Retrodictive quantum optical state engineering

Abstract

Although it has been known for some time that quantum mechanics can be formulated in a way that treats prediction and retrodiction on an equal footing, most attention in engineering quantum states has been devoted to predictive states, that is, states associated with a preparation event. Retrodictive states, which are associated with a measurement event and propagate backwards in time, are also useful, however. In this paper it is shown how any retrodictive state of light that can be written to a good approximation as a finite superposition of photon number states can be generated by an optical multiport device. The composition of the state is adjusted by controlling predictive coherent input states. It is shown how the probability of successful state generation can be optimized by adjusting the multiport device and also a versatile configuration that is useful for generating a range of states is examined.     

Homodyne tomography of classical and non-classical light

Abstract

States with explicit quantum character, such as squeezed vacuum and bright squeezed light, as well as coherent states and incoherent superpositions of coherent states were generated and analysed by tomographical methods. Wigner functions, photon-number distributions, density matrices and phase distributions were reconstructed with high accuracy. Features such as photon number oscillations, sub-Poissonian and super-Poissonian photon statistics, bifurcations of the phase distribution, and loss of coherence were observed, demonstrating the usefulness of quantum state reconstruction as an analysing tool in quantum optics experiments.     

Experimental realization of ‘universal homodyne tomography’ with a single local oscillator

We report preliminary experimental measurement of the twin-beam quantum state via optical homodyne tomography using a single local oscillator. The experiment is a realization of the recently reported ‘universal homodyne tomography’ technique. The results agree well with theoretical predictions and reveal the non-classical photon-number correlation between the signal and idler photons of the twin-beam state.     

Measuring the phase variance of light

Abstract

The results of experiments designed to measure the operational phase cosine and sine variances of weak states of light disagree with the variances predicted by canonical phase formalisms. As these variances are fundamental manifestations of the quantum nature of phase, it is important to be able to measure the canonical variances also. A recent suggestion to do so, based on the use of a two-component probe, involves the difficult preparation of exotic states of light which have not yet been produced. In this paper we show how the variances can be measured with simple coherent state inputs. The retrodictive formalism of quantum mechanics provides useful insight into the physics involved.     

Simulations of continuum coherent states and its use in quantum cryptographic systems

Abstract

The continuum states formalism is suitable for field quantization in optical fibre; however, they are harder to use than discrete states. On the other hand, a Hermitian phase operator can be defined only in a finite dimensional space. We approximated a coherent continuum state by a finite tensor product of coherent states, each one defined in a finite dimensional space. Using this, in the correct limit, we were able to obtain some statistical properties of the photon number and phase of the continuum coherent states from the probability density functions of the individual, finite dimensional, coherent states. Then, we performed a simulation of the BB84 protocol, using the continuum coherent states, in a fibre interferometer commonly used in quantum cryptography. We observed the fluctuations of the mean photon number in the pulses that arrive at Bob, which occurs in the practical system, introduced by the statistical property of the simulation.     

Photon-number-resolving detection using time-multiplexing

Abstract

Detectors that can resolve photon number are needed in many quantum information technologies. In order to be useful in quantum information processing, such detectors should be simple, easy to use, and be scalable to resolve any number of photons, as the application may require great portability such as in quantum cryptography. Here we describe the construction of a time-multiplexed detector, which uses a pair of standard avalanche photodiodes operated in Geiger mode. The detection technique is analysed theoretically and tested experimentally using a pulsed source of weak coherent light.     

Detecting photons: Properties and challenges

This paper reports on work being carried out on detector characterisation at the National Physical Laboratory in the UK. It focuses on the development of a new technique based on correlated photons produced via parametric downconversion which can be used to directly measure the quantum efficiency of photon counting detectors. The main drivers for these measurements are the wide uptake of few photon optical technologies and the rapidly progressing field of quantum information processing which operates in the photon counting regime. Photodetection in the fields of biology, nuclear physics and astrophysics will also benefit from this work. The potential of this technique for realising primary radiometric scales will also be briefly discussed.     

