations may be completely deterministic. Simulations of this system show high fidelity operation for realistic semiconductor microcavity systems and qubit-communication rates approaching 100 Hz.
Single-Photon Detector & Source Efforts at NIST
NIST is engaged in a number of efforts involving single-photon technology with quantum information applications as an ultimate focus. As the quantum information field advances, the need for improved single-photon devices becomes more critical. We will present some of our efforts to address that need. With respect to single photon detection, quantum information systems are often limited by the detector deadtime to operate at count rates of a few MHz, at best, and often at significantly lower rates. We have modeled a multiplexed detection system that offers a way to photon count at much higher rates than are possible with individual detectors. We show that such systems are more promising than simply reducing deadtime of individual detectors. We find that a system of N detectors, with a given deadtime, can photon count at faster rates than a single detector with its deadtime reduced by 1/N (even if it were practical to make such a large improvement). We also present our efforts to develop a compact entangled photon source for quantum cryptography using microstructure fiber. Because the properties of these fibers can be controlled through engineering, they offer potential as a bright flexible photon pair source with a wide range of selectable output wavelengths. In addition, these highly nonlinear fibers and resulting high wavelength conversion efficiencies, can operate with convenient low-power laser pumps. One key to the success of this type of source are the relative levels of two photon output to background Raman processes. We present the results of our effort so far.
Single photonics: the future is not so bright
The concept of an N-photon state of light will be carefully developed with an emphasis on the optical properties of pulsed and CW beams. While the possible application of single photonics to quantum computing is exciting, single photonics will likely have a greater impact on future communication systems.
Quantum Computation via Communication
Quantum computation requires two types of operations: single-qubit manipulation and two-qubit operation. However, it is very difficult to realize these two types of operations, keeping quantum coherence at the same time. We propose a new scheme that computational qubits are connected via continuous-variable bus mode, and show that quantum computation via quantum bus (Qubus computation) is universal in QIP. The scheme exploits the advantages both qubits and continuous variables (CV), and hence is viable today and is applicable to many physical systems.
Distinguishing N photons in a single temporal mode from N separate photons
We present a multimode model to describe an arbitrary N-photon state. In general, the N photons can be distinguished through their temporal modes. From this model, we can find the criterion for the N photons in an indistinguishable state of a single temporal mode. We find that simple multi- photon detection scheme cannot distinguish N photons in different temporal modes and only a multi-photon interference experiment can accomplish the goal. We apply the theory to the four-photon case in the process of parametric down- conversion. We will present the results for various four-photon interference schemes and identify a quantity to characterize how well the four photons are indistinguishable. We will present some latest experimental results for four-photon and six-photon cases in support of the theory.
Experimental quantum teleportation of a complex system
We present the first experimental realization of quantum teleportation of a two-qubit system. In the experiment, we exploit a six-photon interferometer to teleport an arbitrary polarization state of two photons. The average fidelity of the teleported two-photon state is about 70%, which is well beyond the classical limit of 40% for optimal estimation of an unknown two-qubit state. The technology developed in the experiment is not only an important step towards quantum teleportation of complex systems, but also a critical ingredient for quantum communication and quantum computation networks.
Characterizing Single Photons for QIP
I will describe a method for representing single photon states that includes their spatio-temporal structure. I will discuss some consequences of this structure for optical quantum information protocols and present experimental data which illustrates some of these effects.
Technologies for optical quantum logic
The photon is a near ideal carrier of quantum information showing little or no decoherence. The main sources of error become losses and small technical errors due to imperfect components. Although the photon is an ideal carrier of quantum information the absence of a single photon non-linearity makes optical quantum logic difficult. Linear optical logic has thus been developed exploiting multiphoton interference to make probabilistic gates. These optical quantum logic schemes require high efficiency sources of single and pair photons [1]. These components in the quantum logic toolbox could be realised by exploiting wavelength scale engineering of optical structures. We have developed a high brightness pair photon source based on four-wave mixing in micro-structured optical fibre [2]. We are also developing high efficiency single photon sources based on microcavity structures. These sources should be bright enough to build the multi-photon states needed for linear logic schemes.
[1] J.G.Rarity, Roy. Soc. Phil. Trans. 361, 1507 (2003)
[2] J.G.Rarity et al, Optics Express 13, 7572 (2005).
