Table of contents

This Special Issue of Journal of Optics B: Quantum and Semiclassical Optics brings together the contributions of various researchers working on theoretical and experimental aspects of fluctuational phenomena in photonics and quantum optics. The topics discussed in this issue extend from fundamental physics to applications of noise and fluctuational methods from quantum to classical systems, and include:

• Quantum measurement • Quantum squeezing • Solitons and fibres • Gravitational wave inferometers • Fluorescence phenomena • Cavity QED • Photon statistics • Noise in lasers and laser systems • Quantum computing and information • Quantum lithography • Teleportation.

This Special Issue is published in connection with the SPIE International Symposium on Fluctuations and Noise, held in Santa Fe, New Mexico, on 1-4 June 2003. The symposium contained six parallel conferences, and the papers in this Special Issue are connected to the conference entitled `Fluctuations and Noise in Photonics and Quantum Optics'. This was the first in a series of symposia organized with the support of the SPIE that have greatly contributed to progress in this area. The co-founders of the symposium series were Laszlo B Kish (Texas A&M University) and Derek Abbott (The University of Adelaide). The Chairs of the `Fluctuations and Noise in Photonics and Quantum Optics' conference were Derek Abbott, Jeffrey H Shapiro and Yoshihisa Yamamoto. The practical aspects of the organization were ably handled by Kristi Kelso and Marilyn Gorsuch of the SPIE, USA.

Sadly, less than two weeks before the conference, Hermann A Haus passed away. Hermann Haus was a founding father of the field of noise in optics and quantum optics. He submitted three papers to the conference and was very excited to attend; as can be seen in the collection of papers, he was certainly present in spirit. In honour of his creativity and pioneering work in this field, we have dedicated this Special Issue to him. The first item is an obituary reflecting on his life and work. The first technical paper in this issue represents Hermann's last sole author publication; a special thanks is due to A P Flitney for organizing this manuscript into publishable form.

We thank the members of the International Programme Committee, listed below, and all those who contributed to making the event such a success. At this point we take the opportunity to express our gratitude to both the authors and reviewers, for their unfailing efforts in preparing and ensuring the high quality of the papers in this Special Issue.

International Programme CommitteeDavid A Cardimona Air Force Research Laboratory, USAHoward Carmichael University of Auckland, New ZealandCarlton M Caves University of New Mexico, Albuquerque, USAPeter D Drummond University of Queensland, St Lucia, AustraliaPaul J Edwards University of Canberra, AustraliaLuca Gammaitoni Università degli Studi di Perugia, ItalyBrage Golding Michigan State University, East Lansing, USAGabriela Gonzalez Louisiana State University, Baton Rouge, USAGuangcan Guo University of Science and Technology of China, Hefei, ChinaSalman Habib Los Alamos National Laboratory, NM, USAMurray Hamilton University of Adelaide, AustraliaBei-Lok Hu University of Maryland/College Park, USADaniel K Johnstone Virginia Commonwealth University, Richmond, USAFranz X Kärtner Massachusetts Institute of Technology, Cambridge, USAPrem Kumar Northwestern University, Evanston, IL, USAZachary Lemnios DARPA, Arlington, VA, USAGerd Leuchs Friedrich-Alexander Universität Erlangen--Nürnberg, GermanyHideo Mabuchi California Institute of Technology, Pasadena, USAPeter W Milonni Los Alamos National Laboratory, NM, USAAdrian C Ottewill University College Dublin, IrelandMartin B Plenio Imperial College, London, UKRajeev J Ram Massachusetts Institute of Technology, Cambridge, USAFarhan Rana Massachusetts Institute of Technology, Cambridge, USAPeter R Smith Loughborough University of Technology, UKRodney S Tucker University of Melbourne, AustraliaHoward M Wiseman Griffith University, Brisbane, AustraliaStuart A Wolf DARPA, Arlington, VA, USAAnton Zeilinger University of Vienna, AustriaXi-Cheng Zhang Rensselaer Polytechnic Institute, Troy, NY, USA