Kerr cat states from the four-photon Jaynes-Cummings model

We investigate the dynamics of a four-photon Jaynes—Cummings model for large photon number. It is shown that at certain times the cavity field is in a pure state which is a superposition of two Kerr states, analogous to the Schrödinger cat state (superposition of two coherent states) which occurs in the one and two photon cases.     

Quantum interference between an arbitrary-photon Fock state and a coherent state

Using the phase space method, we study the quantum interference through a Mach–Zehnder interferometer with an arbitrary-photon Fock state and a coherent state as two inputs. The statistical properties, in terms of the Wigner function, average photon number, photon number distribution and parity, are derived analytically for the field of the individual output port. These results indicate that the output state is actually a statistical mixture between a bunch of Fock state and coherent states. In addition, the phase sensitivity is also examined by using the detection scheme of intensity difference measurement.     

Non-classical Properties of Two-mode SU(1, 1) Coherent States

Abstract

We examine the non-classical properties of two-mode coherent states based on different unitary irreducible representations of SU(1, 1). Such states are generated by the action of the two-mode squeezing operator on initial states of the field containing arbitrary numbers of photons in each of the two modes. If the initial state of the field is a two-mode vacuum state, the final state is of course the two-mode squeezed vacuum. An initial occupation generalizes the idea of a squeezed vacuum to the SU(1, 1) coherent states. We show that fields in such states have remarkable quantum properties such as sub-Poissonian statistics, violations of the Cauchy-Schwarz inequality, strong correlations in the photon number fluctuations and squeezing. Using information theory formalism, we show that these coherent states are less correlated than the usual two-mode squeezed vacuum. Moreover, we show that an initial coherent amplitude contribution, in a large amplitude limit, can result in the reduction of correlations between modes.     

Photosynthetic light harvesting: excitons and coherence

Photosynthesis begins with light harvesting, where specialized pigment–protein complexes transform sunlight into electronic excitations delivered to reaction centres to initiate charge separation. There is evidence that quantum coherence between electronic excited states plays a role in energy transfer. In this review, we discuss how quantum coherence manifests in photosynthetic light harvesting and its implications. We begin by examining the concept of an exciton, an excited electronic state delocalized over several spatially separated molecules, which is the most widely available signature of quantum coherence in light harvesting. We then discuss recent results concerning the possibility that quantum coherence between electronically excited states of donors and acceptors may give rise to a quantum coherent evolution of excitations, modifying the traditional incoherent picture of energy transfer. Key to this (partially) coherent energy transfer appears to be the structure of the environment, in particular the participation of non-equilibrium vibrational modes. We discuss the open questions and controversies regarding quantum coherent energy transfer and how these can be addressed using new experimental techniques.     

High-stability time-domain balanced homodyne detector for ultrafast optical pulse applications

Abstract

Low-noise, efficient, phase-sensitive time-domain optical detection is essential for foundational tests of quantum physics based on optical quantum states and the realization of numerous applications ranging from quantum key distribution to coherent classical telecommunications. Stability, bandwidth, efficiency, and signal-to-noise ratio are crucial performance parameters for effective detector operation. Here we present a high-bandwidth, low-noise, ultra-stable time-domain coherent measurement scheme based on balanced homodyne detection ideally suited to characterization of quantum and classical light fields in well-defined ultrashort optical pulse modes.     

Invariant polarimetric contrast parameters of coherent light

Many applications use an active coherent illumination and analyze the variation of the polarization state of optical signals. However, as a result of the use of coherent light, these signals are generally strongly perturbed with speckle noise. This is the case, for example, for active polarimetric imaging systems that are useful for enhancing contrast between different elements in a scene. We propose a rigorous definition of the minimal set of parameters that characterize the difference between two coherent and partially polarized states. Indeed, two states of partially polarized light are a priori defined by eight parameters, for example, their two Stokes vectors. We demonstrate that the processing performance for such signal processing tasks as detection, localization, or segmentation of spatial or temporal polarization variations is uniquely determined by two scalar functions of these eight parameters. These two scalar functions are the invariant parameters that define the polarimetric contrast between two polarized states of coherent light. Different polarization configurations with the same invariant contrast parameters will necessarily lead to the same performance for a given task, which is a desirable quality for a rigorous contrast measure. The definition of these polarimetric contrast parameters simplifies the analysis and the specification of processing techniques for coherent polarimetric signals.     

