A few decades ago, quantum optics stood out as a new domain of physics by exhibiting states of light with no classical equivalent. The first investigations concerned single photons, squeezed states, twin beams and EPR states, that involve only one or two modes of the electromagnetic field. The study of the properties of quantum light then evolved in the direction of more and more complex and rich situations, involving many modes, either spatial, temporal, frequency, or polarization modes. Actually, each mode of the electromagnetic field can be considered as an individual quantum degree of freedom. It is then possible, using the techniques of nonlinear optics, to couple different modes, and thus to build in a controlled way a quantum network in which the nodes are optical modes and that is endowed with a strong multipartite entanglement. In addition, such networks are easily reconfigurable and subject only to weak decoherence. They open indeed many promising perspectives for optical communications and computation.
Because of the linearity of Maxwell equations a linear superposition of two modes is another mode. This means that a "modal superposition principle" exists hand in hand with the regular quantum state superposition principle. The purpose of the present review is to show the interest of considering these two aspects of multimode quantum light in a global way. Indeed using different sets of modes allows to consider the same quantum state under different perspectives: a given state can be entangled in one basis, factorized in another. We will show how to produce, characterize and tailor multimode quantum light. Finally we will describe some applications to quantum technologies, such as parameter estimation and measurement-based quantum computation.
We show that a universal set of gates for quantum computation with optics can be quantum teleported through the use of EPR entangled states, homodyne detection, and linear optics and squeezing operations conditioned on measurement outcomes. This scheme may be used for fault-tolerant quantum computation in any optical scheme (qubit or continuous variable). The teleportation of nondeterministic nonlinear gates employed in linear optics quantum computation is discussed.
Introducing creation and annihilation operators for negative frequency components extends the algebra of smeared local observables of quantum optics to include an associated classical random field optics.
This article provides a brief overview of some fundamental effects of quantum fields under extreme conditions. For the Schwinger mechanism, Hawking radiation, and the Unruh effect, analogies to quantum optics are discussed, which might help to approach to these phenomena from an experimental point of view.
In this work, we propose two optical setups for two-players, non-zero and zero sum, quantum games in optical networks using light polarization of single-photon pulses, single-photon detectors and linear optical devices. The optical setups proposed can be easily implemented permitting a fast experimental realization of quantum games with present technology.
Several quantum protocols for data security having been proposed and, in general, they have different optical implementations. However, for the implementation of quantum protocols in optical networks, it is highly advantageous if the same optical setup can be used for running different quantum communication protocols. In this direction, here we show an optical scheme that can be used for quantum key distribution (QKD), quantum secure direct communication (QSDC) and quantum secret sharing (QSS). Additionally, it is naturally resistant to the attack based on single-photon detector blinding. At l…
We present a constructive method to translate small quantum circuits into their optical analogues, using linear components of present-day quantum optics technology only. These optical circuits perform precisely the computation that the quantum circuits are designed for, and can thus be used to test the performance of quantum algorithms. The method relies on the representation of several quantum bits by a single photon, and on the implementation of universal quantum gates using simple optical components (beam splitters, phase shifters, etc.). The optical implementation of Brassard et al.'s tele…
Linear optics has seen a resurgence for applications in quantum information processing owing to its miniaturisation on-chip, and increase in production efficiency and quality of single photons. Time-bin encodings have also become feasible owing to architectural breakthroughs, and new processing capabilities. Theoretical efforts have found new ways to implement universal quantum computations with linear optics requiring less resources, and to demonstrate the capabilities of linear optics without requiring a universal optical quantum computer.