Hermann Anton Haus, an Institute Professor at the Massachusetts Institute of Technology (MIT), was to have been a Keynote Speaker at the Fluctuations and Noise in Photonics and Quantum Optics Conference, from which the papers in this special issue derive. Sadly, on May 21, 2003 – less than two weeks before the conference – Professor Haus succumbed to a heart attack after arriving home in Lexington, Massachusetts, from his regular, 15-mile commute by bicycle from MIT. He was 77. Throughout his lengthy and illustrious career, Professor Haus had repeatedly and very successfully addressed problems of fluctuations and noise, with special focus on the fundamental issues that arise in quantum optics. To honour Professor Haus' legacy to our technical community, this special issue of Journal of Optics B: Quantum and Semiclassical Optics is dedicated to his memory.

Professor Haus was born in Ljubljana, Slovenia, in the former Yugoslavia, on 8 August 1925. After attending the Technische Hochschule, Graz, and the Technische Hochschule, Wien, in Austria, he received his Bachelor of Science degree from Union College in Schenectady, New York in 1949. In 1951, he graduated from Rensselaer Polytechnic Institute with a Master of Science in Electrical Engineering, and came to MIT, where he earned his Doctorate of Science and joined the faculty in 1954. He was promoted to Associate Professor in 1958, to Professor in 1962, and to Elihu Thomson Professor in 1973. In 1986, he was conferred the honour of Institute Professor.

Professor Haus had a lifelong fascination with noise. While still an undergraduate at Union College, he became aware of Norbert Wiener's theories of statistical phenomena – the new mathematics needed to understand and quantify the random fluctuations we refer to as noise. So it was that noise theory formed the core of Professor Haus' research during the 1950s: noise in electron beams, noise in microwave amplifiers, and noise in amplifier cascades. Two of his notable achievements from that era are his elegant four-terminal impedance transformation for the treatment of noise in electron beams [1], and the single noise measure for optimizing linear amplifier cascades that he developed with Richard B Adler [2]. In 1960 the first working laser was reported, and Professor Haus' noise work shifted from microwaves to higher frequencies – light waves – and to the most fundamental source of fluctuations, the inescapable noise introduced by quantum mechanics. In 1962, he and Charles H Townes used the number-phase uncertainty principle to derive the sensitivity advantage that optical homodyne detection enjoys over optical heterodyne detection [3]. That same year he and James A Mullen tied the fundamental noise limits on linear amplification to the quadrature-noise uncertainty principle [4]. Four years later he and Charles Freed reported the first measurements of photoelectron statistics for a laser operating below and above its oscillation threshold [5]. All three of these works have continuing echoes through more recent research on the quantum theory of coherent detection, the noise limits of phase-insensitive and phase-sensitive amplifiers, and quantum noise measurements via photodetection.

It took some time for laser technology to fulfil its initial promise of inexpensive, long-haul, broadband communications, and Professor Haus' work on modelocked, distributed-feedback, and soliton lasers played no small role in that development. Nevertheless, from the 1980s onward, Professor Haus' research interest returned again and again to quantum noise. In collaboration with colleagues from the Raytheon Company he showed that their ring-laser gyroscope was operating at the noise limit set by the number-phase uncertainty principle [6]. In collaboration with Nobuyuki Imoto and Yoshihisa Yamamoto from Nippon Telegraph and Telephone Research Laboratories he proposed a practical route to the quantum nondemolition (QND) measurement of photon number [7]. Together with James P Gordon he elucidated the quantum timing jitter that afflicts soliton propagation down optically-amplified fibre lines [8]. He and Masataka Shirasaki introduced the nonlinear Sagnac loop as a technique for generating squeezed states in optical fibre [9]. Together with his student Yinchieh Lai, Professor Haus established a physically-motivated decomposition that accounts for the various noise contributions seen in soliton squeezing [10]. The impact of these works has continued to reverberate through more recent efforts devoted to optical QND measurements, long-haul soliton transmission systems, and Sagnac loop quantum-noise manipulation.

