This summary of the second Terrestrial Very-Long-Baseline Atom Interferometry (TVLBAI) Workshop provides a comprehensive overview of our meeting held in London in April 2024 (Second Terrestrial Very-Long-Baseline Atom Interferometry Workshop, Imperial College, April 2024), building on the initial discussions during the inaugural workshop held at CERN in March 2023 (First Terrestrial Very-Long-Baseline Atom Interferometry Workshop, CERN, March 2023). Like the summary of the first workshop (Abend et al. in AVS Quantum Sci. 6:024701, 2024), this document records a critical milestone for the international atom interferometry community. It documents our concerted efforts to evaluate progress, address emerging challenges, and refine strategic directions for future large-scale atom interferometry projects. Our commitment to collaboration is manifested by the integration of diverse expertise and the coordination of international resources, all aimed at advancing the frontiers of atom interferometry physics and technology, as set out in a Memorandum of Understanding signed by over 50 institutions (Memorandum of Understanding for the Terrestrial Very Long Baseline Atom Interferometer Study).

The journey from great research to practical realization is a difficult one, where building a collaborative ecosystem engaging researchers, entrepreneurs, investment capital, companies and government early adopters is essential. I will describe how such a committed ecosystem can be built, drawing together a diverse community, accelerating the journey from fundamental science to product. Full-text article not available; see video presentation

In this short perspective article we present our personal highlights on how the Jaynes-Cummings model has become a central model to describe spin-boson couplings underpinning much of modern quantum optics. To the current authors, the key contribution is a demonstration of a measurable effect that showed the discreteness of the quantized radiation field.

When quantum state amplitudes interfere, surprising non-classical features emerge which emphasis the roles of indistinguishability and discreteness in quantum mechanics. A famous example in quantum optics is the Hong Ou Mandel interference effect,a major ingredient in current quantum information processing using photonics. Traditionally the HOM features interference between amplitudes for two one-photon number states. Surprisingly, interference can be manifested when one amplitude represents that most classical of light field states, the coherent state, provided the partner state is non-classical (eg a single photon state or an odd photon number state). Imposing such nonclassical features on an otherwise classical state is the focus of this article. Recently, the HOM effect has been generalized to the multi-photon case, termed the extended HOM effect by the authors.The implication of the extended HOM effect is that if an odd parity state, comprising only odd numbers of photons, enters one input port of a 50:50 beam splitter, then regardless of the state entering the other input port, be it pure or mixed, there will no output coincident counts. In this work, we explain the extended HOM as arising from a sequence of pairwise HOM-like complete destructive interferences occurring simultaneously in the multicomponent amplitude for the output coincidence counts. We first demonstrate this diagrammatically in order to build physical intuition, before developing a general analytical proof. We then examine the case of a single photon interacting with a coherent state (and idealized laser), and consider prospects for experimental detection by including the effect of imperfect detection efficiency. This work highlights the importance of the non-classicality of light, and in particular the interference effects stemming from the discreteness of photon quanta.

The quantum interference effects of mixing the most non-classical states of light, number states, with the most classical-like of pure field states, the coherent state, are investigated. We demonstrate how the non-classicality of a single photon when mixed with a coherent field can transform the statistical properties of the output and further demonstrate that the entanglement of the output is independent of the coherent state amplitude. This article is part of the theme issue ‘The quantum theory of light’.

This established textbook provides an accessible but comprehensive introduction to the quantum nature of light and its interaction with matter. The field of quantum optics is covered with clarity and depth, from the underlying theoretical framework of field quantization, atom–field interactions, and quantum coherence theory, to important and modern applications at the forefront of current research such as quantum interferometry, squeezed light, quantum entanglement, cavity quantum electrodynamics, laser-cooled trapped ions, and quantum information processing. The text is suitable for advanced undergraduate and graduate students and would be an ideal main text for a course on quantum optics. This long-awaited second edition builds upon the success of the first edition, including many new developments in the field, particularly in the area of quantum state engineering. Additional homework problems have been added, and content from the first edition has been updated and clarified throughout.

This established textbook provides an accessible but comprehensive introduction to the quantum nature of light and its interaction with matter. The field of quantum optics is covered with clarity and depth, from the underlying theoretical framework of field quantization, atom–field interactions, and quantum coherence theory, to important and modern applications at the forefront of current research such as quantum interferometry, squeezed light, quantum entanglement, cavity quantum electrodynamics, laser-cooled trapped ions, and quantum information processing. The text is suitable for advanced undergraduate and graduate students and would be an ideal main text for a course on quantum optics. This long-awaited second edition builds upon the success of the first edition, including many new developments in the field, particularly in the area of quantum state engineering. Additional homework problems have been added, and content from the first edition has been updated and clarified throughout.

We revisit a method for mapping arbitrary single-mode pure states into superpositions of N00N states using an asymmetric non-linear Mach–Zehnder interferometer (ANLMZI). This method would allow one to tailor-make superpositions of N00N states where each axis of the two-mode joint-photon number distribution is weighted by the statistics of any single-mode pure state. The non-linearity of the ANLMZI comes in the form of a χ(3) self-Kerr interaction occurring on one of the intermediary modes of the interferometer. Motivated by the non-classical interference effects that occur at a beam splitter, we introduce inverse-engineering techniques aimed toward extrapolating optimal transformations for generating N00N state superpositions. These techniques are general enough so as to be employed to probe the means of generating states of any desired quantum properties.