We investigate the computational power of passive and active linear optical elements and photo-detectors. We show that single photon sources, passive linear optics and photo-detectors are sufficient for implementing reliable quantum algorithms. Feedback from the detectors to the optical elements is required for this implementation. Without feedback, non-deterministic quantum computation is possible. A single photon source sufficient for quantum computation can be built with an active linear optical element (squeezer) and a photo-detector. The overheads associated with using only linear optics …
Quantum optics is the study of the intrinsically quantum properties of light. During the second part of the 20th century experimental and theoretical progress developed together; nowadays quantum optics provides a testbed of many fundamental aspects of quantum mechanics such as coherence and quantum entanglement. Quantum optics helped trigger, both directly and indirectly, the birth of quantum technologies, whose aim is to harness non-classical quantum effects in applications from quantum key distribution to quantum computing. Quantum light remains at the heart of many of the most promising an…
Frequency conversion between microwave and optical photons is a key enabling technology to create links between superconducting quantum processors and to realize distributed quantum networks. We propose a microwave-optical transduction platform based on long-coherence-time superconducting radio-frequency (SRF) cavities coupled to electro-optic optical cavities to mitigate the loss mechanisms that limit the attainment of high conversion efficiency. In the design, we optimize the microwave-optical field overlap and optical coupling losses, while achieving long microwave and optical photon lifeti…
A heavy focus for optical quantum computing is the introduction of error-correction, and the minimisation of resource requirements. We detail a complete encoding and manipulation scheme designed for linear optics quantum computing, incorporating scalable operations and loss-tolerant architecture.
We review the electronic level structure of the nitrogen-vacancy in diamond and some common experimental techniques to study its optical properties at low temperatures. We then summarize several recent experiments and advances in using nitrogen-vacancy centers for quantum optics.
A fully optical method to perform any quantum computation with optical waveguide modes is proposed by supplying the prescriptions for a universal set of quantum gates. The proposal for quantum computation is based on implementing a quantum bit with two normal modes of multi-mode waveguides. The proposed universal set of gates has the potential of being more compact and easily realized than other optical implementations, since it is based on planar lightwave circuit technology and can be constructed by using Mach-Zehnder interferometer configurations having semiconductor optical amplifiers with…
We show that a cavity optomechanical system formed by a mechanical resonator simultaneously coupled to two modes of an optical cavity can be used for the implementation of a deterministic quantum phase gate between optical qubits associated with the two intracavity modes. The scheme is realizable for sufficiently strong single-photon optomechanical coupling in the resolved sideband regime, and is robust against cavity losses.
By the newly developed technique of integration within an ordered product (IWOP) of operators, we explore quantum optical version of classical optical transformations such as optical Fresnel transform, Hankel transform, fractional Fourier transform, Wigner transform, wavelet transform and Fresnel-Hadmard combinatorial transform etc. In this way one may gain benefit for developing classical optics theory from the research in quantum optics, or vice-versa. We can not only find some new quantum mechanical unitary operators which correspond to the known optical transformations, deriving a new theo…
We present a proposal for optically implementing the quantum game of the two-player quantum prisoner's dilemma involving nonmaximally entangled states by using beam splitters, phase shifters, cross-Kerr medium, photon detector and the single-photon representation of quantum bits.
Lecture Notes for the Les Houches Summer School LXIII on Quantum Fluctuations in July 1995 to appear in Elsevier Science Publishers B.V. 1997, edited by E. Giacobino and S. Reynaud.
All-quantum signal processing techniques are at the core of the successful advancement of most information-based quantum technologies. This paper develops coherent and comprehensive methodologies and mathematical models to describe Fourier optical signal processing in full quantum terms for any input quantum state of light. We begin this paper by introducing a spatially two-dimensional quantum state of a photon, associated with its wavefront and expressible as a two-dimensional creation operator. Then, by breaking down the Fourier optical processing apparatus into its key components, we strive…
We propose a scheme to realize deterministic quantum teleportation using linear optics and hybrid qubits. It enables one to efficiently perform teleportation and universal linear-optical gate operations in a simple and near-deterministic manner using all-optical hybrid entanglement as off-line resources. Our analysis shows that our new approach can outperforms major previous ones when considering both the resource requirements and fault tolerance limits.
We propose a scheme for conditional implementation of a quantum phase gate by using distant atoms trapped in different optical cavities. Instead of direct interaction between atoms, the present scheme makes use of quantum interference of polarized photons decaying from the optical cavities to conditionally create the desired quantum phase gate between two distant atoms. The proposed scheme only needs linear optical elements and a two-fold coincidence detection, and are insensitive to the quantum noise. The scheme can be directly used to prepare any quantum state of many distant atoms.