During the last decade of Professor Haus' life, he revisited – in very modern terms – some topics that he had studied early in his career. In a collaboration between his group and researchers at Bell Laboratories he used amplified spontaneous emission noise measurements to accurately predict the performance of a 10-Gbit/s optically-preamplified receiver [11], thus reprising – in the context of broadband optical communications – issues of photodetection noise statistics that he had confronted 30 years earlier with Charles Freed. In an invited paper he described a single noise figure for amplification that is valid from radio to optical frequencies [12], i.e., in both the classical and quantum regimes, thus bringing him back, full circle, to his earliest interest in amplifier noise measures. The culmination of his life's work, however, was his book, Electromagnetic Noise and Quantum Optical Measurements. Published in 2000 [13], it is a distillation of 45 years of his research. Generations of students to come will learn quantum noise from this masterwork.

Professor Haus authored or co-authored five books, published more than 300 articles, and presented his work at virtually every major conference and symposium on lasers, quantum electronics, and quantum optics around the world. He was one of very few engineers in the USA to become a member of both the National Academy of Engineering and the National Academy of Sciences. He was a Fellow of the American Academy of Arts and Sciences, the American Physical Society, the Institute of Electrical and Electronics Engineers, and the Optical Society of America. He received Guggenheim and Fulbright Fellowships and several honorary degrees, including one from the University of Vienna, and he received the Austrian government's Wittgenstein Prize for outstanding contributions to humanity. Professor Haus was selected by his MIT colleagues for the 1982–1983 James R Killian Faculty Achievement Award, the highest honour that the MIT faculty bestows. In 1984, the Optical Society of America recognized Professor Haus' contributions with its Frederic Ives Medal, the Society's highest award. In 1995, Professor Haus was awarded the National Medal of Science by President William Jefferson Clinton.

In a 1998 interview, Professor Haus was asked about his philosophy of life. He replied, 'Try to do your best, because that's all part of the fun. The greatest thing is that once in a while something clicks. It happens every three of four years. It can't happen more often than that, except for some exceptional people.' Things clicked for Hermann Anton Haus. This happened not just once, not just every three or four years, but regularly and throughout his long career. He was a truly exceptional man.

Jeffrey H ShapiroMassachusetts Institute of Technology, Cambridge, USA

References

[1]  Haus H A 1955 Noise in one-dimensional electron beams J. Appl. Phys.26 560–71 [2]  Haus H A and Adler R B 1958 Optimum noise performance of linear amplifiers Proc. IRE46 1519–33 [3]  Haus H A and Townes C H 1962 Comment on `Noise in photoelectric mixing' Proc. IRE50 1544 [4]  Haus H A and Mullen J A 1962 Quantum noise in linear amplifiers Phys. Rev.128 2407–13 [5]  Freed C and Haus H A 1966 Photoelectron statistics produced by a laser operating below and above the threshold of oscillation IEEE J. Quantum Electron.QE-2 190–5 [6]  Dorschner T A , Haus H A, Holz M, Smith I W and Statz H 1980 Laser gyro at quantum limit IEEE J. Quantum Electron.QE-16 1376–9 [7]  Imoto N, Haus H A and Yamamoto Y 1985 Quantum nondemolition measurement of the photon number via the optical Kerr effect Phys. Rev. A 32 2287-92 [8]  Gordon J P and Haus H A 1986 Random walk of coherently amplified solitons in optical fiber transmission Opt. Lett.11 665–7 [9]  Shirasaki M and Haus H A 1990 Squeezing of pulses in a nonlinear interferometer J. Opt. Soc. Am. B 7 30–4 [10]  Haus H A and Lai Y 1990 Quantum theory of soliton squeezing: a linearized approach J. Opt. Soc. Am. B 7 386–92 [11]  Wong W S, Haus H A, Jiang L A, Hansen P B and Margalit M 1998 Photon statistics of amplified spontaneous emission noise in a 10-Gbit/s optically preamplified direct-detection receiver Opt. Lett.23 1832–34 [12]  Haus H A 2000 Noise figure definition valid from RF to optical frequencies IEEE J. Sel. Topics Quantum Electron.6 240–7 [13]  Haus H A 2000 Electromagnetic Noise and Quantum Optical Measurements (Berlin: Springer)

This is the edited text of the Keynote Speech that Professor Haus had been invited to give at the Conference on Fluctuations and Noise in Photonics and Quantum Optics, held at Santa Fe, NM, on 1–4 June 2003. He introduces it as partly an overview, partly a retrospective, finishing with some remarks about the future, addressing the topics as he knew them best, from his own perspective. Sadly, Professor Haus died shortly before he was due to present this speech to conference delegates.

