- The first one is the generation of temporally entangled light, in which separate temporal parts of the light pulses are correlated at the quantum level. The technology of femtosecond trains of pulses (or "frequency combs") has in the last decade enjoyed a great wave of developments, so that the instantaneous phase and amplitude of these pulses can now be shaped at will. We propose to extend the very successful domain of "coherent control" of light pulses, used up to now to tailor transition probabilities in atoms and molecules, to the quantum optics domain, and to use such methods for a coherent control of quantum fluctuations and correlations in ultra-short pulses. This section of the project will tackle the experimental study of synchronously pumped optical parametric oscillators (SPOPOs), which have been theoretically shown to produce trains of non-classical light. More precisely, we expect they will generate several well-defined temporal supermodes (i.e. superpositions of phase-locked modes of different frequencies) that are either squeezed or entangled.
- The use of frequency combs has revolutionized the domain of metrology of frequencies. As a second objective, this WP will investigate how the quantum frequency combs can be used to improve information extraction in pulses of arbitrary shapes. In a first step, we shall consider the case of time and frequency metrology, in which quantum fluctuations begin to be a limiting factor. We shall study in particular the techniques of ultra-precise synchronization of clocks situated at remote places (see Figure) 1) a subject of paramount importance, both from a fundamental and practical point of view, which can impact the synchronization of satellites.
- The third objective is in connection with WP5. The consortium will study the ways of interfacing such a temporally multimode light with broadband quantum memories. Two-photon processes, like Raman or two-photon absorption, must be considered, because in such processes all the "teeth" of the entangled frequency comb contribute to the interaction with the material medium. Inhomogeneously broadened media have been already extensively studied as broadband memories in classical computing. We plan to use the various domains of expertise of the consortium to assess the possibilities of these media for making broadband quantum memories.
- The use of spatially entangled light for the improvement of highly sensitive image processing techniques beyond the standard quantum limit will be investigated. More precisely, we will focus on the experimental realization of ultra-precise simultaneous measurement of position and orientation of objects in space, to detect ultra-small 3D displacements and rotations at the sub-nanometer scale. This research targets an important impact on the improvement of position sensors. This turns out to be a difficult task when the level of quantum fluctuations is reached, requiring the use of spatially entangled light beams, because the position and the angular orientation of light beams are quantum conjugate variables, obeying Heisenberg uncertainty relations.
- Similarly to the third objective of WP1, here we will study the precise properties of spatially multimode light suitable to be interfaced with multimode quantum memories. In view of the general goal of our project, which is to increase the bandwidth and capacity of quantum information devices, we shall investigate the various ways allowing us to imprint and read-out in a parallel way the maximum amount of quantum information in a cloud of N atoms, without loss of quantum coherence, and to maximize the writing and reading rate of this information.

**Concepts and Objectives of the HIDEAS project**

Entanglement and quantum correlations are the fundamental tools for building protocols of Quantum
Information Processing and Communication (QIPC).These fields passed in the last years the
proof-of-concept stage, asking now for real-world implementations. In this context, light plays a
fundamental role as the natural carrier of information over large distances and between logic elements
within a processor.

However, the standard approach of quantum optics, that deals with single-or two-mode systems, turns
out to be inadequate to analyse and tackle the problems posed by practical implementations of QIPC: not
only since it does not allow for a realistic modelling but, even more, because it creates a bottleneck in the
information capacity of the communication, manipulation and storage of quantum information.

Our proposal aims at a breakthrough in the information capacity of quantum communication, by
exploiting the intrinsic multivariate and multi-modal character of the radiation field, which involves
spatial, temporal and polarization degrees of freedom. The long term vision underlying our project is that
of a broadband quantum communication, where all the physical properties of the photons are utilized to
store information. This proposal intends to do crucial steps towards the realization of this ambitious vision.
The general objectives are to study, on the one hand, how to produce in a controlled way quantum
entanglement of light in high dimensional and multimodal spaces; on the other hand, we need to create
multimode quantum interfaces between light and matter so that quantum states of light can be stored and
processed in long-lived matter degrees of freedom.