We formulate and argue in favor of the following conjecture: There exists an intimate connection between Wigner's quantum mechanical phase space distribution function and classical Fresnel optics.
We present a brief review of the impact of the Heisenberg uncertainty relations on quantum optics. In particular we demonstrate how almost all coherent and nonclassical states of quantum optics can be derived from uncertainty relations.
We demonstrate a device that allows for the coherent analysis of a pair of optical frequency sidebands in an arbitrary basis. We show that our device is quantum noise limited and hence applications for this scheme may be found in discrete and continuous variable optical quantum information experiments.
Here we review some of the recent developments in Quantum Optics. After a brief introduction to the historical development of the subject, we discuss some of the modern aspects of quantum optics including atom field interactions, quantum state engineering, metamaterials and plasmonics, optomechanical systems, PT (Parity-Time) symmetry in quantum optics as well as quasi-probability distributions and quantum state tomography. Further, the recent developments in topological photonics is briefly discussed. The potent role of the subject in the development of our understanding of quantum physics an…
Linear optics is a promising candidate to enable the construction of quantum computers. A number of quantum protocols gates based on linear optics have been demonstrated. However, it is well-known that these gates are non-deterministic and that higher order nonlinearity is necessary for deterministic operations. We found the quantum leader election protocol (QLE) can be operated deterministically only with linear optics, and we have demonstrated the nearly deterministic operation which overcomes classical limit.
This Habilitation manuscript describes the work done at JQI-NIST and LKB-ENS-Sorbonne University since 2010. After a brief introduction of the needed concepts for non-linear and quantum optics in optically dense atomic medium, I review several experiments about the Gradient Echo Memory protocol in warm atomic vapors and in cold atomic clouds, and especially the multi-mode properties of this memory. In the next chapter I describe two experiments of quantum optics in dense atomic medium : the possibility to image using quantum noise and the propagation of quantum mutual information in a fast-lig…
What is light and how to describe it has always been a central subject in physics. As our understanding has increased, so have our theories changed: Geometrical optics, wave optics and quantum optics are increasingly sophisticated descriptions, each referring to a larger class of phenomena than its predecessor. But how exactly are these theories related? How and when wave optics reduces to geometric optics is a rather simple problem. Similarly, how quantum optics reduces to wave optics has been considered to be a very simple business as well. It's not so. As we show here the classical limit of…
Quantum collision models (CMs) provide advantageous case studies for investigating major issues in open quantum systems theory, and especially quantum non-Markovianity. After reviewing their general definition and distinctive features, we illustrate the emergence of a CM in a familiar quantum optics scenario. This task is carried out by highlighting the close connection between the well-known input-output formalism and CMs. Within this quantum optics framework, usual assumptions in the CMs' literature - such as considering a bath of non-interacting yet initially correlated ancillas - have a cl…
Applications of Integrated Optics to quantum sources, detectors, interfaces, memories and linear optical quantum computing are described in this review. By their inherent compactness, efficiencies, and interconnectability, many of the demonstrated individual devices can clearly serve as building blocks for more complex quantum systems, that could also profit from the incorporation of other guided wave technologies.
In quantum information and communication, optical schemes provide simple and intuitive experimental implementations. Of particular importance is quantum state preparation. In this thesis, the creation of polarisation entanglement using a particular class of optical circuits is studied. I give a mathematical description of this class of circuits in terms of Hermite polynomials. In this context, single photon resolution and single photon sensitivity detectors are discussed and compared with detector cascading. In addition, I study applications of state preparation such as quantum teleportation a…
We consider transmission of an (unknown) quantum state between two distant atoms via photons. Based on a quantum-optical realistic model, we define a noisy quantum channel which includes systematic errors as well as errors due to coupling to the environment. We present a protocol that allows one to accomplish ideal transmission by repeating the transfer operation as many times as needed.