Quantum equations of motion are developed for broadband soliton propagation in optical fibres with an instantaneous Kerr effect. New terms appear in the nonlinear Schrödinger equation. Hyperbolic secant soliton solutions exist. The initial pulse perturbations are evaluated.

Following the pioneering work of Professor Haus, a general quantum theory for bi-directional nonlinear optical pulse propagation problems is developed and applied to study the quantum properties of fibre Bragg grating solitons. Fibre Bragg grating solitons are found to be automatically amplitude squeezed after passing through the grating and the squeezing ratio saturates after a certain grating length. The optimal squeezing ratio occurs when the pulse energy is slightly above the fundamental soliton energy. One can also compress the soliton pulsewidth and enhance the squeezing simultaneously by using an apodized grating, as long as the solitons evolve adiabatically.

Conditional homodyne detection of quadrature squeezing is compared with standard nonconditional detection. Whereas the latter identifies nonclassicality in a quantitative way, as a reduction of the noise power below the shot noise level, conditional detection makes a qualitative distinction between vacuum state squeezing and squeezed classical noise. Implications of this comparison for the realistic interpretation of vacuum fluctuations (stochastic electrodynamics) are discussed.

An all-fibre source of amplitude squeezed solitons utilizing the self-phase modulation in an asymmetric Sagnac interferometer is experimentally demonstrated. The asymmetry of the interferometer is passively controlled by an integrated fibre coupler, allowing for the optimization of the noise reduction. We have carefully studied the dependence of the amplitude noise on the asymmetry and the power launched into the Sagnac interferometer. Qualitatively, we find good agreement between the experimental results, a semi-classical theory and earlier numerical calculations (Schmitt et al 1998 Phys. Rev. Lett. 81 2446). The stability and flexibility of this all-fibre source makes it particularly well suited to applications in quantum information science.

Combinations of quadratic nonlinear crystals with different phase mismatches are studied numerically in terms of amplitude squeezing in the second-harmonic generation. It is predicted that an appropriate choice of phase mismatches can lead to large amplitude squeezing in the fundamental field with much larger stability than in the phase-matched case. It is also predicted that another choice of phase mismatches can yield amplitude squeezing in the harmonic field beyond the theoretical limit of the phase-matched case.

We demonstrate the possibility of surpassing the quantum noise limit for simultaneous multi-axis spatial displacement measurements that have zero mean values. The requisite resources for these measurements are squeezed light beams with exotic transverse mode profiles. We show that, in principle, lossless combination of these modes can be achieved using the non-degenerate Gouy phase shift of optical resonators. When the combined squeezed beams are measured with quadrant detectors, we experimentally demonstrate a simultaneous reduction in the transverse x- and y-displacement fluctuations of 2.2 and 3.1 dB below the quantum noise limit.

We present an overview of quantum noise in gravitational-wave interferometers. Current gravitational-wave detectors are modified variants of a Michelson interferometer and the quantum noise limits are strongly influenced by the optical configuration of the interferometer. We describe recent developments in the treatment of quantum noise in the complex interferometers of present-day and future gravitational-wave detectors and explore prospects for beating the standard quantum limit by use of both injected and ponderomotive squeezing in future interferometers.