This established textbook provides an accessible but comprehensive introduction to the quantum nature of light and its interaction with matter. The field of quantum optics is covered with clarity and depth, from the underlying theoretical framework of field quantization, atom–field interactions, and quantum coherence theory, to important and modern applications at the forefront of current research such as quantum interferometry, squeezed light, quantum entanglement, cavity quantum electrodynamics, laser-cooled trapped ions, and quantum information processing. The text is suitable for advanced undergraduate and graduate students and would be an ideal main text for a course on quantum optics. This long-awaited second edition builds upon the success of the first edition, including many new developments in the field, particularly in the area of quantum state engineering. Additional homework problems have been added, and content from the first edition has been updated and clarified throughout.

This special issue "Coherent Control: Photons, Atoms and Molecules", honors the life and work of Bruce W. Shore who passed away on January 9, 2021 at the age of 85.

We investigate entanglement in various photonic states interfering on a 50:50 BS and obtain some, at first sight, unexpected results, that we subsequently explain.

We show that any odd parity state entering one input port of a 50:50 beam splitter, with an arbitrary state entering the other input port, produces zero coincidence counts. This result extends the HOM effect.

The groundbreaking research and ideas introduced by Emil Wolf continue to inspire researchers and motivate ongoing research in the wave properties of light. This special issue commemorates the legacy of Emil Wolf with research in physical optics, with specific focus on those areas where Wolf was active, such as optical coherence theory, inverse problems, singular optics, imaging, and polarization, and the intersection of these fields of study. Here we discuss the life of Emil Wolf and his influence on optical science and the optics community.

We show that the parity (evenness or oddness) of a nonclassical state of light has a dominant influence on the interference effects at a balanced beam splitter, irrespective of the state initially occupying the other input mode. Specifically, the parity of the nonclassical state gives rise to destructive interference effects that result in deep valleys in the output joint number distribution of which the Hong-Ou-Mandel (HOM) effect is a limiting case. The counter-intuitive influence of even a single photon to control the output of a beam splitter illuminated by any field, be it a coherent or even a noisy thermal field, demonstrates the extraordinary power of non-classicality. The canonical example of total destructive interference of quantum amplitudes leading to the absence of coincidence counts from a 50/50 beam splitter is the celebrated HOM effect, characterized by the vanishing of the joint probability of detecting singe photons in each of the output beams. We show that this is a limiting case of more general input states upon which a 50/50 BS can create total, or near total, destructive interference of quantum amplitudes. For odd photon number input Fock states of arbitrary value n>0 we show that the joint photon number probabilities vanish when detecting identical photon numbers in each output beams. We examine the mixing of photon number states of n = 1, 2, and 3 with a CV state, such as a coherent state of arbitrary amplitude, and a thermal state. These vanishing joint probabilities form what we call a central nodal line -- a contiguous set of zeros representing complete destructive interference of quantum amplitudes. For odd or even photon number Fock states with n>1 there will be additional off-diagonal pseudo-nodal curves along which the joint photon number probabilities are either zero, or near zero, which constitute a near, but not complete, destructive interference.

The first demonstration of laser action in ruby was made in 1960 by T. H. Maiman of Hughes Research Laboratories, USA. Many laboratories worldwide began the search for lasers using different materials, operating at different wavelengths. In the UK, academia, industry and the central laboratories took up the challenge from the earliest days to develop these systems for a broad range of applications. This historical review looks at the contribution the UK has made to the advancement of the technology, the development of systems and components and their exploitation over the last 60 years.

A two-level system driven by a classical single frequency field in rotating-wave approximation is a basic model for resonance in quantum optics. The probability of making a transition depends sinusoidally on time with a characteristic frequency called the Rabi frequency. The Jaynes-Cummings model (JCM) consists of a two-level atomic system driven by a single quantized electromagnetic field mode. The field entropy in the case of an atom interacting with an initially coherent field is expected to reflect the collapse and revival of Rabi oscillations. The photon statistics of the JCM are examined and the entropy concepts are used to describe the apparently disordered collapses. A density matrix method is used to describe the influence of photon statistics in the JCM. The quantum generalization defines entropy through where the trace is taken over a convenient basis set. The thermal field JCM shows enhanced photon variances as expected for an initially Bose-Einstein field with large fluctuations.

Cold atoms offer a wonderful platform for quantum technologies for novel sensing, timing and of course quantum computation. I will describe how atoms and ions are cooled and state prepared for such applications, drawing on the UK National Quantum Technology Programme. Prospects for applications will be explored for time standards and sensors. In the longer term, laser cooled atoms and ions offer great potential for information processing. Universal quantum computers will be able to act as simulators of any system. But a simpler quantum device, able to mimic a real system, does not have to be a quantum computer. Such devices are quantum simulators; they are not universal but are simpler to construct. We expect early quantum simulators to be developed relatively soon, allowing certain regimes of problems, intractable for classical computers, to be solved. Cold atoms make good simulators: they provide naturally identical qubits without the need for high-quality materials fabrication. Quantum simulators with networked laser cooled trapped ions or cold atoms in optical lattices are already able to provide information about problems inaccessible to classical computers. Scaling of quantum processors to hundreds of qubits or more is a major engineering challenge, but arrays of ion or atom-based qubits offer great potential that is being rapidly explored around the world.

Join us in this panel discussion to explore the challenges and opportunities of converting global innovation initiatives into a thriving sector: are we in a super position to realise the full potential of quantum technology for all?

The UK has, through a mix of government and industry funding, committed more than £1Bn over ten years to a coordinated programme in quantum technology. Five years into this programme, the UK National Quantum Technology Programme has induced a step change in the nation’s capabilities for establishing a new sector in future quantum information technologies. We describe how the programme arose and the activities it has supported and influenced to deliver these new capabilities, building on a first phase of over £385M investment across several UK government agencies. As the programme enters its second phase, with a further substantial investment by UK government and global industries, we review the prospects for ensuring the advanced quantum science and demonstrator platforms in imaging, sensing, timing, communications and computing developed over the past five years drive the formation of the sector and embed quantum tech in a broad range of industries by means of new products and services.