Photon Wave Mechanics
It is often tempting to use the term "photon" in reference to individual quantum objects, or particles, rather than as excitations of fields. Yet, quantum mechanics textbooks contain no satisfactory wave equation for photon wave functions. We are led to seek the analog of the Dirac equation for photons, which would completely describe the evolution of the photonic quantum wave function in coordinate space. For the single-photon state of positive helicity, the quantum wave function is a complex, divergenceless, three-component vector obeying the complex form of the Maxwell equations [1,2]. We have carried out quantum tomography to measure the transverse spatial part of such wave functions for an ensemble of single photons [3]. Considering two photons, we find that the wave function is a complex, divergenceless, nine-component tensor field that obeys a generalized complex Maxwell equation. We prove that a recently cited duality between the two-photon detection amplitude of quantum optics [4] and the Wolf equations of partial coherence theory [5] is a consequence of the two-photon Maxwell equation.
[1] I. Bialynicki-Birula, "Photon Wave Function" in Progress in Optics XXXVI, E. Wolf, ed. (Elsevier, Amsterdam, 1996).
[2] J. E. Sipe, "Photon wave functions" Phys. Rev. A 52, 1875-1883 (1995).
[3] B. J. Smith, B. Killett, M. G. Raymer, I. A. Walmsley, and K. Banaszek, "Measurement of the transverse spatial quantum state of light at the single photon level" Opt. Lett. 30, 3365 (2005), quant-ph/0507142.
[4] M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, UK, 1997).
[5] E. Wolf, "Optics in terms of observable quantities" Nuovo Cimento 12, 884-888 (1954).
Single Photons for Quantum Networks
Recently, the storage of a single atom inside a high-finesse optical cavity for an average time of 17 s has been demonstrated [1]. Such atom-cavity systems with the ability to generate single photons [2] can form the nodes in a quantum network, where the photons act as flying qubits and couple or entangle distant nodes [3]. In order to do so the photons need to be mutually coherent and thus indistinguishable. With this backdrop, we have developed a new scheme for the generation of polarized single photons in a coupled atom-cavity system. Together with the cavity, a pump laser drives Raman transitions between the mF = ±1 Zeeman states of the F = 1 hyperfine ground state of a single 87Rb atom. This allows us to generate a stream of photons with alternating polarization. The mutual coherence of subsequent photons is characterized in a two-photon interference experiment [4], where their suitability for applications in quantum information processing such as linear optical quantum computing [5] is verified.
[1] Nußmann et al., Nature Phys. 1, 122 (2005).
[2] Kuhn et al., Phys. Rev. Lett. 89, 67901 (2002).
[3] Cabrillo et al., Phys. Rev. A 59, 1025 (1999).
[4] Legero et al., Phys. Rev. Lett. 93, 70503 (2004).
[5] Knill et al., Nature 409, 46 (2001).
Towards optical cluster state computation with realistic devices
The primary technological hurdle facing linear optical Quantum computation is commonly thought to be the construction of efficient sources and detectors. I will argue that the primary hurdle is in fact theoreticians who haven't devoted enough time to thinking about whether we can get by with the devices we have. In defense of this thesis I will discuss how, by making use of some neat features of cluster state computation, we can get by with much more noisy devices than one might have hoped, and why I am optimistic that smarter theoreticians then me should be able to relax these fault tolerant thresholds even further.
Engineering Optical Entanglement for Quantum Communication
Sources of entangled photons are of primary importance for practical realizations of quantum-optical information processing techniques. Traditionally such sources are based on the use of the process of spontaneous parametric down conversion (SPDC) when nonlinear crystal is pumped by a continuous wave (cw) or a pulsed laser. The pump photon disintegrates spontaneously giving birth to two twin photons that are strongly correlated in frequency, polarization and wave vector (direction of propagation). Photonic entanglement results from the fact that the possible values of correlated parameters of twin photons are made indistinguishable from each other either at the generation or at the single-photon detection stage. This leads to non-classical interference effects. Polarization entanglement is one of the most frequently used types of entanglement in quantum information processing and in precise optical measurement. The indistinguishability of the polarization outcome can be achieved by superimposing photon paths with optical elements (mirrors and beam splitters). The required two-photon pair correlated in polarization is usually produced form a non-linear crystal selected for a type-II phase matching or from two perpendicularly oriented type-I phase-matching crystals positioned next to each other. We combined an advantage of generating photon pairs in Periodically Poled Lithium Niobate (PPLN) with the possibility of using two perpendicularly oriented type-I phase-matching crystals when they are spatially separated. We have demonstrated that such a design represents very flexible and efficient system for engineering entangled states with desired frequency, polarization, and spatial properties. We demonstrated that the spatial profile of SPDC could be tailored appropriately to achieve the desired spatial and temporal overlap of photon pairs born from separate crystals inside a telecommunication fiber. This guarantees necessary indistinguishability and high-contrast quantum interference that is sufficient for performing a quantum key distribution at the telecommunication wavelength 1550 nm. We also review the role of single-photon detectors in quantum optics and quantum information processing with entangled-photon states. We show that such properties of single-photon detectors as timing resolution (jitter), number-photon resolution, size of photosensitive area, and quantum efficiency can be extremely important in quantum cryptography applications.