From a different perspective, our research will contribute fundamentally to the field of metrology, a
domain where multimode aspects have been introduced with great success ("frequency combs"), and
quantum noise tailoring demonstrated a powerful tool to increase the sensitivity of high-precision
measurements ("quantum metrology").

The path to reach such general objectives proceeds along five research lines (workpackages, WPs) that
address both the light (WP1-WP4) and the matter (WP5) aspects, spanning the continuous variable
(WP1,WP2) and the photon-pair (WP3,WP4)
regimes and encompassing temporal (WP1), spatial
(WP2,WP3) and spatio-temporal (WP4) degrees of freedom.

Researches in quantum optics in the regime of continuous variables have produced many impressive
achievements, thanks to more and more subtle ways of mastering quantum fluctuations and correlations in
light beams, which found applications in QIPC and quantum metrology protocols. So far studies have dealt
mainly with single-mode light beams, characterized by a single number, its complex amplitude. A general
goal of this and of the following WPs is to go beyond this step, and to deal with multimode light, which is
able to convey a much larger amount of information. To cope with the complexity of multimodal
configurations, we have a powerful tool: the possibility of changing the basis of modes used to describe the
system. In most cases it is advantageous to introduce new physical objects, that we call supermodes, which
are proper combinations of standard modes. These are in a way the eigenmodes of the physical system, and
represent the natural structures where entanglement lives.

An important tool for broadband information technologies is to use light in a well defined transverse
spatial mode (for example the guided mode of an optical fibre), in which the information is conveyed by
the temporal variation of the light amplitude and phase, in an analogous or digital way. In this case, the
multimode optical system under consideration is the set of all possible temporal shapes of the light pulses.
This workpackage aims at studying this field from a quantum perspective. We identify three main
objectives:

In our present technological world, images are a privileged way to convey a great deal of information in
a massively parallel way. Recording, storing, processing and displaying images require broadband
information channels and large size memories. In this workpackage we propose to study all these problems
at the quantum level. Such a task requires to simultaneously consider from a quantum perspective the
millions of pixels forming the image. On the one hand, the laws of quantum mechanics impose that
quantum fluctuations are always present on such pixels, and degrade to some extent the information. On
the other hand the possible existence of spatial quantum correlations between different pixels, or between
different parts of the image, is a specific quantum property which provides a powerful tool that can be used
to improve the processing of the spatial information contained in the image.

The first objective of this WP is to study the best ways of generating spatially entangled multimode
light, which will be the highly-entangled quantum resource necessary for broadband quantum information
processing of images. The sources of spatially entangled multimode light that have been used up to now for
first-principle demonstrations are inadequate in view of practical applications, and a qualitative leap is
necessary. In this workpackage, in order to substantially improve the performances of the devices, different
promising avenues will be pursued They are either based on merging several appropriately designed
single-mode quantum light beams, or on directly using nonlinear processes such as parametric
down-conversion (PDC), or four-wave mixing, which are intrinsically multimode, and improving their
efficiency.

The second objective is to use these multimode quantum resources to improve various functions of
quantum information processing. This requires a thorough conceptual and theoretical effort in the design
of new approaches and the realization of a few experiments. Within HIDEAS project we will focus our
efforts on the two following topics:

This work package shares with WP2 the interest towards entanglement in the spatial degrees of freedom
of light. In WP2 this was studied within the context of continuous light beams ("continuous variables"),
involving intensity measurements where the photons cannot be distinguished individually. In contrast, in
this WP we will turn our interest to the quantum correlations between single-photon counts registered in
the spatial domain, in particular two-photon coincidence counts.

The main concept here is to increase **the quantum bandwidth of photonic communication channels**
by employing channels that are spatially multi-mode, either implemented in free space or with fibre optics.
We feed these channels with twin photons that are highly entangled in a spatial sense; this allows
communication with a larger alphabet (qudits) as compared to the usual binary alphabet (qubits) that is
allowed by the polarization degree of freedom. This larger alphabet increases the capacity of the quantum
channel involved and may thus greatly improve, for instance, the quality of quantum cryptography
(interestingly, in classical cryptography a higher-dimensional alphabet, e.g. the ASCII instead of a binary
code, brings no advantages).