We give an overview of linear optics quantum computing, focusing on the results from the original KLM paper. First we give a brief summary of the advances made with optics for quantum computation prior to KLM. We next discuss the KLM linear optics scheme, giving detailed examples. Finally we go through quantum error correction for the LOQC theory, showing how to obtain the threshold when dealing with Z-measurement errors.
We present a theoretical analysis of the connection between classical polarization optics and quantum mechanics of two-level systems. First, we review the matrix formalism of classical polarization optics from a quantum information perspective. In this manner the passage from the Stokes-Jones-Mueller description of classical optical processes to the representation of one- and two-qubit quantum operations, becomes straightforward. Second, as a practical application of our classical-\emph{vs}-quantum formalism, we show how two-qubit maximally entangled mixed states (MEMS), can be generated by us…
We discuss mode-entangled states based on the optical transverse modes of the optical field propagating in multi-mode waveguides, which are classical analogs of the quantum entangled states. The analogs are discussed in detail, including the violation of the Bell inequality and the correlation properties of optical pulses' group delays. The research on these analogs may be important, for it not only provides useful insights into fundamental features of quantum entanglement, but also yields new insights into quantum computation and quantum communication.
One approach to quantum information processing is to use photons as quantum bits and rely on linear optical elements for most operations. However, some optical nonlinearity is necessary to enable universal quantum computing. Here, we suggest a circuit-QED approach to nonlinear optics quantum computing in the microwave regime, including a deterministic two-photon phase gate. Our specific example uses a hybrid quantum system comprising a LC resonator coupled to a superconducting flux qubit to implement a nonlinear coupling. Compared to the self-Kerr nonlinearity, we find that our approach has im…
We propose and fully analyze the simplest technique to date to generate light-based universal quantum computing resources, namely 2D, 3D and, in general, n-hypercubic cluster states. The technique uses two standard optical components: first, a single optical parametric oscillator pumped below threshold by a monochromatic field, which generates Einstein-Podolsky-Rosen entangled states, a.k.a. two-mode-squeezed states, over the quantum optical frequency comb; second, phase modulation at frequencies multiple of the comb spacing (via RF or optical means). The unprecedented compactness of this tech…
We present a linear optics quantum computation scheme with a greatly reduced cost in resources compared to KLM. The scheme makes use of elements from cluster state computation and achieves comparable resource usage to those schemes while retaining the circuit based approach of KLM.
We discuss the unique capabilities of programmable logic devices (PLD's) for experimental quantum optics and describe basic procedures of design and implementation. Examples of advanced applications include optical metrology and feedback control of quantum dynamical systems. As a tutorial illustration of the PLD implementation process, a field programmable gate array (FPGA) controller is used to stabilize the output of a Fabry-Perot cavity.
We analyze a fiber-optic component which could find multiple uses in novel information-processing systems utilizing squeezed states of light. Our approach is based on the phenomenon of photon-number squeezing of soliton noise after the soliton has propagated through a nonlinear optical fiber. Applications of this component in optical networks for quantum computation and quantum cryptography are discussed.
Atom optics, a field which takes much inspiration from traditional optics, has advanced to the point that some of the fundamental experiments of quantum optics, involving photon correlations, have found atomic analogs. We discuss some recent experiments on atom bunching and anti-bunching as well as some prospects for extending them to the field of many body physics.
We propose a novel interferometer by using optical transverse modes in multimode waveguide that can beat the standard quantum limit. In the scheme, the classical simulation of $N$-partical quantum entangled states is generated by using $N$ independent classical fields and linear optical elements. Similar to the quantum-enhanced measurements, the classical simulation can also achieve $\sqrt{N}$ enhancement over the precision of the measurement $N$ times for independent fields. Due to only using classical fields and linear optical elements, the scheme can be realized much more easily.