Optical qubit generation by state truncation using an experimentally feasible scheme

Generation of arbitrary superposition of vacuum and one-photon states using a quantum scissors device (QSD) is studied. The device allows the preparation of states by truncating an input coherent light. Optimum values of the intensity of the coherent light for the generation of any desired state using the experimentally feasible QSD scheme are found.     

Realistic eight-port homodyne detection and covariant phase space observables

We consider the quantum optical eight-port homodyne detection scheme in the case that each of the associated photon detectors is assigned with a different quantum efficiency. We give a mathematically rigorous and strictly quantum mechanical proof of the fact that the measured observable (positive operator measure) in the high-amplitude limit is a smearing of the covariant phase space observable related to the ideal measurement, that is, the measurement performed with fully efficient detectors. The result is proved for an arbitary parameter field. Furthermore, we investigate some properties of the measured observable. In particular, we show that detector inefficiencies do not affect the observable's ability to distinguish between different states.     

Quantum nature of laser light

All compositions of a mixed-state density operator are equivalent for the prediction of the probabilities of future outcomes of measurements. For retrodiction, however, this is not the case. The retrodictive formalism of quantum mechanics provides a criterion for deciding that some compositions are fictional. Fictional compositions do not contain preparation device operators, that is operators corresponding to states that could have been prepared. We apply this to Mølmer's controversial conjecture that optical coherences in laser light are a fiction and find agreement with his conjecture. We generalize Mølmer's derivation of the interference between two lasers to avoid the use of any fictional states. We also examine another possible method for discriminating between coherent states and photon number states in laser light and find that it does not work, with the equivalence for prediction saved by entanglement.     

Measuring the absolute photodetection efficiency using photon number correlations

We present two methods for determining the absolute detection efficiency of photon-counting detectors directly from their singles rates under illumination from a nonclassical light source. One method is based on a continuous variable analog to coincidence counting in discrete photon experiments, but it does not actually rely on high detector time resolutions. The second method is based on difference detection, which is a typical detection scheme in continuous variable quantum optics experiments. Since no coincidence detection is required with either method, they are useful for detection efficiency measurements of photodetectors with detector time resolutions far too low to resolve coincidence events.     

A simple scheme with coupled down converters with type-I phase matching as resource for conditional preparation of macroscopic entangled states

It is shown that macroscopic entangled states can be generated using an experimental arrangement consisting of coupled spontaneous parametric down-converters with type-I phase matching (SPDCI) pumped simultaneously by optical fields in coherent state and two beam splitters. Two beam splitters in auxiliary generated modes are used to conditionally prepare macroscopic entangled states in output pumping modes of the studied system. Identification of two macroscopic entangled states is produced by use of photon number resolving detection. In contrast to all previous schemes, our scheme does not need Kerr-type nonlinear interaction and is purely based on second-order susceptibility of the crystal which is stronger for the Kerr nonlinearity. We calculate concurrence of the states as a measure of the amount of entanglement stored in the states and present analysis concerning ‘separation’ between components forming studied entangled states.     

Coherent superposition states of light and their interference in three-photon absorption process

Abstract

For the process of three-photon absorption in the case of a cubic parametric perturbation a possibility to obtain quantum superposition states of three coherent components is shown. The one-photon and two-photon absorption processes are shown to destroy the interference between the state components: the quantum superposition state decays into the classical mixture of its components. It is shown that the interference between different three-component coherent superposition states formed in the system can, depending on the initial state of the field, result in almost full localization of the optical system in a two-component state, or in destruction of the interference between different coherent components. The Wigner functions and quantum entropy of the system are calculated for a variety of initial states.     

Two-photon processes in faint biphoton fields

The goal of this research is to determine and study a physical system that will enable a fast and intrinsically two-photon detector, which would be of interest for quantum information and metrology applications. We consider two types of two-photon processes that can be observed using a very faint, but quantum-correlated biphoton field. These are optical up-conversion and an external photoelectric effect. We estimate the correlation enhancement factor for the biphoton light compared to coherent light, report and discuss the preliminary experimental results.