Twin photons are naturally created in spontaneous parametric down-conversion, where a pump photon
is split into two photons. The main objective is to demonstrate experimentally high-D spatial
entanglement of such photon-pairs and to establish its usefulness for quantum communication. To this
end, as a secondary objective we will investigate whether optical fibres can be used for quantum
communication based upon multi-mode spatially entangled photons.

At difference with WP2, in WP3 we will not consider the translational degrees of freedom but instead
focus on the angular degrees of freedom, also known as orbital angular momentum (OAM) [Allen 1992,
Allen 2003]. The key physical principle that underlies our work is the notion that angular momentum and
angular position are Fourier-conjugate observables, just as the momentum and the position of a particle.
Photon pairs produced in PDC naturally exhibit entanglement in the form of coexistence of quantum
correlations in pairs of incompatible observables including, famously, position and momentum and
non-orthogonal components of polarization. We will focus here on the transverse spatial degrees of
freedom and, in particular, on OAM.

It is convenient to present our, closely integrated, plans under two headings.

**Momentum domain:** The basic idea is to project the two-photon state on a specific superposition of
angular eigenstates ("orbital angular momentum" eigenstates) (Fig.2). To achieve this goal we will
construct angular projectors that play the same role as the polarization projectors (polarizers) in the case of
polarization entanglement. The essential element in such an angular projector is an angular phase plate
coupled to a single-photon detector via a single-mode fibre (Fig.3); by rotating the phase plate one changes
the projected superposition of OAM eigenstates that corresponds to a detection event.

The number of eigenstates that is coupled by the phase plate (i.e. the entanglement dimension D) depends
on the choice of the phase-plate profile. The secret to realize a large value of D is then to use a sufficiently
complicated angular phase profile; our goal is to demonstrate in this way angular two-photon entanglement
with a dimensionality D well above 50, a (soft) limit set by technical considerations.

**Position domain:** Our second approach is very close to the spirit of the original EPR paradox, formulated
in terms of position and momentum as conjugate quantum observables. The conjugate observable to orbital
angular momentum is angular position and we shall undertake a demonstration of high-dimensional
quantum entanglement between down-converted photons based on measurements of azimuthal angular
position and orbital angular momentum. Essential to this approach (and in contrast to that described above)
is the use of an effectively array-type detector based upon temporal multiplexing (Fig. 4). Another key
technological advance of our work is the integration of computer-addressable spatial light modulators
working at the single-photon level in PDC. This approach will allow us full freedom in selecting detected
mode patterns and thus allow us to demonstrate EPR type paradoxes. The effective dimensionality of the
entanglement will be determined by the largest values of orbital angular momentum that are
experimentally accessible; experience suggests that D » 30 should readily be possible, with yet higher
values requiring only technical improvements. It is intriguing that this estimate is basically identical to that
obtained in the momentum domain (D »50) in spite of the fact that the experimental methods used are
rather different. Testing this presumably similar performance is a strong motivation to have both
approaches on board in the same program; each will doubtless be able to feed off of the technical advances
of the other.

Mastering the techniques that involve sources of entangled pairs of photons and of single photons in a
pure state has become vital for implementations of many quantum networks and quantum computing
schemes [Bouwmeester2000,Nielsen2000]. So far, parametric down-conversion (PDC) demonstrated the
most efficient and practical room-temperature source of entangled photon pairs, that has been used in
successful implementation of quantum communication schemes, such as quantum dense coding
[Mattle1996], teleportation [Bouwmeester1997, Boschi1998], and entanglement swapping [Pan1998]. At
the very heart of such QIPC technologies lies the quantum interference between photonic wave functions,
which depends crucially on the spatio-temporal mode structure of the generated photons. Tailoring and
mastering the coherence and correlation properties of PDC photon pairs in the spatio-temporal domain is
therefore of paramount importance in modern QIPC technologies.