The sensitivity in interferometric measurements such as those made by gravitational-wave detectors is ultimately limited by the quantum noise of light. We discuss the use of feedback mechanisms to reduce the quantum effects of radiation pressure. Recent experiments have shown that it is possible to reduce the thermal motion of a mirror by cold damping. The mirror motion is measured with an optomechanical sensor based on a high-finesse cavity, and reduced by a feedback loop. We show that this technique can be extended to lock the mirror at the quantum level. In gravitational-wave interferometers with Fabry–Perot cavities in each arm, it is even possible to use a single feedback mechanism to lock one cavity mirror on the other. This quantum locking greatly improves the sensitivity of the interferometric measurement. It is furthermore insensitive to imperfections such as losses in the interferometer.

We show that the quantum locking scheme recently proposed by Courty et al (2003 Phys. Rev. Lett. 90 083601) for the reduction of back-action noise is able to significantly improve the sensitivity of the next generation of gravitational wave interferometers.

In this note we review some recent results on corrections to the Casimir–Polder retardation force due to atomic motion and present a preliminary critique on one recently proposed cavity QED scheme for detection of the Unruh–Davies–DeWitt–Fulling effect. These two well-known effects arise from the interaction between a moving atom or detector and a quantum field under some boundary conditions introduced by a conducting mirror/cavity or dielectric wall.

The Casimir–Polder force is a retardation force on the atom due to the dressing of the atomic ground state by the vacuum electromagnetic field in the presence of a conducting mirror or dielectric wall. We have recently provided an improved calculation by treating the mutual influence of the atom and the (constrained) field in a self-consistent way. For an atom moving adiabatically, perpendicular to a mirror, our result finds a coherent retardation correction up to twice the stationary value.

The Unruh–Davies–DeWitt–Fulling effect refers loosely to the fact that a uniformly accelerated detector feels hot. Two prior schemes have been proposed for the detection of 'Unruh radiation', based on charged particles in linear accelerators and storage rings. Here we are interested in a third scheme proposed recently by Scully et al involving the injection of accelerated atoms into a microwave or optical cavity. We analyse two main factors instrumental to the purported success in this scheme, the cavity factor and the sudden switch-on factor. We conclude that the effects engendered from these factors are unrelated to the Unruh–Davies–DeWitt–Fulling effect.

Phase-sensitive squeezing in the resonance fluorescence of two-level atoms, that are coherently driven by a near-resonant laser field in free space, was observed recently (Lu et al 1998 Phys. Rev. Lett. 81 3635). This was accomplished via homodyne detection at a phase near ± 45° relative to the driving field for strong off-resonant excitation of 'long-lived' atoms (where the atomic lifetime far exceeded the laser–atom interaction time, meaning that relaxation effects could be ignored). On the other hand, traditional theoretical predictions of phase-sensitive squeezing in the resonance fluorescence from two-level atoms have emphasized in- and out-of-phase (i.e., 0° and 90°) quadratures, and weak, on-resonant excitation of 'short-lived' atoms (where the observation time for laser–atom interaction far exceeded the natural atomic lifetime, meaning that relaxation effects dominate). Here, we calculate the probability of a delayed-coincidence detection in the interference field of a fluorescing dipole with a local oscillator (LO). We show that, despite the strikingly different conditions in which squeezing occurs in short- and long-lived atoms, squeezing in both cases can be shown to arise from a joint detection of two photons which are related by a quantum jump in the following way: the first photodetection precipitates a quantum jump of the atom to the ground state, and the second measures the mean amplitude of the fluorescent field subsequent to the quantum jump.

The output of a degenerate optical parametric oscillator (DOPO), for weak driving fields, is highly bunched. The photons tend to come out in pairs. Nonclassical behaviour is evident in the output of the DOPO, but usually involves interferometric investigations, as in the spectrum of squeezing, or a Mandel–Hong–Ou interferometer. We discuss a conditioned measurement of the second-order intensity correlation function g⁽²⁾(τ) that yields antibunching. By only measuring the second-order intensity correlation function g⁽²⁾(τ) after a photon has been detected, large bunching is turned into almost perfect antibunching.