Triggered Single Photons and Entangled Photon Pairs from Quantum Dots
There is currently great interest in using the radiative emission of a quantum dot as a source of indistinguishable single photons and entangled photon pairs. This approach to quantum light generation has the advantage of allowing a robust and compact source to be designed with contacts for electrical injection. A cavity may be integrated into the semiconductor structure to enhance the photon collection efficiency and control the recombination dynamics. The radiative emission of the doubly excited biexciton state of the quantum dot is also a potential source of entangled photon pairs. We reported[1] that, provided the splitting of the intermediate exciton is erased, the polarisation correlations of the pair show clear evidence for entanglement. A remaining problem is the high level of background emission from other layers in the device which degrades the degree of correlation. The 2-photon density matrix of a more recent device, for which this background emission is suppressed, violates the Peres criterion for non-classical correlations by ten standard deviations without any background subtraction. It suggests it may be possible to realise a simple semiconductor LED for generating entangled photon pairs, as well as single photons, on demand.
[1] R M Stevenson, R J Young, P Atkinson, K Cooper, D A Ritchie and A J Shields, Nature 439 179 (2006).
Manipulating and measuring quantum information with multiple photons
Throughout the 20th century, the question of quantum measurement has confused and intrigued physicists. At the dawn of the 21st, these issues have taken on new practical importance due to the birth of the interdisciplinary science of quantum information. The realization that quantum mechanics allows communications more secure than one could ever have classically, and computation exponentially more efficient than any classical known algorithms, has incited a huge amount of research into this new area, which has in turn provided an exciting new perspective on quantum mechanics. Motivated in part by these considerations, my lab has been carrying out a variety of experiments on controlling simple quantum systems and comparing different techniques for "measuring" their wave functions, density matrices, or phase-space distributions. I will describe some of the current issues in measurement and characterisation of quantum systems, and show the results of some of our recent experiments. In particular, I will discuss various schemes for creating path-entangled "noon" states of more than 2 photons, and some interesting problems which arise when one tries to perform characterisations of these states, either in terms of density matrices or in terms of Wigner functions.
Toward the realization of optical quantum circuits
We have been working on the experiments of linear optics quantum computation. We will report our current status of our technologies toward the realization of small scale quantum circuits using linear optics.
Verifying entanglement between atomic ensembles
I'll discuss the theory behind a recent experiment [C.W. Chou et al., Nature 438, 828 (2005)] that entangled two atomic ensembles. I'll explain why verifying entanglement is (even) harder than generating entanglement.
Characterization of conditionally prepared nonclassical photon states
We experimentally investigate a method of directly characterizing the photon number distribution of nonclassical light beams that is tolerant to losses and makes use only of standard binary detectors. This is achieved in a single measurement by calibrating the detector using some small amount of prior information about the source. We demonstrate the technique on a heralded two-photon number state created by conditional detection of a two-mode squeezed state generated by a parametric downconverter, and propose how this can be extended to determine the degree of squeezing of the twin beams.
Linear Optics Gates and Multi-Photon Entanglement
Parametric downconversion became the standard tool to generate entangled photon pairs. For the observation of multi-photon entanglement there are now two options. Either one employs interference effects ocuring in the emission process and uses again parametric downconversion to directly observe some four-photon entangled states. Alternatively, starting with multiple entangled photon pairs, linear logic quantum gates enable one to observe a number of different states exhibiting genuine multi-photon entanglement. We give an overview of the methods to observe and to analyze a variety of different three and four-photon states. The significant differences should enable many different applications in new quantum communication protocolls.
Optical entangling gates
Entangling gates lie at the heart of quantum information. We discuss our recent efforts building, applying and characterising optical entangling gates in quantum computing and metrology protocols. These include: multi-qubit logic gates; nonlocality without entanglement; weak-valued and non-demolition quantum measurements; and phase super resolution.
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Last Modified: Monday, April 3, 2006 by Pavel Lougovski