This WP addresses a quite peculiar and novel issue, that is, the non factorability in space and time of
the spatio-temporal structure of PDC bi-photon entanglement. Our interest is driven by recent
investigations in nonlinear optics [DiTrapani2003, Trull2004, Conti2003], that outlined how in nonlinear
media the angular dispersion relations impose a hyperbolic geometry involving both temporal and spatial
degrees of freedom in a non-factorable way. The wave object that captures such a geometry is the so-called
X-wave (the X being formed by the asymptotes of the hyperbola), which is a stationary and localized
wave-packet, not separable in space and time. Intense X-shaped wave-packets strongly localized in time
and in the transverse plane, with an extension of a few tens of femtoseconds and microns, respectively,
have been indeed observed in second-harmonic generation [DiTrapani2003, Trull2004]. In the context of
nonlinear optics, the X-wave structure emerges as the natural eigenmode of quadratic media governed by
phase-matching constraints.

Within this WP we intend to adopt the X-wave description for investigating the spatio-temporal
entanglement in PDC. The general objective is to demonstrate the X-shaped geometry, non-separable in
space and time, of the bi-photon entangled state. This will require:

**i)**
A precise and quantitative characterization of the spatio-temporal structure of entanglement in various
regimes and type of phase matching of PDC. This study will provide a far-reaching characterization of the
entanglement in the fully spatio-temporal domain, that will be of fundamental interest for both the
community working with discrete variables (i.e. counting photon pairs) or continuous variables.

**ii)**
To identify and implement a proper scheme of measurements able to disclose the X-shaped geometry
of entanglement. Two avenues will be followed, the first one involving Hong-Ou-Mandel (HOM) type of
interferometers, able to discriminate coherence times on the order of few fs, the second one involving a
measurement of the cross-correlation via a second harmonic generation process.
We remark that the predicted non-factorability of the state will open the relevant possibility of tailoring
the temporal bandwidth of one photon by a conditional measurement in the spatial domain or, viceversa, of
tailoring the spatial bandwidth by conditional measurements in the temporal domain. A third objective will
be thus that of

**iii)**
assessing this possibility, and in particular exploring the impact of the non-factorability of the state
on the purely spatial entanglement of photon pairs explored by WP3.

A quantum communication network is impossible without a quantum interface between light – the
carrier of information – and matter – the storage medium for quantum information. The need for such an
interface comes from the need for quantum state purification and quantum error correction. That is why a
quantum communication protocol usually contains a phase of Local Operations and Classical
Communication (LOCC). This stage requires that quantum states of light are stored in atomic memories.
Obviously multi-mode memories for multi-mode (broadband) quantum communication with light offer a
decisive advantage of compactness and scalability when compared to single mode memories. A
particularly well known, but certainly not the only, example of the use of light-matter interface for
communication is a quantum repeater, a fundamental concept in quantum communication
[Childress2004].

Two approaches to the light-atoms quantum interface emerged in the past decade, one of them based on
single atoms or other emitters in a high Q cavity (cavity QED) and the other one based on atomic
ensembles. The atomic ensemble approach has proven to be extremely successful for the interface
purposes. But most importantly, besides its many technical advantages, this method is fundamentally more
suitable for the multi-mode interface, for the simple reason that a single atom can, as a rule, store a single
light mode, whereas an ensemble of N atoms can, in principle, store N modes.

Up to now, the work on light-atoms interface has been mostly limited to the case of a single spatial mode
of light and a single spatial mode of atomic ensembles. With this workpackage we intend to extend this
approach to a multi-mode light-atoms quantum interface. We will concentrate on the high-fidelity
quantum interface, in the sense of a fidelity higher than that achievable by any classical interface or
memory. The objectives here will be to investigate theoretically and experimentally i) the generation of a
new type of spatial multi-mode entanglement between light and matter and ii) multi-mode quantum
memories for light based on spatially extended atomic ensembles, which we call quantum holograms.

The ultimate goal will be the experimental demonstration of the extended spatial memory capacity of the
quantum hologram, compared to a classical hologram. On the theoretical side the objective is to develop a
model for the multi-mode quantum memory for light and to choose the optimal method for the high-fidelity
interface.