The fluorescence intensity and quadrature spectra from a two-level atom embedded in a photonic bandgap crystal and resonantly driven by a classical pump light are calculated. The non-Markovian nature of the problem caused by the non-uniform distribution of the photonic density of states is handled by linearizing the generalized optical Bloch equations with the Liouville operator expansion. Unlike the case in free space, we find that the bandgap effects will not only modify the fluorescence spectral shape but also cause squeezing in the in-phase quadrature spectra.

We investigate intensity cross-correlation functions for two cavity QED systems. These are a driven optical cavity containing a single two-level atom interacting with a single mode of the cavity field with quantized centre of mass motion, and a two-level atom in an optical parametric oscillator. We find analytic results in the weak driving field limit using quantum trajectory theory. We find large violations of inequalities that must be satisfied by classical fields. One of these inequalities is well known, , where i and j denote two modes of the field. We also derive a new inequality that cross-correlations must satisfy, . Large violations of classical inequalities and asymmetrical behaviour in delay time τ are found in complimentary regimes for the cavity QED system with quantized centre of mass motion. They always exist for the two-level atom inside an optical parametric oscillator.

We present a theoretical study of the relationship between entanglement and entropy in multi-qubit quantum optical systems. Specifically we investigate quantitative relations between the concurrence and linear entropy for a two-qubit mixed system, implemented as two two-level atoms interacting with a single-mode cavity field. The dynamical evolutions of the entanglement and entropy are controlled via time-dependent cavity–atom couplings. Our theoretical findings lead us to propose an alternative measure of entanglement, which could be used to develop a much needed correlation measure for more general multi-partite quantum systems.

We study collective spontaneous emission from arbitrary distributions of N two-state atoms using quantum trajectory theory and without an a priori single-mode assumption. Assuming a fully excited initial state, we calculate the angular distribution of the average intensity, focusing on pencil- and disc-shaped samples. The formalism is developed around an unravelling of the master equation in terms of source mode quantum jumps. A modified boson approximation is made to treat the many-atom case, where it is found that strong directional superradiance with shot-to-shot fluctuations occurs for a few hundred to a few thousand atoms.

The theory of the photon statistics of a beam propagated over a horizontal path in air is described and applied to the counting distribution and fade probability for weak laser pulses. Good agreement is obtained between theory and experiment for values of the refractive-index structure constant within an expected range and for various simplifying assumptions, including the assumption of a log-normal distribution for the fluctuations of the mean photon number due to atmospheric turbulence.

The zero-point fluctuations in an L–C circuit of finite Q are revisited. The zero-point energy is shown to approach the value of only in the limit of an infinite Q. A Fabry–Perot resonator, on the other hand, has bounded zero-point energies of its modes that are equal to for each resonance. Based on the Fabry–Perot resonator with broadband noise, we analyse the noise of an ultrafast mode-locked laser when the slowly varying envelope approximation (SVEA) is not valid. This is achieved by reinterpreting the quantized form of the master equation of mode locking as an equation of motion for the electric field rather than for the creation operator of a photon. It is found that in this formulation quantum correlations exist that are not present in the SVEA. The correlations become evident in the spectrum of the zero-point fluctuations and therefore in the background noise of the laser. This behaviour can be detected by homodyne detection of the laser output. The linewidth of the frequency comb generated by the mode-locked laser is not affected by these correlations and is given by the Schawlow–Townes linewidth of an equivalent continuous wave taking the additional intracavity loss due to the mode locking process into account.

A theoretical analysis is performed of the quantum noise properties of multi-element laser diode arrays. A general formalism is presented which facilitates the estimation of the quantum noise arising due to cross contamination between lasing modes of the array. By consideration of three-element laser arrays a specific strategy is advanced for effecting quantum noise management in laser diode arrays.

The non-zero response time of the Kerr (χ⁽³⁾) nonlinearity determines the quantum-limited noise figure of χ⁽³⁾ parametric amplifiers and wavelength converters. This non-zero response time of the nonlinearity requires coupling of the parametric amplification process to a molecular-vibration phonon bath, causing the addition of excess noise through Raman gain or loss. The effect of this excess noise on the noise figure of the amplifier can be significant. We derive analytical expressions for this quantum-limited noise figure in the case of non-degenerate phase-insensitive operation of a χ⁽³⁾ parametric amplifier and show excellent agreement with experiment without any fitting parameter. We also derive analytical expressions for the quantum limited noise figure for χ⁽³⁾-based wavelength converters.