Knill, Laflamme, and Milburn (KLM) proved that it is possible to build a scalable universal quantum computer using only linear-optics elements and conditional dynamics [Nature (London) {\bf 409}, 46 (2001)\cite{Knill}]. However, the practical realization of the quantum logic gate for the scheme is still technically difficult. A major difficulty is the requirement for sub-wavelength level stabilization of the interlocking interferometers. Following our recent experimental work[Phys. Rev. Lett.{\bf 92}, 017902 (2004)\cite{Sanaka2}], we describe a more feasible scheme to implement the gate that g…
Probabilistic quantum non-demolition (QND) measurements can be performed using linear optics and post-selection. Here we show how QND devices of this kind can be used in a straightforward way to implement a quantum relay, which is capable of extending the range of a quantum cryptography system by suppressing the effects of detector noise. Unlike a quantum repeater, a quantum relay system does not require entanglement purification or the ability to store photons.
We show that atomic spin motion can be controlled by circularly polarized light without light absorption in the strong pumping limit. In this limit, the pumping light, which drives the empty spin state, destroys the Zeeman coherence effectively and freezes the coherent transition via the quantum Zeno effect. It is verified experimentally that the amount of light absorption decreases asymptotically to zero as the incident light intensity is increased.
As quantum optical phenomena are based on Maxwell's equations, and it is becoming important to understand quantum optical phenomena at short distances, so it is important to analyze quantum optics using short distance corrected Maxwell's equation. Maxwell's action can be obtained from quantum electrodynamics using the framework of effective field theory, and so the leading order short distance corrections to Maxwell's action can also be obtained from the derivative expansion of the same effective field theory. Such short distance corrections will be universal for all quantum optical systems, a…
In this paper, we review recent developments in the emerging field of electron quantum optics, stressing analogies and differences with the usual case of photon quantum optics. Electron quantum optics aims at preparing, manipulating and measuring coherent single electron excitations propagating in ballistic conductors such as the edge channels of a 2DEG in the integer quantum Hall regime. Because of the Fermi statistics and the presence of strong interactions, electron quantum optics exhibits new features compared to the usual case of photon quantum optics. In particular, it provides a natural…
An optical realization of the damped quantum oscillator, based on transverse light dynamics in an optical resonator with slowly-moving mirrors, is theoretically suggested. The optical resonator setting provides a simple implementation of the time-dependent Caldirola-Kanai Hamiltonian of the dissipative quantum oscillator, and enables to visualize the effects of damped oscillations in the classical (ray optics) limit and wave packet collapse in the quantum (wave optics) regime.
Quantum optics and classical optics have coexisted for nearly a century as two distinct, self-consistent descriptions of light. What influences there were between the two domains all tended to go in one direction, as concepts from classical optics were incorporated into quantum theory's early development. But it's becoming increasingly clear that a significant quantum presence exists in classical territory-and, in particular, that the quintessential quantum attribute, entanglement, can be seen, studied and exploited in classical optics. This blurring of the classical-quantum boundary has opene…
We present a broad summary of research involving the application of quantum feedback control techniques to optical set-ups, from the early enhancement of optical amplitude squeezing to the recent stabilisation of photon number states in a microwave cavity, dwelling mostly on the latest experimental advances. Feedback control of quantum optical continuous variables, quantum non-demolition memories, feedback cooling, quantum state control, adaptive quantum measurements and coherent feedback strategies will all be touched upon in our discussion.
The recent developments of electron quantum optics in quantum Hall edge channels have given us new ways to probe the behavior of electrons in quantum conductors. It has brought new quantities called electronic coherences under the spotlight. In this paper, we explore the relations between electron quantum optics and signal processing through a global review of the various methods for accessing single- and two-electron coherences in electron quantum optics. We interpret electron quantum optics interference experiments as analog signal processing converting quantum signals into experimentally ob…
The interaction of an atom with an electromagnetic field is discussed in the presence of a time periodic external modulating force. It is explained that a control on atom by electromagnetic fields helps to design the quantum analog of classical optical systems. In these atom optical systems chaos may appear at the onset of external fields. The classical and quantum chaotic dynamics is discussed, in particular in an atom optics Fermi accelerator. It is found that the quantum dynamics exhibits dynamical localization and quantum recurrences.