Semiconductor cascade lasers have larger photon noise than conventional semiconductor lasers as a result of positive correlations in photon emission in different gain stages which are connected electrically in series. The photon noise of a cascade laser can be related to the photon noise of a single-stage laser with a scaled external circuit impedance. This scaling relation for the photon noise holds for bipolar as well as unipolar cascade lasers.

The relative intensity noise (RIN) of a semiconductor laser diode subject to optical feedback has been numerically calculated for both weak and strong optical feedback levels. Good agreement with recent experiment results was only obtained after a modified Lang–Kobayashi model was used. Multiple reflections in the external cavity are required to explain the experimentally observed variation of the upper boundary of the coherence collapse regime with injection current. RIN measurements are shown to offer a convenient method of identifying the various feedback regimes both experimentally and theoretically. The importance of incoherent optical feedback in regime IV is also stressed.

The joint influence of stochastic frequency drift and optical injection on the dynamical behaviour of a rate-equation laser model is studied. When the autocorrelation time of the frequency fluctuations is larger than the typical timescales of the system's dynamics, and the amplitude of the frequency drift is larger than the injection locking range, the laser exhibits bursting behaviour at irregular times, each burst being followed by relaxation oscillations towards the unlocked state. The conditions under which this type of phenomenon occurs are fulfilled in fibre lasers. Accordingly, numerical simulation results of the model agree satisfactorily with the experimentally observed behaviour of an injected fibre ring laser.

Liquid transmission studies at terahertz frequencies (0.1–10 THz) are valuable for understanding solvation dynamics of salts, exploring long-range structure in mixtures and probing biomolecules in suspension. T-ray (or THz) time-domain spectroscopy, based on terahertz pulse generation from ultrafast lasers, is a sensitive technique for measuring material parameters in this frequency range. This paper proposes and demonstrates a novel technique for increasing the sensitivity and repeatability of liquid studies with T-ray time-domain spectroscopy (TDS), reducing relative parameter measurement errors below 0.0001. The proposed technique combines dual-thickness liquid measurement with rapid modulation (double-modulated differential TDS) to reduce the effect of both thickness-measurement errors and T-ray noise errors below 0.0001. The possible reduction in error is calculated and a liquid differential TDS (DTDS) prototype is demonstrated, incorporating amplitude and mean detection for near-simultaneous measurement of two T-ray waveforms.

The working principles of linear optical quantum computing are based on photodetection, namely, projective measurements. The use of photodetection can provide efficient nonlinear interactions between photons at the single-photon level, which is technically problematic otherwise. We report an application of such a technique to prepare quantum correlations as an important resource for Heisenberg-limited optical interferometry, where the sensitivity of phase measurements can be improved beyond the usual shot-noise limit. Furthermore, using such nonlinearities, optical quantum non-demolition measurements can now be carried out easily at the single-photon level.

The primary resource for quantum computation is the Hilbert-space dimension. Whereas Hilbert space itself is an abstract construction, the number of dimensions available to a system is a physical quantity that requires physical resources. Avoiding a demand for an exponential amount of these resources places a fundamental constraint on the systems that are suitable for scalable quantum computation. To be scalable, the number of degrees of freedom in the computer must grow nearly linearly with the number of qubits in an equivalent qubit-based quantum computer. These considerations rule out quantum computers based on a single particle, a single atom, or a single molecule consisting of a fixed number of atoms or on classical waves manipulated using the transformations of linear optics.

How fast can a quantum system evolve? In this paper we study the relation between entanglement and the time it takes for a composite system to perform a given evolution. In particular, we analyse how the order of the interactions shapes the dynamics.

We explore the intimate relationship between quantum lithography, Heisenberg-limited parameter estimation and the rate of dynamical evolution of quantum states. We show how both the enhanced accuracy in measurements and the increased resolution in quantum lithography follow from the use of entanglement. Mathematically, the hyper-resolution of quantum lithography appears naturally in the derivation of Heisenberg-limited parameter estimation. We also review recent experiments offering a proof of the principle of quantum lithography, and we address the question of state preparation and the fabrication of suitable photoresists.

We show that by using the strongly correlated photon pairs generated in a Raman quantum erasure scheme (Scully M and Drühl K 1982 Phys. Rev. A 25 2208), it is possible to exceed the Rayleigh resolution limit of classical microscopy. The complete analysis of the underlying physics is given here. Further discussion of the physics and potential applications are presented in a companion paper (Scully M O 2004 Improving quantum microscopy and lithography via Raman photon pairs: I. Biological applications, submitted).

An important and well established area of quantum optics is the theory of Markovian stochastic Schrödinger equations (or by another name quantum trajectory theory). Recently stochastic Schrödinger equations have been developed for non-Markovian systems. In this paper we extend the current known stochastic Schrödinger equations for non-Markovian systems to include the position unravelling. We also discuss and illustrate that this stochastic Schrödinger equation can have an interpretation under both the orthodox and the de Broglie–Bohm hidden variable interpretation of quantum mechanics. We conclude that only the de Broglie–Bohm hidden variable theory provides a continuous-in-time interpretation of the non-Markovian stochastic Schrödinger equation.

We outline a toolbox comprised of passive optical elements, single photon detection and superpositions of coherent states (Schrödinger cat states). Such a toolbox is a powerful collection of primitives for quantum information processing tasks. We illustrate its use by outlining a proposal for universal quantum computation. We utilize this toolbox for quantum metrology applications, for instance weak force measurements and precise phase estimation. We show in both these cases that a sensitivity at the Heisenberg limit is achievable.

In this work, we describe the process of teleportation between Alice in an inertial frame, and Rob who is in uniform acceleration with respect to Alice. The fidelity of the teleportation is reduced due to Davies–Unruh radiation in Rob's frame. In so far as teleportation is a measure of entanglement, our results suggest that quantum entanglement is degraded in non-inertial frames. We discuss this reduction in fidelity for both bosonic and fermionic resources.

We describe a new protocol where, by using a non-maximally entangled basis as the measurement basis, one can use a general pure entangled state as a resource for quantum teleportation. Using this protocol one can teleport a state with unit fidelity though less than unit probability. We also use the more natural language of quantum operations to describe this probabilistic teleportation. We also provide success and failure probabilities for this protocol. This scheme could be of use in real experiments which may be tested in the near future.

It has been argued (Rudolph and Sanders 2001 Phys. Rev. Lett.87 077903) that continuous-variable quantum teleportation at optical frequencies has not been achieved because the source used (a laser) was not 'truly coherent'. Van Enk and Fuchs (2002 Phys. Rev. Lett.88 027902), while arguing against Rudolph and Sanders, also accept that an 'absolute phase' is achievable, even if it has not been achieved yet. I will argue to the contrary that 'true coherence' or 'absolute phase' is always illusory, as the concept of absolute time (at least for frequencies beyond direct human experience) is meaningless. All we can ever do is to use an agreed time standard. In this context, a laser beam is fundamentally as good a 'clock' as any other. I explain in detail why this claim is true, and defend my argument against various objections. In the process I discuss super-selection rules, quantum channels, and the ultimate limits to the performance of a laser as a clock. For this last topic I use some earlier work by myself (1999 Phys. Rev. A 60 4083) and Berry and myself (2002 Phys. Rev. A 65 043803) to show that a Heisenberg-limited laser with a mean photon number μ can synchronize M independent clocks each with a mean-square error of .

In game theory, a popular model of a struggle for survival among three competing agents is a truel, or three-person generalization of a duel. Adopting the ideas recently developed in quantum game theory, we present a quantum scheme for the problems of duels and truels. In the classical case, the outcome is sensitive to the precise rules under which the truel is performed and can be counterintuitive. These aspects carry over into our quantum scheme, but interference amongst the players' strategies can arise, leading to game equilibria different from the classical case.